Frequency splitting and collisional de-correlation for removing superadiabatic barriers in ECRH experiments

Abstract

A series of test-particle calculations are presented which measure the ECRH velocity diffusion coefficients for two mirror devices – the simple mirror SM-1 and the tandem mirror TMX-U – for monochromatic electron-cyclotron waves. The diffusion coefficients are compared to those from quasi-linear theory. The role of wave-particle resonance overlap and collisional de-correlation for producing stochastic instead of superadiabatic particle motion is investigated. The use of two or more waves with different frequencies is found to increase the number of resonances and thus the chance of resonance overlap; a frequency separation of the axial bounce frequency is optimum for two waves. A spectrum of axial wavenumbers making up a standing wave does not increase the number of resonances and thus does not increase stochasticity. Pitch-angle collisions can also produce significant de-correlation between the wave and particle, owing to the large geometrical enhancement of the gyrophase diffusion in an inhomogeneous magnetic field. Results for fundamental (\U0001d6da = \U0001d6dac) heating in SM-1 show that using two frequencies instead of one increases heating at an energy of ~ 10 keV by a factor of about three. Calculations for the tandem mirror TMX-U for an energy of SO keV show that stochasticity is assured by either resonance overlap or collisional gyrophase diffusion.