Kinetic Description of Plasmas

Abstract

We have come back full circle! In Chapter 2, we started with the phase — space description of N discrete particles and then transformed it into a continuum two-fluid and finally one fluid descriptions using several averaging processes. After investigating some characteristics of the one-fluid and two-fluid descriptions, we now deal head-on with N discrete particles, electrons and protons, using the Vlasov equation. In this description, we work with particle distribution functions in the phase space of velocities and positions. The time evolution of the distribution function defines the stability or otherwise of the system. Plasmas are particularly interesting because they often submit to, or support, or generate, nonthermal (non-Maxwellian) and non-equilibrium distributions for finite durations of time. In other words, different species of particles can have unequal temperatures. Even a single species of particles can have different temperatures corresponding to different degrees of freedom. The free energy contained in these non-equilibrium distribution functions is then released in the form of heat and radiation. Plasmas are valued for their intrinsic cooperative nature due to which the transport, dissipative and radiative processes proceed at anomalously large rates as compared to single particle processes. Several astrophysical sources with extremely high luminosities with spectral energy distribution far from that of the blackbody, often showing variability on extremely short time scales, warrant the operation of coherent plasma processes. In this chapter, we shall study what is known as the kinetic or microscopic equilibrium and stability of an electron — proton plasma