Simulation of ion confinement during ion cyclotron heating in the TMX-U tandem mirror

Abstract

Particle and energy confinement of ions during ion cyclotron heating (ICH) in the centre cell of a tandem mirror is simulated by a Monte Carlo code. The interaction of the ion cyclotron wave with the ions is calculated using reduced equations of motion, and Coulomb collisions are modelled using a Monte Carlo algorithm. An axial electrostatic potential profile is generated by an iteration procedure, assuming Maxwellian electrons. The axial profile of neutral gas which fuels the ions from a localized gas box is determined from a neutral particle Monte Carlo code. Steady state calculations are reported for the Tandem Mirror Experiment Upgrade (TMX-U). The calculated energy confinement time τE is about twice that measured for off-midplane fuelling. The calculated τE can be decreased to the experimental value by either introducing extra gas at the ICH antenna to model the effect of ions striking the antenna or assuming anomalous radial loss. However, the enhanced radial loss also increases the end loss current well above that measured. Experimental and calculated τE agree more closely for midplane fuelling with heating from one antenna.

Effect of magnetic field ripple on parallel electron transport during microwave plasma heating in the Proto-MPEX linear plasma device

“…In the present work, a Monte-Carlo (MC) based approach is used to solve equation (3) for an 'ensemble' of trace or test particles [24][25][26][27][28][29]. This technique correctly describes the evolution of both low energy particles whose scattering length is short compared to the device length and high energy particles whose long scattering lengths lead to adiabatic confinement effects.…”

“…We note that the trapped particle kinetic energies observed in Profiles D (2300 A) and above exceed the 2 keV value described in appendix D; hence, under these conditions, superadiabatic effects due to wave and gyro-phase correlation between RF kicks needs to be incorporated. This means that the particle's gyro-phase needs to be tracked either by solving the full orbit equations of motion or a modified guiding center description as in [24].…”

“…For trapped test-particles with > a E 4 keV and undergoing multiple RF kicks, superadiabatic effects may become important and the velocity space diffusion model for the RF heating process is no longer valid [44]. Under these circumstances the particle gyro-phase information between consecutive RF kicks needs to be tracked [24,44].…”

“…This is trivially satisfied when the particle receives a single RF kick and leaves the plasma volume as in a passing particle in an open magnetic configuration like a linear plasma device. However, for trapped particles which encounter a turning point and travel back to the cyclotron resonance region, consecutive RF kicks may become correlated leading to superadiabatic effects [24,44] and the assumption of RF heating as diffusion due to a random walk in velocity space is no longer satisfied. Collisional processes can cause decorrelation of the gyro-phase between successive RF kicks.…”