Analysis of heat transport in the continuum model of self-organized criticality: Implications for heat avalanches in magnetic fusion plasmas

We analyze heat transport within a continuum model of self-organized criticality (SOC) that incorporates nonlinear threshold-driven dynamics and joint reflection symmetry. This SOC model is shown to be reduced to a nonlinear Guyer–Krumhansl-like constitutive relation, suggesting a fundamental similarity between SOC dynamics and the second sound phenomenon observed in solids. We demonstrate that heat avalanches emerge from the strong nonlinearity inherent in the threshold dynamics. These avalanches in the SOC model correspond to traveling nonlinear thermal waves. Interpreting avalanches as nonlinear waves improves physics understanding of global transport phenomena within SOC systems. A comprehensive flux balance analysis shows that the propagation of these nonlinear waves requires metastability, a critical factor for avalanche generation and propagation in conventional cellular automata models. Finally, we discuss the potential implications of this thermal wave perspective for understanding avalanching heat transport in magnetic fusion plasmas, including the possible origins of key physical parameters in the SOC model.