磁界中のプラズマ振動のCauchy積分型分散式の誘導

Abstract

The dispersion formula of Cauchy integral type for longitudinal plasma waves in a magnetic field has been for the first time exactly derived, in order to obtain a general instability criterion for magnetoplasma waves, on the basis of Vlasov's collision-free kinetic equation for arbitrary velocity distributions. It reads∫Φ(k, v)/v-ζ dv=k2/ωpwhereΦ(k, v)=φ_(k, v)=2π/NkII[kII∫A2l(k1/Ω)2l+k1∑A2l+1(v)(k1/Ω)2l+1]and ζ=ω/kII, 1mζ>0N and Ω are the total density and the gyration frequency of electrons. A2l and A2l+1 are fully determined by the 2/-th moment of the elelctron velocity distribution function integrated perpendicularly to the external magnetic field.The motion of the ions is easily taken into account by replacing Φ(k, v) by φ-(k, v)+φ+(k, v)m_/m+. The formula being important for the drift instability can be written ask2-ω_∫∞-∞g0(v)/v-ζ dv+(k1/kII)2∫∞-∞D(v.Ω/kII)/v-ζ dv=0The first two terms correspond to the dispersion relation either for the case of strong magnetic field approximation or for the case of grazing angle propagation. The third term contributes to the drift instability in the case of wave propagation at an appreciable angle to a finite magnetic field.The fourth or higher order terms give rise to the instability due to anisotropic velocity distributions.