Plasma Instabilities in Ring and Bi-Maxwellian Electron Distributions

Abstract

Kinetic plasma instabilities affect a wide range of plasmas, from the small scales of laser-generated plasmas, up to the very largest scales of astrophysical plasmas. These instabilities depend on details of the velocity distribution of the particles. However, it is experimentally challenging to initialize the system with a sufficiently accurately known distribution function, that can be used for quantitative studies of kinetic instabilities. Recent results have shown the possibility of tailoring the velocity distribution through rapid ionization in laser-generated plasmas. Examples of such distribution functions are the bi-Maxwellian and the ring distributions. In this thesis, we have examined the electrostatic instability of a ring distribution function. It was found analytically that the ring distribution is electrostatically stable. Moreover, numerical simulations using the particle-incell approach show that certain incomplete (anisotropic) ring distributions can collapse to a complete (isotropic) ring distribution, through an electrostatic instability. In additional particle-in-cell simulations, we confirm the prediction of a previous analytical model of the effects of collisions on the Weibel instability of a bi-Maxwellian electron distribution. Using the previously known analytical model, it is found that collisions could play a major role in the Weibel instability in laboratory plasmas. We find that the evolution of the non-fluctuating part of the distribution is important during the time the instability grows to significant amplitudes. Thus, the strength of the seed fluctuations in the beginning of the simulation or experiment can impact the observed growth.