Theoretical issues in tokamak confinement: (i) Internal/edge transport barriers and (ii) runaway avalanche confinement

This paper summarises a number of distinct, but related, pieces of work on key confinement issues for tokamaks, in particular the formation of internal and edge transport barriers, both within turbulent and neoclassical models, and radial diffusion of avalanching runaway electrons. First-principle simulations of tokamak turbulence and transport using the two-fluid, electromagnetic, global code CUTIE are described. The code has demonstrated the spontaneous formation of internal transport barriers near mode rational surfaces, in qualitative agreement with observations on JET and RTP. The theory of neoclassical transport in an impure, toroidal plasma has been extended to allow for steeper pressure and temperature gradients than are usually considered, and is then found to become nonlinear under conditions typical of the tokamak edge. For instance, the particle flux is found to be a nonmonotonic function of the gradients, thus allowing for a bifurcation in the ion particle flux. Finally, it is shown that radial diffusion caused by magnetic fluctuations can effectively suppress avalanches of runaway electrons if the fluctuation amplitude exceeds δB/B∼10-3. (author)