Erratum: Trapped-Particle Asymmetry Modes in Single-Species Plasmas [Phys. Rev. Lett. 87, 225002 (2002)]

Abstract

The fluid motion of Eq. (3) is written in a form that inadvertently omits a contribution from the rise in the trapped (and the fall in the untrapped) particle density at the interface between trapped and untrapped particles (i.e., at r r s ). The equation should readwhere the trapped and untrapped densities are written in terms of Heaviside step functions Q as follows:and n u ͑r͒ n 0 ͑r͒Q͑r s 2 r͒ .The dispersion relation of Eq. (4) for top hat density profiles [n 0 ͑r͒ n 0 Q͑R p 2 r͒] then becomes µ R p r swhere I m ϵ I m ͑r s ͞l D ͒ are modified Bessel functions of the first kind and f 0 ϵ m 2 f͞f E . This new dispersion relation has two solutions, with only the lower frequency solution being relevant here. The remaining discussion and results in the paper are not affected by this correction, since the two dispersion relations are equivalent in the limit of l D ! 0, and the correct equation was used in the kinetic treatment for comparison to experiments.

Trapped-Particle-Mediated Damping and Transport

“…Even for small V sq , the trapped particle mode is essentially uniform with z on either side of the barrier, changing sign at the barrier. A simple kinetic theory model with a zero-length trapping barrier [1] predicts mode frequencies agreeing with measurements to within about 10%.…”

“…Two years ago, "trapped particle asymmetry" modes were reported to occur when an applied "squeeze" voltage causes some particles to be trapped axially; and a simple theory explained the observed mode frequencies [1]. Now, it appears likely that trappedparticle-mediated (TPM) effects are dominant in plasma lifetime scalings, in transport from applied asymmetries, and in diocotron mode damping.…”

Trapped particles and asymmetry-induced transport

“…This subtlety was missed in prior experiments. 15 The trapped particle mode is observed to be strongly damped, with ␥ a Ϸ1ϫ10 3 s Ϫ1 ͑i.e., ␥ a / f a ϳ1/15) for small V sq at Bϭ10 kG. Figure 4 shows that the damping rate decreases as V sq increases, with ␥ a ϳ0 when the column is cut in half.…”

Numerical Non-neutral Plasmas

“…This code has been used to study the instability of the m = 1 diocotron mode for hollow density profiles, and has been used more recently to simulate the trapped-particle asymmetry modes discovered by Kabantsev, et al [9].…”