Instabilities of charged particle beams in plasmas

Instabilities in ion beam implanters are the results of multiple processes caused by the motions of a large number of plasma particles. The study of beam plasma instabilities is critical to the optimization of transport systems for low energy beams. Due to instabilities, low energy beam currents are limited even if complete space charge compensation (i.e. d.c. space potential=0) is achieved. Minor instabilities deplete electrons from the beam causing it to blow up. Severe instabilities inhibit beams by forming virtual cathodes for electron beams or virtual anodes for ion beams. This paper reviews beam plasma instabilities and a dispersion relation for beam plasmas is developed based upon three fluid equations (beam ions, thermalized electrons and slow ions) and Poisson´s equation. From the dispersion relation, an instability threshold dependent on ion beam current density is derived. Criteria to postpone the occurrence of the instabilities are outlined