Non-local gyrokinetic model of linear ion-temperature-gradient modes

The non-local properties of anomalous transport in fusion plasmas are still an elusive topic. In this work, a theory of non-local linear ion-temperature-gradient (ITG) drift modes while retaining non-adiabatic electrons and finite temperature gradients is presented, extending the previous work [S. Moradi et al., Phys. Plasmas 18, 062106 (2011)]. A dispersion relation is derived to quantify the effects on the eigenvalues of the unstable ion temperature gradient modes and non-adiabatic electrons on the order of the fractional velocity operator in the Fokker-Planck equation. By solving this relation for a given eigenvalue, it is shown that as the linear eigenvalues of the modes increase, the order of the fractional velocity derivative deviates from two and the resulting equilibrium probability density distribution of the plasma, i.e., the solution of the Fokker-Planck equation, deviates from a Maxwellian and becomes Levy distributed. The relative effect of the real frequency of the JIG mode on the deviation of the plasma from Maxwellian is larger than from the growth rate. As was shown previously the resulting Levy distribution of the plasma may in turn significantly alter the transport as well