Effects of Collisions and Finite Length on Plasma Waves in a Single-Species Plasma Column.

摘要

This dissertation discusses the effects of collisions and finite plasma length on Trivelpiece-Gould waves on a magnetized, single-species plasma column. Starting from Poisson's equation and a drift-kinetic equation with an energy- and momentum-conserving Fokker-Planck collision term, a dispersion equation is obtained for an azimuthally symmetric wave on an infinitely long column. The dispersion relation includes the effect of velocity-scattering collisions with impact parameters less than the cyclotron radius and recovers Landau damping as collisionality approaches zero. For wavenumbers such that ( klambdaD) 1---where k ≡ &parl0;k2z+k2⊥ &parr0;1/2 is the total wavenumber, kz and k⊥ are the wavenumbers along and transverse to the magnetic field, and lambdaD is the Debye length---Landau damping is exponentially small, and the complex frequency of the wave is approximately o ≅ (kzop / k)[1 + (3 / 2)( klambdaD)2 x x(1 + 10 ialpha / 9) / (1 + 2ialpha)], where op is the plasma frequency, alpha ≡ knuD / (kzop) is a collisionality parameter, and nuD is the collision frequency. When the Debye length is larger than the cyclotron radius, long-range interactions between particles on different field lines are also significant but cannot be treated by a Fokker-Planck collision operator. Fluid theory provides a simpler context for incorporating these long-range interactions, since their primary effect is the enhancement of transport across the magnetic field. Fluid analysis reveals that the damping rate obtained from kinetic theory corresponds to bulk viscosity and that viscous relaxation of radial shear in the parallel flow, due to long-range collisions, gives an important additional contribution to the damping rate. Lastly, azimuthally symmetric normal modes are calculated for a cold, finite-length plasma column. The dispersion equation o = kzop / &parl0;k2z+k2⊥ &parr0;1/2 for Trivelpiece-Gould waves on a cold, strongly magnetized plasma has the property that two waves with wavenumbers (kz, k⊥) and ( k'z,k'⊥ ) have the same frequency if kz / k⊥ = k'z/k'⊥ . Such degenerate waves are mixed upon reflection at the ends of the plasma column, and consequently each normal mode involves many such waves. The modes often exhibit sharp features along resonance cones with slope dz / dr = +/-( w2p/w2-1 )1/2.