Particle Dynamics in Asymmetry-Induced Transport: a Computational Study

We have developed a simple computer code as an aid to resolving the discrepanies between our experiments\footnote{D.L. Eggleston and B. Carrillo, Phys. Plasmas {\bf 10}, 1308 (2003).} and the theory\footnote{D.L. Eggleston and T.M. O'Neil, Phys. Plasmas {\bf 6}, 2699 (1999).} of asymmetry-induced transport. The code employs the fourth- order Runge-Kutta method to advance the particles in prescribed fields matching our experiment. For a single helical asymmety $\phi(r)\cos{(kz+l\theta-\omega t)}$, significant motion in the radial direction is restricted to those particles near the resonant velocity. Both the location and the width of this resonance are consistent with expectations. When a standing wave asymmetry is used (i.e., two counter-propagating helical waves), additional dynamical behaviors are observed. Stocastic motion occurs when the resonant regions of the two waves overlap, allowing a larger population of particles to undergo large radial excursions. There is also a class of particles with restricted axial motion, as in trapped particle modes\footnote{A.A. Kabantsev et al., Phys. Rev. Lett. {\bf 89}, 245001 (2002).}. These particles, which also make large radial excursions, are located near the radius where $\dot{\theta}= \omega/l$. Further progress in understanding asymmetry-induced transport may require inclusion of these effects.