### Excitation of a Gould-Trivelpiece (TG) Mode by Relativistic Electron Beam (REB) in Magnetized Dusty Plasma

#### Abstract

Gould-Trivelpiece (TG) mode is excited by a relativistic electron beam (REB) via Cerenkov interaction in a magnetized dusty plasma and dusty plasma cylinder. The unstable wave's frequency increases with relative density of negatively charged dust grains \(\delta\) \((=n_{i0}/n_{e0})\), where \(n_{i0}\) is the equilibrium ion density, \(n_{e0}\) is the equilibrium electron density, respectively) in both infinite and finite geometry. The growth rate of the unstable mode increases with beam density and scales as one third power of beam density in both the cases. In addition, the growth rate of the unstable mode decreases with relativistic gamma factor. Moreover, comparison between the infinite and finite geometry indicates that the unstable mode's growth rate is more in case of infinite geometry than that of the finite geometry. Our theoretical results are in line with some of the experimental observations and theoretical findings of previous investigations.

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DOI: http://dx.doi.org/10.26713%2Fjamcnp.v5i2.922

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