The guiding centre dynamics of fast particles can alter the behaviour of energetic particle (EP) driven modes with chirping frequencies. In this paper, the applicability of an earlier trapped/passing locus model (Hezaveh et al 2017 Nucl. Fusion 57 126010) has been extended to regimes where the wave trapping region can expand and trap ambient particles. This extension allows the study of waves with up-ward and down-ward frequency chirping across the full range of EP orbits. Under the adiabatic approximation, the phase-space of EPs is analysed by a Lagrangian contour approach where the islands are discretised using phase-space waterbags. In order to resolve the dynamics during the fast formation of phase-space islands and find an appropriate initialisation for the system, full-scale modelling is implemented using the bump-on-tail code. In addition to investigating the evolution of chirping waves with deepening potentials in a single resonance, we choose specific pitch-angle ranges in which higher resonances can have a relatively considerable contribution to the wave-particle interaction. Hence, the model is also solved in a double-resonance scenario where we report on the significant modifications to the behaviour of the chirping waves due to the 2nd resonance. The model presented in this paper gives a comprehensive 1D paradigm of long range frequency chirping signals observed in experiments with both up-ward and down-ward chirping and multiple resonances.

快速粒子的引导中心动力学可以改变具有啁啾频率的高能粒子 (EP) 驱动模式的行为。在本文中，早期捕获/通过轨迹模型的适用性（Hezaveh等人2017 Nucl. Fusion 57126010）已扩展到陷波区域可以扩展并捕获环境粒子的区域。这种扩展允许研究在整个 EP 轨道范围内具有向上和向下频率啁啾的波。在绝热近似下，EP 的相空间通过拉格朗日等高线方法进行分析，其中使用相空间水袋离散岛。为了解决相空间岛快速形成过程中的动力学问题并为系统找到合适的初始化，使用尾部碰撞代码实现全尺寸建模。除了研究单个共振中具有加深电位的啁啾波的演化之外，我们还选择了特定的俯仰角范围，在这些范围内，较高的共振可以对波粒相互作用产生相对较大的贡献。因此，该模型也在双共振场景中得到解决，我们报告了由于第二次共振对啁啾波行为的重大修改。本文中提出的模型给出了在实验中观察到的长程频率啁啾信号的综合一维范式，这些信号在向上和向下啁啾和多次共振的实验中观察到。