<RESEARCH REPORT>Collision-Induced Instability in a Magnetoactive Plasma

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The dispersion relations for the waves propagating in a magnetoactive plasma are obtained from the Boltzmann equation with a collision term of the electrons. Two cases in which the wave vector parallel and perpendicular to a uniform magnetic field are studied. Assuming a δ-function for velocity distribution function, in each case, we have two dispersion relations for the zeroth approximation in k as follows : (A) ω(ω+iυ)^2=ω^2_p(ω+iν-i(V/3)(dν/dV)) and (B) ω(ω±ω_c+iν)^2=ω^2_p(ω±ω_c+iν-i(V/3)(dν/dV)) where ω_c, ω_p and υ are the cyclotron, the plasma and the collision frequency respectively. After detailed calculations under the assumption υ(v)=const. x v^h it is found that the initial perturbation grows exponentially for h<-3 in (A) and h>3 in (B), and that the growth rate of the latter case attains its maximum value at Re (ω)=ω_c independently of the other plasma parameters. In the first approximation, Re (ω) shifts from ω_c to a larger frequency and Im (ω) grows more, but their corrections decrease with the ratio ω_c/ω_p increasing.
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