Space charge waves in a trapped, relativistic plasma

Abstract

Equations are set up to describe collective longitudinal plasma waves in a trapped, one-dimensional relativistic plasma. It is shown that, provided the background plasma is immobile, the system is unstable if the relativistic plasma frequency is somewhat higher than the typical 'bounce' frequency in the trap. It is further shown that inclusion of a cold, but mobile, background plasma quenches the instability provided only that the thermal plasma frequency is greater than about the relativistic plasma frequency. The calculation has been performed in order to ascertain the role that collective plasma waves may play in inhibiting, or enhancing, Fermi acceleration of cosmic rays in astrophysical plasma situations.