Sideways Force Produced During Disruptions

We extend previous studies [1] of vertical displacement events (VDE) which can produce disruptions. The emphasis is on the non axisymmetric ``sideways'' wall force $F_x.$ Simulations are performed using the M3D [2] code. A VDE expels magnetic flux through the resistive wall until the last closed flux surface has $q < 3.$ At this point the plasma is unstable to an $(m,n) = (2,1)$ mode. A theory of sideways force produced by this mode in the presence of a VDE is presented. The wall force depends strongly on $\gamma\tau_w,$ where $\gamma$ is the mode growth rate and $\tau_w$ is the wall resistive penetration time. The force $F_x$ is largest when $\gamma\tau_w $ is a constant of order unity, which depends on the initial conditions. For large values of $\gamma \tau_w,$ the wall force asymptotes to a relatively smaller value, well below the critical value ITER is designed to withstand. The principle of disruption mitigation by massive gas injection is to cause a disruption with large $\gamma\tau_w$. \\[4pt] [1] H. R. Strauss, R. Paccagnella, and J. Breslau,Phys. Plasmas \textbf{17}, 082505 (2010) \par\noindent [2] W. Park, E.V. Belova, G.Y. Fu, X. Tang, H.R. Strauss, L.E. Sugiyama, Phys. Plasmas \textbf{6}, 1796 (1999).