Nonlinear co-existence of beta-induced Alfvén eigenmodes and beta-induced Alfvén-acoustic eigenmodes

A toroidal particle-in-cell (PIC) code, suitable for investigating nonlinear phenomena in radio frequency (RF) heating and current drive, is developed and verified thereafter through a series of fidelity tests for field solvers and single particle motions in toroidal geometry, where simulation results show good coincidence with analytical prediction. The RF capability is then demonstrated through the integrated benchmarks with linear lower hybrid wave and ion Bernstein wave theory in cylindrical geometry, where the analytic result is easily available. The frequency and mode structure in the simulations agree well with the theoretical prediction.

Figure 1 Vector field solver fidelity test, black dot is the solver’s numerical solution, while the red line is the theoretical curve.

Figure 2 Particle trajectory integrator benchmark, right panel shows a typical 'banana' particle. In the right panel, dots indicates various properties measured form the integrator, while the black line is the theoretical calculation using simple guiding center drift theory.

Figure 3 Lower hybrid wave simulation result obtained, left panel shows the field history, and right panel shows the mode structure on a poloidal cross section.

Figure 4 The frequency spectrum (left) of the ion Bernstein wave benchmark with the ion temperature set to 3 keV. The right panel shows the dispersion relation plot, where various dots indicate the measured result from the simulation and the line represents the analytical solution.