C. Oberman

High-Frequency Conductivity and the Emission and Absorption Coefficients of a Fully Ionized Plasma

The problem of the ac conductivity of a fully ionized plasma is investigated for frequencies embracing the plasma frequency. The finite duration of encounters is taken into account in a self‐consistent fashion which includes collective effects. The concomitant processes of absorption and emission of electromagnetic radiation are investigated and in particular the bremsstrahlung emission and absorption coefficients near the plasma frequency are given. The conversion of longitudinal to transverse waves by scattering from ions is discussed.

Nonlinear gyrokinetic equations

Nonlinear gyrokinetic equations are derived from a systematic Hamiltonian theory. The derivation employs Lie transforms and a noncanonical perturbation theory first used by Littlejohn for the simpler problem of asymptotically small gyroradius. For definiteness, only electrostatic fluctuations in slab geometry are considered; however, there is a straightforward generalization to arbitrary field geometry and electromagnetic perturbations. An energy invariant for the nonlinear system is derived, and several limiting forms are considered. The weak turbulence theory of the equations is examined. In particular, the wave kinetic equation of Galeev and Sagdeev can ony be derived by an asystematic truncation of the equations, implying that this equation fails to consider all gyrokinetic effects. The equations are simplified for the case of small but finite gyroradius and put in a form suitable for efficient computer simulation. Although it is possible to derive the Terry–Horton and Hasegawa–Mima equations as limit...

On the Stability of Plasma in Static Equilibrium

Criteria useful for the investigation of the stability of a system of charged particles are derived from the Boltzmann equation in the small m/e limit. These criteria are obtained from the examination of the variation of the energy due to a perturbation, when subject to the general constraint that all regular, time‐independent constants of the motion (including the energy) have their equilibrium values.The first‐order variation of the energy vanishes trivially, and the second‐order variation yields a quadratic form in the displacement variable ξ (which may be introduced because of the well‐known properties of this limit). The positive‐definiteness of this form is a sufficient condition for stability.Several theorems are stated comparing stability under the present theory with that under conventional hydromagnetic fluid theories where heat flow along magnetic lines of force is neglected. Generalizations can be made to systems where the effect of collisions is included.

Plasma transport in stochastic magnetic fields. Part 3. Kinetics of test particle diffusion

A discussion is given of test particle transport in the presence of specified stochastic magnetic fields, with particular emphasis on the collisional limit. Certain paradoxes and inconsistencies in the literature regarding the form of the scaling laws are resolved by carefully distinguishing a number of physically distinct correlation lengths, and thus by identifying several collisional subregimes. The common procedure of averaging the conventional fluid equations over the statistics of a random field is shown to fail in some important cases because of breakdown of the Chapman-Enskog ordering in the presence of a stochastic field component with short autocorrelation length. A modified perturbation theory is introduced which leads to a Kubo-like formula valid in all collisionality regimes. The direct-interaction approximation is shown to fail in the interesting limit in which the orbit exponentiation length L/sub K/ appears explicitly. A higher order renormalized kinetic theory in which L/sub K/ appears naturally is discussed and used to rederive more systematically the results of the heuristic scaling arguments.

Some Stable Hydromagnetic Equilibria

Hydromagnetic equilibria are obtained for a variety of situations which differ little from that of a zero pressure uniform axial magnetic field. Criteria for ascertaining the stability of these equilibria are found by means of an energy principle. In particular, if helically invariant fields are present, stable equilibria with nonzero pressure and net axial current can be found.

Effect of Ion Correlations on High‐Frequency Plasma Conductivity

In an earlier work the ac conductivity of a plasma was investigated by means of an elementary model. The validity of this model has been borne out by a rigorous treatment of plasma at thermal equilibrium. The elementary model is now extended to include the effects of ion correlations for arbitrary fixed ion distributions. For thermal equilibrium correlations it is found that the ion shielding reduces the maximum effective impact parameter by the factor (1 + Z)½ (i.e., both ions and electrons contribute to the shielding) for frequencies low compared to the plasma frequency ωp. For frequencies high compared to ωp, the previous results obtain. The resistance due to the excitation of longitudinal waves at frequencies just in excess of ωp is reduced by the factor (1 + Z)−1. However, if large‐amplitude (nonthermal) ion fluctuations are present, the longitudinal wave contribution to the resistance may be greatly enhanced.

High‐Frequency Conductivity of a Fully Ionized Plasma

ABS>A complete classical derivation of the frequency dependent conductivity is presented that properly takes into account collective dynamics. This treatment rests on the joint solution of the first two members of the BBGKY hierarchy, in the plasma limit, when both are able to change on the same time- scale. For arbitrary frequencies this leads to an integral equation for the one- particle distribution function that can be solved by conventional variational and/ or numerical procedures. For irequencies high compared to the collision frequency, an explicit statement of the conductivity is possible. This high frequency limit is further examined in the limit of small electron to ion mass ratio, and these limiting results are compared with those of other authors. (auth)

ON THE KINETIC THEORY OF STABLE AND WEAKLY UNSTABLE PLASMA. PART 1.

A kinetic theory is presented which is valid for both weakly unstable and stable plasma. The theory corrects the conventional Balescu—Guernsey—Lenard description for the weakly stable portions of the fluctuation spectrum. The theory is no longer Markoffian in the distribution function F alone but is in the pair F and I k the spectrum of fluctuations. Further the evolution in time from an initially weakly unstable distribution to the stable regime can be described. Even after passage into the stable state the fluctuations can be large nd lead to enhanced diffusion across a magnetic field. The coefficient of spatial diffusion is given in this weakly stable (or untable) state. A strong coupling is found between plasmons and the particles in the distribution with velocities near the phase velocities of the plasmons. There is only weak thermal contact between the plasmons and these particles with the main body of the distribution whenever certain nonlinear processes are of secondary importance.

Theory of dissipative drift instabilities in sheared magnetic fields

Several different techniques are used to study the stability of electrostatic drift wave eigenmodes in a resistive plasma with finite magnetic shear. It is found that in the slab approximation, where usual shear damping is operative, resistivity contributes to an enhancement of this damping and the enhancement factor increases with the electron-ion collision frequency νei. Thus no unstable eigenmodes result. If the shear damping is nullified, either by introducing a strong spatial variation of the density gradient or by working in toroidal geometry with strong toroidal coupling effects, then unstable eigenmodes with growth rates increasing with νei are recovered. A perturbation calculation shows that retention of electron temperature fluctuations associated with the mode and inclusion of temperature gradients do not alter these conclusions. Extensive numerical calculations are also presented.

OSCILLATIONS OF A FINITE COLD PLASMA IN A STRONG MAGNETIC FIELD

Of prime concern in plasma investigations is the coupling of a bounded plasma with external electromagnetic fields. In the present paper the properties of the normal modes of a cold plasma slab, and cylinder, situated in a strong magnetic field are derived, and then used to discuss the transmission and reflection of radiation, the scattering by a plasma cylinder, the response to driving sources in the vicinity of the plasma, and the radiation due to plasma oscillations.