| Based on a physically reasonable plausibility argument, we have formulated a nonlinear dynamic model for the behavior of a localized magnetohydrodyamic (MHD) mode (slinky mode) that appears in reversed-field pinch toroidal magnetic confinement systems. The slinky mode is formed when magnetic fluctuations in the plasma coalesce and form a localized deformation that travels in a helical path around the torus. Under certain conditions, the slinky mode will stop moving, (lock) often resulting in localized heating and the potential of wall damage to the vacuum chamber as well as loss of plasma confinement. Thus, understanding and controlling the locking phenomenon is important in the use of magnetically confined plasmas. The model was developed for the slinky mode by summing the torques acting on the slinky mode around the magnetic axis. It was found that the slinky mode obeys the nonlinear sine-Gordon (SG) equation, which has a number of analytic solutions that can be either a soliton-type of disturbance or a periodic type. To account for the various torques that act on the slinky mode, the SG equation was modified by including terms for dissipation, driving forces and localized "gap" regions. The modified SG equation was solved analytically using a perturbation method and numerically using a finite-difference scheme. The resulting model can be fit to match a variety of experimental results in the Madison Symmetric Torus (MST) reversed-field pinch experiment by varying three parameters. |
