Nonlocal Theory of Excitation of Electron Bernstein Waves by a Relativistic Electron Beam in Plasma with Loss-Cone Distribution of Electron

A nonlocal theory of excitation of electron Bernstein waves in a magnetized plasma slab by a relativistic electron beam with loss-cone distribution of electrons is presented. Kinetic theory is employed to obtain the susceptibility of plasma electrons whereas fluid theory is used to obtain the susceptibility of beam electrons. The mode structure and growth rate of the electron Bernstein wave are obtained. The growth rate in the case of Cerenkov and slow cyclotron interactions are proportional to ωb01/3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\omega }_{b0}}^{1/3}$$\end{document} and ωb0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\omega }_{b0}$$\end{document}, respectively. For typical parameter, the normalized growth rate attains maximum value at b≈1.743\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$b\approx 1.743$$\end{document} with different normalized beam velocities. These parameters control the growth rate due to nonlocality which rapidly decreases. The present theoretical scheme may be possible application in the field of heating of spherical torus plasmas.