Resonance frequency broadening of wave-particle interaction in tokamaks due to Alfv\'{e}nic eigenmode

TL;DR

This study investigates how resonance frequency broadening in wave-particle interactions within tokamaks depends on mode amplitude, confirming theoretical predictions under realistic conditions and exploring the limits of the pendulum approximation.

Contribution

It demonstrates the first experimental confirmation of the resonance frequency width to bounce frequency ratio being 4 in realistic tokamak conditions and analyzes how this ratio changes with mode amplitude.

Findings

Resonance frequency width to bounce frequency ratio equals 4 at small mode amplitudes.

The ratio decreases as mode amplitude increases due to nonlinear effects.

The pendulum approximation applies at small amplitudes but breaks down at larger amplitudes.

Abstract

We use a guiding center code ORBIT to study the broadening of resonances and the parametric dependence of the resonance frequency broadening width $\Delta\Omega$ on the nonlinear particle trapping frequency $\omega_b$ of wave-particle interaction with specific examples using realistic equilibrium DIII-D shot 159243 (Collins et al. 2016 Phys. Rev. Lett. 116 095001). When the mode amplitude is small, the pendulum approximation for energetic particle dynamics near the resonance is found to be applicable and the ratio of the resonance frequency width to the deeply trapped bounce frequency $\Delta\Omega/\omega_b$ equals 4, as predicted by theory. This factor 4 is demonstrated for the first time in realistic instability conditions. It is found that as the mode amplitude increases, the coefficient $a=\Delta\Omega/\omega_b$ becomes increasingly smaller because of the breaking down of the nonlinear pendulum approximation for the wave-particle interaction.