The dispersion relation for parallel propagating waves in the ion-cyclotron branch is investigated
numerically by considering that the velocity distribution of the ion population is a function of type
product-bi-kappa. We investigate the effects of the non-thermal features and of the anisotropy associated with this type of distribution on the ion-cyclotron instability, as well as the influence of different forms of the electron distribution, by considering Maxwellian distributions, bi-kappa distributions, and product-bi-kappa distributions. The cases of ions described by either Maxwellian or bi-kappa distributions are also considered, for comparison. The results of the numerical analysis show that the increase in the non-thermal character associated with the anisotropic kappa distributions for ions contributes to enhance the instability as compared to that obtained in the Maxwellian case, in magnitude and in wave number range, with more significant enhancement for the case of ion product-bi-kappa distributions than for the case of ion bi-kappa distributions. It is also shown
that the ion-cyclotron instability is decreased if the electrons are described by product-bi-kappa distributions, while electrons described by bi-kappa distributions lead to growth rates which are very
similar to those obtained considering a Maxwellian distribution for the electron population.