Relativistic ion cyclotron instability driven by energetic alpha particles in plasma under magnetic field with sinusoidal nonuniformities

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.