Pfc/ja-82-25 on Impurity Transport in Tokamaks

We study theoretically the effects of diffusion, convection, and sawteeth on impurity profile evolution in tokamaks. Sawtooth effects are modeled after our' experimental observations that internal disruptions flatten radial profiles of impurity densities in the Alcator-C plasma core. We present numerical simulations and analytic results for confinement times and profile shapes, and we predict that sawteeth may significantly decrease impurity confinement times under some circumstances. Because impurities play a crucial role in determining plasma characteristics in tokamaks, it is important to understand impurity transport. Here we investigate theoretically some general consequences of diffusion, convection and sawtooth oscillations (periodic "internal disruptions"), using experimental observations as a guide to modeling effects of sawteeth. Internal disruptions are known to affect the transport of electrons and working-gas ions, flattening radial profiles of temperatures and densities in the plasma core (presumably by momentarily providing a radial magnetic field component and allowing rapid radial transport along field lines). We show here that disruptions also flatten radial profiles of individual charge states of impurities. A numerical code is then used to simulate impurity profile evolution in impurity injection experiments and in "steady-state" plasmas; and an analytic model, based on eigenfunctions of the transport equation, is used to explicitly relate confinement times and profile shapes to properties of the impurity flux and to sawtooth effects. Our earlier worki along these lines neglected convection, but experimental results2,3 indicate that convection may be important -in some tokamaks, and our theoretical results here indicate that the effects of sawteeth on impurity confinement can be much more important if convection is present. Silicon has been injected4 into the Alcator-C plasma for impurity transport experiments; it appears first as a shell at the outer surface of the plasma, then penetrates to the plasma core, and finally leaves the system with an exponential decay rate. Using a method we've described recently, we have followed the evolution of absolute radial density profiles of different silicon ionization states and of the sum of all states.1,5 Figure la shows what happens to the helium-like and hydrogen-like ions as a consequence of an internal disruption during the inflow stage, when the silicon density profile