On How Decoherence of Vorticity Flux by Stochastic Magnetic Fields Quenches Zonal Flow Generation

Recent experiments indicate that RMP fields can reduce fluctuation-driven Reynolds forces and so inhibit the initiation of the L-H transition. We present a theory of vorticity flux decoherence and its implications for zonal flow evolution. This theory builds upon recent fundamental work on vorticity mixing in a tangled magnetic field. We calculate the decoherence of the vorticity flux due to stochastic magnetic field scattering in presence of a strong toroidal field. The three relevant rates are: (1) the bandwidth of the ambient electrostatic micro-instabilities ($\Delta \omega$), (2) the bandwidth of Alfv\'en waves excited by Drift-Alfv\'en coupling ($|v_A\Delta k_{\parallel}|$), and (3) the stochasticity-induced decorrelation rate ($1/\tau_c = max(k^2_{\perp} D, (k_{\theta}^2 v_A^2 D/L_s)^{1/3})$), where $D$ accounts for scattering by the stochastic field. Decoherence requires (3) $>$ (1) and (3) $>$ (2) (i.e. Kubo number $Ku \geq 1$). These inequalities define the critical value of $\langle (\delta B)^2 /B^2 \rangle$ for an effect on the transition. The analysis proceeds by considering the Els\"asser population responses. The implications for decoherence of the particle and heat flux are discussed, as well.