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 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 collisional regimes. The direct-interaction approximation is shown to fail in the interesting limit in which the orbit exponentiation length LK appears explicitly. A higher-order renormalized kinetic theory in which LK appears naturally is discussed and used to rederive more systematically the results of the heuristic scaling arguments.

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.

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.