>I just wanted to let you know that I redid our SOCA calculation 
>from the 2015 PRE, but removing the pressure force with constant 
>desnity (i.e., burgulence). I actually found exactly zero for 
>both the kinetic and magnetic shear-current effects, for arbitrary 
>viscosity or resistivity (although, being SOCA, it's only really 
>valid when they are large). There is still a nonzero rotational 
>(Radler effect) contribution for both, but it looks quite different 
>from the case with turbulence – happy to provide the expression if 
>you're interested for some reason.

Thanks for the further clarifications.

> The difference compared to the result in your appendix is probably
>because our calculation is perturbative in the shear. 

Our analysis was also perturbative in S.


>So it is a bit of a different limit, and simpler. We did notice some 
>differences between our CE2 calculations (which are effectively 
>SOCA but non-perturbative in the shear) and the analytic ones, 
>so this is not altogether surprising. 

>One other thing worth mentioning: without the pressure you 
>indeed see a magnetic contribution to the standard (diagonal) 
>beta effect (i.e., turbulent diffusion), whereas with the 
>pressure this goes away to zero, as well known. This isn't 
>surprising (it fits with previous results and our JPP cartoon) 
>but it's nice to see in the formal calculation.