ION-CYCLOTRON INSTABILITIES IN A MILDLY RELATIVISTIC HYDROGEN-DEUTERIUM FUSION PLASMA

A dispersion relation for the perpendicular propagation of the electro magnetic ion cyclotron wave around the second harmonic of the deuteriu m ion gyrofrequency in a mildly relativistic, anisotropic Maxwellian p lasma with hydrogen as the majority species and deuterium as the minor ity component has been derived. The work has been carried out in the f rame of reference of the majority hydrogen ions; to these ions the wav es at 2 Omega(D) would be at its own gyrofrequency. Using a small quan tity epsilon to order all relevant parameters of the plasma, it was po ssible to derive the dispersion relations in a simple form. To the low est order the relativistic factors do not enter the dispersion relatio n. 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 justif ying the correctness of the ordering scheme. In the next higher order, the dispersion relation is a quartic equation and is sensitively depe ndent on the relativistic factors. The plasma can now support four mod es, both above and below the hydrogen gyrofrequency and consistent wit h the ordering scheme used. However the modes can now coalesce resulti ng in complex conjugate roots to the dispersion relation thereby indic ating an instability. The advantage of such a scheme is that two dispe rsion relations - one of which is independent of the relativistic fact ors and the other which is sensitively dependent on them can be separa ted out.