Nonlinear evolution of the resistive interchange mode in the cylindrical spheromak

Results are presented of a study of various aspects of the single helicity nonlinear development of the resistive interchange mode in the cylindrical spheromak. A formulation of the helically symmetric resistive magnetohydrodynamic (MHD) equations that partially separates the ideal MHD characteristics is developed. Mode saturation can occur because of the quasilinear flattening of the pressure profile in the vicinity of the mode rational surface. However, this saturation process is defeated when the plasma overheats and in regions of the plasma where the shear is low. Finite fluid compression has significant, and optimistic, consequences on the long-term nonlinear behavior of this mode. For a tearing mode stable cylindrical spheromak equilibrium configuration with an axial beta value of 6%, complete overlap of the m = 1 islands occurs in about 3% of the resistive skin time for a magnetic Reynolds number of S = 10⁵. For typical parameters of the S-1 device at Princeton, this time corresponds to nearly one millisecond.