We present modifications to the sandpile model [Chapman, Phys. Rev. E 62, 1905 (2000)] (Classic Model). A feedback loop is added to the Classic Model, elements of which may have relevance to the behaviour of a fusion plasma. Those elements include variation of the total energy of the system in proportion to a proxy for the Larmor radius, ρ, and resulting variations in mass loss event (MLE) size and waiting times between MLEs. We also show other variants of the Classic Model which produce pedestals, without introducing feedback. The modifications produce a pedestal similar to that seen in a fusion plasma, as well as feedback effects. We observe that maximum MLE sizes, and maximum waiting times between MLEs, grow with pedestal size only in the presence of feedback. If, as we purport, the edge localised mode (ELM) process is captured by an MLE model with feedback, then a conclusion is that ELMs can be reduced if feedback effects are reduced.

The sandpile paradigm is widely used to model aspects of the phenomenology of magnetically confined fusion (MCF) plasmas, including enhanced confinement, edge pedestals and, potentially, the impulsive energy and particle release process known as ELMing. Here we identify new points of contact between ELMing and the systemwide avalanches in a sandpile. We compare the quantified response [Calderon et al., Phys. Plasmas 20, 042306 (2014)] to increased fuelling of the time sequence of edge localised mode events in a series of similar Joint European Torus plasmas with the response to increased fuelling of the time sequence of systemwide avalanches in a sandpile model [Chapman et al., Phys. Rev. Lett. 86, 2814 (2001)] that has well established links to MCF plasma phenomenology. Both the probability density functions of inter-event time intervals, and delay time embeddings of event time sequences, at different fuelling rates, show common features and point to shared underlying physics.

Sandpile models have been used to provide simple phenomenological models without incorporating the detailed features of a fully featured model. The Chapman sandpile model (Chapman et al Physical Review Letters 86, 2814) has been used as an analogue for the behaviour of a plasma edge, with mass loss events being used as analogues for ELMs. In this work we modify the Chapman sandpile model by providing for both increased and intermittent driving. We show that the behaviour of the sandpile, when continuously fuelled at very high driving, can be determined analytically by a simple algorithm. We observe that the size of the largest avalanches is better reduced by increasing constant driving than by the intermittent introduction of 'pellets' of sand. Using the sandpile model as a reduced model of ELMing behaviour, we conject that ELM control in a fusion plasma may similarly prove more effective with increased total fuelling than with pellet addition.

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