Pascal Elleaume's Comments about phase dependent skew quadrupole terms in EPUs:

Pascal’s thoughts about the variation in vertical beamsize versus EPU phase (April 2002 email)

• Change in the beamsize is likely to be due to the very nature of the coupling which is a set by a 2D vector to which you add one contribution from the EPU.
• Depending if the two vectors are parallel or orthoganal the resulting vector can have a different modulus
• The effect can change as the coupling distribution in the ring changes
• This has been observed at ESRF and the change can happen rather rapidly (within one week)
• They keep the effect small by correcting the nearest coupling resonances.
• Question 1: What do they actually do to correct the nearest resonances?
• Pascal then speculates about what is contributing to the shift dependent EPU coupling.
• A contribution to the field itself quadratic with the field and the energy and linear to the length of the device – similar in nature to the vertical and horizontal tuneshift with phase
• Effect of the permeability of the permanent magnets which deviates from 1. It is of the same nature as the change in the vertical and horizontal field integrals with phase and should be well simulated with Radia.
• First check is a comparison of the field integrals versus phase
• Accidental presence of some iron near the ends and close to the chamber.
• It may also come from small positionning errors of the magnetic blocks in the bulk of the undulator
• Pascal then discusses possible cures
• Depending on the cause one can design an end block to eliminate the phase dependent field integrals which could also eliminate phase dependent skew quadrupole.
• Get rid of the induced coupling with a local skew quadrupole feed forward correction look up table (gap, phase symmetric and gap, phase antisymmetric) or a global correction scheme.

Pascals recent email (October 7, 2002)

• I am indeed surprised that a measurable skew quad precisely periodic with phase with extremum on circular polarisation cannot be simulated with Radia. Besides possible error in the problem description, is the termination described in the modelling (very important) ?, could there be some magnet block displacement induced by changing magnetic forces ? In any case the best person to contact on this subject is Joel Chavanne (chavanne@esrf.fr), send him the documented notebook and I am sure he will be happy to have a look at it.
• Concerning the coupling correction. At ESRF we correct the nearest sum and difference resonances Qx-Qy=22 and Qx+Qy=61 using a set of 16 skew quads located all along the ring circumference (coils in the sextupoles). This is made using a SVD algorithm with the additionnal constraints of minimizing the induced vertical dispersion. If you need more information on this conatact Laurent Farvacque (laurent@esrf.fr).