Accessing the symmetric component of quadrupole misalignment through counter-rotating closed orbits in EDM storage rings

Abstract

In the storage ring proposed to measure the proton electric dipole moment (EDM), quadrupole misalignments of a few microns mimic a genuine EDM through a geometric (Berry) phase; at a 10 micron rms misalignment the false signal is up to a thousand times the target sensitivity of 1e-29 e-cm. The misalignment splits into an antisymmetric component, which distorts the closed orbit and is visible to the beam-position monitors, and a symmetric component, whose orbit signature is strongly suppressed. Standard single-beam orbit correction therefore removes only the antisymmetric part. The proposed design reaches the symmetric one by beam-based alignment (BBA), which is effective but relatively slow and invasive. Using symplectic beam and spin tracking, we show that correcting the two counter-rotating beams jointly recovers the symmetric component from the orbit itself; it is carried by the sum of the two orbits, whereas their difference is blind and a single beam is far too weak to recover it. The static BPM offset is degenerate with the symmetric misalignment in this sum, so the scheme does not replace the initial absolute alignment. However, the drift is differential and the offset cancels, so continuous two-beam correction maintains the alignment after a single initial BBA calibration, reducing the repeated realignment required by the original proton EDM proposal.