Analytical estimates of the vertical displacement growth rate in tokamaks with a resistive wall

Analytical evaluation of the vertical displacement event (VDE) growth rate is the main subject here. The attention is attracted to the fact that the model with the plasma and wall boundaries treated as confocal ellipses, introduced by Laval et al. [Phys. Fluids 17, 835 (1974)] and used up until now in analytics, not only restricts the applicability range, but also strongly affects the outcome. In particular, improper utilization of the aforementioned model (i.e., by neglecting the assumption of the wall's confocality) leads to the prediction that the resistive wall with circular cross section cannot slow down the VDE—a conclusion beyond the applicability of the model. Here, we propose a new model and a new approach assuming rigid plasma motion, where the plasma is separated from the wall, and the main element in the task is the plasma–wall electromagnetic interaction. First, we propose a VDE growth time evaluation based on integral equation for the poloidal flux diffusion through the thin resistive shell, which is applicable for the walls of arbitrary shape. Then, the task is simplified by using the large-aspect-ratio expansion of the Green's function. As a result, a slow wall-stabilized motion is predicted in wide ranges of the plasma elongations and the width of the plasma–wall gap. The differences between the existing results and our new predictions are explained.