UC San Diego

First in Chapter 2, we discuss the collisional relaxation of a strongly magnetized pure ion plasma that is composed of two species with slightly different masses, but both with singly-ionized atoms. In a limit of high cyclotron frequencies Ωj, the total cyclotron action Ij for the two species are adiabatic invariants. In a few collisions, maximizing entropy yields a modified Gibbs distribution of the form exp[-H/T_para-α1 I1-α2 I2]. Here, H is the total Hamiltonian and αj's are related to parallel and perpendicular temperatures through 1/T_(perp,j)=1/T_para+αj/Ωj. On a longer timescale, the two species share action so that α1 and α2 relax to a common value $\alpha$. On an even longer timescale, the total action ceases to be a constant of the motion and $\alpha$ relaxes to zero.

Next, weak transport produces a low density halo of electrons moving radially outward from the pure electron plasma core, and the m=1 mode begins to damp algebraically when the halo reaches the wall. The damping rate is proportional to the particle flux through the resonant layer at the wall. Chapter 3 explains analytically the new algebraic damping due to both mobility and diffusion transport. Electrons swept around the resonant ``cat's eye" orbits form a dipole m=1 density distribution, setting up a field that produces ExB-drift of the core back to the axis, that is, damps the mode.

Finally, Chapter 4 provides a simple mechanistic interpretation of the resonant wave-particle interaction of Landau. For the simple case of a Vlasov plasma oscillation, the non-resonant electrons are driven resonantly by the bare electric field from the resonant electrons, and this complex driver field is of a phase to reduce the oscillation amplitude. The wave-particle resonant interaction also occurs in 2D ExB-drift waves, such as a diocotron wave. In this case, the bare electric field from the resonant electrons causes ExB-drift motion back in the core plasma, thus damping the wave.