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This article reports on 1D+2V heat pulse propagation studies using the COGENT guiding center kinetic code. The model uses magnetized kinetic ions and a simple Boltzmann electron model. Results agree with previous kinetic and fluid modeling benchmark studies that correspond to the parameters of edge localized modes (ELMs) observed on the JET tokamak. The plasma parameters for the edge pedestal and ensuing ELM dynamics are in the low collisionality regime. Hence, the dominant balance between the assumed Maxwellian ELM source and collisionless parallel advection causes the ion PDF to develop a significantly anisotropic velocity distribution. Adding nonlinear Coulomb ion-ion collisions to the model acts to smooth the sharp features of the ion distribution function, but the anisotropy remains robust due to the low collisionality. 2010 MSC: 00-01, 99-00, Kinetic theory, Vlasov equation, Magnetic fusion energy, Tokamak, Edge localized mode

In this study, COGENT is a continuum gyrokinetic code for edge plasmas being developed by the Edge Simulation Laboratory collaboration. The code is distinguished by application of the fourth order conservative discretization, and mapped multiblock grid technology to handle the geometric complexity of the tokamak edge. It is written in v∥-μ (parallel velocity – magnetic moment) velocity coordinates, and making use of the gyrokinetic Poisson equation for the calculation of a self-consistent electric potential. In the present manuscript we report on the implementation and initial testing of a succession of increasingly detailed collision operator options, including a simple drag-diffusion operator in the parallel velocity space, Lorentz collisions, and a linearized model Fokker-Planck collision operator conserving momentum and energy (© 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

We consider the treatment of electrons in kinetic simulations of edge plasmas. A fully kinetic treatment of electrons is expensive because of the short timescales associated with rapid streaming along field lines. Hence we survey a number of reduced options, of varying complexity, with particular attention to the “adiabatic model” commonly used for core plasmas. We note that the adiabatic model is the linear limit of a Boltzmann model, whose nonlinear form is more appropriate for the large potential variations in edge plasmas, and then consider extensions to the Boltzmann model which render it applicable to a plasma which includes end-loss in the scrape-off layer (© 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

The following results are presented from the development and application of TEMPEST, a fully nonlinear (full-f) five-dimensional (3d2v) gyrokinetic continuum edge-plasma code. (1) As a test of the interaction of collisions and parallel streaming, TEMPEST is compared with published analytic and numerical results for endloss of particles confined by combined electrostatic and magnetic wells. Good agreement is found over a wide range of collisionality, confining potential and mirror ratio, and the required velocity space resolution is modest. (2) In a large-aspect-ratio circular geometry, excellent agreement is found for a neoclassical equilibrium with parallel ion flow in the banana regime with zero temperature gradient and radial electric field. (3) The four-dimensional (2d2v) version of the code produces the first self-consistent simulation results of collisionless damping of geodesic acoustic modes and zonal flow (Rosenbluth–Hinton residual) with Boltzmann electrons using a full-f code. The electric field is also found to agree with the standard neoclassical expression for steep density and ion temperature gradients in the plateau regime. In divertor geometry, it is found that the endloss of particles and energy induces parallel flow stronger than the core neoclassical predictions in the SOL.

This paper describes a numerical method for the solution of plasma fluid equations on block-structured, locally refined grids. The plasmas under consideration are typical of those used for the processing of semiconductors. The governing equations consist of a drift?diffusion model of the electrons, together with an energy equation, coupled via Poisson's equation to a system of Euler equations for each ion species augmented with electric field, collisional, and source/sink terms. A discretization previously developed for a uniform spatial grid is generalized to enable local grid refinement. This extension involves the time integration of the discrete system on a hierarchy of levels, each of which represents a degree of refinement, together with synchronization steps to ensure consistency across levels. This approach represents an advancement of methodologies developed for neutral flows using block-structured adaptive mesh refinement (AMR) to include the significant additional effect of the electrostatic forces that couple the ion and electron fluid components. Numerical results that assess the accuracy and efficiency of the method and illustrate the importance of using adequate resolution are also presented.

This paper describes a numerical method for the solution of a system of plasma fluid equations. The fluid model is similar to those employed in the simulation of high-density, low-pressure plasmas used in semiconductor processing. The governing equations consist of a drift-diffusion model of the electrons, together with an internal energy equation, coupled via Poisson's equation to a system of Euler equations for each ion species augmented with electrostatic force, collisional, and source/sink terms. The time integration of the full system is performed using an operator splitting that conserves space charge and avoids dielectric relaxation timestep restrictions. The integration of the individual ion species and electrons within the time-split advancement is achieved using a second-order Godunov discretization of the hyperbolic terms, modified to account for the significant role of the electric field in the propagation of acoustic waves, combined with a backward Euler discretization of the parabolic terms. Discrete boundary conditions are employed to accommodate the plasma sheath boundary layer on underresolved grids. The algorithm is described for the case of a single Cartesian grid as the first step toward an implementation on a locally refined grid hierarchy in which the method presented here may be applied on each refinement level.

Experiments demonstrate energy and power transfer between copropagating, same frequency, beams crossing at a small angle in a plasma with a Mach 1 flow. The process is interpreted as amplification of the low intensity probe beam by the stimulated scatter of the high intensity pump beam. The observed probe amplification increases slowly with pump intensity and decreases with probe intensity, indicative of saturation limiting the energy and power transfer due to ion-wave nonlinearities and localized pump depletion. The results are consistent with numerical modeling including ion-wave nonlinearities.

We present edge gyrokinetic simulations of tokamak plasmas using the fully non-linear (full-f) continuum code TEMPEST. A non-linear Boltzmann model is used for the electrons. The electric field is obtained by solving the 2D gyrokinetic Poisson equation. We demonstrate the following. (1) High harmonic resonances (n > 2) significantly enhance geodesic-acoustic mode (GAM) damping at high q (tokamak safety factor), and are necessary to explain the damping observed in our TEMPEST q-scans and consistent with the experimental measurements of the scaling of the GAM amplitude with edge q 95 in the absence of obvious evidence that there is a strong q-dependence of the turbulent drive and damping of the GAM. (2) The kinetic GAM exists in the edge for steep density and temperature gradients in the form of outgoing waves, its radial scale is set by the ion temperature profile, and ion temperature inhomogeneity is necessary for GAM radial propagation. (3) The development of the neoclassical electric field evolves through different phases of relaxation, including GAMs, their radial propagation and their long-time collisional decay. (4) Natural consequences of orbits in the pedestal and scrape-off layer region in divertor geometry are substantial non-Maxwellian ion distributions and parallel flow characteristics qualitatively like those observed in experiments.

Experiments show that power is transferred between two copropagating 351nm laser beams crossing in an Al plasma when the frequency of the driven ion wave is shifted by a Mach 1 flow. The resonant amplification of a low-intensity (⩽2.5×1014W∕cm2) beam intersected by a high-intensity (7.0×1014W∕cm2) pump beam is determined by comparing the transmitted beam power to that measured in experiments where the plasma flow direction is reversed and the ion wave is evidently detuned. The polarization of the amplified light is also observed to align to the pump polarization consistent with ion-wave scattering. The amplification is found to reduce with probe-beam intensity demonstrating a nonlinear saturation mechanism that is effective when the ion-wave damping is weak, which is modeled with a calculation including both the nonlinear ion-wave frequency shifts due to ion trapping and whole-beam pump depletion.

A new method is presented for calculating the scattering of an arbitrary electromagnetic wave by a bounded, perfectly conducting body of general shape. The strategy is to replace the corresponding exterior boundary-value problem by an approximate problem on the boundary of the scattering body. This involves the introduction of a certain bilinear form and non-local boundary operator, together with the use of a special class of known solutions of the reduced Maxwell's equations satisfying the Sommerfeld radiation boundary conditions at infinity. Two computer programs implementing this method are described and numerical results showing the successful application of this method to some model problems are presented.