Instability in a relativistic magnetized plasma

We present a general relativistic linear growth rate formula of electromagnetic waves for any wave normal angle and a general distribution function in a uniform magnetized plasma with a dominant cold plasma component and a tenuous hot plasma component. Such a general linear growth rate formula can be applied to different plasma environments, such as the Jovian Magnetosphere and laboratory plasma. The relativistic resonant condition for different wave modes is discussed and summarized. Then, the formula is applied to a parametric study for local instability of Earth's plasmaspheric hiss. We study the effects of the electron temperature, electron temperature anisotropy, types of distribution functions, plasma density, background magnetic field, and wave normal angle on the relativistic linear growth rate of the whistler mode. We find that (1) the energetic electrons with larger energy resonate with the lower frequency wave. The relativistic effect becomes significant for the electron with energy >100 keV. (2) The anisotropy only increases the growth rate and expands the growth wave band. (3) The high density and low background magnetic field tend to decrease the wave frequency and increase the growth rate. (4) The field-aligned growth rate is larger than the oblique growth rate, and the lower frequency whistler waves are easier to propagate obliquely. Published under license by AIP Publishing.