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

TL;DR

This paper develops a non-local linear ITG drift mode theory incorporating non-adiabatic electrons, revealing that increased turbulence leads to a Levy distribution, significantly affecting plasma transport and mode characteristics.

Contribution

It extends previous models by deriving a dispersion relation with fractional derivatives, showing how turbulence causes plasma distribution to shift from Maxwellian to Levy, impacting transport.

Findings

Plasma becomes Levy distributed with increased turbulence.

Fractional derivatives more strongly affect real frequency than growth rate.

Transport properties are significantly altered by Levy distribution.

Abstract

A theory of non-local linear ion-temperature-gradient (ITG) drift modes while retaining non-adiabatic electrons is presented, extending the previous work [S. Moradi, et al {\em Phys. Plasmas} {\bf 18}, 062106 (2011)]. A dispersion relation is derived to quantify the effects of the fractional velocity operator in the Fokker-Planck equation modified by temperature gradients and non-adiabatic electrons on the real frequency and growth rate. Solving the dispersion relation, it is shown here that as the plasma becomes more turbulent, it deviates from a Maxwellian distribution and becomes L\'{e}vy distributed. The resulting L\'{e}vy distribution of the plasma may thus significantly alter the transport. The relative effect of the fractional derivative is larger on the real frequency than on the growth rate of the ITG mode.