Rippling modes in the edge of a tokamak plasma

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Abstract
A promising resistive magnetohydrodynamic candidate for the underlying cause of turbulence in the edge of a tokamak plasma is the rippling instability. In this paper a computational model for these modes in the cylindrical tokamak approximation was developed and the linear growth and single-helicity quasi-linear saturation phases of the rippling modes for parameters appropriate to the edge of a tokamak plasma were explored. Large parallel heat conduction does not stabilize these modes; it only reduces their growth rate by a factor sacling as K−4/3∥. Nonlinearly, individual rippling modes are found to saturate by quasi-linear flattening of the resistivity profile. The saturated amplitude of the modes scales as m−1, and the radial extent of these modes grows linearly with time due to radial Ẽ×B0 convection. This evolution is found to be terminated by parallel heat conduction.