Bruce I. Cohen

Comparisons and physics basis of tokamak transport models and turbulence simulations

The predictions of gyrokinetic and gyrofluid simulations of ion-temperature-gradient (ITG) instability and turbulence in tokamak plasmas as well as some tokamak plasma thermal transport models, which have been widely used for predicting the performance of the proposed International Thermonuclear Experimental Reactor (ITER) tokamak [Plasma Physics and Controlled Nuclear Fusion Research, 1996 (International Atomic Energy Agency, Vienna, 1997), Vol. 1, p. 3], are compared. These comparisons provide information on effects of differences in the physics content of the various models and on the fusion-relevant figures of merit of plasma performance predicted by the models. Many of the comparisons are undertaken for a simplified plasma model and geometry which is an idealization of the plasma conditions and geometry in a Doublet III-D [Plasma Physics and Controlled Nuclear Fusion Research, 1986 (International Atomic Energy Agency, Vienna, 1987), Vol. 1, p. 159] high confinement (H-mode) experiment. Most of the mo...

Direct implicit large time-step particle simulation of plasmas

Abstract A recently developed implicit method for solving the set of coupled particle and field equations arising in particle-in-cell plasma simulation is described in detail. This implicit integration scheme is motivated by the desire to study efficiently low-frequency, long-wavelength plasma phenomena using a large time step. In particular, this method allows the use of a time step which is larger than the electron plasma period, when electron plasma oscillations are not of interest, and provides selective damping of the distorted remnant of the electron plasma oscillation. The implicit scheme presented here uses particle data directly without introducing fluid moment equations as an intermediary between the field and particle equations. In an electrostatic model, the essence of our scheme is a linearization of the charge density at the advanced time about an explicit approximate density and the computation of the incremental correction to the charge density that is linear in the advanced field. We are led to an elliptic field equation whose coefficients depend directly on particle data accumulated on the spatial grid in the form of an effective linear susceptibility. Prediction and iterative refinement of the solution of the implicit equations, and spatial difference representations of the equations are given. Residual restrictions on time step are described. It is demonstrated that convergence is superior when spatial diferencing and filtering are done in a consistent manner.

Theory and three‐dimensional simulation of light filamentation in laser‐produced plasma

A desire to interpret recent experiments on filamentation with and without beam‐smoothing techniques led to the development of a three‐dimensional fluid model that includes the effects of nonlocal electron transport and kinetic ion damping of the acoustic waves. The damping of the electron‐temperature perturbations that drive thermal filamentation by nonlocal electron conduction, valid in the diffusive limit, is supplemented in the present model by electron Landau damping in the collisionless limit when the wavelength of the perturbation is much less than the electron–ion scattering mean‐free path. In this collisionless limit, Landau damping of the ‘‘temperature’’ fluctuations makes ponderomotive forces universally more important than thermal forces. Simulations in plasmas of current interest illustrate the relative importance of thermal and ponderomotive forces for strongly modulated laser beams. Although thermal forces may initiate filamentation, the most intense filaments are associated with ponderomot...

Laser–plasma interactions in ignition‐scale hohlraum plasmas

Scattering of laser light by stimulated Brillouin scattering (SBS) and stimulated Raman scattering (SRS) is a concern for indirect drive inertial confinement fusion (ICF). The hohlraum designs for the National Ignition Facility (NIF) raise particular concerns due to the large scale and homogeneity of the plasmas within them. Experiments at Nova have studied laser–plasma interactions within large scale length plasmas that mimic many of the characteristics of the NIF hohlraum plasmas. Filamentation and scattering of laser light by SBS and SRS have been investigated as a function of beam smoothing and plasma conditions. Narrowly collimated SRS backscatter has been observed from low density, low‐Z, plasmas, which are representative of the plasma filling most of the NIF hohlraum. SBS backscatter is found to occur in the high‐Z plasma of gold ablated from the wall. Both SBS and SRS are observed to be at acceptable levels in experiments using smoothing by spectral dispersion (SSD).

Hybrid simulations of quasineutral phenomena in magnetized plasma

A new class of numerical algorithms for computer simulation of low frequency electromagnetic and electrostatic phenomena in magnetized plasma is presented. Maxwells equations are solved in the limits of quasineutrality and negligible transverse displacement current (Darwins model). Electrons are modeled as a fluid with polarization effects ignored. Ions are described as particles. A novel feature of these algorithms is the use of the electron fluid equation of motion to determine the electric field, which renders these numerical schemes remarkably simple and direct. The simulation plasma is either periodic or bounded by particle reflecting conducting walls. Both fully nonlinear codes with spatial grids and linearized gridless codes have been implemented.

Implicit time integration for plasma simulation

Abstract To increase the size of the time step, and thereby extend the applicability of kinetic plasma simulation, analysis of the stability and accuracy of implicit time integration schemes for plasma particle-in-cell simulation and the synthesis of new algorithms have been undertaken. Three classes of implicit algorithms are considered in general form. Stability and accuracy calculations provide guidelines for the design and application of implicit simulation algorithms, as illustrated in the construction of new difference schemes with desirable properties. Of particular interest- are the relaxation of stability constraints on the time step, strong damping of unwanted high-frequency modes, accuracy of the simulation of low-frequency phenomena, numerical secular acceleration, and numerical stability of fast and slow space-charge waves. The potency of higher order accurate differencing schemes in reducing undesirable numerical effects is demonstrated.

Stimulated scattering of light by ion modes in a homogeneous plasma: Space-time evolution

Stimulated Brillouin scattering, filamentation, and induced Thomson scattering are studied for a coherent electromagnetic plane wave propagating in a uniform plasma. A generalized Green’s function is found that describes the impulse response for stimulated scattering by electron and ion modes. Explicit asymptotic Green’s functions are calculated for those parametric instabilities involving ion modes or quasi‐modes. Special attention is given to whether the instabilities are convective or absolute. For a traveling wave pump in a uniform plasma, Brillouin and induced Thomson backscatter can be absolute, but sidescatter is convective; filamentation of traveling waves is always convective. Spatial growth rates are calculated for convectively unstable modes. Finally, the competition of filamentation and stimulated Brillouin scattering is considered for parameters typical of real laser‐fusion experiments.

Resonantly excited nonlinear ion waves

One- and two-dimensional simulations and supporting analysis of nonlinear ion acoustic waves as might be associated with the saturation of stimulated Brillouin backscattering (SBBS) are presented. To simulate ion wave phenomena efficiently, while retaining a fully kinetic representation of the ions, a Boltzmann fluid model is used for the electrons, and a particle-in-cell representation is used for the ions. Poisson’s equation is solved in order to retain space-charge effects. We derive a new dispersion relation describing the parametric instability of ion waves, evidence for which is observed in our simulations. One- and two-dimensional simulations of plasma with either initially cold or warm ions (and multi-species ions) exhibit a complex interplay of phenomena that influence the time evolution and relaxation of the amplitude of the excited ion wave: ion trapping, wave steepening, acceleration, heating and tail formation in the ion velocity distribution, parametric decay into longer wavelength ion waves...

Effects of ion trapping on crossed-laser-beam stimulated Brillouin scattering

An analysis of the effects of ion trapping on ion acoustic waves excited by the stimulated Brillouin scattering of crossing intense laser beams is presented. Ion trapping alters the dispersion of ion acoustic waves by nonlinearly shifting the normal mode frequency and by reducing the ion Landau damping. This in turn can influence the energy transfer between two crossing laser beams in the presence of plasma flows such that stimulated Brillouin scattering (SBS) occurs. The same ion trapping physics can influence the saturation of SBS in other circumstances. A one-dimensional analytical model is presented along with reasonably successful comparisons of the theory to results from particle simulations and laboratory experiments. An analysis of the vulnerability of the National Ignition Facility Inertial Confinement Fusion point design [S. W. Haan et al., Fusion Sci. Technol. 41, 164 (2002)] is also presented.

Performance and optimization of direct implicit particle simulation

Performance characteristics obtained from particle simulations using the direct implicit method are presented. Parameter studies of simulation behavior for an expanding plasma slab have been made determining code performance as functions of ..omega../sub p//sub e/..delta..t and ..delta..x/lambda/sub D//sub e/, where ..omega../sub p//sub e/ is the plasma frequency, lambda/sub D//sub e/ is the electron Debye length, ..delta..t is the time step, and ..delta..x is the grid spacing. A range of time steps ..omega../sub p//sub e/..delta..tless than or equal to200 and mesh sizes ..delta..x/lambda/sub D//sub e/less than or equal to100 were explored. Accurate results for low-frequency phenomena resolved by the time step can be obtained without limit on ..omega../sub p//sub e/..delta..t in this range (and higher) with a careful choice of algorithms. This choice of algorithms defeats a potential nonlinear instability that occurs when (..omega../sub p//sub e/..delta..t)/sup 2/ exceeds the number of particles per cell. copyright 1989 Academic Press, Inc.