We use the guiding center code ORBIT to study the broadening of resonances and the parametric dependence of the resonance frequency broadening width on the nonlinear particle trapping frequency 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 equals 4, as predicted by theory. It is found that as the mode amplitude increases, the coefficient becomes increasingly smaller because of the breaking down of the nonlinear pendulum approximation for the wave-particle interaction.
Dynamics of electrons in a parabolic magnetic field perturbed by an electromagnetic wave