A continuum one - dimensional SOC model for thermal transport in tokamaks

We discuss here the adaptation of a well - known continuum model of SOC to the thermal transport problem in tokamaks. The model consists of a coupled set of two evolution equations. The first equation is the characteristic radial transport equation for the mean plasma temperature. The second equation is an evolution equation for the thermal conductivity coefficient (associated with temperature gradient instability) and exhibits a characteristic relaxation time, a source term which alternates between two values (depending on the local value of temperature gradient) and hysterisis. Numerical studies of this coupled set of equations illustrate many features of SOC like thermal transport in tokamaks such as profile consistency, slow loading and fast unloading cycles of stored thermal energy, propagation of fast moving fronts of enhanced transport through the discharge etc. The speed of propagating fronts are found to be in excellent agreement with measurements on machines like doublet DIII-D. (author)