USING RADIA TO MODEL SUPERCONDUCTING WIGGLERS AT THE CANADIAN LIGHT SOURCE

The Canadian Light Source (CLS) operates two superconducting wigglers (SCW): a 2 Tesla, 63 pole wiggler, and a 4 Tesla, 27 pole wiggler. Both SCWs have a negative impact on the facility’s injection efficiency. Beam based measurements indicate a larger than expected sextupole moment, and the 4T wiggler produces a horizontal tune shift. To better understand these effects, computer models were developed for the SCWs using the magnetic modeling software package, RADIA [1]. The RADIA models accurately predict the wiggler on-axis field strength and vertical tune shift. By introducing physical misalignments, the models can also produce sextupole moments on the same order of magnitude as the measured quantities. However, the modeled horizontal tune shift is orders of magnitude smaller than the 4T wiggler’s observed tune shift. Various model parameters were investigated for their effect on horizontal tune shift, but the cause of the 4T wiggler’s horizontal tune shift remains unknown. MODEL CONSTRUCTION Overview The RADIA model was built according to the design drawings represented in Fig. 1 and Fig. 2. As indicated, the pole model can be considered as three main components: the core, the yoke, and the coils. The core is the lowermost section of an ARMCO-iron yoke and is partly enclosed by the current-carrying coils. The yoke returns magnetic flux and supports the coils. Figure 1: 2T SCW pole, side view. For the purpose of orientation and alignment, special pins with rounded heads are molded into the cores. In order to include these pin cavities in the model, the core is modeled in upper and lower sections, as shown in Fig. 3. Figure 2: 2T SCW cores and coils, bottom view. Figure 3: Three half-cores modeled in RADIA. The SCW’s superconducting coil is modeled as uniform current-carrying racetracks. Coil design differs slightly between the two SCWs; while the central poles of the 4T device each have two separately powered windings (see Fig. 4), the 2T device only has one coil per core. Figure 4: 4T SCW’s dual coil winding. Proceedings of IPAC2012, New Orleans, Louisiana, USA MOPPP061 02 Synchrotron Light Sources and FELs T15 Undulators and Wigglers ISBN 978-3-95450-115-1 699 C op yr ig ht c ○ 20 12 by IE E E – cc C re at iv e C om m on sA tt ri bu tio n 3. 0 (C C B Y 3. 0) — cc C re at iv e C om m on sA tt ri bu tio n 3. 0 (C C B Y 3. 0) Figure 5 shows the cores, yoke, and current-carrying coils combined to form a model SCW with six poles. Figure 5: Six pole SCW model in RADIA. Summary of Assumptions and Approximations Construction of the RADIA models made use of the following approximations:  Modeled superconducting current windings as uniform current-carrying racetracks.  Approximated pin cavity’s cylindrical shape.  Approximated core’s rounded edge.  Ignored stainless steel structural components.  Manufacturer (Budker) design reports describe core and yoke’s material as ARMCO-iron, the magnetic properties of which we do not know in detail. The RADIA model uses the built-in material RadMatXc06, which is “an inexpensive low carbon steel with C<0.06%”.  Ignored vacuum chamber. MODEL PERFORMANCE Field Strength The initial benchmark for the RADIA models was ramp tables, which were supplied by the device manufacturer and later refined by CLS; these tables map power supply current to the device’s peak field. As shown in Fig. 6, the models and ramp tables agree very well for fields above 1T. Results diverge for lower field strengths, but there is no foreseeable reason to use the model (or the devices) at such fields. Integrated Sextupole Moment Measurements of the 2T and 4T SCWs show sextupole terms of -670 ± 230 G/cm and -680 ± 120 G/cm, respectively [2]. RADIA models containing no misalignments do not produce sextupole moments of this order; the 2T SCW model predicts 50 G/cm, and the 4T SCW model predicts 215 G/cm. 70

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