A turbulent cascade model of bounce averaged gyrokinetics

A shell model is derived for the description of nonlinear bounce averaged gyrokinetics, which is one of the simplest kinetic descriptions in magnetized plasmas. In order to validate the numerical implementation, detailed linear evolution of the system is compared with a linear benchmark based on solving the linear dispersion relation numerically. The resulting wave number spectrum, which extends over 3-4 decades, is shown to have a robust general structure to model parameters, such as dissipation or the ratio of linear energy injection to nonlinear transfer. In a range of wave numbers where the nonlinear transfer term is dominant, a power law spectrum, roughly of the form k - 4, is observed for the spectral electrostatic potential energy density. The model, being fully kinetic, can be used to obtain the free energy spectra for ion and electron distribution functions as functions of E. This model constitutes the first numerical implementation of a kinetic shell model.