Non-resonant beam instability driven by the ring-beam ion distribution

Beams are one of the features that nearly commonly appear in various plasma realizations in nature. A systematic study of non-resonant ion-beam instability is presented for the ring-beam distribution, corresponding to a gyrotropic, helical beam along the large-scale magnetic field. We work on the rationalized, polynomial dispersion relation of the fourth-order and obtain the wave properties (dispersion relation) and the instability profile (the growth rate) at low and high beam speeds. The beam instability shows a smooth transition from the right-hand resonant instability at a moderate beam velocity to the non-resonant instability at a higher beam velocity. Moreover, the non-resonant beam instability occurs both forward and backward with respect to the beam direction. The non-resonant mode reduces to the firehose instability of anisotropic magnetohydrodynamics in the long-wavelength limit, where the beam component virtually serves as the field-aligned pressure. Simultaneous excitation of both the resonant and the non-resonant beam instabilities is possible at distinct wavelengths if the beam has a ring distribution, indicating that the set of the excited wave frequencies or wavelengths serves as a fingerprint of the ring-beam distribution.