Plasma Oscillations in a Magnetic Field

Abstract

In the presence of a uniform external magnetic field, the initial value problem for a longitudinal electron oscillation in a fully ionized plasma is treated in the range of the linear theory under the assumption that collisions are negligible and that the angle θ between wave vector and magnetic field is not equal to π/2, and \(\textRe(s){\neq}0\) on the complex s -plane. It is shown that, if we determine the indicial condition that the solution of initial value problem varies as exp ( i k · r +α t ), where α is a complex valued frequency, then for \(\textRe(\alpha){ }0\) (amplified wave) each dispersion equation of the proper plasma oscillations, the perturbed velocity distribution function, and the potential are coincident. As a typical example, the case in which the equilibrium distribution is Maxwellian is discussed.