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This is a follow-up on my last B-Team suggestion to correct the extraction (E02) BPM positions. It involves a straight-forward change in BPM sensitivity scale factor plus an empirical offset, and should result in the extracted and recirculating beam XPOS values
showing the "correct" values when only one is present and at the desired positions.</div>
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I attach a png image of ideal 1:1 BPM response overiaid with target points (which I chose to be +5.5 mm and -16 mm, not recalling exactly the values). I used a simple low-range divide-by-exponential to model a sub-linear response for a hypothetical BPM.</div>
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Than I took the model response at the two target positions, and found the difference to be about 77% of the more-appropriate 21.5 mm real-world position difference. I scaled the model response up by 30% (a 1.3 multiplier) to regain the actual positon difference
between recirculated and extracted beams. This made the actual positions improper, but in error by the same amount, which I then added back as pushing the XSOF would do. In this case, mocking up XSOF = -0.9 mm.</div>
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You can see the plot of "x" and the sublinear model with the target points added (in yellow). Scaling up by 30% plus 0.9 mm puts the target points at the desired positions. The recirculated (+5.5mm) point retains nearly 1 mm per mm response to beam misplacement,
but the extracted beam position error is under-reported by about a third because the 30% boost does not recover increasing shortfall in incremental response.</div>
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I think that we ought to be able to use the correctors as reasonably calibrated items, steer beam to about where we think the recirculated beam should be and record the XPOS. Then deflect the beam magnetically by the amount we think is appropriate for the
extraction position. The BPM response will be less than we anticipate. Then multiply the BPM scale factor by the ratio of </div>
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(designDiff) / (BPMrec - BPMextr) and offset by whatever is required to make the extraction and recirculation points indicate what they "ought to be."</div>
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I hope this is of interest. It appears to be something which can be implemented with little difficulty and no hazard.</div>
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Michael Tiefenback</div>
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