Nonlinear phase dynamics of ideal kink mode in the presence of shear flow
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Graphical Abstract
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Abstract
We investigate nonlinear phase dynamics of an ideal kink mode, induced by E × B flow. Here the phase is the cross phase (θc) between perturbed stream function of velocity (ф˜) and magnetic field (φ˜ ), i.e. θc = θф − θψ. A dimensionless parameter, analogous to the Richardson number, Ri = 16γkink2/ωE2 (γkink: the normalized growth rate of the pure kink mode; ωˆE: 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 Ri> 1, θc is locked to a fixed value, corresponding to the conventional eigenmode solution. When Ri ≤1, θc 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 ynamical behavior of the kink mode in the presence of E × B shear flow.
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