Simulation of linear and nonlinear Landau damping of lower hybrid waves

Abstract

The linear physics of lower hybrid waves (LHWs) and their nonlinear interaction with particles through Landau damping are studied with the gyrokinetic electron and fully kinetic ion (GeFi) particle simulation model in the electrostatic limit. Unlike most other wave modes, the LHWs can resonantly interact with both electrons and ions, with the former being highly magnetized and latter nearly unmagnetized around the lower hybrid frequency. Direct interactions of LHWs with electrons and/or ions are investigated for cases with various k∥/k,Ti/Te, and wave amplitudes. In the linear electron Landau damping (ELD), the dispersion relation and the linear damping rate obtained from our simulation agree well with the analytical linear theory. As the wave amplitude increases, the nonlinear Landau effects are present, and a transition from strong decay at smaller amplitudes to weak decay at larger amplitudes is observed. In the nonlinear stage, the LHWs in the long time evolution finally exhibit a steady Bernstein-Greene-Kruskal mode, in which the wave amplitude is saturated above the noise level. While the resonant electrons are trapped in the wave field in the nonlinear ELD, the resonant ions are untrapped in the LHW time scales. The ion Landau damping is thus predominantly in a linear fashion, leading to a wave saturation level significantly lower than that in the ELD. On the long time scales, however, the ions are still weakly trapped. The results show a coupling between the LHW frequency and the ion cyclotron frequency during the long-time LHW evolution.

Nonlinear electromagnetic formulation for particle-in-cell simulation of lower hybrid waves in toroidal geometry

“…(1), (3)(4), (7)(8)(9) and (26-29) form a closed system for electron model with canonical momentum, while Eqs. (1), (3), (10), (13)(14), (18) and (26-29) form a closed system for electron model with kinetic momentum. In linear and nonlinear regimes, both electron models with kinetic and canonical momentum can be used in LH wave studies with similar complexity and numerical performance.…”

“…[9][10][11] Particle-in-cell simulation approach is a powerful tool for studying nonlinear physics. Several algorithms and models of particle simulation of radio frequency (RF) waves in simple geometry (slab or cylinder) have been developed, e.g., GeFi [12][13][14] , Vorpal 15,16 and G-gauge 17,18 codes. However, nonlinear RF simulation capability is unavailable for the toroidal geometry before our earlier work, in which we developed the electrostatic particle simulation of LH wave propagation in tokamaks.…”

Verification of particle simulation of radio frequency waves in fusion plasmas

“…Such an approach has been taken by gyrokinetic (GK) simulation codes, which have revolutionized studies of turbulent transport driven by low frequency drift waves 19,20 . Nonlinear phenomena a) Electronic mail: akuley@uci.edu of the RF waves have been studied in the slab geometries with particle codes such as GeFi 21 , Vorpal 22 and G-gauge 23 . For waves in the intermediate frequency range, between the ion and electron cyclotron frequencies (e.g., lower hybrid wave, ion Bernstein wave, etc.…”

Particle simulation of lower hybrid wave propagation in fusion plasmas

“…5 Present address: Plasma Physics Laboratory, Princeton University, PO Box 451, Princeton, NJ 08543, USA. the nonlinear issues related to RF heating and current drive in the slab geometry [22,23].…”