Fast heat pulse propagation with a nonlocal flux-gradient model

Time dependent solutions of the heat diffusion equation in a slab geometry are studied for a spatially nonlocal flux-gradient model of thermal diffusivity (χ) proposed by Taylor et al. [J. B. Taylor, J. W. Connor, and P. Helander, Phys. Plasmas 5, 3065 (1998)]. This model is distinguished by the presence of a parameter α in the expression for χ, which is related to the strength of velocity shear in the plasma. It is shown that when α is nonzero one can obtain a rapid propagation of heat pulse towards the core due to the cooling of the edge, exhibiting similar features as in 'edge-cooling core-heating' experiments. A rapidly increasing α(t) also gives encouraging qualitative match with observed nonlocal signatures of current ramp-up in tokamak experiments. General issues of linear and nonlinear stability have also been presented