The scattering of energetic particles by waves in a finite beta plasma

Solutions are presented for the dispersion relation of waves propagating parallel to the ambient magnetic field, in a plasma having an arbitrary ratio of thermal to magnetic pressure, beta. Previous results applicable only to wave frequencies much lower than the ion cyclotron frequency are extended to include all frequencies lower than the electron cyclotron frequency. The cyclotron turnovers are found to occur at significantly lower frequencies in finite beta plasmas. Cyclotron damping is significant for small wavelength waves. These results show that in energetic particle scattering by electromagnetic turbulence in a plasma with beta value greater than 40, scattering by waves with wave frequencies greater than the ion cyclotron frequency can be neglected. This condition is satisfied in many astrophysical plasmas.