Nonclassical Theory of Turbulent Collisionless Plasmas

Abstract

A transport theory is developed for the proton component of collisionless plasmas; nonclassical is taken to mean that Maxwellian distributions and Coulomb collisions are nonexistent or cannot be assumed outright. Novel features include a self-consistent description of the coupling between nonthermal distributions and the bulk fluid velocity. This theory combines results from several well-established research disciplines in the field of space plasma theory: turbulence, particle acceleration, and fluid dynamics. Key to the present treatment is basing the plasma description on the ensemble average of the proton distribution function, and complementing it with the bulk fluid velocity, for a complete description of the proton component of turbulent collisionless plasma. The information contained in the distribution and fluid velocity encompasses that in a conventional MHD description of velocity, density, and pressure. This approach also provides transport coefficients, viscosity and conductivity, and these can be used to fill out a conventional MHD description. Motivation for this work is to supply a description of collisionless plasmas appropriate for investigating nonthermal effects in the creation of stellar coronae and acceleration of stellar winds. The basic assumption of this approach is that magnetic fluctuations in the turbulent collisionless plasma will tend to isotropize the ensemble average of the proton distribution. This average may be identified observationally as the same time average used to construct the average fluid velocity and magnetic field of standard solar wind turbulence theory. Expansion about isotropy replaces the expansion about a Maxwellian in classical plasma models, allowing closure of the moment equations. Because isotropization need not proceed in the usual flux-defined fluid frame, one finds contributions to the fluid pressure from a fluid-frame mass flux driven by gradients and fluid acceleration. Such terms must, in general, accompany any fluid description of the solar wind or other collisionless plasma in which dissipation of fluctuations affects the dynamics of the average fluid variables. The equation describing the proton distribution reduces to the cosmic-ray transport equation at high particle speeds and describes heating of the distribution due to shears, compressions, and accelerations at low proton speeds. This description thus unifies our understanding of dissipation in collisionless plasmas over the range of particle speeds.