Analytical solutions to the general problem of oblique wave growth and damping

Analytical solutions are presented for the linear growth or damping rate caused by resonant particle interactions with plasma waves propagating in any arbitrary direction relative to the ambient magnetic field. For the case of three realistic and widely adopted representations for the particle distribution function, namely for a bi-Maxwellian, a bi-Lorenzian, and a loss-cone distribution, the angular dependence of the net growth rate can be expressed in terms of simple, smoothly varying functions involving modified Bessel functions of the first and second kind. Furthermore, in the limits of both quasilongitudinal and quasitransverse wave propagation, the analytical results reduce to simple algebraic expressions that may readily be used to compare the contributions from any specific harmonic resonance. These analytical solutions eliminate the need for costly and time-consuming numerical integration that hitherto was the standard procedure for obtaining growth rates for oblique waves