C. W. Nielson

NUMERICAL SIMULATION OF THE WEIBEL INSTABILITY IN ONE AND TWO DIMENSIONS.

Particle‐in‐cell simulation methods for doing full electromagnetic simulations of collisionless plasma phenomena are described and applied to the Weibel instability in one and two dimensions. Magnetic particle trapping and subsequent mode coalescing are seen. Magnetic field energy is seen to reach 10% of the total particle energy. The different electromagnetic simulation methods are compared.

Numerical Simulation of Warm Two‐Beam Plasma

One‐dimensional numerical simulation of plasmas consisting of two unequal warm beams has shown flattening of the small beam and, in most cases, a strong single mode structure at about the wavelength of largest linear growth rate, accompanied by an eddylike arrangement of trapped particles in phase space. The total electrostatic field energy first increases at the linear growth rate and then, after saturating abruptly, decreases at about the same rate to an intermediate level where a much slower decay begins.

Hybrid model studies of ion dynamics and magnetic field diffusion during pinch implosions

A one‐dimensional numerical hybrid model (Vlasov ions, fluid electrons) which includes all nontrivial field components has been devised and its predictions have been compared with experimental pinch results. The effect of microscopic electron dynamics is included on the average by the specification of (anomalous) resistivity and thermal conductivity coefficients. The model has reproduced the magnetic field profiles observed during the implosion and post implosion phases of several screw pinch experiments. The behavior of the imploding plasma as various physical parameters are changed is discussed. The foot in the front of an experimentally determined density profile of a high density theta pinch is reproduced and shown to be due to a reflected ion beam. For some conditions the formation of a reflected ion beam is found to be dependent upon whether the bias is parallel or antiparallel to the driving field.

Occurrence of high‐energy electrons and surface expansion in laser‐heated target plasmas

It is shown that limitations on collisionless electron thermal conduction place a lower limit on the range of energies of electrons in the surface of target plasmas which are heated by incident electromagnetic radiation, and that in cases of contemporary experimental interest these energies can be hundreds of keV. It is then shown that these high‐energy electrons can cause a much faster expansion of plasma from the heated surface than would be predicted by a single fluid theory. Numerical simulations demonstrate both effects.

Numerical Simulation of Axisymmetric, Collisionless, Finite‐β Plasma

A numerical simulation method for time‐dependent, axisymmetric, collisionless, finite‐β plasma is described and applied to mirror modes in θ pinches and to rotational and tearing modes in Astron. It is shown that the mirror modes cause an increase of axial thermal velocities and the long time development of a gross bumpy structure in the θ‐pinch plasma. The Astron plasma layer first develops tearing modes in agreement with linear theory, but at later times the wavelength of this mode increases by coalescence until the plasma is completely reassembled.

Electron Cyclotron Drift Instability and Turbulence

The linear theory of the electron‐cyclotron drift instability, including off angle and collisional effects, is discussed in the context of applications to controlled fusion and collisionless shocks. With the help of numerical simulations it is then shown in detail that a strong nonlinear development of the instability causes anomalous resistance to current flow perpendicular to magnetic field lines, which is large enough to be consistent with the anomalous diffusion seen in these applications. In particular a repeated trapping and untrapping of electrons in combined electrostatic‐magnetic wells is an essential part of the nonlinear resistive heating process. A relatively steady resistance and turbulence level is seen, in contrast with the short burst of turbulence produced by many magnetic field free beam plasma instabilities.

Thermal Relaxation in One‐ and Two‐Dimensional Plasma Models

Thermal relaxation of stable one‐ and two‐dimensional plasmas is followed in time by particle‐in‐cell numerical computation. The predicted dependences of relaxation rate on plasma parameter are observed.

Vlasov confinement equilibria in one dimension

A method for constructing one‐dimensional Vlasov equilibria from assumed macroscopic moments is described and examples are given. General properties of these equilibria, in particular, the fact that temperature anisotropy in the two directions perpendicular to the magnetic field is required, are discussed. Results of particle simulations which verify the validity of these equilibria and illustrate the effects of temperature anisotropy are presented.

Simulation of Binary Collision Processes in Plasmas

A numerical procedure for adding the effects of binary collisions to previously collisionless plasma simulation programs has been developed. It is shown that the model faithfully reproduces a numerical solution to the Fokker‐Planck equation. As an illustration of the effect of collisions, a mirror mode problem is solved in θ‐pinch geometry. Solutions are displayed for varying collision frequencies and qualitative as well as quantitative differences are readily apparent.

Initial Comparison of Transform and Particle‐in‐Cell Methods of Collisionless Plasma Simulation

Two fundamentally different methods are used to simulate the nonlinear development of a strong two‐stream instability. Transform and particle‐in‐cell simulations are shown to agree for the growth rate and limiting amplitude.