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Figures 89 and 90 show the electron phasespace distributions
evaluated at equally spaced times for a twostream instability calculation
performed with electrons. It can be seen that the distribution
initially takes the form of two uniform bands, corresponding to two
counterstreaming electron beams. However, as time progresses, the
bands spontaneously develop structure which grows in magnitude and
eventually converts the phasespace distribution into a set of connected
vortices. In this final state, the electrons are basically bouncing backwards
and forwards in a quasiperiodic electric potential generated by nonuniformities
in the electron density. In other words, the instability effectively destroys the two
beams. For this reason, the twostream instability is of major
concern in particle accelerators, which often consist of counterpropagating
charged particle beams.
Figure 90:
The electron phasespace distribution evaluated
at various times for a 1dimensional twostream instability calculation performed with , , , , and .

Richard Fitzpatrick
20060329