Study on the dissipative trapped-particle instability using the Connor-Hasti-Taylor transformation

The trap-ion instability is studied by applying the Connor-Husti-Taylor transformation. Unlike the previous studies, it has been shown now that there are two regimes corresponding to strong and weak overlapping of harmonics (large and small shears). Integral equations and variational principles have been obtained for the trapped-particle instabilities. This instability is found to have two regimes, at small and large shears, which differ essentially. At small shear the instability increment is found which takes into account the Landau damping by flight ions. The regime of a large shear has been examined for the first time. Frequencies and increment are found. The real part of the frequency is shown to decrease essentially. The Landau damping has a slight effect and the instability may be stabilized by ion collisions