Excitation of Trivelpiece–Gould mode in a magnetized plasma having dust by relativistic electron beam?

Abstract

Excitation of various modes by a beam propagation through a partially or fully ionized plasma has been a subject of great interest. Trivelpiece–Gould (TG) mode are the electrostatic waves having frequency in between the ion plasma frequency and electron cyclotron frequency. In the investigations, scientists have included dust grains in the plasma. We have noticed that in a theoretical investigation, the speed of electron beam propagating through a dusty plasma has been taken relativistic. Since the inclusion of dust grains in plasma and consideration of relativistic speed of electron beam could be a challenging task for theoretical treatment, we have looked into the details of such work and have found that for such situation, the dispersion relation is so complicated that its analysis is not feasible. We have found that earlier work has several discrepancies.