Transformation approximation method for an electromagnetic ion-cyclotron instability caused by proton temperature anisotropy

The transformation approximation for the plasma dispersion fonction is applied to an electromagnetic ion-cyclotron instability caused by proton temperature anisotropy. The transformation method gives an improved dispersion relation and instability growth rate compared with the asymptotic expansion for the plasma dispersion fonction. It is found that the maximum growth rate is slightly suppressed when the transformation approximation for the plasma dispersion function is used. However, it is shown that the transformation approximation method yields an unreliable estimate of the growth rate for values greater than a critical thermal anisotropy. Cold-heavy-ion effects on the ion-cyclotron instability are also investigated.