Streaming Instabilities in Plasmas with Zero-Order Density Gradients

Abstract

Current-carrying plasmas with zero-order density gradients are analyzed for instability using the Vlasov and Maxwell's equations. The plasmas are confined by a strong axial magnetic field, and the densities are nonuniform in the transverse directions. By means of a variational method, it has been found that the density inhomogeneity (1) decreases the real frequency of oscillation, (2) reduces the maximum unstable wave number, and (3) increases the minimum current required for instability and imposes an upper limit on the streaming velocity beyond which the plasma is stable against perturbations of all wavelengths. Explicit results are given for Gaussian and exponential density profiles with resonant, Maxwellian, and delta function velocity distributions. The physical mechanisms that are responsible for these changes are discussed.