DIOCOTRON INSTABILITY OF A RELATIVISTIC SHEET ELECTRON-BEAM PROPAGATING THROUGH A RECTANGULAR CONDUCTING WALL

Properties of the diocotron instability in a relativistic sheet electr on beam propagating through a rectangular conducting wall are investig ated within the framework of a macroscopic cold fluid model. The elect ron beam is assumed to be partially neutralized by the positive immobi le ions with the fractional charge neutralization f. The eigenvalue eq uation is obtained for low-frequency perturbations in standing waves. The dispersion relation of the diocotron instability is derived and us ed to investigate stability properties for a broad range of system par ameters including the ratio a/d of the beam thickness (2a) to the cond uctor gap (2d) and the charge neutralization f. The dispersion relatio n indicates that the system is stabilized by increasing the neutraliza tion f to 1/gamma(b)2, where gamma(b) is the characteristic value of t he beam relativistic factor. It is also shown that the diocotron pertu rbations are completely stabilized by increasing the beam thickness to more than one-half the conductor gap (i.e., a/d>0.5) for f=0. The gro wth rate of instability is a substantial fraction of the diocotron fre quency if the system is unstable.