Localized electrostatic wave modes due to relativistic ion cyclotron instabilities are observed in a hybrid particle-in-cell simulation under a magnetic field with sinusoidal nonuniformity. In order to investigate the physical mechanism of the simulation results, an analytical theory, adopting a parabolic approximation around a magnetic field minimum, has been developed based on an absolute instability condition along with systematic expansion procedures. The spatial structure, growth rate and frequency of the localized wave modes predicted by the theory are found to agree well with those of simulation. In this work, we demonstrate that the instabilities can survive even when the magnetic variation is much larger than the Lorentz factor minus one. Furthermore, both the simulation and the theory show that the wave mode can exist where its frequency is smaller than the local harmonic cyclotron frequency, violating the well-known requirement for driving relativistic cyclotron instabilities.
正弦波的不均匀性磁场中，相对论性离子回旋不稳定性导致的局域静电波模在混合粒子-网格模拟中被观测到。为探究该模拟结果的物理机制，本研究基于绝对不稳定性条件，并采用系统展开方法，建立了围绕磁场极小值的抛物线近似解析理论。理论所预测的局域波模的空间结构、增长率及频率与模拟结果吻合良好。本工作进一步证明，即使磁场变化幅度远大于洛伦兹因子减一，不稳定性仍可存在。此外，模拟与理论均表明，该波模可在其频率低于局域谐波回旋频率时存在，从而违反了驱动相对论性离子回旋不稳定性的已知必要条件。