Fluctuations of a plasma (I)

Abstract

We consider a fully ionized plasma. At time t the state of the system is represented by a point X in the phase space of all the particles. We define D s dXdX' ... dX (s) as the joint probability that at time t the system will be in ( X, dX ), at time t ' in ( X', dX '), etc. A systematic procedure has been developed for calculating any desired moment of D s as an expansion in the discreteness parameters e, m and 1/ n . Spectral densities and autocorrelation functions can thus be obtained without any "Stoßzahlansatz" or Markoffian assumption. A comprehensive treatment of a plasma in thermal equilibrium has been carried out. A large class of non-equilibrium states may exist in a hot plasma for sufficient time to be considered stationary. Fluctuations have been calculated for the class of spatially homogeneous states of an infinite plasma. It is of some interest that thermal equilibrium relationships such as Kirchhoff's radiation law and the fluctuation-dissipation theorem survive. As an application we have calculated the degree of excitation of the collective modes such as plasma waves, ion oscillations, etc. For distribution functions which approach instability as some parameter is varied, the energy for some modes becomes very large and ultimately becomes infinite as instability is approached.