Dimits transition in electromagnetic ITG turbulence

A two-species (one main ion and electrons) fluid model for describing ion temperature gradient

(ITG) turbulence in a Z-pinch magnetic geometry has been derived from gyrokinetics. First,

we carry out a mass ratio expansion ( me /mi ≪ 1) similar to the procedure introduced in

(Schekochihin et al., 2009). It is then followed by a subsidiary expansion in small k⊥ ρi , where

k⊥ is the typical wavenumber perpendicular to the mean field line and ρi is the ion gyroradius.

Since we study ITG in the long-wavelength limit k⊥ ρi ≪ 1, it requires shifting the driving scale

of ITG also to long wavelength, leading to the cold-ion assumption, which is used in electro-

static ITG fluid models studied previously (Ivanov et al., 2020, 2022). The novelty of the model

presented here is that it retains electromagnetic (EM) effects and aims to provide a physical

mechanism by which the ITG turbulence transitions from a low-transport, zonally dominated

state to a high-transport state with weak zonal flows. It is found that Maxwell stress tends to

shift the Dimits transition to lower temperature gradients. Generally as β is increased, where

β is the ratio between plasma pressure and magnetic pressure, Maxwell stress starts to erode

the zonal flow, setting a threshold β above which the turbulence can no longer support a strong

zonal flow and hence produces relatively large transport. Studying this model is an attempt to

understand why many local gyrokinetic simulations of ITG turbulence lead to divergent heat

fluxes at finite β(Pueschel et al., 2013b).