Numerical solution of continuity equation with a flux non-linearly depending on density gradient

An approach to integrate transport equations with fluxes being complex non-linear functions of physical parameters and their gradients, as it is predicted by theoretical models for micro-instabilities in plasma, is proposed. This approach operates without any splitting of the flux on diffusive and convective components normally involved in transport calculations. Introduction By considering transport processes in fusion plasma it is conventional to speak about such characteristics as particle and heat diffusivities, advection velocity etc. This approach is originated in the traditional view on the mass and heat transfer as caused by collisions of individual particles. In toroidal fusion plasmas such a situation is described by the neoclassical theory. However, diverse micro-instabilities, developing in these plasmas, lead to turbulence, tremendously enhancing mass and heat transfer [1]. The resulting anomalous fluxes are complex nonlinear functions of the parameter spatial gradients. By computing profiles of the plasma parameters, these fluxes are normally splitted on diffusive and convective contributions in order to apply well developed approaches for numerical integration of the second order differential equations. Such a separation serves also as an approximate tool for interpretation of experimental data in customary concepts of diffusion and advection. However, there is not any definitive answer to the question: are the individual transport coefficients, both reconstructed from experimental measurements under usually ambiguous assumptions about the time and spatial behavior of these characteristics and obtained by a splitting of theoretically predicted fluxes, unique? Therefore, development of direct methods for integration of transport equations without flux splitting on diffusive and convective contributions would be very helpful in order to clarify this situation and to offer a firm basis for the prediction of parameter profiles in future devices. In the present contribution such an approach is elaborated and demonstrated on the example of the well known Weiland transport model [1] for the charged particle flux. 33rd EPS Conference on Plasma Phys. Rome, 19 23 June 2006 ECA Vol.30I, P-1.179 (2006)