Numerical studies of relativistic ion cyclotron instabilities

The novel physics of relativistic ion cyclotron instabilities is numericall y investigated. The growth rate spectrums and the possibility being absolut e instability of two fast ion cases (that the fast ions are energetic proto n and alpha particle, respectively) are numerically studied and compared wi th the analytical theory. The fundamental difference in the characteristics of the instabilities due to a slight change in fast ion mass per nucleon i s emphasized; it is determined by the relative normalized mass deficit per nucleon of fast and slow ions, and by the difference of their Lorentz facto rs. For the energetic proton case, both a cubic instability and a high harm onic quadratic instability can be driven; while, for the energetic alpha pa rticle case, only the quadratic instability can occur at the high alpha cyc lotron harmonics in the lower hybrid frequency regime and above; the thresh old is determined by the dielectric constant of the slow ion. The peak grow th rate is highest at the harmonics just over the threshold. Many new physi cs discovered by the numerical results are explained. A numerical polynomia l expansion method with curve fitting is developed to conclude that the ins tabilities studied are absolute, because the analytical results cannot be u sed to address this important issue. (C) 2000 American Institute of Physics . [S1070-664X(00)05602-0].