Instability of nonlinear Trivelpiece-Gould waves. II. Weakly trapped particles

Abstract

This paper discusses a novel parametric instability mechanism caused by particles that are weakly trapped in the potential wells of a nonlinear “pump” wave. The pump wave is unstable to the growth of daughter waves with longer wavelength and nearly the same phase velocity as the pump. This induces adjacent potential peaks in the wave to slowly approach one-another, receding from other pairs of peaks. Particles that are weakly trapped between approaching peaks, with kinetic energies just below the potential maxima, are heated by compression and escape the well, and then become retrapped on the other side of the approaching peaks, where they amplify the compression by pushing the peaks together. The mechanism applies to low-collisionality plasmas supporting waves with near-acoustic dispersion relations such as ion sound waves, magnetized Langmuir waves, or Alfvén waves. The theory is compared to particle in cell simulations of Trivelpiece-Gould (TG) traveling waves, as well as to experiments on pure ion plasmas that observe parametric instability in TG standing waves.