Bounds on Instability Growth Rates for Cold Plasmas Streaming along an Infinite Magnetic Guide Field

We derive two bounds on growth rates for streaming instabilities of cold plasmas with inhomogeneous density and velocity profiles transverse to a unidirectional infinite magnetic field: 1) a uniform bound which is independent of wavenumber, and 2) a wavenumber-dependent bound which is less than the uniform bound for long wavelengths. Here streaming instabilities include both multistream instabilities in which two or more streams with different velocities overlap in configuration space, and the slipping stream instability in which a stream has a transverse velocity gradient. The bounds obtained are functions of only global steady-state parameters and are useful in bounding growth rates in experimental devices.