Numerical Investigation of Saturation Mechanism of the Dissipative Trapped Ion Instability

A set of model equations of the dissipative trapped ion instability is derived and solved numerically. Multiple time scale expansion scheme is applied to the non-linear fluid equations of Kadomtsev and Pogutse by taking μ=ω⁄ν_e as a small parameter, where ω is the frequency of the wave and ν_e is the effective collision frequency of the electrons. All the modes except for the linearly most unstable one die away due to the mode coupling. Final saturation of the mode is attributed to the modification of background trapped ion number density averaged over the poloidal direction. The coefficient of trapped ion anomalous diffusion, which scales as D∝ν_ia² (ν_i is the effective collision frequency of the ions and a is the minor radius of a torus) is also derived.