Dispersion and Damping of Oscillations in Maxwellian Plasmas with Nonuniform Zero-Order Densities

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Abstract
The dispersion and damping of oscillations in Maxwellian plasmas with zero-order density gradients are studied 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 oscillation characteristics are governed by a parameter γ which depends on the ratio of wavelength to the scale of inhomogeneity. Physically, γ is a measure of the weighted average density, with the square of the electric field as the weighting factor. It is always greater than or equal to unity; unity being the limiting case of an infinite and homogeneous medium. As γ increases, the effective plasma density is decreased and the following changes occur: (1) The real frequency of oscillation and the phase velocity are reduced. (2) The group velocity is increased. (3) Landau damping is increased. These changes are evaluated quantitatively for Gaussian and exponential density profiles.

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