Hole Equilibria in a Quasi-Cold Plasma

Abstract

The present paper is a theoretical investigation of hole equilibria in phase space, such as being observed in numerical experiments on the two stream instability of counterstreaming, equal, electron-beams in a background of fixed ions. It is assumed that the thermal velocity of the plasma surrounding holes in phase space is suffciently small. The equilibria are classified into two groups: Quasi-cold hole equilibria, and dressed hole equilibria. The former equilibria are characterized by the smallness of the shielding distance that is the distance between adjacent holes required to shield the charge of holes, whilst in the latter, adjacent holes are separated by long shielding distance even for sufficiently small thermal velocity.