Transition from weak to strong turbulence in magnetized plasmas

The scaling of turbulent heat flux with respect to electrostatic potential is examined in the framework of a reduced ($4$D) kinetic system describing electrostatic turbulence in magnetized plasmas excited by the ion temperature gradient instability. Numerical simulations were instigated by, and tested the predictions of generic renormalized turbulence models like the $2$D fluid model for electrostatic turbulence [Y.~Z.~Zhang and S.~M.~Mahajan, Phys.~Fluids B 5 (7), pp.~2000 (1993)]. A fundamental, perhaps, universal result of this theory-simulation combination is the demonstration that there exist two distinct asymptotic states (that can be classified as Weak turbulence (WT) and Strong turbulence (ST) states) where the turbulent diffusivity $Q$ scales quite differently with the strength of turbulence measured by the electrostatic energy $\|\phi\|^2$. In the case of WT $Q \propto \|\phi\|^2$, while in ST $Q$ has a weaker dependence on the electrostatic energy and scales as $\|\phi\|$.