Long range frequency chirping of Bernstein-Greene-Kruskal modes, whose existence is determined by the fast particles, is investigated in cases where these particles do not move freely and their motion is bounded to restricted orbits. An equilibrium oscillating potential, which creates different orbit topologies of energetic particles, is included into the bump-on-tail instability problem of a plasma wave. With respect to fast particles dynamics, the extended model captures the range of particles motion (trapped/passing) with energy and thus represents a more realistic 1D picture of the long range sweeping events observed for weakly damped modes, e.g. global Alfven eigenmodes, in tokamaks. The Poisson equation is solved numerically along with bounce averaging the Vlasov equation in the adiabatic regime. We demonstrate that the shape and the saturation amplitude of the nonlinear mode structure depends not only on the amount of deviation from the initial eigenfrequency but also on the initial energy of the resonant electrons in the equilibrium potential. Similarly, the results reveal that the resonant electrons following different equilibrium orbits in the electrostatic potential lead to different rates of frequency evolution. As compared to the previous model [Breizman B.N. 2010 Nucl. Fusion 50 084014], it is shown that the frequency sweeps with lower rates. The additional physics included in the model enables a more complete 1D description of the range of phenomena observed in experiments.
Frequency Chirping of Energetic-Particle-Driven Geodesic Acoustic Modes in Tokamaks
De Vinci Higher Education, De Vinci Research Center（德芬奇高等教育中心，德芬奇研究中心）；Center for Nonlinear Plasma Science and C.R. ENEA Frascati（非线性等离子体科学中心与ENEA弗拉斯卡蒂研究中心）；Max Planck Institute for Plasma Physics（马克斯·普朗克等离子体物理研究所）
Theoretical description of chirping waves using phase-space waterbags
快粒子的引导中心动力学可以改变高能粒子驱动模式的啁啾频率的行为。本文讨论了早期的捕获/传递轨迹模型[H. Hezaveh et al 2017 Nucl. Fusion 57 126010]已经扩展到波捕获区域可以扩展并捕获周围粒子的区域。这种扩展允许研究波向上和向下的频率啁啾在整个范围内的高能粒子轨道。在绝热近似下，高能粒子的相空间分析的拉格朗日轮廓的方法，使用相空间水袋离散的岛屿。为了解决在快速形成的相空间岛的动态，并找到一个适当的初始化系统，全尺寸的建模实施使用凸尾（BOT）代码。除了调查的啁啾波深化潜力在一个单一的共振的演变，我们选择特定的节距角范围内，更高的共振可以有一个相对相当大的贡献的波粒相互作用。因此，该模型也解决了在双共振的情况下，我们报告的显着修改的啁啾波的行为，由于$2^{\text{nd}}$共振。本文提出的模型给出了一个全面的一维范式的长距离频率啁啾信号的实验观察向上和向下啁啾和多共振。
