Delay time embedding of mass loss avalanches in a fusion plasma-oriented sandpile model

Abstract

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 modeling of pellet pacing in fusion plasmas

“…For 'macro' pellets, we show here results for two values of ∆t P -70000 and 100000. Short and long ∆t N are typically [25] observed in the model: the 'short' ∆t N for this model with dx = 1.2 is ≈ 70000, with a longer ∆t N at ≈ 140, 000. The values of ∆t P selected therefore represent different stages in build-up prior to, or post, avalanching (recognizing that the additional fuel added by way of 'pellets' also increases total fuelling).…”

“…As will be observed from Table I, we are primarily concerned here with variation in driving. Unlike some, [17,19,[22][23][24] but not all, [25,26] implementations of the Chapman model, Z c is single valued, rather than being randomized. The phenomenology generated by this model has several features resembling tokamak plasmas, including edge pedestals, enhanced confinement [19] ternal transport barriers [23].…”

“…Effectively, fuelling is paused until the system is stable, which reflects the instantaneous nature of an avalanche, by comparison to the slow addition of single grains of sand. In the 'running model' which was first explored by Bowie, Dendy and Hole [25], the sandpile is fuelled again as soon as the first iteration of the avalanche is complete, while the sandpile remains in a critical state. In the low fuelling regime, little difference is observed between the classic and running models: the sandpile may take ≈ 500 iterations to reach stability, during which time enough sand has been added at the first cell to cause the critical gradient to be exceeded between the first and second cells a further one or two times.…”

Applications of Sandpile Algorithms to Modelling Edge Localised Mode Phenomenology in Magnetically Confined Fusion Plasmas

“…Importantly, in the model developed here, avalanche size reduction is achieved via continuous (or quasi-continuous) addition of fuel in the pedestal, rather than by synchronising pellets to waiting times between avalanches, and it is conjectured that this may also be true for a fusion plasma. Some of this research has been published in [1][2][3][4][5].…”