Nonlinear phase dynamics of ideal kink mode in the presence of shear flow

Abstract

We investigate nonlinear phase dynamics of an ideal kink mode, induced by E × B flow. Here the phase is the cross phase (θ c) between perturbed stream function of velocity () and magnetic field (), i.e. θ c = θ ϕ − θ ψ . A dimensionless parameter, analogous to the Richardson number, (γ kink: the normalized growth rate of the pure kink mode; : normalized E × B shearing rate) is defined to measure the competition between phase pinning by the current density and phase detuning by the flow shear. When R i > 1, θ c is locked to a fixed value, corresponding to the conventional eigenmode solution. When R i ≤ 1, θ c enters a phase slipping or oscillating state, corresponding to a nonmodal solution. The nonlinear phase dynamics method provides a more intuitive explanation of the complex dynamical behavior of the kink mode in the presence of E × B shear flow.