Fokker-Planck Simulations Of Some Plasma Processes

Laser-produced plasmas generally fall between collisionless and collisional regimes. In some spatial regions, saying the critical surface, the well-known hydrodynamic or Vlasov descriptions break down. A Fokker-Planck (FP) description, a kinetic model widely used to describe long-range interactions between charged particles becomes necessary. In this thesis, we exploit Fokker-Planck equation to simulate some typical processes such as electron thermal conduction and plasma waves.In order to investigate electron transport process in a laser-produced plasma, we develop a Fokker-Planck code. The diffusive approximation is adopted to simplify the electron Fokker-Planck equation. Our code is numerically implemented by finite difference method with inclusion of processes such as electron thermalization, inverse bremsstrahlung heating, and electron transport. The numerical implementation is achieved essentially as the same numerical scheme presented in Epperlein's work [Laser Part. Beams 12, 257 (1994)]. We simulate the thermalization of a nearly monoenergetic electron velocity distribution as the standard test problem to check the number and energy conservation laws of the collision operator. In the. process of inverse bremsstrahlung absorbtion, electron velocity distribution in a uniform plasma is well fitted by a super-Gaussian distribution. In a non-uniform plasma, as a result of the transport of high energetic electrons, the tail of electron velocity distribution slighth, deviates from super-Gaussian function and turns out to be smaller. The comparisons among our computational heat flux and the classical Spitzer-Harm (SH) transport theory and non-local Epperlein-Short(E-S) models have been presented. It is found that the heat flux inhibition occurs in the vicinity of the critical-density surface and the non-lotal model of heat flux is in reasonable agreement with the FP simulation in overdense region and becomes invalid in the hot underdense plasmas. It is also found that preheat phenomenon occurs at the base of heat front where the electron velocity distribution presents a structure of double-Maxwellian. The high energy tail is due to the unthermalized energetic electrons that are generated in hot underdense region and diffuse into overdense region with negligible collisions, while the bulk of the electron velocity distribution function presents a Maxwellian dependence. Linearized ion Fokker-Planck equation is solved as an eigenvalue problem to investigate ion-acoustic waves (IAWs). The frequencies and damping rates as a function of kλ_ii and kλ_D are computed, where k is the wave number,λ_it is the ion mean-free path,λ_D is the electron Debye length. The effects of electron Debye screen on the solution are discussed. Ion heat flux is also investigated in the process of ion-acoustic waves. We find the FP computed ion conductivity has a Braginskii value of 3.95 in the collisonal limit, and decreases as kλ_ii increases, which indicates the ion heat flux become nonlocal in the rare collisional case. The two nonlocal formulas, i.e., E-S model and Luciani, Mora, Virmont (LMV) model, are applied to fit the computed ion conductivity. We find that E-S model and LMV model become invalid, and that the charge state Z should been taken into consideration when nsing noulocal formulas fo fit the ion conductivity. The fitting parameters in the nonlocal formulas as a function of Z are investigated and presented. Thus the ion nonlocal heat transport formulas are developed, which can provide an efficient and practical implementation in fluid descriptions.We also investigate, pair plasmas and pair-ion-electron plasmas by solving linearized Fokker-Planck equations of positive- and negative-charged particles. In the pair-ion- electron plasmas, electrons are assumed collisionless. The sound waves and Langmuir waves in pair plasmas, and the pair-ion-acoustic waves and ion-Langmuir waves in pairion-electron plasmas are computed. The fluid or Vlasov descriptions are consistent with FP computed results in collisionat limit or collisionless limit, respectively. The valid regimes of fluid descriptions for the waves are also discussed by comparing with the computational results. When Landau damping is negligible, the two-fluid hydrodynamic descriptions can give good approximations to the FP results. For a pair plasma, it is found that the sound wave does not suffer any Landau damping and its dissipation is only due to the Coulomb collisions.