Rotational pumping and damping of the m=1 diocotron mode

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Abstract
An effect called rotational pumping by the authors (by analogy with magnetic pumping) causes a slow damping of the m=1 diocotron mode in non-neutral plasmas. In a frame centered on the plasma and rotating at the diocotron mode frequency, the end confinement potentials are nonaxisymmetric. As a flux tube of plasma undergoes E×B drift rotation about the center of the column, the length of the tube oscillates about some mean value, and this produces a corresponding oscillation in T∥. In turn, the collisional relaxation of T∥ toward T⊥ produces a slow dissipation of electrostatic energy into heat and a consequent radial expansion (cross-field transport) of the plasma. Since the canonical angular momentum is conserved, the displacement of the column off axis must decrease as the plasma expands. In the limit where the axial bounce frequency of an electron is large compared to its E×B drift rotation frequency theory predicts the damping rate γ=−2κ2ν⊥,∥ (r2p/R2w)(λ2D/L20)/(1−r2p R2w), where κ is a numerical constant, λD is the Debye length, Rw is the radius of the cylindrical conducting wall, rp is the effective plasma radius, L0 is the mean length of the plasma, and ν⊥,∥ is the equipartition rate. A novel aspect of this theory is that the magnetic field strength enters only through ν⊥,∥. As the field strength is increased, the damping rate is nearly independent of the field strength until the regime of strong magnetization is reached [i.e., Ωc≳v̄/b=(kT)3/2/√me2], and then the damping rate drops off dramatically. This signature has been observed in recent experiments. For completeness, the theory is extended to the regime where the bounce frequency is comparable to the rotation frequency, and bounce-rotation resonances are included.