Kinetic Theory of Plasma Adiabatic Major Radius Compression in Tokamaks
Authors: M.V. Gorelenkova, N.N. Gorelenkov, E.A. Azizov, A.N. Romannikov, H.W. Herrman
A kinetic approach is developed to understand the individual charged particle behavior as well as plasma macro parameters (temperature, density, etc.) during the adiabatic R-compression in a tokamak. The perpendicular electric field from Ohm's law at zero resistivity E = -vEE x B/c is made use of to obtain the equation for particle velocity evolution in order to describe the particle motion during the R-compression. Expressions for both passing and trapped particle energy and pitch angle change are obtained for a plasma with high aspect ratio and circular magnetic surfaces. The particle behavior near the trapped passing boundary during the compression is also studied to understand the shift induced loss of alpha particles produced by D-T fusion reactions in Tokamak Fusion Test Reactor experiments. Qualitative agreement is obtained with the experiments. Solving the drift kinetic equation in the collisional case, i.e., when the collisional frequency of given species exceeds the inverse compression time, we obtain that the temperature and the density evolution is reduced to the MHD results T ~ R-4/3 and n ~ R-2, respectively. In the opposite case, the collisional frequency of given species is smaller than the inverse compression time, the longitudinal component of the temperature evolve like R-2 and perpendicular component of the temperature is R-1. The effect of toroidicity is negligible in both cases.