Hysteresis and relaxation in bistable diffusive sandpile

Abstract

Several problems in the physics of $\mathrm{L\to H}$ transition and pedestal formation are examined using a simple and universal sandpile model, which incorporates key features of a confined plasma, namely, diffusion, shear induced bistability of turbulent transport, and a local magnetohydrodynamic (MHD) limit on the gradient. The main focus of this study is the effect of ambient diffusion, representative of neoclassical transport, on hysteresis and edge relaxation phenomena. The transport function of the sandpile bifurcates to a multivalued function with increasing deposition, and, as a consequence, a hysteresis in the $\mathrm{L\to H\to L}$ transition is observed. With pedestal formation, diffusive losses increase at the expense of the turbulent flux. This effect prolongs the time needed to reach the MHD stability boundary, and thus provides a positive feedback on the pedestal. The gradient in the pedestal is more rigid and, due to diffusive smoothing, can reach the critical value at all radii simultaneously. Hence an avalanche, starting at the edge, can span the entire pedestal, thus destroying it. The transport in the core is essentially unaffected by the diffusion.