Excitation of upper-hybrid waves by a gyrating relativistic electron beam in a magnetized dusty plasma cylinder

A gyrating relativistic electron beam propagating through a magnetized dusty plasma cylinder drives an upper-hybrid wave to instability via cyclotron interaction. Numerical calculations of the growth rate and unstable mode frequencies have been carried out for the typical parameters of dusty plasma experiments. It is found that as the density ratio of negatively charged dust grains to electrons increases, the unstable mode frequency of the upper-hybrid waves increases. Moreover, the growth rate of the instability also increases with the density ratio. The growth rate of the unstable mode has the largest value for the modes whose eigenfunctions peak at the location of the beam. The growth rate of the unstable mode scales as the one-third power of the beam density.