The propagation of the electromagnetic ion-cyclotron wave in a fusion plasma described by a loss-cone structure is discussed. The wavelength is assumed to be much larger than the ion Larmour radius and the ion plasma frequency ≫ the ion-cyclotron frequency. The two modes that propagate in the plasma interact strongly and fuse together under certain conditions making the plasma unstable. The coalescence of the modes is found to decrease with an increase in electron temperature.

A dispersion relation for the near perpendicular propagation of the electromagnetic ion cyclotron wave has been derived in a fusion plasma that has deuterium as a majority species, hydrogen as a minority species and fully ionized oxygen as an impurity constituent; all being modelled by loss cone distribution functions. The wave has a frequencyω around the deuterium ion gyrofrequency-Ω_D and a wavelength much longer than its Larmor radiusγ_LD(k_⊥γ_LD<1); the plasma itself being characterized by large ion plasma frequencies (ω_PD²>Ω_D²). Two modes, a low frequency (LF) and a high frequency (HF) mode of opposite electrical energy can propagate in the plasma; the instabilities that arise are thus due to an interaction of modes of opposite energies. We find that while hydrogen tends to destabilize the plasma, the impurity oxygen ions have the reverse effect. Also the plasma is most stable when the ratios of the perpendicular components of oxygen-to-deuterium and hydrogen-to-deuterium temperatures are kept low. Detailed studies of the wave propagation characteristics and energy reveal the close resemblance of a loss cone plasma containing oxygen to a stable Maxwellian plasma in regard to wave stability, propagation and energy.

A dispersion relation has been derived to study the stability of ion cyclotron (IC) propagation at the second harmonic of the minority component deuterium in a mirror confined plasma that has hydrogen as the majority species. We have worked in the frame of the majority ions; our dispersion relation can thus be used to study IC propagation in a single ion plasma also. Analysis of the dispersion relation yields two modes — one below and the other above the ion gyro-frequency Θ_H of hydrogen. The expression for the growth rate is used to explicitly show that an instability can arise in the plasma when the loss-cone indexj⩾3; this instability being a result of the coalescing of the two modes supported by the plasma. Unfortunately, the minority component deuterium does not decrease this instability and thus the proposed scheme of IC heating at the second harmonic of the minority component seems unsuited to mirror devices.

A dispersion relation for the perpendicular propagation of the electromagnetic ion cyclotron wave around the second harmonic of the deuterium ion gyrofrequency in a mildly relativistic, anisotropic Maxwellian plasma with hydrogen as the majority species and deuterium as the minority component has been derived. The work has been carried out in the frame of reference of the majority hydrogen ions; to these ions the waves at 2Θ_D would be at its own gyrofrequency.

Using a small quantityɛ to order all relevant parameters of the plasma, it was possible to derive the dispersion relations in a simple form. To the lowest order the relativistic factors do not enter the dispersion relation. The plasma can now support two modes—one above and the other below the hydrogen gyrofrequency in agreement with the assumptions. This was also verified numerically using a standard root solver thereby justifying the correctness of the ordering scheme.

In the next higher order, the dispersion relation is a quartic equation and is sensitively dependent on the relativistic factors. The plasma can now support four modes, both above and below the hydrogen gyrofrequency and consistent with the ordering scheme used. However the modes can now coalesce resulting in complex conjugate roots to the dispersion relation thereby indicating an instability.

The advantage of such a scheme is that two dispersion relations — one of which is independent of the relativistic factors and the other which is sensitively dependent on them can be separated out.

We have studied the stability of the electrostatic ion cyclotron wave in a plasma consisting of isotropic hydrogen ions ($H^{+}$) and temperature-anisotropic positively ($O^{+}$) and negatively ($O^{−}$) charged oxygen ions, with the electrons drifting parallel to the magnetic field. Analytical expressions have been derived for the frequency and growth/damping rate of ion cyclotron waves around the first harmonic of both hydrogen and oxygen ion gyrofrequencies. We find that the frequencies and growth/damping rates are dependent on the densities and temperatures of all species of ions. A detailed numerical study, for parameters relevant to comet Halley, shows that the growth rate is dependent on the magnitude of the frequency. The ion cyclotron waves are driven by the electron drift parallel to the magnetic field; the temperature anisotropy of the oxygen ions only slightly enhance the growth rates for small values of temperature anisotropies. A simple explanation, in terms of wave exponentiation times, is offered for the absence of electrostatic ion cyclotron waves in the multi-ion plasma of comet Halley.