Enstrophy non-conservation and the forward cascade of energy in two-dimensional electrostatic magnetized plasma turbulence

Abstract

A fluid system is derived to describe electrostatic magnetized plasma turbulence at scales somewhat larger than the Larmor radius of a given species. It is related to the Hasegawa-Mima equation, but does not conserve enstrophy, and, as a result, exhibits a forward cascade of energy, to small scales. The inertial-range energy spectrum is argued to be shallower than a −11/3 power law, as compared to the −5 law of the Hasegawa-Mima enstrophy cascade. This property, confirmed here by direct numerical simulations of the fluid system, may help explain the fluctuation spectrum observed in gyrokinetic simulations of streamer-dominated electron-temperature-gradient driven turbulence (Plunk et al., Phys. Rev. Lett., vol. 122, 2019, 035002), and also possibly some cases of ion-temperature-gradient driven turbulence where zonal flows are suppressed (Plunk et al., Phys. Rev. Lett., vol. 118, 2017, 105002).