Weak Turbulence and Quasilinear Diffusion for Relativistic Wave-Particle Interactions Via a Markov Approach

We derive weak turbulence and quasilinear models for relativistic charged particle dynamics in pitch-angle and energy space, due to interactions with electromagnetic waves propagating (anti-)parallel to a uniform background magnetic field. We use a Markovian approach that starts from the consideration of single particle motion in a prescribed electromagnetic field. This Markovian approach has a number of benefits, including: 1) the evident self-consistent relationship between a more general weak turbulence theory and the standard resonant diffusion quasilinear theory (as is commonly used in e.g. radiation belt and solar wind modeling); 2) the general nature of the Fokker-Planck equation that can be derived without any prior assumptions regarding its form; 3) the clear dependence of the form of the Fokker-Planck equation and the transport coefficients on given specific timescales. The quasilinear diffusion coefficients that we derive are not new in and of themselves, but this concise derivation and discussion of the weak turbulence and quasilinear theories using the Markovian framework is physically very instructive. The results presented herein form fundamental groundwork for future studies that consider phenomena for which some of the assumptions made in this manuscript may be relaxed.

Langevin Equations, Fokker–Planck Equations and Entropic Analysis of a Model-Independent Classical Plasma

Plasma dynamics have been studied extensively and there is a fair amount of understanding where the scientific community has reached at. However, there is still a very big gap in completely explaining plasma physics at the classical as well as the quantum level. The dynamics of plasma from an entropic approach are not very well understood or explained. There is too much chaos to account for and even a small deviation in terms of perturbations of any kind makes a sizeable difference. This study is based on the entropic approach where we take a model independent classical plasma. Then we apply Langevin equations and Fokker–Planck equations to explain the entropy generated and entropy produced. Then we study various conditions in which we apply an electric field and a magnetic field and understand the various trends in entropy changes. When we apply the electric field and the magnetic fields independently of each other and together in the plasma model, we see that there is a very important change in the increase in entropy. There are also changes in the plasma flow, but the overall flow does not drastically change since we have considered a model independent plasma. Finally, we show that there are indeed changes to the entropy in a model-independent classical plasma in the various cases as mentioned in this study.