Plasma temperature and density dynamics including particle and heat pinch effects

The spatial and temporal evolutions of temperature and density of plasmas, governed by coupled nonlinear diffusion equations with source terms and finite boundary effects, are studied by means of a central expansion technique for "bell-shaped" plasma profiles. Four coupled first order nonlinear equations in time are obtained for the amplitudes (central values) and widths of the temperature and density distributions. The roles played by the various processes, considering also particle and heat pinch effects, are discussed and the conditions for possible equilibria are formulated.