Authors: Igor D. Kaganovich

Abstract:  This  paper  presents  a study  of the  two-stream  instability of an electron  beam  propagating in a finite-size plasma  placed  between  two electrodes.  It  is shown  that  the  growth  rate  in such  a system  is much smaller than  that  of an infinite plasma or a finite size plasma with periodic  boundary conditions. Even if the width  of the  plasma  matches  the resonance  condition  for a standing wave, a spatially growing wave is excited  instead with the  growth  rate  small  compared  to  that  of the  standing wave in a periodic  system.   The  approximate expression  for this growth  rate  is 1(1/13)wpe(nb/np)(Lwpe/vb)ln(Lwpe /vb) [1- 0 .18cos(Lwpe/Vb       + rr/2)], where Wpe is the electron  plasma frequency, nb and np are the beam and the plasma densities,  respectively, Vb is the  beam velocity, and L is the  plasma  width.  The  frequency,  wave number  and the spatial and temporal growth  rates  as functions  of the  plasma  size exhibit  band  structure.  The  amplitude of saturation of the instability depends  on the  system  length,  not  on the  beam  current.  For short  systems,  the  amplitude may exceed values predicted  for infinite  plasmas  by more than  an order  of magnitude.

Submitted to: Physics of Plasmas
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Download PPPL-5327 (pdf 2.0 MB 13 pp)
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