On the Effect of Eddy Current Induced Field Wanming Liu, Sergey Antipov and Wei Gai HEP, ANL

Conditions Undulator: k=0.92, u=1.15cm, 100m long Target: 0.4 r.l. Ti, 500m drift OMD:5T-0.25T,50cm Eddy current induced field: from Femlab simulation at 900rpm for 1m radius wheel of titanium under 5T magnetic field. Conductivity of target: 1.5e6 and 3e6

Bz on yz plane near the target  =1.5e6 Induced fieldOMD field Beam axis z (mm) Y (mm)

Bz of Induced field + OMD field near the target z (mm) Y (mm) Distortion caused by eddy current induced field is observed near the target

By of OMD field on yz plane near the target Beam axis By of OMD field By of induced field Transverse component of induced field is small comparing with those from OMD itself. It’s effective domain is a small vicinity near both the beam axis and target.

x-x’ comparison of captured positrons with and without induced field Induced field kicked some out but also kicked some in. The final yield doesn’t change for  =1.5e6

Induced field,  =3e6 y-z planex-z plane By Bz Beam axis

Induced field + OMD field y-z planex-z plane Beam axis By Bz

Initial x-x’ of captured positrons Induced field kicked some positrons out but also kicked some in. The lost of yield is only ~5%( from ~1.27 down to ~1.20).

Summary For  =1.5e6, since the eddy current induced field is small comparing with the OMD field, and also due to the broad band matching provided from OMD field, the distortion of field doesn’t caused any noticeable change to the e+ yield. For  =3e6, the eddy current induced field is nearly twice as much as of  =1.5e6 and we noticed a lost of yield of about 5%( from ~1.27 down to ~1.20). Lower the conductivity will suppress the effect eddy current induced field.