Two-Stream Instability in a Cold Inhomogeneous Plasma in a Strong Magnetic Field

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Abstract
The two-stream instability in a cold plasma in a very strong magnetic field is considered. The density distribution is assumed to be the same for all species and varies arbitrarily in directions perpendicular to the field. For a given wavenumber in the direction of streaming there is a discrete set of normal modes. The stability of the system is determined by the lowest eigenvalue of a differential equation. A variational principle is devised for this lowest eigenvalue. The variational principle is applied to Gaussian and exponential density distributions. It is indicated how the eigenvalues corresponding to higher modes may be found by a Wentzel-Kramers-Brillouin method.

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