Study on Kinetic Control-Mechanisms for ITER-like Plasma

A new computer time saving method is presented for the calculation of the charge separation and electric field at the plasma edge of a tokamak. This problem has been recently presented in one spatial dimension using an adiabatic equation for the electrons and a kinetic Vlasov equation for the ions with three velocity dimensions. These equations were solved using a method of fractional steps for the solution of the kinetic equation. Extending these results to two spatial dimensions requires extending the phase- space dimensionality of the ions Vlasov equation from four to five. Also, including a kinetic equation for the electrons will make the computation lengthy and expensive, due to the important ratio of masses between electrons and ions. This problem, however, can be tackled if we take advantage of exact invariance of the solution present in the Vlasov equation. Expressing the distribution function in terms of the invariant allows to reduce the dimensionality of the phase-space of the Vlasov equation, since the invariant only appears as a label of the Vlasov equation, and can be coarsely discretized. This method of invariant has been applied for the previously presented ID solution , where we were able to reproduce exactly the same results with a gain of a factor of 10 in the computation time, using only 10 invariants instead of 50 points in velocity space. We present in this work the application of this method of invariants to a two-dimensional problem, for the calculation of the charge separation at a plasma edge.