Parametric Instability Driven by Weakly Trapped Particles in Nonlinear Plasma Waves*

This talk discusses a new parametric instability mechanism caused by particles that are “weakly trapped” in the potential wells of a nonlinear wave[1]. The mechanism applies to low-collisionality plasmas supporting waves with near-acoustic dispersion relations such as ion sound waves, magnetized Langmuir waves, or Alfven waves. The theory is compared to particle in cell [PIC] simulations of Trivelpiece-Gould [TG] waves, as well as to experiments[2] on pure ion plasmas that observe parametric instability in TG standing waves. For TG waves, the standard parametric instability mechanism induced by wave-wave coupling is suppressed. The new mechanism predicts instability only if weakly trapped particles are present, at rates found to be in agreement with the simulations, and consistent with the experiments.

In the parametric instability studied here, a nonlinear “pump” wave is unstable to the growth of daughter waves with twice the 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.   Distributions with weakly trapped particle populations (appearing as phase space “holes”  or “rings” in the trapped particle distribution) often occur in nonlinear plasma waves and BGK states, and such distributions can be unstable to this new trapped particle mechanism.

[1] D. Dubin, Phys. Rev. Lett. 2018 (accepted).

[2] F. Anderegg, M. Affolter, A. Ashourvan, D. Dubin, F. Valentini and C. F. Driscoll, AIP Conf. Proc. 1668,  020001 (2015).