Undulator Field Integral Measurements Page: 1 of 9
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Undulator Field Integral Measurements
August 5, 2005
The LCLS undulator field integrals must be very small so that the beam trajectory slope
and offset stay within tolerance. In order to make accurate measurements of the small field
integrals, a long coil will be used. This note describes the design of the coil measurement
The primary tuning of the LCLS undulators will be done by sampling the magnetic field at many
points and numerically calculating quantities of interest. The sampling will be done with Hall
probes. For some measurements, however, the errors associated with this technique are too large.
An example is the calculation of the field integrals. A small DC offset from the Hall probe, when
integrated over the undulator length, can exceed the required field integral tolerances. A better
technique to measure field integrals involves the use of a long coil. As the coil is moved through
the field, the induced voltage is integrated to give the flux change. The field integrals can be
calculated from the measured flux changes. Small offsets are easily dealt with by measuring in both
the forward and backward directions. In this note, the coil measurement system under construction
The maximum values for the field integrals have been specified2. The first integral of both Bx
and By must be less than 40 x 10-6 Tm. The second integral of both Bx and By must be less than
50 x 10-6 Tm2. The exact definitions of these integrals and a discussion of their importance will
be given below.
The field integrals should be measured better than the required maximum values for the undu-
lators. This is very difficult, if not impossible, to do even with the best Hall probes. Consider a
Sentron Hall probe as used at ANL and many other laboratories for precision undulator measure-
ments. The specified DC offset drift of the Sentron probe is 0.1 G, or 10-5 T (average output
noise in the bandwidth 0.01 Hz to 100 Hz3). Over the 3.4 m length of the undulator, a 10-5 T
offset would contribute 3.4 x 10-5 Tm to the first field integral, which is roughly the specified limit.
Because the required Hall probe offset is at the limit of what can be achieved, a second method of
measuring the field integrals is desired.
Field integral measurements are fairly easy to do with a long integrating coil, and offsets can
be easily dealt with by measuring as the coil moves both forward and back, then subtracting and
dividing by 2. An additional benefit is that the equipment is somewhat mobile, unlike the granite
bench required for Hall probe measurements, allowing measurements to also be done in the tunnel.
Coil measurements similar to those required for the field integrals are done routinely in the magnetic
'Work supported in part by the DOE Contract DE-AC02-76SF00515. This work was performed in support of the
LCLS project at SLAC.
2H. D. Nuhn et al, "LCLS Undulator Requirements", LCLS Specification # 1.4-001 rev 2.
3Sentron model 3M12-2-2-0.2T data sheet.
SLAC National Accelerator Laboratory, Menlo Park, CA 94025
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Wolf, Zachary. Undulator Field Integral Measurements, report, December 7, 2010; United States. (digital.library.unt.edu/ark:/67531/metadc836025/m1/1/: accessed July 17, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.