Electrostatic Instabilities in a Plasma with Anisotropic Velocity Distribution

An anisotropic magnetized plasma, in which the distribution of particle velocities is a bi-Maxwellian characterized by the temperatures $T_{\perp }$ and $T_{\mathrm{II}}$, is considered in order to delimit as much as possible the location of possibly unstable roots to the dispersion equation. We find that marginally unstable roots of the dispersion equation can occur only if both $[l+\frac{1}{2}]<\mathrm{}\omega <[l+1-(\frac{T_{\mathrm{II}}}{T_{\perp }}\left)\right]$ and $\omega <\frac{(T_{\perp }-T_{\mathrm{II}})}{T_{\mathrm{II}}}$, where $l$ is an integer and $\omega$ is the real part of the frequency in units of the cyclotron frequency. Thus, in particular, the system is stable if $T_{\perp }<2\mathrm{}{T}_{\mathrm{II}}$.