Transport formulation of the gyrokinetic turbulence

Nonlinear gyrokinetic equation is formulated in the Fokker-Planck form that puts the effects of the turbulent wave scattering into the divergence of a diffusive-convective flux in the phase space, unified with the binary collision operator. The macroscopic transport fluxes of the particle and heat transport due to the gyrokinetic turbulence are systematically derived, with the diffusive and convective fluxes and the nonlinear turbulence heating rate identified. The proposed theory includes the ponderomotive effects on the turbulent convection and heating, which were not included in the previous quasilinear theory.