Non-Markovian renormalization of kinetic coefficients for drift-type turbulence in magnetized plasmas

The problem of derivation of the kinetic equations for inhomogeneous plasma in an external magnetic field is considered. The Fokker–Planck-type equations with the non-Markovian kinetic coefficients are proposed. In the time-local limit (small correlation times with respect to the distribution function relaxation time) the relations obtained recover the results known from the appropriate quasilinear theory and the Dupree–Weinstock theory of plasma turbulence. Kinetic calculations of the dielectric response function are also performed with regard to the influence of turbulent fields on particle motion. The equations proposed are used to describe zonal flow generation and to estimate the diffusion coefficient for saturated turbulence.