Formation and locking of the "slinky mode" in reversed-field pinches

The formation and breakup of the "slinky mode'' in a Reversed-Field Pinch (RFP) is investigated analytically. The slinky mode is a toroidally localized, coherent interference pattern in the magnetic field, which corotates with the plasma at the reversal surface. This mode forms, via a series of bifurcations, as a result of the nonlinear coupling of multiple m = 1 core tearing modes. The slinky mode breaks up via a second series of bifurcations. However, the typical mode amplitude below which slinky breakup is triggered is much smaller than that above which slinky formation occurs. Analytic expressions for the slinky formation and breakup thresholds are obtained in all regimes of physical interest. The locking of the slinky mode to a static error field is also investigated analytically. Either the error field arrests the rotation of the plasma at the reversal surface before the formation of the slinky mode, so that the mode subsequently forms as a nonrotating mode, or the slinky mode forms as a rotating mode and subsequently locks to the error field. Analytic expressions for the locking and unlocking thresholds are obtained in all regimes of physical interest. (C) 1999 American Institute of Physics. [S1070-664X(99)02604-X].