Resonantly unstable off-angle hydromagnetic waves

We consider semi-quantitatively the cyclotron resonance instability of ion cyclotron and magnetosonic waves propagating at an angle to the magnetic field in an infinite uniform plasma. The velocity distributions of electrons and ions consist of a dense cold component and a diffuse high-energy tail. If the high-energy protons are sufficiently intense and their pitch angle distributions sufficiently anisotropic, instability occurs for those waves propagating parallel to the magnetic field. If the spectrum of resonant protons is sufficiently hard, a reasonably large cone of propagating angles about the magnetic field can be unstable. Observed fluxes of trapped protons in the magnetosphere should destabilise the ion cyclotron wave at a lower intensity threshold than for at least one class of electrostatic waves.