Longitudinal electron oscillations in a cold plasma penetrated through by a beam of charged particles with anisotropic temperature

A study is made for a gyrating electron beam interaction with a cold plasma in the presence of an external magnetic field. We derived the appropriate dielectric tensor components for a gyrating electron beam with anisotropic temperature (for different parallel T_||a and perpendicular T_⊥a temperatures with respect to external magnetic field H&oarr;₀). The importance of special cases for isotropic (T_||a=T_⊥a) and anisotropic (T_||a≪T_⊥a, i.e., if T_||a→0) beam temperature, is investigated. We derived the dispersion equation of longitudinal oscillations in a cold electronic plasma penetrated through by a beam of charged particles with anisotropic temperature (for different parallel T_||a and perpendicular T_⊥a temperatures). As an application, the derived dispersion relation is solved in due course to investigate the current-convective instability (CCI) due to helical beam-plasma interaction. We determined the self longitudinal plasma oscillations in the absence of the beam. We investigated the derived dispersion equation in the two special cases for isotropic (T_||a=T_⊥a ) and anisotropic (T_||a≪T_⊥a, i.e., if T_||a→0) beam temperatures. The theory of a helical beam interaction with a plasma can be applied in astrophysics and in the study of the Sun-Earth environment. The study of instabilities in a system of gyrating charges is of special interest for elucidating the conditions of plasma confinement in magnetic traps