Possibility of a direct solution of Vlasov–Maxwell equations in tokamaks in the ion cyclotron range of frequencies

Abstract

The possibility of a solution of the Vlasov–Maxwell equations as a time-dependent problem in a tokamak geometry at ω∼ωci is studied. The major approximations in the analysis are the following: small Larmor radius relative to the wavelength, particle orbits deviate little from a magnetic surface during the time of the dominant contribution to the orbit integral. This direct integration becomes possible due to a rapid growth of the computing power and the development of multiprocessing. A proper description of the plasma dielectric properties in this time-dependent approach is made. Due to a limited computing power and not completely optimized procedure applied in the analysis, the time evolution of Maxwell equations is limited to cases of relatively small perpendicular wave numbers. The results demonstrate that it is computationally feasible to perform a direct integration of the time-dependent Vlasov–Maxwell equations in a tokamak geometry on a substantially long time interval. The directions of the further optimization of this method are discussed and the suggestions for the further analysis are made.