Verification of particle simulation of radio frequency waves in fusion plasmas

Abstract

Radio frequency (RF) waves can provide heating, current and flow drive, as well as instability control for steady state operations of fusion experiments. A particle simulation model has been developed in this work to provide a first-principles tool for studying the RF nonlinear interactions with plasmas. In this model, ions are considered as fully kinetic particles using the Vlasov equation and electrons are treated as guiding centers using the drift kinetic equation. This model has been implemented in a global gyrokinetic toroidal code (GTC) using real electron-to-ion mass ratio. To verify the model, linear simulations of ion plasma oscillation, ion Bernstein wave, and lower hybrid wave are carried out in cylindrical geometry and found to agree well with analytic predictions.

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

“…(2) to its canonical form: Furthermore, the 6-D Vlasov equation has been adopted for describing fully kinetic ion dynamics in GTC and can be utilized when ion kinetic effects are important. 19,26,27 …”

“…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. 19,20 In this work, we further extend the electrostatic particle model to a fully nonlinear electromagnetic particle model, which has been successfully implemented into the gyrokinetic toroidal code (GTC). 21 The electromagnetic dispersion relation and the nonlinear particle trapping of the LH waves have been verified by using current particle model.…”

“…[9][10][11] In such cases, ion kinetic effect can be incorporated by using 6-D Vlasov equation. 19,26,27 Due to the fact that LH wave frequency is much smaller than electron cyclotron frequency ce   and LH wavelength is much bigger than electron gyro-radius 1 e k , the electron dynamic is described by drift kinetic equation using either kinetic momentum or canonical momentum. At the same time, electron continuity equation is used for calculating the perturbed density from the perturbed current to avoid the numerical instabilities due to the inconsistency between electron density and current when calculated from the first two moments of the perturbed distribution function.…”

Nonlinear particle simulation of ion cyclotron waves in toroidal geometry

“…In our simulation we compute the marker particle trajectory [Eq. (2)] by the time centered Boris push method [3,7]. To verify this integrator we carried out the single particle motion in this toroidal geometry.…”

“…However, this method does not capture the crucial nonlinear physics. To address these crucial nonlinear physics we have developed a toroidal PIC simulation model based on the initial value approach [3][4]. Nonlinear phenomena of the RF waves have been studied in the slab geometries with particle codes such as GeFi [5] and Vorpal [6].…”