The transverse kink instability of electron phase-space holes

Electron holes (solitary BGK modes) routinely form in one dimension as the stable, long-lived, non-linear result of two-stream or bump-on-tail unstable electron distributions. In multiple dimensions, however, they break up unless there is a strong magnetic field, by a 'transverse instability', which kinks and often destroys the hole. Many prior simulations have observed the instability, but its mechanism has not previously been correctly identified. I show that the instability mechanism is in fact kinematic, arising from the jetting of electrons as the kink accelerates in the trapping electric field direction. The growth rate at long wavelength can be deduced by a conceptually simple consideration of conservation of total hole momentum. PIC simulations of unmagnetized-hole kink growth show wavelengths and growth rates in agreement with heuristic estimates of the fastest growing mode². In addition, a comprehensive linear kinetic analytic calculation at non-zero magnetic field has been completed for the relevant shift eigenmode, providing the full dispersion relation of the instability, and verifying the heuristic estimates³.
² I H Hutchinson, Phys. Rev. Lett. 120, 205101 (2018).
³ I H Hutchinson, submitted to J. Plasma Phys. (2018).