  An analytic theory of edge localized mode (ELM) suppression in an H-mode
tokamak plasma via the application of a static, externally generated, resonant
magnetic perturbation (RMP) is presented. This theory is based on the plausible
hypothesis that mode penetration at the top of the pedestal is a necessary and
sufficient condition for the RMP-induced suppression of ELMs. The theory also
makes use of a number of key insights gained in a recent publication
(Fitzpatrick R 2019). The first insight is that the response of the plasma to a
particular helical component of the RMP, in the immediate vicinity of the
associated resonant surface, is governed by nonlinear magnetic island physics,
rather than by linear layer physics. The second insight is that neoclassical
effects play a vital role in the physics of RMP-induced ELM suppression. The
final insight is that plasma impurities play an important role in the physics
of RMP-induced ELM suppression. The theory presented in this paper is employed
to gain a better understanding ELM suppression in DIII-D and ITER H-mode
discharges. It is found that ELM suppression is only possible when q_95 takes
values that lie in certain narrow windows. Moreover, the widths of these
windows decrease with increasing plasma density. Assuming a core plasma
rotation of 20 krad/s, the window width for a model ITER H-mode discharge is
found to be similar to, but slightly smaller than, the window width in a
typical DIII-D H-mode discharge.
