## 2014 Theory Department Weekly Highlights

### August 8~

**THEORY**

J. Squire and A. Bhattacharjee have published a paper in PRL on a new nonmodal analysis of the magnetorotational instability (MRI), which is widely believe to play an important role in controlling angular momentum transport in rotating astrophysical objects such as accretion disks (PRL 113, 025006, 2014). Their findings are quite different from standard eigenmode analyses, illustrating that shearing wave energy can grow at a universal growth rate for any choice of azimuthal and vertical wavelengths in the disc. They thus demonstrate that fast linear growth is possible at all wavelengths, suggesting that nonmodal linear physics could play an important role in MRI turbulence. The methodology used in the paper is potentially useful in the study of instabilities in rotating fusion plasmas.

A. Bhattacharjee and G. Hammett were invited to attend and give talks at the conference "From the MRI to the Sun" in honor of the 60th Birthday of Steven Balbus, Savilian Professor at the University of Oxford at Chamonix, France, July 14-18.

W. Fox traveled to the University of Rochester Laboratory for Laser Energetics (LLE) to participate in experiments on the OMEGA EP facility. He collaborated with Gennady Fiksel and other colleagues at the LLE in experiments pertaining to the dynamics of magnetic reconnection in colliding high-energy-density density plasmas. The goal of the experiments was to study secondary instabilities of current sheets and their consequences during magnetic reconnection varying the magnitude of an externally imposed magnetic field. The experiments involved collisions of plumes of magnetized and unmagnetized plasma and observations with proton radiography and optical probing diagnostics. A. Bhattacharjee and W. Deng collaborated on developing theory and simulations for the experiments.

### July 25~

**THEORY **

Professor R. Ganesh of Institute of Plasma Research of India has just finished his one-month summer visit at PPPL. During his stay, he worked with W.-L. Lee and S. Ethier on the implementation of the two-weight delta-f to full-F scheme along with the neoclassical drive in the GTC-P code. The physics of steady state transport with and without collisions has also been investigated. The results will be reported at the upcoming International Congress on Plasma Physics (ICPP) Conference in Lisbon, Portugal in September. Professor Ganesh also interacted with W. Wang on the use of the GTS code.

**COMPUTATIONAL PLASMA PHYSICS GROUP **

S. Ethier represented PPPL at the DOE Laboratory Poster Session of the CSGF Annual Program Review held in Arlington, Virginia. The Department of Energy Computational Science Graduate Fellowship (DOE CSGF, http://www.krellinst.org/csgf/) program provides outstanding benefits

and opportunities to students pursuing doctoral degrees in fields of study that use high performance computing to solve complex science and engineering problems. As part of the program, CSGF fellows are required to complete a practicum project in one of the many DOE laboratories, giving them practical work experiences while strengthening collaborative ties between the national academic community and DOE laboratories.

### Jul 18~

### Jul 11~

The special theory seminar on July 8 was presented by Dr. Bruce Scott from Max-Planck-IPP EURATOM Association, entitled "Relaxation to neoclassical flow equilibrium in gyrofluid simulations". The abstract of the talk is "The theorem for toroidal angular momentum conservation within gyrokinetic field theory is used as a starting point for consideration of slow transport of flows under quasistatic force balance. The content of the momentum by itself yields a relation between the electric field and the parallel flow, if conserved/transported quantities are taken as given. The relation of poloidal to parallel flow then yields the radial electric field in terms of the poloidal flow as in the standard case. If the toroidal Mach number is not small this gives an iterable solution for the electric field provided neoclassical theory has given the poloidal flow of each ion species. In a gyrokinetic computation, provided the collision operator is sufficient (is conservative) this is enough to recover neoclassical results in the appropriate limit but is also applicable to more general situations. This treatment serves merely to underpin the ability of global gyrokinetic computations to treat neoclassical physics even when conventional ordering is relaxed. Finally, the pathway of relaxation to slowly varying conditions from an arbitrary initial state is detailed. The time scale hierarchy is separated to have Alfven and then geodesic oscillations damp away, and then on the ion collisional time scale the electric field is established, and then on the much slower confinement time the conserved quantities are transported. All of the important effects go through first order drifts, with the quadratic term in the Hamiltonian accounting for polarization."

### Jul 4~

A paper titled "Two-stream instability with time-dependent drift velocity" by H. Qin and R. C. Davidson was published in Physics of Plasmas http://dx.doi.org/10.1063/1.4885076 . In this paper, the classical two-stream instability driven by a constant relative drift velocity between two plasma components is extended to the case with time-dependent drift velocity. A solution method is developed to rigorously define and calculate the instability growth rate for linear perturbations relative to the time-dependent unperturbed two-stream motions. Stability diagrams for the oscillating two-stream instability are presented over a large region of parameter space. It is shown that the growth rate for the classical two-stream instability can be significantly reduced by adding an oscillatory component to the relative drift velocity.

A. Reiman presented a poster at the European Physical Society (EPS) meeting, held June 23-27 in Berlin, Germany, on "A Cross-Benchmarking and Validation Initiative for Tokamak 3D Equilibrium Calculations". The initiative involves eleven codes: two tokamak perturbative equilibrium codes, three time-dependent extended MHD codes, a gyrokinetic code, and five stellarator codes. Disagreements between some of the codes appear to arise from differences in their handling of localized currents at low order rational surfaces. Comparison of synthetic diagnostic data generated by the codes with experimental data may provide indirect evidence of the existence or nonexistence of such localized currents in contemporary experiments. Dedicated experiments for the purpose of generating data for code validation were performed on the DIII-D tokamak in May. As a first step towards analysis of the data, kinetic EFIT reconstructions are currently being generated for a selected set of shots and time slices within those shots.

N. Fisch attended the International Workshop on Runaways at Chalmers University in Gothenburg, Sweden, where on June 19 he gave an invited talk on "Backwards Runaways".

Together with H. Qin, W. Wu, and J. Liu, Dr. Fisch then gave a poster at the EPS meeting in Berlin, Germany on "Velocity Space Signature of Backwards Runaways."

### Jun 27~

Members of the PPPL Theory Department's Space Plasma Group attended the Geospace Environment Modeling (GEM) Summer Workshop at Portsmouth, Virginia on June16-20. Dr. P. Damiano presented a poster entitled "2D Gyrofluid-kinetic electron simulations of dispersive

scale Alfven waves in a dipole geometry" Dr. E.-H. Kim gave two oral talks entitled "Global Modeling of EMIC waves in Earth's Inner magnetosphere" and "Inferring magnetopsheric heavy ion density using EMIC waves". She also presented a poster entitled "Global Modeling of EMIC

waves in Earth's Inner magnetosphere: Generation and Application of linearly Polarized EMIC waves". Dr. J. Johnson gave a talk on "Role of kinetic Alfven waves on plasma heating and transport into the plasma sheet and Dr. P. Porazik presented a poster entitled "Modeling of Low

Frequency Anisotropic Instabilities."

### Jun 20~

E. Belova presented Theory Department Research & Review Seminar entitled “Using the HYM code for numerical simulations of NSTX and FRC” on June 20. Abstract reads: "The talk outlines progress in simulation studies of the effects of energetic beam ions on stability properties of sub-cyclotron frequency Alfven eigenmodes in the NSTX and global modes in FRCs, and numerical studies of FRC rotation control. Experimental observations from the NSTX have linked strong activity of global (GAEs) and compressional (CAEs) Alfven eigenmodes with a flattening of the electron temperature profile in beam-heated plasmas in NSTX. Previous theoretical studies attributed this effect to an enhanced electron transport due to these modes. This work presents self-consistent simulations of neutral-beam-driven AEs demonstrating an alternative mechanism, namely an energy channeling mechanism that will occur for any unstable CAE in NSTX or other toroidal devices. Also, the stability properties of a hybrid FRC in which field reversal is created both by plasma currents and by a low-density energetic component of large-orbit ions, have been studied by means of a generalized energy principle, and also by using three-dimensional numerical simulations using the HYM code. Effects of various boundary conditions on FRC spin-up and stability of the n=2 rotational and the n=1 wobble mode have been studied using the hybrid version of the HYM code."

### Jun 6~

W. Fox attended the Meeting of the American Astronomical Society, and presented a talk titled “Astrophysical Weibel Instability in Counter-Streaming Laser-Produced Plasmas”.

On May 30, L.E. Zakharov gave a Research & Review Seminar to the Theory Department, titled “Li-Wall Fusion - no alternative, no other option". He explained an innovative "particle diffusion based" confinement regime and introduced the LiWF theory. The implementation of this best possible confinement regime requires the plasma pumping from its edge, which is made realistic by the recent invention of a system with a continuous flow of thin lithium film (called 7/24 FLiLi) along the plasma facing surface of limiters or divertor plates. A lithium limiter based on this concept was manufactured, and delivered from PPPL to EAST tokamak in Hefei, China, where it was installed and prepared for the plasma experiments in July. An initial cylindrical version of a new vertical disruption code (CylVDE) was written by the Theory Department visitor Xujing Li. First results of CylVDE clarified the important details of plasma-wall interactions and MHD processes during disruptions. The simulations confirmed the generation of Hiro and Evans currents previously predicted by Zakharov and measured on EAST in 2012. These simulations stimulate the development of new diagnostics, which will measure the radial profile and localization of the Evans currents during disruptions. The corresponding proposal was submitted to NSTX-U management for future implementation.

**May 30~**

The theory seminar on May 29 was presented by Professor Julia Mikhailova from Department of Mechanical and Aerospace Engineering, Princeton University, entitled "Laser-driven synchrotron-type emission from solid surfaces". The abstract of the talk is "High-order harmonic emission from the interaction of relativistic-intensity laser pulses with solids offers the potential for intense ultrashort XUV/x-ray pulse generation. This highly nonlinear phenomenon was predicted by numerical simulations and later observed in many experiments. It is commonly explained in terms of the so-called “relativistic oscillating mirror” model (Doppler frequency upshift of light reflected by a moving surface). Here, a clear physical picture is presented for the generation of attosecond XUV/x-ray pulses from the interaction of relativistic-intensity laser pulses with overdense plasma slabs. The sub-cycle, field-controlled release and subsequent nanometer-scale acceleration of relativistic electron bunches under the combined action of the laser and ionic potentials give rise to synchrotron-like emission. This insight into the fundamental properties of the relativistic high-harmonic emission process allows for an analytical treatment of the effect. The high-frequency cutoff in the emission spectrum is explained in terms of the basic laws of synchrotron radiation. The emerging synchrotron-like radiation is confined to time intervals much shorter than the half-cycle of the driver field. This intuitive approach will be instrumental in analyzing and optimizing laser-driven relativistic sources of intense ultrashort XUV/X-ray pulses."

### May 23~

A paper entitled "Ponderomotive forces on waves in modulated media", by I. Y. Dodin and N. J. Fisch, was published in Physical Review Letters [Phys. Rev. Lett. 112, 205002 (2014)]. It is shown there that nonlinear interactions of waves via instantaneous cross-phase modulation can be cast in the same way as ponderomotive wave-particle interactions in high-frequency fields. The ponderomotive effect arises when rays of a probe wave scatter off perturbations of the underlying medium produced by a second, modulation wave, much like charged particles scatter off an oscillating electromagnetic field. Parallels with the point-particle dynamics, which itself is subsumed under this theory, lead to new methods of wave manipulation, including asymmetric barriers for light.

### May 16~

**THEORY**

A paper entitled "Geometric view on noneikonal waves", by I. Y. Dodin, was published in Physics Letters A [PLA 378, 1598 (2014)]. In this paper, an axiomatic theory of classical nondissipative waves is proposed that is constructed based on the definition of a wave as a ultidimensional oscillator. Waves are represented as abstract vectors in the appropriately defined space with a Hermitian metric. The metric is usually positive-definite but can be more general in the presence of negative-energy waves (which are typically unstable and must not be confused with egative-frequency waves). The very form of wave equations is derived from properties of the vector space. The generic wave equation is shown to be a quantum like Schrödinger equation; hence one-to-one correspondence with the mathematical framework of quantum mechanics is established, and the quantum-mechanical machinery becomes applicable to classical waves "as is". The classical wave action is defined as the density operator. The coordinate and momentum spaces, not necessarily Euclidean, need not be postulated but rather emerge when applicable. Various kinetic equations flow as projections of the von Neumann equation for the density matrix. The previously known action conservation theorems for noneikonal waves and the conventional Wigner-Weyl-Moyal formalism are generalized and subsumed under a unifying invariant theory. Whitham's equations are recovered as the corresponding fluid limit in the geometrical-optics approximation. The Liouville equation is also yielded as a special case, yet in a somewhat different limit; thus ray tracing, and especially nonlinear ray tracing, is found to be more subtle than commonly assumed. Applications of this axiomatization are also discussed, briefly, for some characteristic equations.

### May 9~

**THEORY**

The APS-DPP invited paper by F. Ebrahimi et al., entitled "Physics of forced magnetic reconnection in coaxial helicity injection (CHI) experiments in National Spherical Torus Experiment", was published in PoP online (see NSTX highlight and Publications listing at end).

The theory seminar on May 8 was presented by Professor Huishan Cai from the University of Science and Technology of China, entitled "Influence of energetic ions on resistive wall mode in reversed field pinch". The abstract of the talk is "A stability analysis of the circulating energetic ions (CEIs) on resistive wall mode is carried out in the reversed field pinch (RFP). In contrast to the minor resonant effects of CEI on resistive wall mode (RWM) in tokamak,the resonant interaction between RWM and CEI is important for high toroidal mode number in RFP with high beta value. The resonance provides an energy dissipation channel of free energy, and stabilizes RWM. As the fraction of CEI is large enough, the RWM is fully suppressed by CEI in the low plasma rotation, even vanishing rotation. Further, a possibility to suppress the RWM by CEI is suggested."

**COMPUTATIONAL PLASMA PHYSICS GROUP **

A finite element based Poisson solver has been developed in flux coordinates in GTS code. Various boundary conditions, including Dirichlet boundary condition, Neuman boundary condition, or mixed Dirichlet-Neuman boundary condition, are provided. The new Poisson solver has been rigorously tested against analytical solutions and benchmarked with the original solver in nonlinear ITG and TEM simulations. It is now routinely used for GTS production runs. The same finite element structure/framework can be applied to solving additional equations needed for finite-beta simulations in GTS. Finite element operators to find derivative and zonal flow are also implemented.

### May 2~

**THEORY**

The Center for Heliospheric Physics hosted a workshop on Space Weather at PPPL on April 16- 17. Participants included invitees from Los Alamos National Laboratory, NASA Goddard Space Flight Center, University of California-San Diego, and University of New Hampshire. The primary focus of the workshop was on the integration of kinetic effects into global multi-fluid computer simulation codes of the Earth's magnetosphere. This effort is supported by a multi- institutional grant, led from Princeton University and PPPL, by the NASA/NSF Partnership on Space Weather.

Many members of the Theory Department attended the 2014 U.S. Transport Task Force Workshop held in San Antonio, Texas, April 22-25. G. Fu gave a plenary talk titled “M3D-K simulations of energetic particle transport due to sawteeth, fishbone and TAE”. He also gave a summary talk on the energetic particle breakout sessions. Oral Presentations were made by C-S Chang, "Full-f gyrokinetic study of vorticity merging,meso/macro scale dynamics, and SOL- pedestal-core interaction in diverted geometry", N. N. Gorelenkov, "The effect of fast ion anisotropy and toroidal flow on plasma equilibrium", Robert Hager "Interaction between turbulence and geodesic acoustic modes near the separatrix", S-H. Ku "Effect of neoclassical and turbulence physics on divertor heat-load spread", Jianying Lang "Different Effects of ITG- dominant and TEM dominant turbulence on macro/meso scale ExB shear flow formation in the edge", Zhixin Lu ( long term PPPL visitor from UCSD) "Effects of q-profile on ITG/TEM induced intrinsic torque" and Weixing Wang "Roles of low-k Turbulence in Spherical Tokamak Plasma Transport". A poster presentation was made by Michael Churchill "Effects of a Pedestal on the Flux-Surface Variation of Impurity Density and Flows".

W. Tang participated in the invitation-only International Conference on Comparing HPC in the U.S. and China that was sponsored by the University of California Institute on Global Conflict & Cooperation (IGCC) and held at the San Diego Supercomputer Center in LaJolla, California, April 29-30. He gave an invited presentation on "Scientific Applications of HPC" that surveyed and compared prominent applications on leadership class supercomputers in the U.S. and China and also served on a panel discussing the current status of "Chinese Supercomputing Expertise."

**COMPUTATIONAL PLASMA PHYSICS GROUP**

Different plasma performance (energy confinement, discharge duration) has been observed in operationally close JET discharges with carbon (C) and ITER-like wall (ILW). The presence of tungsten (W) in ILW discharges leads to increased radiation, and this may partly explain the differences observed at JET and have an impact on ITER operation. Therefore, the penetration and accumulation of W impurity during the discharge evolution is a key analysis issue for JET. The first step in this analysis is the estimation of the neoclassical W diffusion and pinch as well as transport of other seeded impurities. The present version of TRANSP, which is the main analysis tool at JET, includes only the transport of an "averaged impurity" as computed by NCLASS. At the request of the JET TRANSP group, the NCLASS output has now been modified to provide detailed information about the different impurity species including their thermal and particle transport and fluxes, as well as poloidal and toroidal velocities on the mid- plane. For further information on this new capability, contact M. Gorelenkova.

### April 25~

**THEORY**

The theory seminar on April 24 was presented by Dr. Eun-Hwa Kim from PPPL entitled "Role of the ion-ion hybrid resonance in the planetary magnetospheres". The abstract is "Ion cyclotron frequency range waves (or electromagnetic ion cyclotron wave, EMIC) have been often observed at Earth and Mercury’s magnetospheres. Because the presence of different ion species has an influence on the plasma’s dispersion characteristics near the ion gyrofrequencies, new multi-ion resonances, such as Buchsbaum and ion-ion hybrid (IIH) resonances, are added with each additional ion species. When the frequency of incoming fast compressional waves matches the ion-ion hybrid resonance condition in an increasing (or decreasing) heavy ion concentration or inhomogeneous magnetic field strength, wave energy from incoming compressional waves concentrates and mode converts to electromagnetic ion cyclotron (EMIC) waves. Mode conversion at this resonance has been simulated using a multi-fluid code showing that the resulting EMIC waves are strongly guided by the ambient magnetic field (B_{0}) and have linear polarization, therefore, the IIH resonance has been suggested to be the field-line resonance at Mercury and linearly polarized EMIC waves at Earth. In addition, because the IIH resonance frequency depends on B_{0} and the ratio of the ion densities, the ratio of the ion densities can be estimated using the IIH resonance frequency of the observed linearly polarized EMIC waves. Using 1D and 2D full wave codes, time-dependent multi-ion wave model, we discuss how such IIH resonance occurs in the Earth and Mercury’s magnetosphere and how to infer heavy ion density using the IIH resonances."

A paper entitled “Analytical methods for describing charged particle dynamics in general focusing lattices using generalized Courant-Snyder theory” by H. Qin, R. C. Davidson, J. W. Burby, and M. Chung published this month in the Physical Review Special Topics – Accelerators and Beams was selected by the Editor as a highlight article for the journal. This paper analyzed the gauge group structure of the generalized Courant-Snyder (CS) theory for coupled beam dynamics. By fixing the gauge freedom with a desired symmetry, the generalized CS parametrization assumes the form of the modified Iwasawa decomposition, whose importance in phase space optics and phase space quantum mechanics has been recently realized. This gauge fixing also symmetrizes the generalized envelope equation and expresses the theory using only the generalized Twiss function beta. The generalized phase advance completely determines the spectral and structural stability properties of a general focusing lattice. For structural stability, the theory enables application of the Krein-Moser theory to greatly simplify the stability analysis. This new theoretical development provides an effective tool to study coupled dynamics and to discover more optimized lattice designs in the larger parameter space of general focusing lattices.

W. Fox attended the annual OMEGA Laser User Group conference at the University of Rochester Laboratory for Laser Energetics and presented a poster, "Colliding Magnetized and Unmagnetized Laser-produced Plasma Plumes for Laboratory Astrophysics"

**COMPUTATIONAL PLASMA PHYSICS GROUP **

E. Feibush presented a hands-on programming workshop at Princeton University on April 24 about scientific computing in Python. The session was a mini-course organized by PICSciE, the Princeton Institute for Computational Science and Engineering. The primary topic was Python's N-dimensional array software "numpy." Topics and programming exercises included the creation and use of computationally efficient arrays, applying Python's numerical functions, and plotting data in Python. There was also a demonstration of how to embed LaTeX commands into Python graph functions to format equations and high quality labels. Matthew Lotocki was the Teaching Assistant for the class. Researchers from ten different departments attended.

J. Chen implemented a new diagnostic in the nonlinear M3D-C1 extended MHD code to calculate and display the toroidal harmonics of the magnetic energy. This complements a similar diagnostic implemented earlier that calculates and displays the toroidal harmonics of the kinetic energy. This capability greatly assists the interpretation of the results of a 3D calculation and provides a consistency check when comparing weakly nonlinear runs with linear runs. Setting ibh_harmonics=nmax in the namelist file will calculate and plot the first nmax harmonics as a function of time.

### April 18~

**THEORY**

L. Zakharov visited Institute of Plasma Physics in Prague, Czech Republic and the COMPASS tokamak group on April 12-18. On April 14, Leonid gave an introduction to the advanced equilibrium reconstruction technique and demonstrated its implementation, the equilibrium code ESC-EEC. On April 16, he gave a talk entitled "Where is the edge in a tokamak plasma? Understanding the temperature pedestal" to the ITPA Pedestal and Edge Plasma meeting. On April 18 he also gave two talks entitled "Understanding disruption" and "LiWall Fusion: No Alternative, No Other Option" and discussed the problems of common interests with the COMPASS group.

The theory seminar on April 17 was presented by Dr. Guoyong Fu from PPPL and entitled "M3D-K simulations of energetic particle transport due to sawteeth, fishbone and TA". This talk was a dry run for Dr. Fu's invited talk at the upcoming TTF meeting. The abstract of the talk is "Recent results of M3D-K nonlinear simulations of energetic particle transport are presented. We investigate energetic particle redistribution due to sawteeth in tokamaks and due to fishbone and TAE in NSTX. The main results are (1) Sawteeth: Test particle simulations are carried out to study the energetic particle transport due to a sawtooth crash. The results show that energetic particles are redistributed radially in plasma core depending on pitch angle and energy. For trapped particles, the redistribution occurs for particle energy below a critical value in agreement with previous theory. For co-passing particles, the redistribution is strong with little dependence on particle energy. In contrast, the redistribution level of counter-passing particles decreases as particle energy becomes large. (2) Fishbone: Nonlinear simulations of beam-driven fishbone instability in NSTX have been carried out for weakly reversed q profiles with minimum of q just above unity. Result show nonlinear saturation with strong frequency chirping and beam ion profile flattening. (3) TAE: Nonlinear simulations of multiple beam-driven TAEs in NSTX have been carried out. Preliminary results show mode saturation, frequency chirping and beam ion distribution flattening."

On April 11, a theory seminar was presented by Dr. Oleg Kirillov from the Helmholtz-Zentrum at Dresden-Rossendorf, Germany, entitled "A unified WKB analysis of instabilities in magnetized Keplerian flows at low magnetic Prandtl number". The abstract reads "I will present recent theoretical results obtained in collaboration with Frank Stefani and Yasuhide Fukumoto. We perform a local stability analysis of rotational flows in the presence of a constant vertical magnetic field and an azimuthal magnetic field with a general radial dependence characterized by an appropriate magnetic Rossby number. Employing the short-wavelength approximation we develop a unified framework for the investigation of the standard, the helical, and the azimuthal version of the magnetorotational instability (MRI), as well as of current-driven kink-type instabilities. Considering the viscous and resistive setup, our main focus is on the case of small magnetic Prandtl numbers, which applies, e.g., to liquid metal experiments but also to the colder parts of accretion disks. We show in particular that the inductionless versions of MRI that were previously thought to be restricted to comparably steep rotation profiles extend well to the Keplerian case if only the azimuthal field slightly deviates from its field-free profile. We also find an explicit criterion for the critical magnetic field at the onset of the Tayler instability (TI) and demonstrate the details of transition between TI and azimuthal MRI in support of the planned MRI-TI experiment." On April 18 Professor A. Cole from Columbia University presented a talk, entitled "Variational Principles with Pade Approximants for Tearing Mode Analysis". The abstract of his talk is "Tearing modes occur in several distinct physical regimes, and it is often important to compute the inner layer response for these modes with various effects. There is a need for an approximate and efficient method of solving the inner layer equations in all these regimes. In this talk I introduce a method of solving the inner layer equations based on using a variational principle with Pade approximants. For all the regimes considered, the main layer equations to be solved are inhomogeneous, and Pade approximants give a convenient and efficient method of satisfying the correct asymptotic behavior at the edge of the layer. Results using this variational principle- Pade approximant method in three of these regimes are presented. These regimes are the constant-psi resistive-inertial (RI) regime, the constant-psi viscoresistive (VR) regime, and the non-constant-psi inviscid tearing regime. The last regime includes the constant-psi RI regime and the inertial regime. The results show that reasonable accuracy can be obtained very efficiently with Pade approximants having a small number of parameters."

### April 11~

**THEORY**

### March 28~

**THEORY**

A PRL by F. Ebrahimi and A. Bhattacharjee entitled "Helicity-Flux-Driven Alpha Effect in Laboratory and Astrophysical Plasmas" has been published online on March 25 at http://dx.doi.org/10.1103/ PhysRevLett.112.125003 It is demonstrated that much can be learned by viewing the dynamo problem in both laboratory and astrophysical plasmas from a common perspective. The constraint imposed by magnetic helicity conservation on the alpha effect is considered for two important and very different examples of tearing instability in laboratory plasmas (magnetically dominated self-organized plasmas) and MRI in flow driven astrophysical disks (flow dominated self-organized plasmas). By analysis and direct numerical simulations (DNS), it is demonstrated that in both cases a dominant contribution to the alpha effect can be cast in the functional form of a total divergence of an averaged helicity flux, called the helicity-flux-driven alpha effect.

Many members of the Theory department and the Princeton University/ Theory team attended the International Sherwood Theory Conference on March 24 -26, in San Diego California. D.P. Brennan, presented a poster“Control of resistive wall modes in a cylindrical tokamak with plasma rotation and complex gain”, J. Breslau, presented a poster, "Halo Currents and the M3D Boundary Condition", F. Ebrahimi presented a poster entitled "Physics of forced magnetic reconnection in coaxial helicity injection experiments in NSTX", Y-M. Huang,gave a talk, "Rapid Change of Field Line Connectivity and Reconnection in Stochastic Magnetic Fields", S. Hudson presented a poster "A new class of magnetic confinement device in the shape of a knot", W.W. Lee, "Effects of Background-Inhomogeneity-Generated Zonal Flows on Microinstabilities and Plasma Pressure Balance".

Theory Department Visiting Research Scholars presented posters; Xujing Li, "The Tokamak MHD (TMHD) plasma model", Michael. R. Halfmoon, University of Tulsa, “Energetic Particle Effects on Tearing Mode Stability with Varying β” and Spencer D. James, University of Tulsa, ‘Self-consistent calculations of the interaction between drift wave turbulence and the tearing mode”. S. James was one of six out of thirty two graduate students that won best student posters.

**COMPUTATIONAL PLASMA PHYSICS GROUP**

E. Feibush presented "Introduction to Python Programming" as a mini-course sponsored by the Princeton Institute for Computational Science and Engineering on March 27. Researchers from 12 different university departments attended. The hands-on programming session emphasized the elements and features of Python and how it can be used in a scientific workflow. Tools and techniques for self-paced learning of Python were demonstrated. PPPL teaching assistants M. Knyszek and M. Lotocki facilitated the programming exercises.

### March 21~

**THEORY**

The theory seminar on March 13 was presented by Professor Gennady Shvets from the University of Texas at Austin, entitled "Multi-Dimensional Collective Instabilities of Laser and Particle Beams Relevant to High Energy Density Laboratory Plasma Science". The abstract of the talk is "I will discuss how two of the oldest-known plasma instabilities, the Weibel Instability and the Raleigh-Taylor Instability, manifest themselves in the context of high energy density relativistic plasmas. The RTI will be described in the context of laser acceleration of thin targets by ultra-intense laser pulses. This acceleration regime, known as Radiative Pressure Acceleration (RPA) is very promising for developing compact sources of high-energy monoenergetic ions that could potentially find numerous applications ranging from fast ignition to cancer treatment. The first analytic model of a uniformly laser-accelerated target and discuss the stability of such targets to RTI will be discussed. PIC simulations reveal that considerable deviations of the growth rate of the RTI from the conventional scaling can emerge for ultra-high laser intensities. Paths to suppressing RTI using multi-ion species targets will be discussed. The Weibel Instability, which occurs when a beam-like plasma propagates through stationary plasma, has been proposed as a candidate for generation of strong magnetic fields and for sustaining collisionless shocks in astronomical environments. It will be demonstrated that there are severe constraints limiting the amount of directed beam energy that can be converted into magnetic field. Analytic results for relativistic beams undergoing filamentation and collisionless thermalization in dense plasma will be presented. A new type of a self-focused beam equilibrium similar to Bennett Pinch will be discussed. Because transverse temperature of the beam can suppress WI entirely, it will be discussed how quasi-electrostatic waves generated by the beam can recover the WI despite high temperature of the beam. The results of modeling WI using reduced-description codes will be presented."

On March 11, D. Stotler, W. Davis and G. Tchilinguirian ran the Robo-Cross competition at the New Jersey Science Olympiad State Tournament. Each of the 24 middle school teams participating in Robo-Cross designed and built a robot capable of moving various objects across a playing field and then placing them in a "goal" box.

A. Hakim gave a talk at the Courant Institute at NYU on "Discontinuous Galerkin schemes for a class of Hamiltonian evolution equations with applications to plasma kinetic problems" (http://math.nyu.edu/webapps/content/mfdd/seminars) describing work performed in collaboration with G. Hammett and graduate student Eric Shi, to develop a new approach for the difficult problem of simulating edge turbulence. While there he had discussions with Harold Weitzner, Antoinne Cerfon, and others, on these and other algorithmic topics.

W. Fox attended the Center for Magnetic Self-Organization Annual Meeting in Santa Fe, New Mexico, and presented an invited talk on recent results from laboratory astrophysics experiments, titled "Astrophysical Weibel instability in counter-streaming laser-produced plasmas."

A paper titled "On the nature of kinetic electrostatic electron nonlinear (KEEN) waves", by I. Y. Dodin and N. J. Fisch, appeared in Physical Plasmas 21, 034501 (2014). The paper reports an analytical theory for the so-called kinetic electrostatic electron nonlinear (KEEN) waves that were originally found in simulations by Afeyan et al [arXiv:1210.8105]. It is suggested that KEEN waves represent saturated states of the negative mass instability (NMI) reported recently by Dodin et al [Phys. Rev. Lett. 110, 215006 (2013)]. Due to the NMI, trapped electrons form macroparticles that produce field oscillations at harmonics of the bounce frequency. At large enough amplitude, these harmonics can phase-lock to the main wave and form stable nonlinear dissipationless structures that are nonstationary but otherwise similar to Bernstein-Greene-Kruskal modes. The theory explains why the formation of KEEN modes is sensitive to the excitation scenario and yields estimates that agree with the numerical results of Afeyan et al. It is also predicted that a new type of KEEN wave may be possible at even larger amplitudes of the driving field than those used in simulations so far.

### March 14~

On March 11, Daren Stotler, Bill Davis and Greg Tchilinguirian ran the Robo-Cross competition at the New Jersey Science Olympiad State Tournament. Each of the 24 middle school teams participating in Robo-Cross designed and built a robot capable of moving various objects across a playing field and then placing them in a "goal" box.

Ammar Hakim gave a talk at the Courant Institute at NYU on "Discontinuous Galerkin schemes for a class of Hamiltonian evolution equations with applications to plasma kinetic problems" (http://math.nyu.edu/webapps/content/mfdd/seminars) describing work performed in collaboration with Greg Hammett and graduate student Eric Shi, to develop a new approach for the difficult problem of simulating edge turbulence. While there he had discussions with Harold Weitzner, Antoinne Cerfon, and others, on these and other algorithmic topics.

Will Fox attended the Center for Magnetic Self-Organization Annual Meeting in Santa Fe NM, and presented an invited talk on recent results from laboratory astrophysics experiments, titled "Astrophysical Weibel instability in counter-streaming laser-produced plasmas."

A paper titled "On the nature of kinetic electrostatic electron nonlinear (KEEN) waves", by I. Y. Dodin and N. J. Fisch, appeared in Phys. Plasmas 21, 034501 (2014). The paper reports an analytical theory for the so-called kinetic electrostatic electron nonlinear (KEEN) waves that were originally found in simulations by Afeyan et al [arXiv:1210.8105]. It is suggested that KEEN waves represent saturated states of the negative mass instability (NMI) reported recently by Dodin et al [Phys. Rev. Lett. 110, 215006 (2013)]. Due to the NMI, trapped electrons form macroparticles that produce field oscillations at harmonics of the bounce frequency. At large enough amplitude, these harmonics can phase-lock to the main wave and form stable nonlinear dissipationless structures that are nonstationary but otherwise similar to Bernstein-Greene-Kruskal modes. The theory explains why the formation of KEEN modes is sensitive to the excitation scenario and yields estimates that agree with the numerical results of Afeyan et al. It is also predicted that a new type of KEEN wave may be possible at even larger amplitudes of the driving field than those used in simulations so far.

### March 7~

### February 28~

### February 21~

Publication appeared online this week: E. A. Startsev and W. W. Lee, "Finite-beta simulation of microinstabilities," Phys. Plasmas 21, 022505 (2014). The paper describes a new split-weight perturbative particle simulation scheme for finite-β plasmas in the presence of background inhomogeneities.

P. Damiano presented an Engineering Physics seminar entitled "Kinetic simulations of multi-scale electron acceleration by Alfven waves" in the Thayer School of Engineering at Dartmouth College on Feb. 18^{th} and engaged in research discussions with colleagues in both the Thayer School and the Department of Physics and Astronomy on topics including auroral physics, magnetosphere-ionosphere coupling and global magnetospheric MHD simulations.

Lan Gao and Chang Liu attended the NNSA Stewardship Science Academic Symposium in Bethesda MD. Lan Gao presented a talk on the progress of PPPL experiments on OMEGA EP, "Particle Acceleration and Small-Scale Structures of Collisionless Magnetic Reconnection Driven by High Energy Petawatt Lasers" and poster “Collisionless Magnetic Reconnection Driven by High Energy Petawatt Lasers”. Chang Liu presented poster titled "Magnetic Field Reconnection Driven by Heat Flux in Laser-Produced Plasmas".

### February 14~

**COMPUTATIONAL PLASMA PHYSICS GROUP**

A 3d Monte Carlo halo model has been developed and implemented in the TRANSP/NUBEAM code. Proper treatment of halo neutrals is crucial for the accurate simulation of Neutral Particles Analyzer (NPA) horizontal and vertical scan measurement. The most effective NPA diagnostics

employ sightlines that intersect the footprint of neutral beam injectors well inside the plasma to measure fast ion distributions ranging from thermal to supra-thermal via the charge exchange process that generates escaping neutrals. At this intersection, the contributions of injected and halo neutrals are larger than the “wall” neutrals that are localized near the plasma boundary. The charge-exchange cross section for halo neutrals is larger than that for primary beam neutrals and the spatial profile is broader which changes the NPA signal temporal evolution. We have added to the code a feature called "beam in box"—a bounded 3d gridded Cartesian domain aligned with each beam. Each neutral beam has its own box that represents the 3d "box" and gathers neutral density for the neutral beam itself,Eb, Eb/2, Eb/3 - lab. frame energy omponents, 3d fast neutral densities due to charge exchange of partially slowed down fast ions in the beam halo region, and, 3d thermal neutral densities due to the charge exchange deposition and fast neutral recapture source. This new feature allows greatly improved TRANSP-based NPA imulations as halo neutrals largely remain near the beam footprint.

### February 7~

**THEORY**

This week on Feb.4th, we had two short special theory seminars presented by M. Choi, from POSTECH, entitled "Improved estimation of the tearing mode stability parameters (D' and wc) with the 2D ECEI data in KSTAR" and by Dr. Y.S. Park from Colombia University, entitled "Investigation of Plasma Rotation Control by n = 2 NTV and Resistive MHD Stability in KSTAR". The abstract of M.Choi's talk is "The 2-D ECE images of the tearing mode with high spatial and temporal resolution provided the data set that can overcome the resolution limit of the conventional 1-D data in estimation of two important tearing mode stability parameters. The experimental images are directly compared with the synthetic ones based on a tearing mode model. An excellent agreement has been found between the measured images and synthetic ones from the model. The confidence level in the estimated tearing mode parameters has improved significantly and the estimated is consistent with the ideal MHD theory."

**COMPUTATIONAL PLASMA PHYSICS GROUP**

S. Ethier attended the annual NERSC Users Group meeting held in Berkeley and Oakland, California, on February 3-6. NERSC was celebrating its 40th anniversary with two days of science talks and retrospective on NERSC's accomplishments. The first day was a training day for new users of NERSC, followed by the 40th anniversary celebrations. The last day was dedicated to the "business meeting", during which the NERSC staff present the status and plans for the supercomputer center, and seek feedback from the user community on how to best support and enhance scientific discovery through high performance computation and storage. As the FES representative and chair of the NERSC Users Group Executive Committee, Ethier chaired the business meeting, which addressed important issues, such as the new data management requirements.

A teleconference was held on Feb 6 between the PPPL TRANSP group and Simon Pinches, Head of the ITER Confinement and Modeling group, and Frederic Imbeaux, Leader of the team developing the ITER Data Model (IDM). The subject of the call was to discuss a path forward for interfacing TRANSP input and output with the IDM, and the related goal of making TRANSP available to the ITER staff. It was decided that the TRANSP developers would begin by familiarizing themselves with the IDM by working through some example exercises on the ITER restricted web site. This requires that the TRANSP developers get accounts not only on the ITER site, but also on the ITER UNIX cluster. This process has begun and we plan to have another call in 1-2 months to discuss the next steps.

### Jan 31~

### Jan 17~

The theory seminar this week was presented by Lei Qi from Auburn University, entitled "GeFi Particle Simulation of Lower Hybrid Waves and Electron-ion Hybrid Instability". The abstract of the talk is "Lower hybrid wave (LHW) is a potential source to heat both electrons and ions to thermonuclear temperature and generate electric currents in fusion plasmas under Landau damping. Although linear Landau damping and nonlinear parametric instability of LHWs were well studied in theories, few particle simulations have been performed. In this talk, physics of LHWs is investigated with a gyro-kinetic electron and fully kinetic ion (GeFi) particle simulation model in the electrostatic limit. GeFi model is particularly suitable for plasma dynamics with wave frequencies lower than the electron gyrofrequency, and for problems in which the wave modes ranging from Alfvén waves to lower-hybrid/whistler waves that need to be handled on an equal footing with realistic electron-to-ion mass ratio. Firstly, the linear physics of lower hybrid waves and their nonlinear interactions with both electrons and ions through Landau amping are studied. Unlike most other wave modes, LHWs can resonantly interact with both electrons and ions, with the former being highly magnetized and the latter nearly unmagnetized around lower hybrid frequency. While the resonant electrons are trapped in the wave field in the nonlinear electron Landau damping, resonant ions are untrapped throughout the wave-particle interaction. Then, electron-ion hybrid instability driven by transversely sheared E×B flow, which plays an important role in laboratory and space plasmas, is studied by the GeFi model in the linear and nonlinear regimes. Electron-ion hybrid instability is in the lower hybrid frequency regime with ρe<LE <ρi, where ρi and ρe are the electron and ion Larmor radii, respectively, and LE represents the scale length of the shear flow profile. Realistic experimental parameters for Auburn Linear Experiment for Instability Studies (ALEXIS) device are adopted in GeFi particle simulations, and the results are compared with ALEXIS measurements."

W. Tang participated in the invitation-only DOE Advanced Scientific Computing Research (ASCR) Workshop on "Software Productivity for eXtreme-Scale Science (SWP4XS)," held at the Hilton Washington DC/ Rockville hotel, January 13-14. The workshop engaged computational scientists from academia, industry, and national laboratories to identify the major challenges of large-scale application software productivity on extreme-scale computing platforms.

Allan Reiman and a group of collaborators have submitted a proposal for a series of experiments on DIII-D that would provide data for validation for a set of 11 codes presently being cross-benchmarked. The collaborators on the proposal are: T. Evans, A. Turnbull, N. Ferraro, J. King, M. Lanctot and F. Turco, all from GA. Dr. Reiman has given presentations on the proposal to the DIII-D Research Opportunities Forum, to the FY 2014 Joint Research Target (JRT) working group, and to the 3D Plasma Response Task Force for DIII-D experimental planning.

### Jan 10~

The Letter by F. Ebrahimi and co-authors entitled "Magnetic reconnection process in transient coaxial helicity injection" http://dx.doi.org/10.1063/1.4821974 was selected for the 2013 PoP editor's list of top-ten letters.

An experiment conducted by W. Fox, A. Bhattacharjee, and collaborators at the University of Rochester Laboratory for Laser Energetics was chosen as the December "centerfold" for the 2014 LLE calendar. The purpose of the experiment is to study magnetic reconnection between counter-propagating, magnetized laser produced plasmas. The calendar is available for download at http://www.lle.rochester.edu/publications/calendars/2014_calendar.php

### Dec 20 & Jan 3~

**THEORY**

This week's theory seminar of this year was presented by Professor Eliezer Hameiri from New York University, entitled "Multi-fluid and MHD plasmas with flow, a variational approach". The abstract of the talk is "Based on an extension to plasmas of Ertel’s classical vorticity theorem in fluid dynamics, it is shown that for each species in a multi-fluid plasma there can be constructed a set of nested surfaces that have this species’ fluid particles confined within them. Variational formulations for the plasma evolution and its equilibrium states are developed, based on the new surfaces and all of the dynamical conservation laws associated with them. A limit of the variational integral yields the two-fluid Hall-Magnetohydrodynamic (HMHD) model. A further special limit yields MHD equilibria and can be used to approximate the equilibrium state of a

Hall-MHD plasma in a perturbative way."

**COMPUTATIONAL PLASMA PHYSICS GROUP**

The CY2014 NERSC computer time allocation awards for PPPL were announced this week. The PI's, Projects, and awards (in millions of core hours) were: A. Bhattacharjee, "Center for Integrated Computation and Analysis of Reconnection and Turbulence", 5M; S. Cohen, "FRC simulations with the Lsp PIC code: 10M; R. Davidson, "Simulations of Field-Reversed Configuration and Other Compact Tori Plasma": 0.070M; S. Jardin, "Study of the Internal Dynamics of ITER", 13M; S. Jardin, "3D Extended MHD Simulation of Fusion Plasmas", 20M; W. Lee, "Turbulent Transport and Multiscale Gyrokinetic Simulation, 25M; D. Mikkelsen, "Experimental Tests of Gyrokinetic Simulations of Microturbulence", 15M; W. Wang, "Investigation of Plasma Rotation Inversion and Profile Structure in Magnetic Fusion Experiments", 3.2M.

## 2013 Theory Department Weekly Highlights

### Dec 13~

**THEORY **

On December 12, Professor Luca Guazzotto (a long-term visitor to the theory department) gave a talk on "Perturbed equilibrium in tokamaks", addressing the hot topic applications, such as (a) thermal quench, (b) runaway electrons, (c) wall touching kinetic mode, (d) resonant magnetic perturbation, (e) plasma boundary perturbations. He described a theoretical and numerical approach to calculation of perturbed equilibria. The interest in the topic comes from the fundamental observation that equilibrium in tokamaks is not represented adequately by axisymmetry. ather, the magnetic configuration is always perturbed. Even in their quiescent phase, the tokamak plasmas are subject to edge perturbations. An equilibrium description is preferable with respect to a stability one because it describes the real state of the plasma without the need to rely on a plasma model. The formalism described has removed the major difficulty in extension of the ideal stability codes to resistive models. The quasi-linear model of the islands was described. A special form of the energy principle used outside islands allows to use the sameisland mode in the toroidal case. The approach has been implemented into a reduced-MHD version of a numerical code, which was supplied to ITER Organization earlier. A plan for the implementation of a full toroidal perturbed equilibrium model was describe.

A. Reiman presented an experimental proposal to the DIII-D Research Opportunities Forum on December 5. General Atomics collaborators on the proposal are T. Evans, A. Turnbull, N. Ferraro, J. King, M. Lanctot, and F. Turco. It is proposed that DIII-D shot 146058 be reproduced,and that systematic scans in plasma parameters and resonant magnetic perturbation spectrum be performed around that equilibrium. The purpose is to provide a rich data set for validation that can be used by stellarator codes as well as tokamak codes. Secondarily, it is believed that there is a strong possibility that these experiments will demonstrate ELM suppression in a stellaratorsymmetric field for the first time. Shot 146058 had a stellarator-symmetric field, and it displayed very strong ELM mitigation, close to ELM suppression. The proposed experiments would llow the application of powerful new diagnostics that have been installed on DIII-D in recent years to stellarator symmetric plasmas for the first time. The information from these diagnostics will be valuable for validation. It will be of particular interest to compare 3D equilibrium solutions with and without strong ELM mitigation.

### Dec 6~

**THEORY**

Paper by W. Fox, A. Bhattacharjee, et al, "Filamentation Instability of Counterstreaming Laser Driven Plasmas" was published in Physical Review Letters on November 27. P. Porazik and J. R. Johnson’s paper entitled "Gyrokinetic particle simulation of nonlinear evolution of mirror instability" has been published in Journal of Geophysical Research at the end of last month. The paper describes gyrokinetic particle simulations of the mirror instability, and discusses simulation results on saturation levels, and nonlinear structure formation.

On November 26, R. Kulsrud presented seminar on his memories of Lyman Spitzer prepared in celebration of Spitzer's 100th birthday. This historic talk was videotaped and the video is available online.

This week's regular theory seminar was presented by Dr. Greg Bewley from Max Planck Institute, Germany, entitled "The decay of turbulence: experimental scrutiny". Abstract: "Fluid turbulence is fascinating in part because it is disordered and therefore seems naturally resistant to organization. Underlying a wide range of natural phenomena like mixing is the as-yet unanswered question of how turbulence dissipates mechanical energy. The practical implication is that turbulence often cannot accurately be modeled, despite a long history of study. Freely decaying laboratory turbulence, a representative for both transient and wake flows, provides a rich environment in which to generate and to test ideas. Descriptions will be provided about systematic experiments that reveal the interplay between large and small scale characteristics of turbulent flow."

The PPPL UNIX "mccune cluster" with 256 cores has been brought online for dedicated use by TRANSP runs. In addition, 80 cores in the fielder cluster are also being made available for use by TRANSP. These additional compute resources are needed due to the increasingly heavy use of the NUBEAM, TORIC and PT_SOLVER mpi components in TRANSP.

S. Ethier gave a tutorial on mixed parallel programming at Princeton University's Institute for Computational Science and Engineering. The event was attended by over 20 researchers and students from several departments at the University, such as physics, engineering, chemistry, economics, political science, and others. Participants learned to exploit the power of parallel computing on distributed memory systems using message passing (MPI) combined with shared memory multi-threaded parallelism using OpenMP directives on multicore processors. GPU programming with recently-developed OpenACC directives was also presented. Mixed parallel programming with all of these methods together allows for very high scalability on the largest computers currently available, such as the hybrid CPU-GPU Cray XK7 "Titan" at the Oak Ridge Leadership Class Facility.

### Nov 22~

**THEORY**

J. Johnson and E.H. Kim attended an electromagnetic ion cyclotron (EMIC) wave workshop at the University of New Hampshire on November 13-14. J. Johnson suggested that the ion-ion hybrid (IIH) resonance can explain magnetospheric compressional waves, which are newly detected by Van Allen probes, and E.H. Kim showed how the IIH resonance can have narrow bandwidth with magnetic compressional components using numerical simulations. They also suggested that mixed polarized EMIC waves could be generated by external sources rather than by locally generated instabilities. Dr. Chung-Sang Ng (University of Alaska) gave a talk entitled "MHD Simulations of the Parker Model of Solar Coronal Heating" for Helio-seminar on November 19. Using new scaling results based on 2D and 3D reduced MHD simulations, he discussed the Parker model which is one of most discussed mechanism of solar coronal heating. His presentation has been posted on http://helio.pppl.gov.

This week, two theory seminars were presented. On November 21, the seminar was presented by Dr. J. Perez from University of New Hampshire entitled "Direct Numerical Simulations of Reflection-Driven, Reduced MHD Turbulence from the Sun to the Alfvén Critical Point". The abstract of this talk is "We present a numerical study of the fundamental properties of reflectiondriven Alfven Wave (AW) turbulence and its applications to the extended solar atmosphere, using realistic profiles that account for the inhomogeneities in density, background flow, and the background magnetic field present in coronal holes. The simulations are performed inside a narrow magnetic flux tube extending from the base of the solar corona to about eleven solar radii. The simulation results address the radial dependence of turbulence spectral slopes, energy cascade rates as well as other important turbulence characteristics in the context of existing phenomenological models and remote observation."

The second theory seminar on November 22 was presented by Dr. F. Halpern from Center for Research in Plasma Physics, Ecole Polytechnique Federale de Lausanne, entitled "A theory for the scrape-off layer width in inner-wall limited plasmas". The abstract reads "We develop predictive theory applicable to the scrape-off layer (SOL) of inner-wall limited plasmas. Using the non-linear flattening of the pressure profile as a saturation mechanism for resistive ballooning modes, we are able to demonstrate and quantify the increase of the SOL width with plasma size, connection length, plasma beta, and collisionality. Individual aspects of the theory, such as saturation physics, parallel dynamics, and system size scaling, are tested and verified using non-linear, 3D flux-driven SOL turbulence simulations. Altogether, good agreement between theory and simulation is found."

A. Reiman organized a lunchtime satellite meeting at APS on cross-benchmarking of codes for calculating 3D equilibrium solutions for DIII-D plasmas. The participants discussed plans for benchmarking activities, and they agreed on a set of specifications for data files from the codes to be used for comparison of equilibrium solutions. There are 11 codes participating in the benchmarking activity: the linearized equiilibrium codes IPEC (J-K Park) and MARS (Turnbull), the time-dependent extended MHD codes M3D-C1 (Ferraro), M3D (Breslau), and NIMROD (Sovinec, Zhu), the guiding center particle code XGC0 (Chang, Hager), as well as VMEC (Lazarus, Lazerson), NSTAB (Garabedian's code: Cerfon, McFadden), PIES (Reiman), HINT (Suzuki in Japan) and SPEC (Hudson). The names in parentheses are the people running

the codes for this exercise.

**COMPUTATIONAL PLASMA PHYSICS GROUP **

J. Lang and S. Ethier attended the SC13 International Conference for High Performance Computing, Networking, Storage, and Analysis. Both Drs. Lang and Ethier were co-authors on a poster presentation entitled "Hybrid MPI/OpenMP/GPU Parallelization of XGC1 Fusion Simulation Code" (Eduardo F. D'Azevedo {ORNL}, J. Lang {PPPL}, Patrick H. Worley {ORNL}, S. Ethier, S.H. Ku, C.S. Chang {PPPL}). Ethier was also a co-author on a talk entitled "Kinetic Turbulence Simulations at Extreme Scale on Leadership-Class Systems" (Bei Wang {Princeton U.}, S. Ethier, W. Tang {PPPL}, Timothy Williams {ANL}, Khaled Ibrahim {LBNL}, Kamesh Madduri {PENN}, Samuel Williams, Leonid Oliker {LBNL}) and another poster, "Scibox: Online Sharing of Scientific Data via the Cloud" (Jian Huang, Xuechen Zhang, Greg Eisenhauer, Karsten Schwan, Matthew Wolf {GATech}, S. Ethier {PPPL}, Scott Klasky {ORNL}).

### Nov 15~

Many researchers from the Theory Department attended the meeting of the APS Division of Plasma Physics in Denver, Colorado, November 11–15. F. Ebrahimi gave invited talk A. Bhattachajee gave invited talk " at the High Energy Density Science Association (HEDSA) Symposium on November 10.

### Nov 8~

**THEORY**

A new theory opens the door to using stochastic variational integrators to perform simulations of stochastic interactions such as Fermi acceleration. Before the discovery of relativity, Einstein solved another riddle of physics, the Brownian motion, in 1905. He derived a Fokker-Planck equation (FPE) for the statistical properties of the Brownian motion, and from this equation the famous Einstein relation. One year later, Langevin recovered Einstein’s result from a different, “infinitely more simple” approach using a differential equation, which now bears his name and is known as the first stochastic differential equation (SDE). In essence, the remarkable achievement of Langevin was to find a SDE that is able to recover the statistical properties of the physical system described by the Fokker-Planck equation derived by Einstein. However, when trying to apply this method to inhomogeneous systems in higher dimensions, one finds that there exist many different SDEs corresponding to one given FPE. Are these different SDEs all equivalent? Is there a unique way to select the correct SDE? This question was answered by Joshua W. Burby, a graduate student at Princeton University, and his collaborators in a paper published this week in Physical Review Letters (see publications section for reference). To put this question to rest, the Einstein-Langevin theory needs to be generalized using a modern geometric method. It turns out that the two-particle FPE uniquely determines a Hamiltonian Langevin equation, and a procedure using the reproducing kernel of a Hilbert space of vector fields is developed to calculate the terms in the Langevin equation. In this geometric framework, the Hamiltonian nature of the underlying microscopic dynamics is retained for both the Fokker-Planck equation and Langevin’s equation, which also opens the door to using stochastic variational integrators to simulate stochastic interactions, such as the Fermi acceleration, with long-term statistical fidelity.

Dr. Scott Boardsen (NASA/GSFC, University of Maryland) gave a talk entitled "Recent progress on ultra low frequency (ULF) waves at Mercury" for theory/helio seminar on November 7. Waves are primarily observed in two frequency ranges in Mercury's inner magnetosphere. Among them, waves in 0.2 to 2 Hz are believed to be related to either/or waves on the magnetopause that feed field-line resonances, or caused by local instabilities. In his talk, he focused on whether these waves could be due to a local instability from the large planetary losscones imposed upon a high proton beta plasma ~0.1 to 0.5. He showed that (1) the proton distribution is highly unstable to the ion-Bernstein mode and that the moderately high proton beta of 0.1 yields solutions with a significant wave magnetic field component; and (2) as the waves propagate, they cycle back and forth across the magnetic equator. For half of each cycle the wave mode is compressional, while in the other half it is moderate/weakly compressional. Fatima Ebrahimi presented a talk entitled "Helicity-Driven Alpha Effect in Laboratory and Astrophysical Plasmas" at the Max Planck/Princeton Plasma Center general meeting on November 1. She presented the results from a recent paper by F. Ebrahimi and A. Bhattacharjee submitted to Phys. Rev. Lett.

**COMPUTATIONAL PLASMA PHYSICS GROUP**

The M3D-C1 code is now fully operational and in production mode on the multi-petaflops Cray XC-30 system at NERSC named Edison. This installation involved considerable collaboration between J. Chen (PPPL), N. Ferraro (GA), the SCOREC team at RPI, CRAY research, the NERSC consultants and the PETSc team in order to track down compiler bugs and software normally memory limited when running on the older NERSC Cray XE6 machine Hopper, and for most jobs uses only 12 of the 24 processors per node because of these memory limitations. Edison has twice the memory per node as Hopper, and so M3D-C1 can make use of all the processors on each node, resulting in a relative speedup of about two comparing two jobs using an equal number of nodes on the two machines.

A TRANSP Users Group meeting will be held on November 14 from 12:30 - 2:00pm in the Directors Row H room in the Sheraton at the APS meeting in Denver, Colorado. The TRANSP team will make short presentations highlighting the progress that has been made in several areas,

among them: (1) parallel solver development, (2) new free-boundary equilibrium and control capabilities, (3) NUBEAM enhancements, (4) automated regression testing, (5) TRANSP at NERSC. The remainder of the meeting will be for discussion and to hear requests from TRANSP

users.

### Nov 1~

**THEORY**

Guiding center simulations play an important role in understanding the effect of ideal andresistive modes on high-energy particle distributions. Both injected beam particle and fusionalpha particle distributions can be significantly modified by Toroidal Alfven instabilities,producing losses and significant wall loading. Until recently, simulations of the effect ofToroidal Alfven eigenmodes (TAE) on beam distributions have taken up to several days ofsimulations on a single processor computer. This summer, Princeton University student Ante Qu implemented a new, highly multi-threaded GPU version of the guiding center code ORBIT under the supervision of S. Ethier and E. Feibush. The new version is 128 times faster than the old version and is currently being used for full-production simulations of induced particle loss by TAE modes in NSTX and TAE-induced avalanches. National Undergraduate Fellowship Award recipient, Ante Qu will present a poster on this research at the APS Division of Plasma Physics in Denver, Colorado on November 12 at 2:00 PM. The poster number is JP8.00025.

A paper by collaborators at the University of Saskatchewan, Canada and PPPL “Sheath-Induced Instabilities in Plasmas with E×B Drift” investigates possible mechanisms of anomalous transport in Hall thrusters. Classical inter-particle collisions alone are too weak to explain experimentally observed electron currents across magnetic field. A new instability was identified. It is shown that ion acoustic waves in plasmas of finite size with E×B electron drift become unstable due to the closure of plasma current in the chamber wall. Such unstable modes may enhance anomalous electron transport in plasma devices with E×B electron drift and unmagnetized ions. The instability is sensitive to the wall material: a high value of the dielectric permittivity of the wall material reduces the mode growth rate by an order of magnitude. This theoretical study may explain previous experimental findings that wall material may strongly affect Hall thruster operation.

### Oct 25 ~

**THEORY**

Jacob Bortnik, from UCLA, visited PPPL on October 23. He gave a space seminar about the role of whistler chorus in energizing electrons in the radiation belt region, and showed how traditional quasilinear approaches do not adequately describe the transport when the wave amplitudes are sufficiently large. He was also the PPPL colloquium speaker and discussed the role of waves in the inner magnetosphere and showed new results on acceleration processes from NASA's Van Allen Probes mission. J. Johnson led an international team working on plasma entry and transport at the International Space Science Institute in Bern, Switzerland October 16-18. The team is preparing a review article on plasma entry and transport in the plasma sheet that will be submitted to Space Science Reviews.

P. Damiano was in Boulder, Colorado between October 15-18 visiting both the High Altitude Observatory (HAO/NCAR) and the Laboratory for Space and Atmospheric Physics (LASP) at the University of Colorado, Boulder. He presented a colloquium at HAO on October 16 entitled "Kinetic simulations of electron acceleration in Alfvenic Aurora" and engaged in research discussions with several colleagues at both institutions on topics including, Alfvenic aurora in terrestrial and giant planet magnetospheres, plasma sheet transport and coronal heating.

**COMPUTATIONAL PLASMA PHYSICS GROUP **

S. Jardin attended the Integrated Modeling Expert Group (IMEG) meeting at the ITER Organization (IO) headquarters as one of the two U.S. representatives (with L. Lao, GA). The meeting served several purposes. (1) Presentations were made by the representatives of each of the seven domestic programs on IM developments of interest to ITER since the last meeting; (2) The IO IM team described progress in developing an Integrated Modeling and Analysis Structure (IMAS) since the last meeting; and (3) The IMEG group served as a program advisory panel and provided advise on prioritizing future activities. It was observed that substantial progress has been made in defining an ITER data model and analysis framework, and recommendations were made that the domestic agencies begin to adapt their analysis tools to be compatible with the emerging ITER data model. Some of this activity is already occurring.

A poster and a two-page paper titled "Hybrid MPI/OpenMP/GPU Parallelization of XGC1 Fusion Simulation Code" by E.F. D’Azevedo, J. Lang (PPPL), P. H. Worley, S.A. Ethier (PPPL), S.-H. Ku (PPPL), and C.-S. Chang (PPPL) was submitted to The International Conference for High Performance Computing, Networking, Storage, and Analysis (SC13). The abstract reads "By exploiting MPI, OpenMP, and CUDA Fortran, the FORTRAN fusion simulation code XGC1 achieves excellent weak scalability out to at least 18,624 GPU-CPU XK7 nodes, enabling science studies that have not been possible before. XGC1 is a full-f gyrokinetic particle-in-cell code designed speci cally for simulating edge plasmas in tokamaks. XGC1 was recently ported to and optimized on the 18,688 node Cray XK7 sited in the Oak Ridge Leadership Computing Facility, making use of both the 16-core AMD processor and the NVIDIA Kepler GPU on each node. XGC1 uses MPI for internode and intranode parallelism, OpenMP for intranode parallelism, and CUDA Fortran for implementing key computational kernels on the GPU. XGC1 also uses the CPU and GPU imultaneously for these computational kernels. The optimized version achieves a four times speed-up over the original CPU-only version."

### Oct 18 ~

**THEORY**

Eun-Hwa Kim gave a talk entitled "Linear mode conversion of Langmuir/z-mode waves to radiation in plasmas with various magnetic field strength" at "STEREO/WAVES & WIND/WAVES workshop on Solar Radio Emissions". This talk provided numerical results of linear mode conversion in warm, magnetized plasmas. The results showed that both left-handed polarized ordinary and right-handed polarized extraordinary mode waves are produced in wide range of magnetic strengths and angles to the ambient magnetic field. In particular, in the intermediately-magnetized plasmas, the right-handed extraordinary waves can be generated for the oblique density gradient to the magnetic field through the linear mode conversion.

Theory seminar this week was presented by R.M. Churchill from MIT entitled "Flux Surface Variation of Impurity Density and Flows in the Pedestal Region of Alcator C-Mod". The asymmetry of boron density and flows measured in the pedestal region of Alcator C-Mod was reported. These asymmetries were observed in localized regions between the low-field side and the high-field side. The talk was well received with many questions raised by participating experimentalists and theoretists. The abstract of his talk is: "Measured impurity density and flows in the pedestal region of Alcator C-Mod can deviate significantly on a flux surface from current model predictions. Comparing localized measurements at the low-field side (LFS) midplane and the high-field side (HFS) midplane, boron (B5+) impurity density asymmetries larger than 10 are observed in H-mode plasmas, with larger densities at the HFS. The LFS density pedestal varies in position and width with varying plasma conditions, while the HFS impurity density profile remains rather fixed. Impurity density asymmetries are not observed in plasmas with small gradients, i.e L-mode, suggesting the drive for the asymmetry may be the strong gradients in the H-mode pedestal region. However, impurity density asymmetries are also absent in I-mode plasmas, despite the presence of a strong radial gradient in temperature (with no main ion density pedestal). This indicates an interplay between the gradient scale lengths of the main ion density and temperature in the drive of the impurity density asymmetry. Possible and probable causes of these density and flow asymmetries will be explored, including localized

sources, poloidally asymmetric radial transport, and ion-impurity friction."

**COMPUTATIONAL PLASMA PHYSICS GROUP**

E. Feibush produced a high quality movie of a simulated complete three-dimensional sawtooth cycle in the DIII-D tokamak as computed by the M3D-C1 extended MHD code using VISIT. The high-resolution M3D-C1 calculations, which spanned about 5 complete cycles, were

performed on Hopper at NERSC using 1500 processors for over 300 hours. The movie is unique in that it clearly shows the evolution of the electron temperature and the current density in the same frames. The movie makes clear that in this calculation, the "crash" of the high temperature that was originally on the magnetic axis occurs substantially faster than the magnetic reconnection time. This movie will be shown at the upcoming Max-Plank/Princeton Center reconnection workshop.

### Oct 11 ~

**THEORY**

This week's theory seminar titled “Magnetic reconnection process in transient coaxial helicity injection" was presented by Dr. Fatima Ebrahimi from Department of Astrophysical Sciences, Princeton University. Dr. Fatima Ebrahimi was awarded an invited talk on this topic at the upcoming APS-DPP meeting. The talk was well-received and generated fruitful discussion. Her simulations show that the reconnection process for the transient coaxial helicity injection in NSTX has a Sweet-Parker characteristics; this conclusion is based on the scaling of width of the elongated current sheet. Future research will involve detailed study of the outflows during reconnection. The abstract reads: "Non-inductive current formation and its sustainment is one of the major physics objectives in NSTX as an advanced Spherical Torus (ST). A promising candidate for start-up current formation is Coaxial Helicity Injection (CHI). We numerically examine the physics of transient CHI for start-up in NSTX. Through resistive MHD simulations, we first obtain the minimum conditions required for generating closed flux and then explain the fundamental mechanism for magnetic reconnection and closed flux generation in transient CHI discharges. We find that at sufficiently low magnetic diffusivity (high Lundquist number), and with a sufficiently narrow injector flux footprint width, the oppositely directed field lines have sufficient time to reconnect (before dissipating), leading to the formation of closed flux surfaces. Simulations show that an X point is formed in the injector region, followed by formation of closed flux surfaces within 0.5 ms after the driven injector voltage and injector current begin to rapidly decrease. As the injector voltage is turned off, the fields lines tend to untwist in the toroidal direction and magnetic field compression exerts a radial J × B force and generates a bidirectional radial Etoroidal × Bpoloidal pinch flow to bring oppositely directed field lines closer together to reconnect. The reconnection process is shown to have transient Sweet-Parker characteristics (http://pop.aip.org/resource/1/phpaen/v20/i9/p090702_s1 ). There are similarities between the transient Sweet-Parker reconnection found here and that reported in forcedreconnection laboratory plasmas of MRX. "

### Oct 4 ~

**THEORY**

This week's theory seminar (on October 3) was presented by Dr. J. P. Boeuf from LAPLACE, CNRS, University of Toulouse on "Rotating instabilities in low temperature magnetized plasmas". The abstract of the talk is "After a short introduction on the activities on low temperature magnetized plasmas at the LAPLACE laboratory in Toulouse (Hall thrusters, negative ion source for the ITER neutral beam injector), we will present and discuss recent results from PIC MCC (Particle-In-Cell Monte Carlo Collisions) simulations of low beta magnetized plasma columns, 1) under conditions of electron beam sustained plasma columns such as the MISTRAL device at the PIIM laboratory in Marseille, and 2) under conditions of cylindrical magnetron discharges. Typical plasma parameters in theses devices are: plasma density in the range [1014-1016 m-3], electron temperature [0.1-5 eV], magnetic field [10-50 mT], gas pressure [10-2 -1 Pa]. In the case of the MISTRAL device, the simulations show a low frequency ExB rotation of the plasma associated with an azimuthal non-uniformity of the plasma potential that reproduces well the experimental results and provides a physical interpretation of the LIF (Laser Induced Fluorescence) measurements of the ion velocity distribution recently performed at the PIIM laboratory1. In the case of cylindrical magnetrons, where a larger current is drawn across the magnetic field by the applied voltage, the simulations predict the formation of a rotating instability associated with an ionization front (« rotating spoke ») whose properties are very similar to those observed in the experiments developed in the 1960s-1980s to study the concept of critical ionization velocity2 (CIV). The CIV concept had been introduced by Alfven in his theory of planet formation.[1] C. Rebont, N. Claire, Th. Pierre, and F. Doveil, Phys. Rev Lett. 106 225006 (2011)[2] A. Piel, E. Möbius and G. Himmel, Astrophysics and Space Science 72 211 (1980); N. Brenning, Space Science Review 59 209 (1992)".

We also had a second theory seminar on October 4 presented by Professor Andrei Smolyakov from the University of Saskatchewan on "Coupling of sheath and bulk plasma fluctuations in plasmas with ExB drift". It was discussed that sheath induced instabilities such as ion sound wave instability can contribute to anomalous electron transport in Hall plasmas (magnetized electrons and unmagnetized ions), e.g. thrusters. Sheath boundary conditions were incorporated in the linear dispersion relation for ion sound wave instability in the presence of ExB drift velocity. The frequency range of these modes was similar to what has been found in the PIC simulations. Here is the abstract of the talk. "It is demonstrated that closure of plasma current in the dielectric or metal wall strongly modifies plasma stability. Generalized sheath boundary conditions are derived for a dielectric wall. It is shown that ion acoustic waves in plasmas with ExB electron drift become unstable due to coupling of plasma and sheath dynamics, which is sensitive to the wall material. Such unstable modes may enhance both near-wall conductivity and turbulent electron transport in plasma devices with ExB electron drift and unmagnetized ions."

### SEP 27 ~

**THEORY **

Drs. N.N. Gorelenkov and G.Y. Fu attended the IAEA technical committee meeting on energetic particles in fusion research held in Beijing, China, September 17-21. Dr. N.N. Gorelenkov gave an oral talk on " Critical Gradient Model for AE Fast Ion Relaxation and its validation against the DIII-D experiments" whereas Dr. G.Y. Fu presented an invited talk "Linear Stability and Nonlinear Dynamics of n=1 Fishbone in NSTX reversed shear plasmas". Few key presentations of the meeting were devoted to the models to describe the fast ion profiles and their relaxation in tokamak plasmas. The experiments were performed and documented on DIII-D, which demonstrated stiff fast ion profiles in the presence of alfvenic instabilities driven by beam ions. Two theories developed independently supported these observations. One of them is developed at PPPL by Drs. N.N. Gorelenkov and K. Ghantous and is relatively approximate. It shows the surprising agreement with experimental measurements. The theory is based on wellvalidated linear stability computations of alfvenic instabilities and is able to predict fast ion beta profile, compute their losses and neutron signal drops. The later was used to compare the predictions of the model with the experiments. Applications of the model for planned burning plasma experiments were argued to be the motivations for future validations. Another theory on this subject was developed at General Atomics and was presented using the code GYRO and is complementary to the critical gradient model of PPPL.

Dr. W. Tang visited the Keldysh Institute of Applied Mathematics (KIAM) in Moscow, Russia and presented an invited talk on "Theoretical Basis and Algorithms for Advanced HPC Fusion Simulations" on September 26. As the US PI for the G8-sponsored Nuclear Fusion Simulations

@ Extreme Scale (NuFuSe) project, which is supported by the NSF, he was hosted by the Russian PI for this G8 project, Academician Boris Chetverushkin – the KIAM director and a distinguished member of the Praesidum of Russia's National Academy of Science (RAS) – to engage in timely strategic planning/future collaborative discussions.

**COMPUTATIONAL PLASMA PHYSICS GROUP**

The Hamiltonian guiding center code ORBIT went through a major performance upgrade this summer thanks to the work of Princeton University undergraduate student Ante Qu, who was the recipient of a DOE OFES National Undergraduate Fellowship. The summer internship project,

under the supervision of CPPG S. Ethier and E. Feibush, consisted in the parallelization of the ORBIT code for multi-threaded architectures, such current multi-core CPUs and high performance Graphical Processing Units (GPUs). By using the OpenMP directive-based approach on CPU, and CUDA-Fortran GPU extensions for GPU. The upgraded ORBIT code was able to reach a 53X speedup improvement on the latest Nvidia GPU compared to its traditional single-core speed. The OpenMP multi-threaded version, which takes advantage of shared memory parallelism on current multi-core CPUs, was shown to achieve more than 20X speedup on a 32-core CPU. These impressive results were achieved without any modifications to the main parts of the code that users interact with. Only the compute-intensive core of the code was modified, minimizing the impact on the users.

### Sep 13~

**THEORY**

Wengjun Deng (coauthored with Dr G.-Y. Fu) titled "Optimization by marker removal for δf particle simulations" has been accepted for publication by Computer Physics Communications and has been available online at http://dx.doi.org/10.1016/j.cpc.2013.08.019 . This paper reports a technique for δf marker particle simulations to save markers and computing time by removing unimportant markers. The technique can be used for phase spaces of arbitrary geometry and dimension. Particularly, the technique has been tested in two particle-in-cell (PIC) simulations: a bump-on-tail simulation in 2D phase space and a toroidal Alfvén eigenmode (TAE) simulation in 5D gyrokinetic phase space. The latter one is performed by the kinetic/MHD hybrid code M3D-K. In these two simulations, the technique has saved markers by about 75% and 95%, respectively. In general, the more localized δf is in the phase space, the more markers can be saved.

This week's theory seminar was presented by Dr. Paul Schmit from Sandia National Laboratories, and Princeton University Plasma Physics Alumn, on "Magnetic fields and tail-ion depletion in inertial confinement fusion". With a good introduction of Z pinch driven Inertial Confinement Fusion targets, he presented the physics of tail-ion transport (losses of fast ions) in ICF. He showed the numerical results of solving the tail-ion kinetic equations and compared with the analytical model of a simple threshold criteria [1]. The effect of B-field on tail-ion trajectories and losses was demonstrated through numerical kinetic modeling and shown that the Maxwell-averaged fusion reactivities are recovered more fully in uniformly magnetized cylindrical targets. Here is the abstract of this talk, "The impact of embedded magnetic fields on Knudsen layer formation and tail-ion depletion [1] near steep density and temperature gradients in inertial confinement fusion is investigated for the first time. Magnetic fields change the energy scaling of the ion diffusivity in a way that eliminates the preferential losses of fast ions compared to thermal ions. Simple threshold criteria give conditions such that the restoration of the ion tail distribution is sufficient to recover much of the lost fusion reactivity. The tail-ion kinetic equations are solved for hot fuel bounded by a cold, nonreacting wall using a numerical stochastic differential equation solver, and the modified fusion reactivities are calculated. We find that modest magnetic fields too weak to magnetize thermal ions are still sufficient to restore much of the lost reactivity, consistent with the threshold conditions. We also find that the Maxwell-averaged fusion reactivities are recovered more fully in uniformly magnetized cylindrical targets compared to uniformly magnetized spherical targets. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000. [1] K. Molvig et al., PRL 109, 095001 (2012)."

### Sep 6~

**THEORY **

The theory seminar this week was presented by Dr. I. Kaganovich from PPPL on "Collective Beam-Plasma Interactions for Fusion and Plasma Processing Applications". Here is the abstract of his talk: The beam-plasma interaction is one of the most important phenomena in plasma physics and its applications. A recent resurgence of interest in beam-plasma interactions is due to the ability of advanced particle-in-cell codes to simulate many aspects of the complex processes observed in experiments on beam-plasma interactions relevant to plasma processing of semiconductors. I will give examples of beam self-organization phenomena that occur because of nonlinear saturation of instabilities and their subsequent evolution. The first example is an electron beam undergoing the Weibel filamentation instability. We demonstrate that the beam splits into many filaments and then the filaments undergo collective interactions and nonlinear mergers. The final state of the process is a single pinched beam surrounded by a wide halo. The second example is an ion beam propagating in background plasma. An ion beam can effectively excite plasma waves and whistler waves when propagating in plasma. The two-stream instability between the beam ions and plasma electrons cause further growth of plasma waves, which in turn leads to a significant enhancement in the plasma return current and a defocusing of the beam. The final example is relevant to plasma processing applications. The two-stream instability of an intense electron beam in finite-length plasma with nonuniform density is investigated numerically. A new regime of the instability is observed where intense plasma oscillations occur near the plasma edges. Here, bulk electrons can be accelerated to substantial energies in the direction opposite to the beam propagation direction. The new regime appears stochastically and only for strong beam currents.

The Edge Particle Code (EPC) was created by PPPL long term visitor Xujing Li and Dr. L.E. Zakharov using recently developed Edge Equilibrium Code (EEC) and Equilibrium and Stability Code (ESC) as a first step for simulating power and particle losses from the magnetically perturbed plasma edge. EPC utilizes the high performance of GPU processors and was validated by comparison of collisional particle diffusion with neoclassical theory

### Aug 30~

**THEORY**

This week's theory seminar was presented by Nick Murphy from Harvard-Smithsonian Center for Astrophysics on "Asymmetric Magnetic Reconnection in the Solar Atmosphere". He presented the concept of asymmetric magnetic reconnection with some observational evidence. The numerical MHD simulations of magnetic reconnection, but with imposed magnetic asymmetry, was then shown for two configurations (i) in a general set up (ii) with plasmoid instability. The abstract of his talk is "Models of solar flares and coronal mass ejections typically predict the development of an elongated current sheet in the wake behind the rising flux rope. In reality, reconnection in these current sheets will be asymmetric along the inflow, outflow, and out-of-plane directions. We perform large-scale simulations to investigate the consequences of asymmetry during solar reconnection. We predict several observational signatures, including flare loops with a skewed candle flame shape, slow drifting of the current sheet, asymmetric hard X-ray emission and motion of flare loop footpoints, and rolling motions within the erupting flux rope. We perform simulations of the plasmoid instability with asymmetric upstream magnetic fields and show that islands grow preferentially into the weak field upstream region. The islands develop net vorticity because the outflow jets impact them obliquely rather than directly. All of these simulations show non-ideal plasma flow across X-points. To understand this, we derive exact expressions for the rate of motion of a magnetic null point. Finally, we discuss how comparisons to observations will necessary to fully understand the roles of global and 3D effects."

### Aug 23~

Gyrokinetic simulations with the GTS code have been employed to investigate the bootstrap current generation in the presence of drift wave turbulence. Plasma self-generated non-inductive currents in fusion devices, e.g, the bootstrap current, have a great impact on overall plasma confinement and, specifically, on key MHD instabilities such as neoclassical tearing mode (NTM) and edge localized mode (ELM). The collisionless trapped electron mode (CTEM) is found to induce a significant, quasi-stationary parallel current. Recent nonlinear GTS simulations, which include both turbulent and neoclassical physics self-consistently and simultaneously, show that bootstrap current generation is significantly enhanced in the presence of CTEM-induced fluctuations. This is consistent with earlier GTS results of CTEM turbulence simulations without neoclassical physics. The total bootstrap current, however, is not a simple addition of turbulence-induced current to the neoclassical bootstrap current. The underlying dynamics is closely related to the nonlinear plasma flow generation by turbulent fluctuations. However, unlike toroidal momentum, which is mostly carried by ions, the turbulent current is mainly carried by electrons and driven by electron residual stress with possible contribution due to turbulent acceleration. The fluctuation-induced current generation exhibits a similar characteristic dependence on plasma parameters as that of neoclassical bootstrap current, but with different physical origins. Specifically, it increases with the pressure gradient, decreases with poloidal magnetic field (and equilibrium current Ip), and increases with the radial variation of the safety factor. Interestingly, the CTEM driven current is essentially carried by trapped electrons, unlike the neoclassical bootstrap current which is mainly carried by passing particles. The work is carried out by W. X. Wang, S. Ethier and their collaborators.

### Aug 16~

**THEORY**

I. Dodin participated in the International Conference "Frontiers of Nonlinear Physics" (Nizhny Novgorod, Russia) and presented an invited talk titled "Nonlinear plasma waves with trapped particles: variational theory and simulations".

A. Reiman is organizing a benchmarking activity for 3D equilibrium calculations for the DIII-D tokamak. There are presently ten codes that are participating: the linearized equiilibrium codes IPEC (J-K Park) and MARS (Turnbull), the time-dependent MHD codes M3D-C1 (Ferraro), M3D (Breslau), and NIMROD (Sovinec, Zhu), as well as VMEC (Lazarus, Lazerson), NSTAB (Garabedian's code: Cerfon, McFadden), PIES (Reiman), HINT (Suzuki in Japan) and SPEC (Hudson). The names in parentheses are the people running the codes for this exercise. This activity is an outgrowth of work on the FY 2012 Fusion Energy Sciences Theory Milestone. In the past week, Dr. Reiman distributed specifications for data files to be used in comparing the solutions of multiple codes.

B. Tang participated in SciDAC-3 EPSi All Hands Meeting at LBNL, August 14-15 in his role as the Chairperson of the Program Advisory Committee for this FES/ASCR jointly-funded project. On August 16 Tang also met with LBNL Deputy Director Horst Simon to discuss collaborations opportunities.

**COMPUTATIONAL PLASMA PHYSICS GROUP **

Aaron Redd, from the University of Wisconsin, visited PPPL this week to receive instruction on using the Tokamak Simulation Code (TSC). His immediate application is to model current penetration in the extremely low-aspect-ratio Pegasus experiment. However, his future modeling will include using techniques developed on Pegasus in the NSTX-U experiment at PPPL.

Four CPPG summer students completed their internships and presented at PPPL's summer poster session. Ante Qu completed his National Undergraduate Fellowship on Multi-threaded GPU Acceleration of ORBIT with Minimal Code Modifications, directed by S. Ethier, E. Feibush, and R. White. Matthew Lotocki worked on Visualization of Gyrokinetic Simulations, directed by E. Feibush. Michael Knyszek presented elvispy - Scientific Graphics for Python, supervised by E. Feibush. Jared Miller developed Validation of in-situ Measurement of Li Coating Thickness on a High Z Substrate through Monte Carlo Methods, with D. Mueller and E. Feibush.

### Aug 9~

**THEORY**

W. Wang participated the Festival de Theorie on "Reduced models of complex plasma dynamics" (Aix-en-Provence, France, July 8-26) and presented an invited talk entitled "Fluctuation Driven Plasma Current, Poloidal Rotation and Flow Structure".

A paper titled "Linear Stability and Nonlinear Dynamics of the Fishbone Mode in Spherical Tokamaks" by F. Wang, G. Fu, J. Breslau, and J. Liu has been submitted to Physical Review Letters. This paper reports the recent work done in collaboration with Feng Wang, a graduate student from Dalian University of Technology, Dalian, China. The abstract reads: "Extensive linear and nonlinear simulations have been carried out to investigate the energetic particle-driven fishbone instability in spherical tokamak plasmas with weakly reversed q profi le and the minimum of q slightly above unity. The global kinetic-MHD hybrid code M3D-K is used. Numerical results show that a fishbone instability is excited by energetic beam ions preferentially at higher q_min values, consistent with the observed appearance of the fishbone before the "long-lived mode" in MAST and NSTX experiments. In contrast, at lower q_min values, the fi shbone tends to be stable. In this case, the beam ion effects are strongly stabilizing

for the non-resonant kink mode. Nonlinear simulations show that the fishbone saturates with strong downward frequency chirping as well as radial flattening of the beam ion distribution. An (m,n)=(2,1) magnetic island is found to be driven nonlinearly by the fi shbone instability, which could provide a trigger for the (2,1) neoclassical tearing mode sometime observed after the fishbone instability in NSTX."

**COMPUTATIONAL PLASMA PHYSICS GROUP **

E. Feibush presented "Python Programming at PPPL" to NSTX physicists on August 6. This introductory workshop included hands-on programming exercises that emphasized the elements and features of Python. Aspects of object-oriented programming were included. Course materials were posted on-line for future reference. Subsequent presentations will cover numerical python and the programming interface to MDSplus. Science Education interns Jared Miller, Michael Knyszek, and Matthew Lotocki served as Teaching Assistants for the workshop.

### Aug 2~

**THEORY**

Dr. Michael Kraus from Max Planck Institute for Plasma Physics, Germany, presented this week's theory seminar entitled "Variational Integrators for Plasma Physics". He introduced the variational integrators scheme which provides a systematic way to derive geometric numericalmethods that preserve a discrete multisymplectic form (and therefore have good long time energy behavior) as well as momenta associated to symmetries of the system by Noether’s theorem. Good long-time energy behavior with no numerical dissipation was shown for three applications, Vlasov-Poisson system in 1D, and ideal and reduced magnetohydrodynamics in 2D. For Vlasov-Poisson integrators the total particle number, momentum and energy, as well as norms of the distribution function, were exactly conserved. However, for cases when filaments of the order of the grid size were developed, a velocity space collision term was needed to damp the subgrid modes. It was mentioned that the oscillations in energy might be due to the potential term as the advection term similar to Arakawa scheme conserves energy. For ideal MHD, the exact conservation of energy and cross helicity were shown for a current sheet (tanh) set up. Collisionless reconnection from reduced MHD by including electron inertia was also demonstrated with exact conservation properties. Questions regarding the higher dimensionality of this scheme and the conservation property of this scheme compared to other techniques such as discrete finite element Galerkin methods were raised.

A second theory seminar on August 2 was given by Dr. Ido Barth from Hebrew University of Jerusalem on "Autoresonance - A Kinetic Perspective". It was shown that a critical amplitude of the oscillating driving perturbation was necessary for transition to the autoresonace (AR). Two effects, first the AR phase-locking transition of a thermally distributed ensemble, and second the bunching effect due to self fields were discussed. Thermal broadening effect was shown that at temperature T, the capture probability is a smoothed step function of the driving amplitude with the step location and width scaling as alpha^(3/4) (alpha being the chirp rate) and (alpha T)^(1/2),

respectively (I. Barth et al . PRL 2009). However, at sufficiently low temperatures this width saturates to a finite value associated with zero point quantum fluctuations. The autoresonance phenomena for a Vlasov-Poisson system was discussed. When the particle density increases, strong repulsive self fields reduce the width of the threshold considerably, as the ensemble forms a localized autoresonant macro-particle. This result played an essential role in the mixing scheme in anti-hydrogen formation experiment at CERN. Finally, the quantum counterpart of the classical AR phenomenon, i.e. the ladder climbing, and the continuous transition between these

two regimes was also addressed (I. Barth, et al. PRL 2011).

### Jul 26~

**THEORY**

S.H. Ku gave an invited talk, entitled "Global multiscale electrostatic turbulence in diverted tokamak geometry with neutral recycling in the XGC gyrokinetic code" at Asia Pacific Physics Conference of AAPPS, Makuhari Messe Chiba, Japan July 14-19.

This week's theory seminar was presented by Dr. Luca Guazzotto from University of Rochester, who is also visiting PPPL. His talk was about two-fluid equilibrium: theory, numerical solution, and applications. The importance of including flows in equilibria for stability analysis was discussed. In particular a two-fluid version of an MHD equilibrium code, FLOW2, was developed to study the "transonic equilibrium", when density and velocity discontinuities form between the edge with the supersonic flows and the core with slower flows. He presented sets of quations for the FLOW2 code and its six free input parameters. By increasing density and decreasing the ion skin depth, MHD equilibrium solutions were recovered for some cases in the FLOW2 code. The work on the two-fluid transonic equilibrium is still in progress. However, as an application of FLOW2 code, NSTX equilibrium was shown for arbitrary poloidal and toroidal flows.

W. Wang participated the EPS Conference on Plasma Physics (Espoo, Finland, July 1-5) and presented a poster on "Gyrokinetic Investigations of Turbulence Driven Plasma Current and Shear Flow Driven Turbulence". He also participated the Festival de Theorie on "Reduced models of complex plasma dynamics" (Aix-en-Provence, France, July 8-26) and presented an invited talk entitled "Fluctuation Driven Plasma Current, Poloidal Rotation and Flow Structure".

**COMPUTATIONAL PLASMA PHYSICS GROUP**

S. Ethier represented PPPL at the DOE Laboratory Poster Session of the CSGF Annual Program Review held in Arlington, Virginia. The Department of Energy Computational Science Graduate Fellowship (DOE CSGF, http://www.krellinst.org/csgf/) program provides outstanding benefits and opportunities to students pursuing doctoral degrees in fields of study that use high performance computing to solve complex science and engineering problems. As part of the program, CSGF fellows are required to complete a practicum project in one of the many DOE labs, giving them practical work experiences while strengthening collaborative ties between the national academic community and DOE laboratories.

### Jul 19~

**THEORY**

Stuart Loch (Auburn University) visited PPPL on July 16-18. He gave an overview of atomic research being done at Auburn and within the Atomic Data and Analysis Structure (ADAS) consortium that will be of particular interest to the NSTX-U program. Loch also engaged in one-on one discussions with T. Abrams, S. Kate, D. Stotler, V. Soukhanovskii and F. Scotti.

### Jul 5-12~

**THEORY **

W. Tang participated in the invitation-only DOE ASCR Workshop on "Accelerating Scientific Knowledge Discovery (ASKD) in Washington, DC on July 11-12. The workshop agenda is located at http://www.orau.gov/ASKD2013/agenda.htm with reference documents posted at http://www.orau.gov/ASKD2013/reference.htm . The vision for this proposed program is to "significantly shorten the time needed to transform scientific data into actionable knowledge by enabling the dynamic creation of advanced discovery ecosystems."

Dr. I. Kaganovich gave a plenary talk at European Physical Society Conference on Plasma Physics titled "Nonlocal Kinetic Theory of Plasma Discharges". The purpose of the talk was to describe recent advances in nonlocal electron kinetics in low-pressure plasmas. Low-pressure discharges are widely used in industry as the main plasma sources for many applications including plasma processing, discharge lighting, plasma propulsion, particle beam sources and nanotechnology. Being partially-ionized, bounded, and weakly-collisional, the plasmas in these discharges demonstrate nonlocal electron kinetic effects, nonlinear processes in the sheaths, beam-plasma interaction, collisionless electron heating, etc. Such plasmas often have a non-Maxwellian electron velocity distribution function. The plethora of kinetic processes supporting the non-equilibrium plasma state is an invaluable tool, which can be used to adjust plasma parameters to the specific needs of a particular plasma application. The talk reports on recent advances in nonlocal electron kinetics in low-pressure plasmas where a non-Maxwellian electron velocity distribution function was “designed” for a specific purpose: in dc discharges with auxiliary biased electrodes for plasma control [1], hybrid DC/RF magnetized and unmagnetized plasma sources, and Hall thruster discharges [2,3]. It was shown using specific examples that this progress was made possible by synergy between full-scale particle-in-cell simulations, analytical models, and experiments. This research was supported by U.S. Department of Energy and Air Force Office of Scientific Research.

1. A. S. Mustafaev, V. I. Demidov, I. Kaganovich, S. F. Adams, M. E. Koepke and A. Grabovskiy, Review of Scientific Instruments 83, 103502 (2012). 2. M. D. Campanell, A. Khrabrov and I. Kaganovich, Phys. Rev. Lett. 108, 235001 and 255001 (2012). 3. Y. Raitses, I. D. Kaganovich, A. Khrabrov, D. Sydorenko, N.J. Fisch, A. Smolyakov, IEEE Transactions on Plasma Science, 39, 995-1006 (2011).

**June 28~**

**THEORY**

The Basic Plasma Physics Group gathered together on June 27. Graduate student J. W. Burby presented a talk titled "The Hamiltonian Mechanics of Stochastic Acceleration" on his recent research performed together with A. I. Zhmoginov (UC Berkeley) and H. Qin (PPPL). The research shows how to find the physical Langevin equation describing collisionless stochastic acceleration. These stochastic differential equations give a more complete description than the Fokker-Planck equation, as they determine the n-particle distribution function for any n and inherit the Hamiltonian nature of the underlying microscopic equations. This opens the door to using stochastic variational integrators to perform Monte-Carlo simulations of collisionless stochastic acceleration processes. The theory was illustrated by an application to a simple toy problem.

**June 21~**

**THEORY**

Dr. C.S. Chang and the XGC code development group reported progress on the “Spontaneous Edge Rotation Source and its Inward Propagation in H-mode Plasma.” These results were included in the talk Dr. Chang gave at the TTF Conference held in Santa Rosa, California on April 9-12. Understanding the spontaneous co-rotation source mechanism in H-mode tokamak edge and its inward propagation into core plasma is an important subject for ITER --as observed in C-Mod, DIII-D and other tokamaks-- but has remained illusive. The full-f gyrokinetic code XGC1 revealed that there is an inward propagation of co-current directional plasma rotation from the edge of an H-mode plasma in the presence of ITG turbulence. XGC1 also finds that the source of the co-current directional edge momentum is mostly from the Pfirsch-Schluter flow at the low field side. The Pfirsch-Schluter flow is asymmetric in poloidal angle, in the co-current direction at the low field side and in the counter-current direction at the high field side, and vanishes when flux-surface averaged. However, XGC1 finds that the ballooning nature of the ITG turbulence preferably transports the co-current directional edge Pfirsch-Schluter flow into core. The orbit loss mechanism reinforces the co-current directional edge momentum generation. The neoclassical nature of the edge rotation source and the turbulence nature of the inward momentum transport have been verified by repeating the same simulation in the pure neoclassical mode: In this case, the edge rotation source remains, but the inward momentum transport vanishes. Detailed analysis showed that the residual stress from the ITG turbulence is responsible for the inward momentum transport. Validation with a DIII-D experimental result [S. Muller, Phys. Plasmas 2011] shows that the finding from XGC1 is in the right ballpark for both the edge rotation profile and the inward transport time scale.

B. Tang participated in a meeting of the G8 NuFuSE Project sponsored in the U.S. by NSF, which provided the support for attending this conference. The key news at ISC-2013 centered on the official Top 500 announcement of the new number one supercomputer in the world, China's TH-2 Intel-MIC based system. Delivering a theoretical peak of nearly 55 TF, TH-2 more than doubled the capability of the previous top-rated Titan GPU-based system at the Oak Ridge National Laboratory. An associated link providing details of this impressive achievement can be found at:http://www.hpcwire.com/hpcwire/2013-06-%2017/top_500_results_reveal_global_acceleration_balance_shift.html

This week's theory seminar titled "Energetic Consistency and Symmetry in Gyrokinetic Field Theory" was presented by Dr. Bruce Scott from Max-Planck-IPP. Dr. Scott presented his theoretical model for gyrokinetic field theory. Global and local toroidal momentum conservations were obtained. Momentum fluxes were calculated using flux tube and global gyrofluid models. It was shown that higher order fluxes are small correction and lowest order terms plus FLR corrections are adequate for momentum transport. The abstract of the talk is: The theorem for toroidal angular momentum conservation within gyrokinetic field theory is used as a starting point for detailed statistical analysis of the momentum fluxes as computed by gyrofluid and gyrokinetic models. Fluxtube and radially finite cases are considered within different representations of magnetic field-aligned geometry. The simple two-dimensional Hasegawa- Wakatani (HW) drift-wave turbulence model is used as a control case. In geometrically symmetric cases the fluxes average to zero, but only in the statistical sense of an ensemble average. In global gyrofluid cases the self consistent flow equilibrium provides a small symmetry breaking, allowing for a finite intrinsic momentum flux in the absence of a seed flow, driven solely by thermal gradients. The main result is that the symmetry properties of both lowand high-order fluxes are similar, so that the effect of high-order fluxes remains a small correction to the usual results."

**COMPUTATIONAL PLASMA PHYSICS GROUP**

Dr. Taisuke Boku from the Center for Computational Sciences, University of Tsukuba, presented a CPPG seminar on "HA-PACS Project with Tightly Coupled GPU communication and XMP Programming Language". The CCS (Center for Computational Sciences) is developing a large scale GPU cluster named HA-PACS with 802 TFLOPS peak performance plus a specially enhanced additional 330 TFLOPS supported by a special hardware/software feature named TCA (Tightly Coupled Accelerators) Architecture. TCA is a novel solution to provide very fast and low latency GPU-GPU direct communication to speed-up various scientific codes. They also are developing a language named XcalableMP-dev (XMP-dev), which provides features to describe large scale scientific codes in easy and suitable way for large scale GPU clusters. GTC-P is selected as the first practical application code to run on this framework. This project is still underway, but the speaker summarized status and near term plans.

### Jun 14~

**THEORY **

This week's theory seminar "Naval Research Laboratory, Space Science Division Research" was presented by Dr. Jill Dahlburg, Superintendent of the Space Science Division at Naval Research Laboratory. She presented a highlight of major research activities of the three research branches of SSD: geospace science, heliospheric physics, and high energy space environment. The importance of the basic research program was emphasized. Most of these research activities (about 85%) are funded externally. For information on individual research and the lead persons, seminar chair Dr. Fatima Ebrahimi (ebrahimi@pppl.gov) has a copy of her talk. Dr. Dahlburg said in her talk: "From the beginning of the Division in 1952 to the present, the Naval Research Laboratory (NRL) Space Science Division (SSD) has pursued a broad-spectrum research,development and experimentation program to study the atmospheres of the sun and the earth, the physics and properties of high energy space environments, and solar activity and its effects on the earth’s atmosphere, and to transition capabilities to operational use." She continued "The importance of basic research in the service of the Navy was robustly championed by Homer Newell, the Division’s 2nd Superintendent, who noted to Congress in 1957 that “a strong basic research program is essential to continuing vitality of applied R&D in missiles or any other military or peacetime applications. New facts, new ideas, new techniques, new materials, new instruments, all come from the basic research effort…”. Extraordinary ranges of research and results have been achieved. Now in its 7th decade, the SSD vigorously continues to envision, design, integrate, test, launch, operate, and experiment with space science RDT&E capabilities for our world’s most extreme environments."

**COMPUTATIONAL PLASMA PHYSICS GROUP**

The new (P)TRANSP nonlinear profile advance routine PTSOLVER has now been extended by X. Yuan to include angular momentum prediction. Test runs have been performed using JET Lmode, H-mode and Hybrid discharges using TGLF and NEO simultaneously to compute turbulent and neoclassical fluxes to predict electron density, electron and ion temperature, together with angular momentum. Results for the shots simulated show good agreement with experimental data and expected dependences. The jobs are being run at PPPL using 64 cores of the Dawson cluster. Results using this capability will be presented at the EPS meeting later this

month by R. Budny. This capability can be made available to other, beta-test, users by request.

### Jun 7~

**THEORY**

A theory seminar was presented by J. Parker, a PPPL Theory graduate student. He presented his work with J. Krommes on "Zonal Flow as Pattern Formation: Merging Jets and the Ultimate Jet Length Scale". Zonal flows are generally known to spontaneously emerge from turbulence by Reynold stress through a fully nonlinear process of an inverse cascade. Parker presented an alternate quasilinear approach, in which statistically homogenous turbulence transitions to an inhomogenous turbulent state with organized zonal flow structure. This transition as a function of a friction parameter was shown through quasilinear simulations of the Hasegawa-Mima equation. The results of this quasilinear approach when retaining the nonlinearity between drift waves and zonal flow was discussed. The stability diagram for these zonal flows was analyzed and compared with the simulations.

**COMPUTATIONAL PLASMA PHYSICS GROUP **

A successful verification benchmark has been carried out by X. Yuan and B. Grierson between the new (P)TRANSP profile advance routine PT_SOLVER and the TGYRO and XPTOR codes. Good agreement between the three codes was obtained when each had implemented a thermal conductivity model including contributions from both the TGLF (turbulent transport) and NEO (neoclassical transport) models. An ITER Hybrid test case constructed by R. Budny that did not have a q < 1 region was used in this benchmark. The simulation region extended from the magnetic axis to the edge region. The final converged ion and electron temperature profiles, as well as the separate TGLF and NEO fluxes were successfully compared for the runs, both with and without flow shear.

### May 31~

**THEORY GROUP**

The paper "Negative-Mass Instability in Nonlinear Plasma Waves" by I. Y. Dodin (PPPL), P. F. Schmit, J. Rocks, and N. J. Fisch (PPPL) was published in Phys. Rev. Lett. 110, 215006 (2013). The paper shows that the negative-mass instability, previously found in ion traps, appears as a distinct regime of the sideband instability in nonlinear plasma waves with trapped particles. As the bounce frequency of these particles decreases with the bounce action, bunching can occur if the action distribution is inverted in trapping islands. In contrast to existing theories that also infer instabilities from the anharmonicity of bounce oscillations, spatial periodicity of the islands turns out to be unimportant, and the particle distribution can be unstable even if it is flat at the resonance. An analytical model is proposed that describes both single traps and periodic nonlinear waves and concisely generalizes the conventional description of the sideband instability in plasma waves. The theoretical results are supported by particle-in-cell simulations carried out for a regime accentuating the negative-mass instability.

This week's theory seminar "Introduction to the Edge Equilibrium Code (EEC)" was presented by Xujing Li from LSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, who is currently visiting PPPL and working with L. Zakharov. The implementation of a new code, the Edge Equilibrium Code (EEC), was discussed. To find solutions faster and more efficiently, this code uses flux coordinates with finite element representation in the edge region coupled with the existing ESC code (based on Fourier representation) in the core region through a virtual boundary. Examples with fixed boundary equilibria were shown.

H. Mynick attended the IAEA Technical Meeting on Theory of Plasma Instabilities in Vienna, and gave an invited talk, "Progress in Turbulent Optimization of Toroidal Configurations Via Shaping".

**COMPUTATIONAL PLASMA PHYSICS GROUP**

Nate Ferraro (GA) visited the M3D-C1 group for 3 days to consult on implementing a new "thick" resistive wall capability in M3D-C1. The finite element computational region is now divided into three sections: plasma, wall, and vacuum. In the wall region, a subset of the MHD equations are solved describing resistive diffusion in a conductor. In the vacuum region, an elliptic equation is solved for the current-free 3D fields. This technique for introducing the

resistive wall does not involve Green's functions, and uses the existing structure of the code with relatively minor modifications. The initial implementation is complete and test problems are being run and evaluated. This development is a joint activity between PPPL, GA, and the SCOREC center at RPI.

### May 24~

**THEORY GROUP**

Snezhana I. Abarzhi, from University of Chicago gave a seminar titled “Rayleigh-Taylor mixing”.

Abstract reads: “Rayleigh-Taylor (RT) mixing plays important role in a variety of plasma systems, spanning astrophysical to atomistic scales and low to high energy densities. Examples include fusion, supernovae, and light-material interaction. We apply the novel theoretical concept, the invariance of the rate of momentum loss, to describe the transports of mass, momentum and energy in RT mixing flow and to capture its anisotropic and inhomogeneous character.We find that invariant, scaling and spectral properties of statistically unsteady RT mixing differ substantially from those of isotropic and homogeneous turbulence. Time- and scale-invariance of the rate of momentum loss leads to non-dissipative momentum transfer, to 1/3 and 3/2 power-law scale-dependencies of the velocity and Reynolds number and to non-Kolmogorov spectra. RT mixing exhibits more order compared to isotropic turbulence, and its viscous and dissipation scales are finite and set by flow acceleration. We suggest how to describe the random character of the unsteady mixing flow and show that the rate of momentum loss is the statistic invariant and a robust diagnostic parameter for either sustained or time-dependent acceleration. Some criteria are outlined for the estimate of the fidelity and information capacity of the experimental and numerical data sets.”

A special Theory seminar was presented by Predrag Krstic (University of Tennessee and TheoretiK) on "Atomistic Science for the Plasma-Material Interface". Recent work with lithium coatings deposited on a variety of metallic and graphitic surfaces, in a number of tokamak fusion machines around the world, has provided evidence of the sensitive dependence plasma behavior has on these ultra-thin deposited films. Krstic's computer simulations, done in collaboration with Japanese and French scientists, and validated by in-situ experiments at Purdue University and at NSTX have contributed to unraveling the mystery of this high fidelity control. Krstic presented quantum-classical atomistic calculations which elucidated the roles of lithium and oxygen in amorphous-carbon on retention of hydrogen and showed that the presence of oxygen in the surface plays the key role in the uptake chemistry, while lithium’s main role is to bring the oxygen to the surface. D atoms preferentially bind with O and C-O when there is a comparable amount of oxygen to Li at surface. This finding well matches a number of experimental results, obtained within the last decade.

John Jenkins from North Carolina State University gave a Theory seminar on May 23 on “Optimization Techniques for Extreme-scale Analytics.” The following is a highlight from his seminar. Recent trends in I/O in an HPC context present significant, multi-dimensional challenges: coping with huge increases in the amount and complexity of scientific data produced, effectively using increasingly complex I/O subsystems and hardware configurations, and allowing for swift data analysis under varying access patterns, to name a few. To address these challenges, advanced data reorganization and analytics techniques must be explored, placing particular focus on data reduction as a first-order constraint. He presented two technologies made to accelerate different data access workloads. First, he introduced a precision-based technique for multi-resolution analysis, extracting favorable performance and accuracy characteristics by exploiting the floating-point data format. He additionally explored the implications of performing varying analyses on reduced-precision GTS and XGC1 electrostatic turbulence potential data, highlighting the efficacy of providing a configurable, multi-resolution data decomposition. Second, he discussed a parallel system for query-driven analysis that drives down storage and query processing costs by operating directly in a compressed data space. He then presented ongoing works that aim to tame the data complexity problem inherent in data layout optimizations: how transparent can these tools be made to the end-user, and can I/O libraries support them effectively?

A paper by D. Stotler "Energy Conservation Tests of a Coupled Kinetic Plasma-kinetic Neutral Transport Code" has been published online in Computational Science and Discovery (Vol. 6, Issue 1): URL;http://stacks.iop.org/1749-4699/6/015006 DOI:10.1088/1749-699/6/1/015006. This article describes the methods used to couple the XGC0 guiding center, neoclassical plasma transport code to the DEGAS2 Monte Carlo neutral transport code. The energy conservation properties of the coupling method are also examined. This work was primarily supported through the Scientific Discovery through Advanced Computing (SciDAC) program funded by the U. S. Department of Energy.

On May 14, L. Zakharov gave a talk "Are Transport Barriers a Zone of Good Confinement or of its Collapse" to the PPPL Experimental Seminar. He addressed the key issue of understanding sharp electron temperature pedestals the plasma edge in H-mode which for more than three decades are being interpreted as regions with suppressed transport – “transport barriers”. RMP experiments, SoL currents and direct measurements of particle deposition to the divertor target plates indicate invalidity of the background assumption of this interpretation, i.e., the existence of the perfect magnetic surfaces at the plasma edge. The theory presented in the talk, emphasizes the role of parallel transport and gives an explanation to (a) the lack of sensitivity of electron temperature pedestal to magnetic perturbations, (b) reduction in the temperature and density gradients in the core near the pedestal, (c) reduction of the width of the pedestal with increase in the amplitude of RMP, etc, all of which are being considered as puzzles associated with the temperature pedestals. The theory also gave the kinetic criterion when the parallel transport destroys the notion of diffusive transport. As a result, in contrast to the widespread interpretation, the pedestal region is located outside the confinement zone with no diffusive transport.

**COMPUTATIONAL PLASMA PHYSICS GROUP **

A milestone in the development of the new PTRANSP parallel predictive profile solver, PT_SOLVER, has been met this week by X. Yuan. It was demonstrated that the neoclassical routine NEO (E. Belli, et al) and the turbulent flux routine TGLF (Stabler, et al) can be simultaneously invoked through PT_SOLVER for a predictive simulation to account for both neoclassical and turbulent transport. The routines NEO and TGLF are treated as independent components with their own communicators. The SOLVER component, which advances the transport equation, controls the NEO and TGLF components. A communication layer is dynamically established to exchange the data from the SOLVER component to the NEO and TGLF components, and to collect the neoclassical and turbulent flux from NEO and TGLF. A test case using a total of 64 cores (32 cores for the TGLF component, 31 cores for NEO component --serial NEO run but parallelized over flux surfaces-- and 1 core for the SOLVER component) produced the same converged profiles with much less wall clock time compared to the same case using the serial PT_SOLVER. This component layer in PT_SOLVER has been developed with flexibility to allow easy extension to include other parallel and/or serial components in the future. This capability is presently in the beta-test mode, and will be made available to select users by request.

### May17~

**THEORY**

The theory seminar was presented by Dr. Wenjun Deng from PPPL on "Marker Particle Optimization for Delta-f PIC Simulation". The technique of marker removal and its implementation in the kinetic/MHD hybrid M3D-K code were shown. So far, this method is mostly applicable for study of instabilities with phase space localized structure in delta-f PIC codes. A detailed convergence study of this method for 2-D simulations of bump-on-tail and n=1 TAE simulations was presented.

### May 10~

**THEORY**

Professor Mike Mauel from Columbia University gave a theory seminar on "Turbulent Pinch, Laboratory Magnetospheres, and the Economic Viability of Fusion". He first reviewed the physics of turbulent pinch in a magnetized plasma. Turbulent pinch due to low-frequency interchange fluctuations and the new results from the superconducting levitated dipole experiment were also presented. In the second part of his talk, he raised the question of economic viability of fusion compared to other energy alternatives, which created a good discussion. We had a large mixed audience from different groups at the lab in attendance at the seminar.

**COMPUTATIONAL PLASMA PHYSICS GROUP**

The PPPL M3D-C1 group received news this week that they are to be awarded an additional 20,000,000 NERSC hours spread over CY13-14 for their successful Advanced Leadership Computing Challenge (ALCC) proposal "Study of the Internal Dynamics of ITER". Through this highly competitive awards program, the M3D-C1 team will have resources to greatly increase the spatial resolution of their 3D two-fluid MHD simulations, allowing them to use parameters approaching those of existing and planned fusion devices. Besides the PPPL team, Co-PIs in this activity are Nate Ferraro of General Atomics and Mark Shephard of RPI.

S. Ethier was recently granted special access to Sequoia -- NNSA's most powerful supercomputer (https://asc.llnl.gov/computing_resources/sequoia/), before it was designated entirely for classified work. Housed at LLNL, Sequoia is the largest Blue Gene/Q system in the world and at 16.3 Pflop/s, currently the second most powerful. Dr. Ethier ran benchmark cases with the recently optimized version of GTCP-C, which was developed in collaboration with members of the Future Technologies group at LBL (L. Oliker, S. Williams, K. Ibrahim), K. Madduri at U. Penn., and Princeton U. G8 postdoc Bei Wang. The code, which already scaled extremely well on the large Blue Gene/Q system at ANL (Mira), continued to scale almost perfectly to all 1,572,864 processor cores on Sequoia. GTCP-C uses a hybrid MPI+OpenMP parallel approach to take full advantage of the BG/Q highly multi-threaded nodes and large scalable interconnect. Sequoia is dedicated to NNSA's Advanced Simulation and Computing (ASC) program for stewardship of the nation's nuclear weapons stockpile, a joint effort by LLNL, Los Alamos National Laboratory and Sandia National Laboratories. ASC advances high performance computing for national security, related science and engineering, and other national challenges.

Arnold Kritz and two associates from Lehigh University visited PPPL on May 8 to receive instruction from X. Yuan on the use of PTSOLVER within the TRANSP code. They are the first beta-users of PTSOLVER outside of PPPL. PTSOLVER replaces the normal TRANSP algorithm for predicting the temperatures by a parallel multivariate Newton-based solver that works with highly nonlinear and stiff transport modules such as GLF23 and TGLF. It is normally able to find smooth solutions for the profiles without imposing additional time or space

smoothing

### May 3~

**THEORY**

L. Zakharov attended ITPA MHD Topical Group Meeting, April 22-25, in Culham Science Center, UK, which is dedicated to disruption mitigation in ITER. In his talk on "Hiro Currents in VDE, Theory, Measurements, Simulations" he emphasized the fundamental role of Hiro currents in disruption physics, and for the first time in ITPA he presented the direct measurement of Hiro currents during vertical disruptions on EAST machine in China. New divertor tile diagnostics was developed to reveal the currents, which were so far were overlooked in interpretations and simulations of vertical disruptions and can make profound impact on assessment of disruption effects on the plasma facing surfaces. In addition, L. Zakharov and S. Sharapov organized a discussion in Culham Science Center on "Are Transport Barriers a Zone of Good Confinement

or of its Collapse?".

G. Hammett is at Oxford University as a Visiting Research Fellow at Merton College for their spring term, through late June. He will be working with Dr. Alex Schekochihin and others at the Peierls Centre for Theoretical Physics at Oxford and at the Culham Centre for Fusion Energy. He gave a talk on May 2 for the UK fusion theory video meeting on "Thoughts About Ways to Improve Confinement for Fusion".

P. Damiano from PPPL presented a theory seminar "Electron Acceleration in Alfvenic Aurora". To support Aurora arcs, electron acceleration in the monoenergetic Alfven waves regime was discussed. The results of 2-D MHD/hybrid simulations of Field Line Resonances in a dipolar magnetic field were presented. It was discussed that mirror effects self-consistently produced sufficient parallel electric field to accelerate electrons. The resulting broadening of the parallel current in the MHD and hybrid models was compared.

**COMPUTATIONAL PLASMA PHYSICS GROUP**

E. Feibush presented "Introduction to Python Programming" as a mini-course sponsored by the Princeton Institute for Computational Science and Engineering on May 1. Researchers from twelve different University departments attended. The hands-on programming session emphasized the elements and features of Python and how it can be used in a scientific workflow. The course material included the "elvispy" software, a new Python Application Programming Interface to the ElVis scientific graphics display program. This enables a Python program to send f(x), f(x,t), and f(x,y) data directly to ElVis for display in a graph. The elvispy API was developed by CPPG intern M. Knyszek who served as a teaching assistant along with J. Miller and M. Lotocki.

Four graduate students from POSTECH University in Korea, supervised by Professor Hyeon Park, spent the last two weeks at PPPL primarily learning to use the M3D-C1 code. Each student is focusing on one or more MHD phenomena in KSTAR: sawtooth, tearing mode, and ELM. The students have a gathered data from the ECEI and MIR systems on KSTAR and are interested in performing simulations with M3D-C1 for benchmarking and increased physics understanding. This collaboration is expected to continue with another visit during the summer.

### April 26~

**THEORY**

Two PPPL Theory graduate students were selected for the 2013 Sherwood Theory Poster Award this week in Santa Fe, NM. The awards, which carry a $500 stipend, went to J. Parker for his poster on "Zonal Flow as Pattern Formation: Merging Jets and the ultimate Jet Length Scale" and to Brendan Lyons for his poster on "A New Drift-kinetic Equation Solver for Coupled Neoclassical-magnetohydrodynamic Simulations in Axisymmetric Systems".

Dr. Dennis from the Australian National University, who is visiting PPPL and has been working with S. Hudson, presented a seminar on "A Minimally Constrained Model of Self-organized Helical States in Reversed-field-pinches". He presented a two-volume model for finding the helical states when energy is minimized against five assumed constraints (magnetic helicities and fluxes) on the two volumes. The SPEC equilibrium code is used to find these helical states by taking the constraints from the VMEC code. The talk stimulated many interesting questions regarding the number the constraints, the location of the domain of the first volume and helicity. This simplified equilibrium model has reproduced the experimental single helical states of RFX.

### April 19~

**THEORY**

The April 12 issue of Physical Review Letters contains an article by V. Geyko (graduate student) and N. Fisch, titled "Reduced Compressibility and an Inverse Problem for a Spinning Gas". Geyko and Fisch show that a rapidly spinning ideal gas exhibits the counter-intuitive propertythat by putting more energy into the spinning, the gas becomes easier to compress. They also show that the spinning breaks an important symmetry, so that gas constituents in a mixture of spinning gases can be determined through pressure measurements only.

Many Theory department members attended the U.S. - E.U. Joint Transport Task Force Workshop in Santa Rosa, California, April 9-12. C.S. Chang presented a talk " Status of the Theory/Simulation on Multi Scale 3D RMP Penetration and Plasma Transport Physics", G. Fu presented a talk titled "Energetic Particle Effects on Non-resonant Kink Mode in Spherical Tokamaks" and N. Gorelenkov presented a talk titled ""Validating The Critical Gradient Model for AE Fast Ion Relaxation in DIII-D". Posters were presented by W. Deng, B. Faber, R. Hager, S.H. Ku, J. Lang and H. Mynick.

Several theory department members attended the International Sherwood Fusion Theory Conference in Santa Fe, MN April 15-17. Poster were presented by J. Burby, F. Ebrahimi, S.Jardin, W. W. Lee, B. Lyons, J. Parker, J. Squire, W. Wang, R. White. L. Zakharov and X. Li also attended the Sherwood meeting.

**COMPUTATIONAL PLASMA PHYSICS GROUP **

The semi-annual meeting of the SciDAC Center for Extended Magnetohydrodynamics was held on Sunday April 14 in Santa Fe, New Mexico, preceding the Sherwood meeting. There were 15 presentation made as well as three discussion sessions on (1) RMP modeling, (2) sawtooth

modeling, and (3) kinetic MHD. All of the presentations can be found on the CEMM web site: http://w3.pppl.gov/CEMM under the "workshops" tab.

### April 12~

**THEORY GROUP**

PPPL scientists participated in an international workshop held last week at the Princeton Center for Theoretical Science (PCTS) on "Stability, Energetics, and Turbulent Transport in Astrophysical, Fusion, and Solar Plasmas: Unifying Theoretical and Computational Tools". This

interdisciplinary workshop aimed to share research strategies and tools (primarily in theoretical and computational research). There were presentations by eight PPPL scientists (seven from the Theory Department), including A. Bhattacharjee, F. Ebrahimi, A. Hakim, G. Hammett, H. Ji, J.

Johnson, J. Krommes, and J. Parker. Most of the workshop was held in the PCTS facilities in Jadwin Hall on the Princeton University main campus. The complete program and abstracts can be found at the following link (slides for many of talks will be posted there soon):

http://www.pctp.princeton.edu/pcts/Stabilityinplasmas2013/Stabilityinplasmas2013.html

Marchh 29~

**THEORY GROUP**

The Theory Department Plasma Material Interaction (PMI) Working Group met on March 27 at PPPL. T. Abrams gave a presentation on experiments performed with M. Jaworski on the Magnum-PSI linear plasma device in the Netherlands. Abrams also discussed semi-analytic modeling of the erosion-redeposition process observed in those experiments. D. Stotler followed with an overview of the state of PMI models used in edge plasma transport codes.

J. Johnson and P. Damiano participated in the AGU Chapman Conference on Fundamental Properties and Processes of Magnetotails in Reykjavik, Iceland from March 10-15 that brought together researchers studying both the terrestrial magnetotail and those at other planets. Johnson presented an invited review talk on “Alfvenic Magnetotail-Ionosphere Coupling at Earth and other Planets” while Peter gave an oral presentation entitled “2D Global Gyrofluid-kinetic Electron Simulations of Magnetotail Alfven Wave Propagation”.

**COMPUTATIONAL PLASMA PHYSICS GROUP**

E. Feibush presented "Scientific Visualization with VisIt" as a mini-course sponsored by the Princeton Institute for Computational Science and Engineering on March 27. Researchers from twelve different departments attended. Representing users' data in the visualization toolkit software was emphasized. This workshop provided hands-on training in using the VisIt visualization software, assembling JPEG images into QuickTime movies, and selecting data from f(x,y,z) data sets. CPPG interns M. Knyszek, J. Miller, and M. Lotocki served as teaching assistants.

Version 4.6 of the DEGAS 2 Monte Carlo neutral transport code (http://w3.pppl.gov/degas2) was released by D. Stotler to external users. The primary improvements to the code are: 1) a more efficient scheme for transmitting data from the "worker" processors to the central processor on massively parallel computers and, 2) a generalized approach to specifying atomic species and reactions when coupling to the XGC0 guiding center neoclassical particle transport code being developed within the Edge Physics Simulation SciDAC 3 project.

### March 22~

**COMPUTATIONAL PLASMA PHYSICS GROUP**

S. Ethier and S. Jardin (along with C.S. Chang, PPPL Theory) participated in the NERSC Program Requirements Review "Large Scale Production Computing and Storage Requirements for Fusion Energy Sciences: Target 2017" in Rockville MD March 19-20. The review brought together the leaders in the FES computational physics community to discuss what computing capabilities would be needed in 2017 in order to conduct their research. More details regarding the review, including the presentations, can be found at:

http://www.nersc.gov/science/hpc-requirements-reviews/FES

B.H. Park, visiting researcher from KSTAR, made a presentation at the weekly CPPG group meeting on "Monte Carlo RF Kick Operator in NUBEAM". The presentation covered the theory and implementation of the RF Kick operator now in a production mode in TRANSP that allows calculation of the effect of the RF fields as calculated by TORIC on the fast ions as calculated by NUBEAM. The talk was broadcast by ReadyTalk to collaborators at ORNL and MIT.

### March 15~

**THEORY**

On March 12, D. Stotler, B. Davis and G. Tchilinguirian ran the Robot Arm competition at the New Jersey Science Olympiad State Tournament. Each of the 20 high school teams participating in Robot Arm designed and built a stationary robot capable of picking up various objects and

placing them in one of four "goal" boxes.

On March 14, X. Li and L. Zakharov visited the Institute of Computational Mathematics and Scientific/Engineering Computing in Beijing. Li gave a talk on "Hiro Currents in Vertical Disruption Events (VDE) and their Simulations". Direct measurements of axisymmetrical Hiro currents during VDE on EAST in May 2012 made it clear that existing disruption simulation codes miss the important effect of Hiro currents and misrepresent the physics of even 2-D vertical instability. New numerical schemes, based on adaptive coordinates, aligned with the magnetic field, should be used to reproduce the Hiro currents. Li presented the steps for development of the VDE simulation code system, which includes the interfacing of the existing core equilibrium code ESC, new plasma edge equilibrium code PEC, and existing conducting shell simulation code SHL. The recently developed PEC is now interfaced with ESC as parallel processes. The details of numerical scheme of PEC, based on Hermite finite elements, were discussed. The special software, CodeBuilder (Cb), which maintains the documentation, communications and the source code consistent with each other, was used for the code development.

On March 14, L. Zakharov gave a talk on "Stationary Flowing Liquid Lithium (FLiLi) System for Tokamaks" to the Professor M.J. Ni group in the College of Physical Sciences, Graduate University of Chinese Academy of Sciences. He explained that unique property of liquid lithium to pump hydrogen isotopes is a key to the plasma regimes relevant to magnetic fusion. Utilization of this property should return magnetic fusion to its original idea of insulation of the high temperature plasma from the wall. The major challenge for using liquid lithium is related to its high chemical activity and interaction with residual outgassing from the wall in the tokamak devices. The talk described how the stationary FLiLi system addresses this technology challenge and make the use of liquid lithium practical and consistent with the safety requirements.

**COMPUTATIONAL PLASMA PHYSICS GROUP**

Dr. J. Lang, Computational Plasma Physics Group (PPPL), presented a CPPG seminar titled "XGC1 Performance on GPU-CPU Hybrid Architecture". XGC1 is a particle-in-cell code including gyrokinetic ions and drift kinetic electrons, which typically uses 5000 particles per cell and the total number of particles exceeds 20 billion. An electron sub-cycling method was developed to push electrons multiple steps for each ion push, and this takes up most of the computing time (>90%). These computationally heavy pushing subroutines are good fits to the recently developed General Purpose Graphics Processing Unit (GPGPU) technologies. The XGC1 code was recently ported to the GPU based TITAN supercomputer using CUDA FORTRAN. In her talk, she presented the CUDA FORTRAN implementation and optimization in XGC1 and demonstrated its performance improvement in the GPU-CPU hybrid architecture.

A new visualization interface has been developed for exploring three-dimensional data, f(x,y,z) or f(x,y,t). Written in Python and using the Tkinter package, the graphical user interface provides an intuitive approach for positioning and animating slice planes through the data and animating the view of the data volume. The rendering is computed in the VisIt software and animations are saved in QuickTime movie files. These techniques are useful for visualizing density data computed by Nubeam and the full wave solution in reflectometry simulations. The visualization interface was developed by M. Lotocki, M. Knyszek, and J. Miller under the direction of E. Feibush.

### March 8~

**THEORY **

A. Hakim presented an invited talk "Discontinuous Galerkin Algorithms for (Gyro) Kinetic Simulations of Turbulence in Plasmas" at the SIAM Computational Science and Engineering 2013 conference in Boston, Massachusetts. Latest kinetic simulation results from underdevelopment code, Gkeyll, were presented. While at the conference, a collaborative effort to benchmark fluid aspects of the code against work done by Francois Waelbroeck and co-workers of the Institute of Fusion Studies in Texas (IFS) was begun. In this effort the transport of blobs in tokamak edge will be studied and compared to a code from IFS as well as BOUT++. Results from this work will be jointly presented at the Sherwood conference later this year.

### March 1~

**THEORY**

A paper by L. Peterson and G. Hammett has just been accepted for publication in the SIAM Journal of Scientific Computing, on "Positivity Preservation and Advection Algorithms With Applications To Edge Plasma Turbulence" http://w3.pppl.gov/~hammett/gyrofluid/papers/2013/peterson_positivity.pdf. Peterson is a former PPPL graduate student and now a research physicist in ICF at LLNL.

E.H. Kim gave a seminar entitled “Role of Linear Mode Conversion Role of Linear Mode Conversion on Generation and Propagation of Space Plasma Waves” at Dartmouth College.

A series of innovative research on geometric theory and algorithms for kinetic system has been carried out recently by J. Squire, a third year Ph.D. student at Princeton University’s Graduate Program in Plasma Physics and PPPL’s Theory Department. A geometric integration algorithm of the Vlasov-Maxwell system with a variational particle-in-cell scheme has been developed and successfully tested [Phys. Plasmas 19, 084501 (2012)]. Using the formalism of discrete exterior calculus, the field solver, interpolation scheme, and particle advance algorithm are derived through minimization of a single discrete field theory action. As a consequence of ensuring that the action is invariant under discrete electromagnetic gauge transformations, the integrator exactly conserves Gauss’s law. This intimate link between the gauge properties of a discrete system with its numerical properties has also been discovered for the variational symplectic algorithm of gyrocenter dynamics [Phys. Plasmas 19, 052501 (2012)]. For explicit algorithms, an instability arises because the discrete symplectic structure does not reproduce the continuous structure in the limit of zero step-size. This numerical instability can be avoided by introducing ageneralized gauge transformation that places Lagrangian in an “antisymmetric discretization gauge”, in which the discrete symplectic structure has the correct form. By designing a model discrete Lagrangian, the algorithms can be made approximately gauge invariant as long as scalar and vector potentials are relatively smooth. A gauge invariant discrete Lagrangian is indispensable for particle-in-cell algorithms because it ensures current continuity and preservation of Gauss’s law. On the theoretical side, a new variational principle for the gyrokinetic system has been developed in the Eulerian frame and based on constrained variations of the phase space fluid velocity and particle distribution function [Phys. Plasmas 20, 022501 (2013)]. To explicitly derive the field theoretic Hamiltonian structure of the system, a Legendre transform with a modified Dirac theory of constraints is used to construct meaningful brackets from those obtained directly from Euler-Poincaré theory. Possible applications of these formulations include continuum geometric integration techniques, large-eddy simulation models, and Casimir type stability methods.

**COMPUTATIONAL PLASMA PHYSICS GROUP**

S. Ethier gave a mini-course entitled "Introduction to Parallel Debugging" as part of the series of mini-courses hosted by the Princeton Institute for Computational Science and Engineering (PICSciE). The lecture introduced the Princeton University participants to different approaches in tackling the task of debugging parallel applications, including the use of open source tools and advanced parallel debuggers, such as Totalview and DDT. The students and researchers attending the lecture were from a wide span of science departments, including chemistry, political sciences, geosciences, physics, and electrical engineering. This shows the major role that advanced parallel computing plays in scientific research across all the departments at the university.

### February 22~

**THEORY **

Discovery of new modes of intense beam propagation in alternating-gradient accelerators. Highintensity charged particle beams have a wide range of applications ranging from basic scientific research in high energy and nuclear physics and ion-beam-driven high energy density matter to practical applications such as heavy ion fusion energy and medical accelerators. To accelerate and transport high-intensity beams, it is critical to understand in what modes the beams can propagate through an alternating-gradient focusing channel. Up to now, the only known class of exactly soluble modes of intense beam propagation including self-electric and self-magnetic field effects is the Kapchinskij-Vladimirskij (KV) distribution discovered in 1959. Recent research at Princeton University’s Plasma Physics Laboratory reveals that there exists a much larger class of self-consistent modes of intense beam propagation in alternating-gradient accelerator systems [Phys. Rev. Lett. 110, 064803 (2013)]. For each of the classical KV solutions, the beam propagation dynamics is specified by two free parameters, i.e., two emittances in the transverse plane. For the newly discovered class of beam modes, which include the classical KV solutions as a sub-class, each mode is specified by ten free parameters. Because the space domain of free parameters has been extended from two-dimensional to ten-dimensional, the new propagation modes that have been discovered enable a large increase in flexibility in the amount of beam control and steering capability. For example, the new modes allow the beam to tumble (rotate) in the transverse plane perpendicular to the propagation direction, which can be utilized as a beam smoothing technique for accelerator applications where smooth illumination is required, such as in the case of heavy ion fusion and medical accelerators. Theoretically, the new modes have been discovered by generalizing the one-dimensional Courant-Snyder theory for charged particles in an alternating-gradient focusing lattice and the associated one-dimensional envelope equation (also known as the Milne-Pinney equation) to a higher-dimensional, non-Abelian space. In particular, the one-dimensional Courant-Snyder invariant (also known as the Lewis invariant in quantum mechanics) is generalized to higher dimensions, and the new class of solutions of the nonlinear Vlasov-Maxwell equations is constructed after applying the Cholesky decomposition technique. [H. Qin and R. C. Davidson, Phys. Rev. Lett. 110, 064803 (2013)]

J. Johnson participated in the STORM kick-off meeting in Brussels, Belgium February 20-21. STORM is a FP7 project involving seven partners from EU and USA to understand turbulence, intermittency, and nonlinearity in Heliospheric plasmas.

W. Tang was invited to serve on the Advisory Board for the DOE-ASCR SciDAC-3 Institute: "Scalable Data Management, Analysis, and Visualization Institute" (SDAV) led by Arie Shoshani of LBNL and attended its initial meeting on February 20. He also participated in the associated SDAV All Hands Meeting February 20-22 in San Francisco, California.

**COMPUTATIONAL PLASMA PHYSICS GROUP **

A. Kritz, T. Rafiq, and A. Pankin from Lehigh University visited PPPL February 15 to discuss their experience with PTRANSP and to learn to use the new solver in TRANSP, PT_SOLVER. S. Ethier attended the annual NERSC Users Group meeting held in Oakland, California, on February 12-15. The first day was dedicated to the business meeting, during which the NERSC staff present the status and plans for the supercomputer center, and seek feedback from the user community on how to best support and enhance scientific discovery through high performance computation and storage. The second day took place at LBNL and focused on trends in HPC, as well as scientific and HPC accomplishments by NERSC users. The final two days were dedicated to training, for both beginners and experienced users, with a focus on NERSC's new Cray XC30 supercomputer, Edison. Documents for the presentations can be found at https://www.nersc.gov/users/NUG/annual-meetings/2013/ .

### Fedruary 15~

**THEORY**

The Theory Department Plasma Material Interaction (PMI) Working Group met on February 8 to discuss the prospects for using small plasma experiments to advance the development of PMI theory and models. Presentations on pertinent experimental devices at PPPL and elsewhere were made by Y. Raitses, I. Kaganovich, and T. Abrams.

Visiting research scholar Jinxing Zheng who is being hosted by J. Breslau continued his research on stellarator coil design with a study of the relationship between the radius of curvature and the maximum field produced by the coils. He has also practiced exercising the COILOPT code by re-deriving a set of optimized coils for the reference plasma configuration of the NCSX device. On February 15, J. Breslau presented an invited talk on "Spline Representations for More Efficient Stellarator Coil Design" at the Workshop on Exploratory Topics in Plasma and Fusion Research (EPR2013) in Forth Worth. The talk described a new software tool developed by Dr. Breslau that computes optimized stellarator coil shapes modeled by spline curves that accurately produce a target plasma configuration while being much easier to construct and maintain than those computed using previous techniques. H. Mynick also attended the Workshop and presented a paper, "Progress in Turbulent Optimization of Toroidal Configurations".

**COMPUTATIONAL PLASMA PHYSICS GROUP **

During the week of February 4-8, Irena Johnson organized an on-site Python Programming Training, which included nine scientists, eight from the Theory Department. Python, is a popular modern object oriented computing language that has the advantage of being open source, easily readable, efficient, portable and scalable to large projects. Those who attended acquired valuable skills that will facilitate improved code development for data management and visualization. On February 13, the entire PPPL TRANSP group (with R. Budny and S. Kaye) held a two-hour video conference call with the JET TRANSP team including I. Voisekhovitch, J. Conboy, and M. Romanelli. The JET side discussed their usage patterns for TRANSP and some JET-specific modifications that they have made. The PPPL team discussed the progress during the last year and future plans in the areas of (1) the new PT_SOLVER, (2) new free-boundary equilibrium capabilities, (3) new NUBEAM capabilities including NUBEAM/RF coupling, and (4) new parallelization options. Plans were made regarding incorporating the JET modifications in to the PPPL code version, and working with JET physicists to utilize some of the newly installed capabilities as they are released.

### February 8~

**THEORY **

Recently, a series of innovative research on the theoretical foundation of modern gyrokinetic theory has been carried out by J. Burby, a third year Ph.D. student at Princeton University’s Graduate Program in Plasma Physics and PPPL’s Theory Department. Using the methods and techniques of differential geometry, Burby proved that in general the gyrocenter phase space coordinates do not exist globally [Phys. Plasmas 19, 052106 (2012)]. However, this does not imply that gyrokinetic theory is invalid in general. He showed that the fundamental justification of the gyrokinetic theory is due to the existence of asymptotic gyro-symmetry, which is a global and coordinate independent fact when the space-time scalelength of the magnetic field is larger than that of the gyromotion of a charged particle. To a more practical side, the application of the methods of differential geometry reveals that the toroidal precession of a charged particle in a toroidal confinement device is a geometric phase [Phys. Plasmas 20, 012511 (2013)], similar to the well-known Berry’s phase in quantum system. Such a revelation enables a general coordinate independent expression of the toroidal precession in tokamaks and quasisymmetric stellarators alike, which can be implemented as an accurate and efficient algorithm for numerical simulations.

On February 5, Dr. Seung-Hoe Ku gave a theory seminar entitled "Introduction to XGC." The presentation focused on basic properties and capabilities of the XGC ( X-point Gyrokinetic Code) code such as the model equations, geometry, collision operators, logical wall-sheath, and the full/delta/total-f numerical techniques. Physical results of global simulations of ITG turbulence, neutral atomic physics, and intrinsic rotation were also discussed. Some of the mentioned future work included simulations of electrostatic turbulence in L-mode, and L-H transition and comparisons with experiments; and enhancement of electromagnetic capability to include low-m/n tearing modes.

### February 1~

**COMPUTATIONAL PLASMA PHYSICS GROUP **

TRANSP off-site collaborators presently authenticate with PKI FusionGrid credentials issued by the ESnet Certificate Authority (CA), a parallel service to the more widely used DOEGrids CA, to submit jobs to the PPPL computer system. Both DOEGrids CA and ESnet CA will cease providing PKI services on March 23, and are transitioning services to a new CA managed by the Open Science Grid (OSG). However, OSG will not support storing credentials on a "MyProxy" server since this does not comply with IGTF policies. Now Certificates will be stored on the user's computer. All TRANSP collaborators have been notified of the changes and instructions and tools have been provided on the TRANSP Website. The TRANSP Production service is now managing and accepting both types of FusionGrid credentials (user-managed and MyProxy-managed) until such time as the old ones gradually expire. Several groups of users have already made the change and have not reported any undue difficulties. Any questions regarding the transition should be referred to Tina Ludescher at ludescher@pppl.gov.

### January 25~

**THEORY**

A paper co-authored by A. Hakim on non-linear simulations of RF propagation has appeared in Physics of Plasmas. In this, both PIC and non-neutral, multi-fluid models are used to study nonlinear wave coupling of IBWs in the edge of a tokamak plasma, leading to a characterization of parametric decay instabilities, a serious parasitic loss mechanism in RF heating systems. The paper is now online at : http://pop.aip.org/resource/1/phpaen/v20/i1/p012116_s1

On January 24, S. Klasky gave a theory seminar entitled "Accelerating Scientific Knowledge Discovery in DOE science." The presentation focused on the effect of data I/O management on code performance and scalability. Efforts in the development of ADIOS, the open source data management framework whose purpose is to increase I/O efficiency of massively parallel codes, while being easy to implement, were also discussed.

### January 18~

**THEORY**

A. Bhattacharjee has been invited to serve on the Standing Committee on Solar and Space Physics (CSSP) of the National Academies for a term effective immediately and ending June 2014.

Recent PPPL kinetic studies of a collisionless plasma slab bounded by dielectric walls with strong secondary electron emission (SEE) predicted a strongly anisotropic, non-monotonic electron velocity distribution function (EVDF), which is depleted in the loss cone. This EVDF reduces the electron wall losses compared to Maxwellian plasmas. Sheath oscillations occur due to coupling of the sheath potential and non-Maxwellian electron energy distribution function when there are intense electron beams emitted from the walls. In a bounded plasma where the electrons impacting the walls produce more than one secondary electron on average no classical Debye sheath or space-charge limited sheath exists. Ions are not drawn to the walls and electrons are not repelled. Hence, the plasma electrons travel unobstructed to the walls, producing extreme particle and energy fluxes. Strong dependence of the wall potential on SEE allows for active control of plasma properties by judicious choice of the wall material. These results are published by M. D. Campanell, A.V. Khrabrov and I. D. Kaganovich, in papers Phys. Rev. Lett. 108,

255001 (2012),Phys. Rev. Lett. 108, 235001 (2012), and Phys. Plasmas 19, 123513 (2012).

### January 11~

**THEORY**

On January 11, Dr. Will Fox gave a theory seminar entitled "Magnetic Reconnection and Laboratory Astrophysics Experiments with Laser-produced Plasmas." Magnetic reconnection experiments using magnetized high-energy-density plasma bubbles produced by ablating a target with a high intensity lasers were described along with the underlying theory. Results obtained from recent experiments on the OMEGA EP facility were discussed and compared with 2D collisional PIC (particle-in-cell) simulations.

A. Bhattacharjee gave an invited talk on the "Physics of Explosive Events Within the Heliosphere" in the Conference on Space Weather at the Annual Meeting of the American Meteorological Society, Austin, Texas, January 6-10.

### Dec. 21- Jan. 4~

**THEORY **

Y.-M. Huang of the University of New Hampshire (UNH) and A. Bhattacharjee of PPPL have published a new study on the "Distribution of Plasmoids in High-Lundquist-Number Reconnection" in Physical Review Letters on December 28, (PRL, 265002, 2012). Over the last three years or so, there has been much interest in the discovery that the secondary instability of thin current sheets in large systems, above a critical value of the Lundquist number, produces a new regime of fast reconnection in which the reconnection rate, within the framework of resistive MHD, becomes independent on the Lundquist number (to a first approximation). By means of an analytic phenomenological model and direct numerical simulations, Huang and Bhattacharjee have obtained a distribution function of plasmoids in a thin current sheet in 2D as a function of the magnetic flux. This distribution function shows a power-law behavior that differs from other recent theoretical predictions. The predictions of the model are presently being tested by laboratory experiments as well as observations of post-flare heliospheric current sheets by graduate student Lijia Guo of UNH, who is presently at Princeton University as a visiting student. The plasmoid instability and its consequences for fast reconnection was also the subject of an invited paper at the 2013 DPP-APS meeting by Huang, an account of which has been submitted recently to the Physics of Plasmas ( http://arxiv.org/abs/1301.0331).

On January 3, Dr. Robert Leamon gave a theory seminar entitled "On the Modulation of the Solar Activity Cycles." The talk addressed the origin of the 11-year sunspot cycle by tying it to the temporally overlapping activity bands of the 22-year magnetic activity cycle. Importance of the temporal asymmetry of solar activity between the Northern and Southern hemispheres was emphasized. The decadal variation in flux distribution on the solar disk which impacts plasma energetics on small scale and on the large scale, such as cosmic ray flux, was attributed to the

lead/lag between the two hemispheres (and their phasing).

**COMPUTATIONAL PLASMA PHYSICS GROUP **

The National Energy Research Supercomputer Center (NERSC) announced its 2013 allocation awards in late December 2012. PPPL researchers received a total of 68,120,000 CPU hours in 8 different awards. The projects, PIs, and awards were as follows: Center for Integrated Computation and Analysis of Reconnection and Turbulence, A. Bhattacharjee (4,000k); Nonlinear Delta-f Particle Simulation of Collective Effects for Heavy Ion Fusion Drivers and High Intensity Particle Accelerators, R. Davidson (50k); Simulations of Field-Reversed Configuration and Other Compact Tori Plasmas, R. Davidson (70k); Center for Edge Physics Simulation, C. S. Chang (25,000k); Center for Simulation of Energetic Particles, G. Fu (6,000k); 3D Extended MHD simulation of fusion plasmas, S. Jardin (10,000k); Turbulent Transport and Multiscale Gyrokinetic Simulation, W. Lee (15,000k); Experimental Tests of Gyrokinetic Simulations of Microturbulence, D. Mikkelsen (8,000k).