Theory for transport in magnetized plasmas

Abstract

We present a two fluid model for anomalous thermal, particle and momentum transport which has been derived from kinetic theory using a small parameter ε ∼ 10−2. This small parameter can come from either the ratio of wave frequency to cyclotron frequency or the ratio of potential to thermal energies. This fluid model is strongly nonlinear and has an exact closure within the accuracy ε. It can be used to simulate the full radius of a tokamak including internal and edge transport barriers at the same time without introducing any local assumptions for physics model or grid size. It involves a full transport matrix, thus giving possibility for both density and heat pinches. The model can be derived from the Vlasov equation, adding also close collisions and includes particle pinches of the type found in the magnetosphere and in the Massachusetts Institute of Technology elevated dipole machine. Pinches are also in agreement for the heat pinch experiments on Doublet III D including simultaneous particle and heat pinches. For tokamaks it gives the right scaling of confinement time versus heating power. Finally, we have also recovered the Turbulent Equipartition result that the density scales as inverse safety factor q in typical simulations. Thus this model is both fundamental and of high practical use.