Logarithmically discretized model of bounce averaged gyrokinetics and its implications on tokamak turbulence

A logarithmically discretized model, which consists of writing the system in log polar coordinates in wave-number domain and reducing the nonlinear interactions to a sum over neighboring scales that satisfy the triad conditions, is proposed for bounce averaged gyrokinetics, where the energy dependence is kept over a semi-regular grid that allows quadrature calculations in order to guarantee quasi-neutrality. The resulting model is a cheaper implementation of nonlinear multi-scale physics involving trapped electron modes, trapped ion modes, and zonal flows, which can handle anisotropy. The resulting wave-number spectrum is anisotropic at large scales, where the energy injection is clearly anisotropic, but is isotropised rapidly, leading generally towards an isotropic k−4 spectrum for spectral potential energy density for fully kinetic system and a k−5 spectrum for the system with one adiabatic species. Zonal flow damping, which is necessary for reaching a steady state in this model, plays an important role...