We consider whether implicit simulation techniques can be extended in time and space scales to magnetohydrodynamics without any change but the addition of collisions. Our goal is to couple fluid and kinetic models together for application to multi-scale problems. Within a simulation framework, transition from one model to the other would occur not by a change of algorithm, but by a change of parameters. This would greatly simplify the coupling. Along the way, we have found new ways to impose consistent boundary conditions for the field solver that result in charge and energy conservation, and establish that numerically-generated stochastic heating is the problem to overcome. For an MHD-like problem, collisions are clearly necessary to reduce the stochastic heating. Without collisions, the heating rate is unacceptable. With collisions, the heating rate is significantly reduced.

A1-Dlinear gyrokinetic code called AWECS is developed to study the kinetic excitation of Alfvénic instabilities in a high-β tokamak plasma, with β being the ratio of thermal to magnetic pressure. It is designed to describe physics associated with a broad range of frequencies and wavelengths. For example, AWECS is capable of simulating kinetic ballooning modes, Alfvénic ion-temperature-gradient-driven modes, as well as Alfvén instabilities due to energetic particles. In addition, AWECS may be used to study drift-Alfvén instabilities in the low-β regime. Here, the layout of the code and the numerical methods used are described. AWECS is benchmarked against other codes and a convergence study is carried out. 

The dynamical evolution of collisionless driven reconnection is investigated by using an electromagnetic particle simulation code in a microscopic open system. Strong in-plane electrostatic field is excited in the central region of current sheet under the influence of an external driving field. As a result of the amplification of unmagnetized meandering motion by the electrostatic field particle distribution function is modified from the shifted Maxwellian to an anisotropic one in the current sheet. An ion hole appears at the center of current sheet in the phase space, where distribution becomes two-peaked and no ions exist in low velocity region between two peaks. The strong modification of distribution function leads to the generation of off-diagonal components of pressure tensor term, which is one of major causes to violate frozen-in constraint and trigger collisionless reconnection.

A spectral element library has been developed and integrated with the M3D extended MHD code. The currently used linear triangular finite element implementation and the new high order quadrilateral spectral element implementation are directly compared on equilibrium, linear stability, and nonlinear evolution calculations run on the same problems.

A gyrokinetic particle simulation model is developed for simulations of the compressional electromagnetic turbulence driven by the mirror instability. Results of the linear simulations of mirror modes agree well with the analytic dispersion relation. Nonlinear simulations of a single mode find that the mirror instability saturates via a phase-space trapping due to the nonlinear wave-particle interaction when the instability drive is weak.

The multi-hierarchy simulation model for magnetic reconnection is developed, where both micro and macro hierarchies are expressed consistently and simultaneously. Two hierarchies are connected smoothly by shake-hand scheme. As a numerical test, propagation of one-dimensional Alfvén wave is examined using the multi-hierarchy simulation model. It is found that waves smoothly pass through from macro to micro hierarchies and vice versa. 

Analysis of the propagation of waves in the lower hybrid range of frequencies in the past has been done using ray tracing and the WKB approximation. Advances in algorithms and the availability of massively parallel computer architectures has permitted the solving of the Maxwell-Vlasov system for wave propagation directly [Wright et al., Phys. Plasmas (2004), 11, 2473-2479]. These simulations have shown that the bridging of the spectral gap (the difference between the high injected phase velocities and the slower phase velocity at which damping on electrons occurs) can be explained by the diffraction effects captured in the full wave algorithm - an effect missing in WKB based approaches. However, these full wave calculations were done with a Maxwellian electron distribution and the presence of RF power induces quasilinear velocity space diffusion that causes distortions away from an Maxwellian. With sufficient power, a flattened region or plateau is formed between the point of most efficient damping on electrons at about 2-3 ν_the and where collisional and quasilinear diffusion balance. To address this discrepancy and better model experiment, we have implemented [Valeo et al., "Full-wave Simulations of LH wave propagation in toroidal plasma with non-Maxwellian electron distributions", 18th Topical Conference on Radio Frequency Power in Plasmas, AIP Conference Proceedings (2007)] a non-Maxwellian dielectric in our full wave solver. We will show how these effects modify the electron absorption relative to what is found for a Maxwellian distribution.

In the Equation-free framework, a macro-coarse projective integration method consists of two parts: the time stepper and time projection on macro scale. The first one consists of lifting, micro simulation and restriction. For extracting directly from microscopic simulations the information which would be obtained from the macroscopic model of two-dimensional microscopic systems, the time stepper based on the one-dimensional cumulative distribution functions, the marginal cumulative and appropriate number of the conditional cumulative distributions, is introduced. Here this procedure is tested on the nonlinear ion acoustic wave in a plasma. The numerical micro-solver is the one dimensional electrostatic particle-in-cell code. It is shown that particle correlations related to wave structures are better preserved by the new model. The lifting step is critically related to the noise in system. The enlarged noise, rise of correlations, trapping of particles during the wave steepening can seriously violate the basic assumptions of the equation-free approach.

Using the gyrocenter-gauge kinetic theory, an electromagnetic version of the high frequency gyrokinetic numerical algorithm for particle-in-cell simulation has been developed. The new algorithm, being an alternative to a direct Lorentz-force simulation, offers an efficient way to simulate the dynamics of plasma heating and current drive with radio frequency waves. Gyrokinetic formalism enables separation of gyrocenter and gyrophase motions of a particle in a strong magnetic field. From this point of view, a particle may be viewed as a combination of a slow gyrocenter and a quickly changing Kruskal ring. In this approach, the nonlinear dynamics of high frequency waves is described by the evolution of Kruskal rings based on first principles physics. The efficiency of the algorithm is due to the fact that the simulation particles are advanced along the slow gyrocenter orbits, while the Kruskal rings capture fast gyrophase physics. Moreover, the gyrokinetic formalism allows separation of the cold response from kinetic effects in the current, which allows one to use much smaller number of particles than what is required by a direct Lorentz-force simulation. Also, the new algorithm offers the possibility to have particle refinement together with mesh refinement, when necessary. To illustrate the new algorithm, a simulation of the electromagnetic low-hybrid wave propagating in inhomogeneous magnetic field is presented.

The new potential model of interlayer intermolecular interaction was proposed to represent “ABAB” stacking of graphite. The bombardment of hydrogen atoms on the graphite surface was investigated using molecular dynamics simulation. Before the first graphene from the surface side was broken, the hydrogen atoms caused the following processes. In the case of the incident energy of 5 eV, many hydrogen atoms were adsorbed on the front of the first graphite. In the case of the incident energy of 15 eV, almost all hydrogen atoms were reflected by the first graphene. In the case of the incident energy of 30 eV, the hydrogen atoms were adsorbed between the first and second graphenes. The radial distribution function and the animation of the MD simulation demonstrated that the graphenes were peeled off one by one, which is called graphite peeling. One C₂H₂ was generated in such chemical sputtering. But the other yielded molecules often had chain structures terminated by the hydrogen atoms. The erosion yield increased linearly with time.

Flute mode turbulence plays an important role in numerous applications, such as tokamak, Z-pinch, space and astrophysical plasmas. In a low beta plasma flute oscillations are electrostatic and in the nonlinear stage they produce large scale density structures co-mingling with short scale oscillations. Large scale structures are responsible for the enhanced transport across the magnetic field and appearance of short scales leads to ion heating, associated with the ion viscosity. In the present paper nonlinear equations which describe the nonlinear evolution of the flute modes treated as compressible electromagnetic oscillations in a finite beta inhomogeneous plasma with nonuniform magnetic field are derived and solved numerically. For this purpose the 2D numerical code FLUTE was developed. Numerical results show that even in a finite beta plasma flute mode instability can develop along with formation of large scale structures co-existing with short scale perturbations in the nonlinear stage.

Three dimensional free-decaying MHD turbulence is simulated by lattice Boltzmann methods on a spatial grid of 8000³ for low and high magnetic Prandtl number. It is verified that ∇·B=0 is automatically maintained to machine accuracy throughout the simulation. Isosurfaces of vorticity and current show the persistence of many large scale structures (both magnetic and velocity) for a long time — unlike the velocity isosurfaces of Navier-Stokes turbulence. 

Accurate prediction of the sawtooth cycle [1] is an important test for nonlinear MHD codes. The sawtooth cycle in the CDX-U tokamak [2], chosen because its small size and low temperature allow simulation using actual device parameters, has been an important benchmark for the comparison of the M3D [3] and NIMROD [5] codes for the last several years. Successive comparisons have led to improvements and refinements in both codes. The most recent comparisons show impressive agreement between the two codes both on the linear instability and on the details of nonlinear cyclical behavior. These tests are somewhat idealized and do not yet agree quantitatively with the experimentally observed sawtooth period. We expect a second generation of CDX-U sawtooth benchmarks based on an analytically specified equilibrium, with source terms that show greater fidelity to the physical device, to produce better agreement.

We present an extended update on the status of a particle-in-cell with Monte Carlo collisions (PIC-MCC) gun code developed at Los Alamos for the study of surface-converter H⁻ ion sources. The program is fully kinetic. Some of the program's features include: solution of arbitrary electrostatic and magnetostatic fields in an axisymmetric (r,z) geometry to describe the self-consistent time evolution of a plasma; simulation of a multi-species (e⁻, H⁺, H₂⁺ , H₃⁺, H⁻) plasma discharge from a neutral hydrogen gas and filament-originated seed electrons; full 2-dimensional (r,z) 3-velocity (v_r, v_z, v_φ) dynamics for all species; detailed collision physics between charged particles and neutrals and the ability to represent multiple smooth (not stair-stepped) electrodes of arbitrary shape and voltage whose surfaces may be secondary-particle emitters (H⁻and e⁻). The status of this development is discussed in terms of its physics content and current implementation details.

A new predictive computer simulation tool targeting the development of the H-mode pedestal at the plasma edge in tokamaks and the triggering and dynamics of edge localized modes (ELMs) is presented in this report. This tool brings together, in a coordinated and effective manner, several first-principles physics simulation codes, stability analysis packages, and data processing and visualization tools. A Kepler workflow is used in order to carry out an edge plasma simulation that loosely couples the kinetic code, XGC0, with an ideal MHD linear stability analysis code, ELITE, and an extended MHD initial value code such as M3D or NIMROD. XGC0 includes the neoclassical ion-electron-neutral dynamics needed to simulate pedestal growth near the separatrix. The Kepler workflow processes the XGC0 simulation results into simple images that can be selected and displayed via the Dashboard, a monitoring tool implemented in AJAX allowing the scientist to track computational resources, examine running and archived jobs, and view key physics data, all within a standard Web browser. The XGC0 simulation is monitored for the conditions needed to trigger an ELM crash by periodically assessing the edge plasma pressure and current density profiles using the ELITE code. If an ELM crash is triggered, the Kepler workflow launches the M3D code on a moderate-size Opteron cluster to simulate the nonlinear ELM crash and to compute the relaxation of plasma profiles after the crash. This process is monitored through periodic outputs of plasma fluid quantities that are automatically visualized with AVS/Express and may be displayed on the Dashboard. Finally, the Kepler workflow archives all data outputs and processed images using HPSS, as well as provenance information about the software and hardware used to create the simulation. The complete process of preparing, executing and monitoring a coupled-code simulation of the edge pressure pedestal buildup and the ELM cycle using the Kepler scientific workflow system is described in this paper.

We study the generation of nonlinear plasma wake fields by intense laser pulses, using an Eulerian code for the numerical solution of the fully relativistic one-dimensional (1D) Vlasov-Maxwell equations. The examination of the phase-space of the distribution function allows to study without numerical noise aspects of the particle acceleration by the wake-field generated by intense laser pulses, in the very low density regions of the phase-space. We study the effect of the thermal spread on the existence of accelerated beams, and we compare between results obtained from a circularly polarized wave and a linearly polarized wave. 

A nonlocal two-fluid formulation has been constructed for describing lower-hybrid drift instabilities in current-sheet configuration with a finite guide magnetic field in the context of magnetic reconnection. As a benchmark and verification, a class of unstable modes with multiple eigenstates are found by numerical solutions with guide field turned off. It is found that the most unstable modes are the electrostatic, short-wavelength perturbations in the lower-hybrid frequency range, with wave functions localized at the edge of the current sheet where the density gradient reaches its maximum. It is also found that there exist electrostatic modes located near the center of the current sheet where the current density is maximum. These modes are low-frequency, long-wavelength perturbations. Attempts will be made to compare the current results with those from kinetic theory in the near future since the validity of the fluid theory ultimately needs to be checked with the more fundamental kinetic theory.