Simulate measurement of cbar in CESR using the method outlined here.
For an initial simulation, use the cta_2085mev_20090516 lattice with zero coupling (no skew quads on). Plot the cbar values from Bmad and from this "measurement," using an initial displacement of (0.1mm,0.1mm) at ele(0) and 1,000 turns. The results using 10,000 turns are almost idential, suggesting 10,000 turns is excessive for this ideal test.
Now take the same lattice and turn on skew quad 2W @ +0.01. Compare results to Bmad's predictions:
Include BPM noise and tilts now. Try a few simple scenarios. BPM resolution = 35 microns, no skew quads, no BPM tilts:
Note: problems with resolution having no effect have been resolved (9/18/09). With no resolution, no skew quads, 10mrad RMS BPM tilts (note the new scale):
Also note that Bmad does not take BPM tilts into account when calculating Cbar elements.
From Rich Helms' thesis, we expect in the limit of zero coupling (Cbar11(actual) = Cbar22(actual) = Cbar12(actual) = 0), Cbar22(meas) = -(BPM tilts), in radians. Plot Cbar22 and -(BPM tilts) simultaneously:
Cbar22 agrees well with our prediction. Cbar11 doesn't have as simple a relation with the tilts.