Behaviour of multiple discrete waiting times between mass loss events in a sandpile model

The avalanche waiting time behaviour of the Chapman sandpile model (Chapman et al, 2001 Phys. Rev. Lett. 86, 2814), compared to the ELM waiting time behaviour of a JET fusion plasma, has been considered by (Bowie et al, 2016 Phys. Plasmas 23, 100 703). Here we extend the analysis of the Chapman sandpile model, by considering cases in which the combinations of variables chosen give rise to three distinct waiting times. It is observed that the short and medium waiting times sum to the long waiting time, suggesting a relationship between all three. Further, it is observed that each of the short, medium, and long waiting times occur independently. We conject that if the short and medium waiting times sum to the long waiting time in a fusion plasma, that may suggest that the Chapman model and the fusion plasma share an underlying common dynamical behaviour, and further, that each of the three waiting times may arise from the same underlying cause. By contrast, if the short and medium waiting times do not sum to the long waiting time, that suggests that the Chapman model would be inappropriate. We remark that the relationship between the short, medium, and long waiting times bears a resemblance to the relationship between the terms of the Fibonacci sequence, and is also consistent with frequency coupling.