Researchers now at York first proposed the so-called peeling-ballooning mode as the key plasma instability responsible for triggering the ELM [1,2]. This led to a long, productive collaboration with General Atomics to develop the ELITE code [3,4], which predicts when the peeling-ballooning mode becomes unstable. This provided the first quantitative comparisons between peeling-ballooning theory and observations of ELM onset, using data from many tokamaks around the world [4,5]. The peeling-ballooning mode is now widely accepted as the plasma instability that drives ELMs.

ELITE is based on so-called linear theory, which is valid provided the perturbation from the equilibrium state is small. While such a theory is valuable for predicting the onset conditions for ELMs, a non-linear theory is required for understanding their evolution and the energy they eject. We developed such a theory in collaboration with Imperial College, which predicted ELMs should result in the explosive ejection of filamentary structures, rather than a uniform shell of plasma as was widely believed at the time [5,6]. Subsequent experiments confirmed the filamentary nature of ELMs, first on MAST and then on many tokamaks around the world [7,8,9]. Developments of our nonlinear theory have demonstrated that when multiple filaments erupt at the same time, those that grow fastest feed off, and suppress the slower ones [10] – this is consistent with observations on the S Korean KSTAR tokamak where a single dominant filament is observed during ELMs. Theory predicts that the filaments do not always accelerate from the plasma explosively – there can be new equilibrium states that the filaments move to and remain for extended periods of time [11]. This new information might explain the dynamics of ELMs on JET with its new metallic, ITER-like, wall [12].

To make quantitative predictions for ELMs requires numerical non-linear simulations. To this end, we have led the development of the BOUT++ code at York in collaboration with researchers at Lawrence Livermore National Laboratory in the US [13]. Our simulations using BOUT++ confirmed the explosive, filamentary nature of ELMs and provided new insight into the mechanism for heat and particle loss [14,15,16]. BOUT++ is now a major community software tool used around the world for simulations of ELMs and tokamak plasma edge turbulence.

The large ELMs driven by peeling-ballooning modes are predicted to cause excessive damage on ITER, and must be either avoided or controlled. The QH mode is one possible ELM-free mode of operation that has been developed on today’s tokamaks. In collaboration with General Atomics, our extensions of ELITE to incorporate the impact of sheared plasma flows on peeling-ballooning stability led to a new picture of the QH mode in which the sheared flows are an essential element [17]. This new understanding has led researchers to propose that this could be a viable operating regime for ITER. Another possible regime is one with small ELMs. So-called grassy ELMs could provide one such option for ITER, but at present there is no widely accepted theory for how these form, and therefore there is significant uncertainty over whether they are ITER-relevant. We have been exploring a model which proposes these small ELMs are a result of bursts of enhanced transport as the flow shear evolves [18].

Our research into ELMS continues, focusing on their dynamics; the search for models of small ELM regimes to assess their relevance for ITER, and to develop a theory for ELM control techniques using so-called resonant magnetic perturbation coils.

[1] J W Connor, R J Hastie, H R Wilson, et al *MHD stability of tokamak edge plasmas* Phys Plasmas **5** 2687 (1998)

[2] H R Wilson, J W Connor, A R Field, et al* Ideal MHD stability of the tokamak high confinement mode edge region* Phys Plasmas **6** 1925 (1999)

[3] H R Wilson, P B Snyder, G T A Huysmans, et al *Numerical studies of edge localised instabilities in tokamaks* Phys Plasmas **9** 1277 (2002)

[4] P B Snyder, H R Wilson, J R Ferron, et al *Edge localized modes and the pedestal: A model based on coupled peeling-ballooning modes* Phys Plasmas **9** 2037 (2002)

[5] H R Wilson, et al *Magneto-hydrodynamic stability of the H-mode transport barrier as a model for edge-localised modes: an overview* Plas Phys Contr Fusion **48** A71 (2006)

[6] H R Wilson and S C Cowley *Theory for explosive ideal magneto-hydrodynamic instabilities in plasmas* Phys Rev Lett **92** 175006 (2004)

[7] A. Kirk, H.R. Wilson, G. F. Counsell, et al, *Spatial and temporal structure of ELMs on MAST,* Phys Rev Lett **92** 245002 (2004)

[8]** **A Kirk, H R Wilson, et al *Structure of ELMs in MAST and the implications for energy deposition* Plas Phys Contr Fusion 47 315 (2005)

[9] A. Kirk, B. Koch, R. Scannell, H.R. Wilson, et al *Evolution of filaments during Edge Localized Modes in the MAST tokamak*, Phys Rev Lett **96** 185001 (2006)

[10] S.A. Henneberg, S.C.Cowley and H.R.Wilson *Interacting filamentary eruptions in magnetised plasmas* Plasma Phys. Control. Fusion **57** 125010 (2015)

[11] C.J. Ham, S.C. Cowley, G. Brochard and H.R. Wilson *Nonlinear stability and saturation of ballooning modes in tokamaks * Phys. Rev. Letts **116** 235001 (2016)

[12] C. Bowman, D. Dickinson, A.E. Lunniss, H.R. Wilson, et al, *Pedestal evolution physics in low triangularity JET tokamak discharges with ITER-like Wall,* Nuclear Fusion, **58** (2017)

[13] B.D. Dudson, et al *BOUT++: A framework for parallel plasma fluid simulations* Comp Phys. Communications **180** 1467 (2009)

[14] B.D. Dudson, et al *Simulation of edge localized modes using BOUT plus plus* Plasma Phys Contr Fusion **53** 054005 (2011)

[15] X. Xu, B.D. Dudson, et al *Nonlinear ELM simulations based on a nonideal peeling-ballooning model using the BOUT plus plus code* Nuclear Fusion **51** 103040 (2011)

[16] S.A. Myers, B.D. Dudson and H.R. Wilson *Nonlinear MHD simulations of the gravitational ballooning mode close to marginal stability*, Plas Phys Contr Fusion **55** 125016 (2013)

[17] P B Snyder, K H Burrell, H R Wilson, et al *Stability and dynamics of the edge pedestal in the low collisionality regime: physics mechanisms for steady state ELM-free operation* Nucl Fusion **47** 961 (2007)

[18] A. Bokshi, D. Dickinson, C.M. Roach and H.R. Wilson *The response of toroidal drift modes to profile evolution:a model for small ELMs in tokamaks?* Plasma Phys. Control. Fusion **58** 075011 (2016)