Effects of offset in distortion maps

At today's TPC meeting, Yuri asked what would be the effect on the distortion maps (particularly SpaceCharge & GridLeak as the largest distortions) if the z-axis of the TPC was offset (e.g. the beam produces SpaceCharge from an axis offset from the TPC's z-axis). It is not a direct answer to the question, but it can give some idea...

I made distortion maps (of all distortions handled by StMagUtilities) for the highest luminosity run from Run 12 (13099025). The maps are distortions vs. radius [60,190] and z [-205,205] in [cm]. I then shifted the maps by 1 cm in the y direction and took the difference of the new map from the original map. I do not believe this is accurate to within a factor of 2 (after all, we calibrate the distortions to match what we see in the data, so re-calibrating with a shifted axis would give a slightly different full distortion map), but is correct for order of magnitude.

In that context, for the largest distortions (highest luminosities), it appears we could have systematic errors on the ~1mm scale.

map of... full distortion absolute difference with offset
δ(rφ) @ φ=0
δ(rφ) @ φ=π/2
δ(r) @ φ=0
δ(r) @ φ=π/2