Recent experiments1 indicate that RMP fields (which induce ambient stochastic magnetic fields in an edge layer) can reduce fluctuation-driven Reynolds forces and so inhibit the initiation of the L-H transition. Here, we present a theory of vorticity flux decoherence and its implications for zonal flow evolution. Note that Reynolds force decoherence is the key effect, and not the competition between Reynolds and Maxwell stress. This theory2 builds upon recent fundamental work on vorticity mixing in a

3 presence of stochastic magnetic field .

The analysis proceeds by considering the Elsässer-like responses, along field lines which wander due to island overlap in this 3D system. The required magnetic Kubo number is modest. Our results show that mean-square stochastic fields strongly

reduce Reynolds stress coherence, and that k⊥2vADM (where DM is stochastic magnetic diffusion) characterizes the rate of stress decoherence. This decoherence of potential vorticity flux due to stochastic field scattering leads to suppression of Reynolds stress

and zonal flow formation. Here, the relevant speed is vA, on an account of the the condition ∇ ⋅ J = 0.

A simple calculation shows that the breaking of the shear-eddy tilting feedback loop by stochastic fields is the key physics mechanism which underlies decoherence. The dimensionless parameter that quantifies the increment in power threshold is

identified as α ≡ [(δB/B0)2q]/(ρ*2 βε) . This is used to assess the impact of stochastic field on the L-H transition. Results indicate that a stochastic magnetic field of

strength (δB/B0)2 ≃ 10−8 is sufficient to inhibit the transition. We also calculate the figure of merit for onset of stochastic decoherence. The evolution of the L-H transition in a stochastic field is examined using the Kim-Diamond model. We also discuss a model of stochastic fields as a resisto-elastic network. Finally, the effect of stochastic fields on staircase formation and structure will be discussed.