Sandpile modelling of dual location fuelling in fusion plasmas

We modify the Chapman sandpile model (Chapman \textit{et al} \textit{Physical Review Letters} 86, 2814 (2001)) to form comparisons with pellet pacing, which is used to reduce or eliminate ELMs in a fusion plasma. We employ a variation of that model in which a pedestal with feedback is introduced (Bowie and Hole \textit{Phys. Plasmas} 25, 012511 (2018)), which we further modify to provide for dual fuelling - sand is added both at the centre of the sandpile, and near the edge. We observe that when the additional sand is added at the top of the pedestal, MLEs are largely suppressed. While this suppression comes at a cost by way of reduction in total energy confinement, that reduction is lower than the reduction in MLE size. The trade-off between MLE suppression and reduction in energy confinement depends not only on the amount of extra sand, but also on its precise location relative to the top of the pedestal. We suggest that the approach of constant dual fuelling may be equally applicable to plasmas, and may suggest a strategy for ELM suppression in fusion plasmas. We observe that when the proposed amount of extra sand is added in 'pellets', using frequencies and amounts based on those proposed for ELM suppression for ITER, MLEs are similarly suppressed, although MLEs are not significantly suppressed when the pellet rate does not substantially exceed the MLE frequency. This suggests that pellet injection at the top of the pedestal at small pellet size and high frequency may represent a reasonable physical proxy for our proposed scheme. However, our results suggest that it is not the synchronisation of pellets to ELM frequencies which is the key factor for ELM suppression in this regime, but rather the introduction of additional fuelling at the top of the pedestal.

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