Toroidal Alfvn eigenmodes excited by energetic particles (EPs) and their transition to energetic particle modes are investigated using a three-dimensional nonlinear kinetic-magnetohydrodynamic hybrid simulation code. Both the symmetric chirping inside the Alfvn continuum gap for upward and downward directions and the asymmetric chirping affected by the Alfvn continuum are found in the simulations depending on the EP drive and the mode damping. For weak drive and damping, symmetric frequency chirping is observed with a chirping rate consistent with the Berk–Breizman theory (Berk et al 1997 Phys. Lett. A 234 213). For moderate drive and damping, upward chirping is dominant because downward chirping is interrupted by interaction with the Alfvn continuum. For strong drive and damping, two branches of frequency chirping are found for different poloidal harmonics. The dominant chirping is downward into the Alfvn continuum and the other is an upward chirping inside the Alfvn continuum gap. The creation and the propagation of holes and clumps are found in EP phase space, which is qualitatively consistent with the Berk–Breizman theory.

使用三维非线性动力学-磁流体力学混合仿真代码研究了由高能粒子（EPs）激发的环形Alfvn本征模式及其向高能粒子模式的转变。取决于EP驱动和模式阻尼，在仿真中都可以找到Alfvn连续间隙内部向上和向下的对称chi以及受Alfvn连续体影响的不对称。对于弱驱动和阻尼，可以观察到对称频率线性调频，其线性调频速率与Berk–Breizman理论一致（Berk等， 1997，Phys.Lett.A 234）。213）。对于适度的驱动和阻尼，向上鸣叫是主要的，因为向下鸣叫会因与Alfvn连续体的相互作用而中断。对于强驱动和阻尼，发现了针对不同的倍频谐波的频率线性调频的两个分支。主导chi是向下进入Alfvn连续谱，而另一个是向上the，即在Alfvn连续谱间隙内。在EP相空间中发现了空穴和团块的产生和传播，这在质量上与Berk–Breizman理论一致。