IEEE Transactions on Nuclear Science, Vol. NS-32, No. 5, October 1985

CSEM-SI EEL HYBRID WIG(LER/UNDULA1TOR MAGNE VIC F IELD STUDIES*

K. Halbach, E. I ioyer, S. Marks, D. Plate, D ShumanLawrence Berkeley Laboratory, University of California,

Berkeley, California 94720

Summary

Current design of permanent magnet wiggler/undulators use either pure charge sheet equivalent material(CSEM) or the CSEM-Steel hybrid configuration. Hiybridconfigurations offer higher field strength at small gaps,field distributions dominated by the pole surfaces and poletuning. Nominal performnance of the hybrid is generallypredicted using a 2-D magnetic design code neglectingtransverse geometry.

Magnetic measurements are presented showingtransverse configuration influence on performance, from acombination of models using CSEMs, REC (He = 9.2 kOe)and NdFe (Hc = 10.7 kOe), different pole widths and endconfigurations. Results show peak field improvement usingNdFe in place of REC in identical models, gap peak fielddecrease with pole width decrease (all results less thancomputed 2-D fields), transverse gap field distributions, andimportance of CSEM material overhanging the poles in thetransverse direction for highest gap fields.

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IntroductionCSE.-STEEL STERlD INERTION DEVIC

Presently there is considerable interest in magneticstructures for insertion devices (wigglers/undulators) used inelectron storage rings to provide both enhanced and quasimonochromatic synchrotron radiation and for free electronlasers generating coherent radiation. I

Permanent magnet structures are particularly attractivefor these applications because of their inherent simplicityand are often the only design alternative with short periodlengths (( 30 cm). With short periods normal conductingelectromagnetic structures become design limited by coilheat transfer; superconducting electromagnetic structuressuffer from complexity and become current density designlimited.2

Current design of permanent magnet structures useeither the pure charge sheet equivalent material (CSEM) or

the CSEM - steel hybrid configuration. Advantages of theCSEM-steel hybrid configuration when compared to the pure

CSEM configuration are:

1. The achievable field strength for small gap toperiod length (g/),) ratios is considerably higher.

2. The field distribution is dominated by the shape ofthe pole surfaces, making the field strength anddistribution much less dependent on the CSEMmaterial prope-rties.

3. The peak field at each pole can be tuned withvariable flux shunts at each pole.

Computational Procedures

1 he computer code PANDIRA3 performs the twodimensional modeling of magnet components. PANDIRAaccounts for nonlinear permeability and the anisotropy ofpermanent magnet materials. Calculations have shownexcellent agreement with measured results where the 2-Dassumptions are appropriate; i.e. where the magnet pole issufficiently wide. F ig. Ia shows a wiggler cross section, cutalong the beam axis. Fig. lb shows the cross sectiongeometry as modeled with PANDIRA, where symmetries are

used to minimize the model size.

*Work supported by the Office of Energy Research,- U.S.Dept. of Energy, Contract No's. DE-AC03-76SF00098 andW-7405-ENG-48.

Figure I

Validity limits of the 2-D assumption forwiggler/undulator (w/u) assemblies was a primarymotivation for the study reported here. Fig. 3 compares themeasured values of central field for pole assemblies ofseveral widths, with the results from a 2-D PANDIRAmodel, which has infinite pole width. As expected,agreement increases with increasing pole width.

However, better agreement can be obtained betweentheory and measurement than is suggested in F ig. 3, byaugmenting the computer modeling with other analyticalprocedures. In considering the 3-D features of w/u

assemblies and relating them to analytical procedures, theeffects which contribute to the scalar potential value on thepole surface are separated from the effects which influencethe resulting magnetic field distribution due to that scalarpotential value. The method can accurately predict polesurface scalar potential value but is limited in relating thescalar potential value to central field value for narrow poles.

Determnining the pole surface scalar potential involvesthe calculation of magnetic flux through the varioussurfaces of the pole that are ignored in the 2-D analysis ofthe configuration shown in Fig lb. These calculations may

use either analytical models or POISSON3 runs. I hecombination of computer and analytical techniques is a

pseudo 3-D analysis that amounts to the integration of 2-Dfield effects over all pole surfaces. All the significantcontributions to the total flux into the pole are accountedfor. This determines the pole surface scalar potentialvalue. (Flux through 3-D pole corners is not accounted for;however, this effect is generally very small). The predictedcentral field value is obtained by comparing the calculatedscalar potential value to the 2-D scalar potential and thecorresponding central field value from the 2-D PANDIRAanalysis. It is assumed that the ratio of central field andscalar potential remnains the same for the actual 3-D poleassembly. This assumption does not take into account thediminution of the transverse field due to finite pole width; a

theoretical/analytical procedure is currently underdevelopment to account for this effect. These techniqueswill be described in detail in a paper to be published.

0018-9499/85/1000-3640$01.003 1985 IEEE

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Model Tests

I o determine experimentally the influence of transversewidth and configuration on performance of the CSFM-Steelhybrid magnetic structure, a nuimber of single poleassemblies were fabricated, each inserted into a steel testfixture and measured magnetically.4 Pole material waseither Vanadium Permendur or steel and the active materialwas either Rare Earth Cobalt (REC) or Neodymium Iron(NdFe). The test fixture simulated the effect of adjacentpoles by providing Neumann boundary conditions atappropriate symmetry planes. Mid pole - midplane gap fieldmeasurements were made transversely with a Hall probe.

To determine the field improvemenit of NdF e whencompared to REC, NdF-e blocks (lic = 10.7 kOe) weresubstituted for REC (Hc = 9.? kOe) in a pole assemblydesigned for optimum performance with REC material.The increase in peak field is shown for various g/X ratiosin F-ig. 2. At large g/A ratios the full 16% increase in thel1c results in a 16% increase in gap field. As the g/.ratio decreases field increase is less due to pole saturation.

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To examine the effect of finite pole width on peak field,tests, using three different pole widths in conjunction withthree different transverse end configurationis of CSEM(REQC) were carried out and results are shown in figures 3and 4. Figure 3 shows the difference betweetn the computedpeak field, using 2-D mnodeling (PANDIRA) and themeasured peak field, which is normalized with the computedpeak field, as a function of the gus ratio. In all cases themeasured field is less (from 3-39% less) than the computedfieldi because of the finite width. Also shown are that thedifferences are less for small g/i, ratios where the widthto pole gap ratio increases. (The PANDIRA computed peakfields used correspond to the computed REC case shown inF iguire 2.) Not shown on Figure 3 is the case where an 8.5cm steel pole with ftlush REC was substituted for theVanadium Permnendtir pole. The steel pole configurationgave only 0.8% less field at a g/A ratio of 0.57, but 5.4%less field at a g/) ratio of 0. 1 14.

F igure 4 is a slice out of Figure 3 at a giA ratio of0.171. Shown clearly is when pole thickness-width ratiodecreases the (lifference between the measured peak fieldand the computed peak field decreases. Also demonstratedis the importance of the transverse end configuration. Ofthe configurations teste(d; highest peak fields were producedin the configuration where the blocks extendbeyond/overhang the pole in all the transverse dimensionexcept toward the Inidplane.

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IN CSEM-STEEL HYBRID CONFIGURATIONS

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To see how transverse field quality is influenced by polewidth and transverse end configuration, transverse fieldprofiles were mreasured for cornbiriations of pole widths andtransverse end configurations at various g/i ratios.F igures 5 and 6 show field quality (expressed as thedifference between the measured central gap field and themeasured gap field away from the pole center normalizedwith the central gap field) as a function of pole overhang(normalized in half-gaps). Figure 5 shows results for a

g/iK ratio of 0.171 and for configuirations with 8.5 cm polewidths. The three (different configurations with theVanadium Permendur pole give very similar curves whichindicate that the transverse field profile is dominatetd by theferromagnetic pole. The less permeable steel pole requiresa greater polet overhang to produce the samne field qualitythan the Vanadium Permendur pole cases. Figures 6a, 6b &6c show field quality for three different g/i. ratios for theflush configuration with three different pole widths. Thedata indicates that for a given field quality, the

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required pole overhang decreases with increased g/\ anddecreases with pole width. Good field aperture width isgiven by pole width less twice the required pole overhang.

Design Example

Receritly, the magnetic design was completed for theLLNL Beam Line VIII Wiggler; a 15 period variable gapwiggler with a 12.85 cm period length.6 Design criteriaincludes a gap field greater than 1.24 1 eslas at. a 2I mm gap(g/\ = 0.163) and a 3% field tolerance for the 2.4 cmaperture over a peak gap field range from 0.01 Teslas to1.24 l-eslas.

The test data4 was used to estimate the magneticstructure dimension. NdF e was selected as the activematerial for its higher field strength and estimated lowerunit cost. Pole material is Vanadium Permendur. F inalconfiguration was based on the 2-D arid pseudo 3-D analysiswhich was verified with a scaled model. The final magneticstructure configuration is shown in Figure 7 along with themagnetic mneasurements from the 7 cm period scaledmodel. For a 21 mm gap (g/X - 0.163) a peak field of 1.39Teslas was measured, the pseudo 3-D analysis computed1.45 l eslas, a 4% difference which shows that thecomputations and measuremeints compare well. With the 3%field tolerance on the peak field, a minimumi good fieldaperture of 2.9 cm is obtained; for a 2% field tolerance thegood field aperture is 2.2 cm.

Acknowle_dgjntThe authors wish to thank Tom Brown, Patul Ebert, and

Glenn 1 irsell of the LLNL XCSF project for theirencouragemnent and support.

References

1. K. Halbach, Permanent Magnets for Production and useof High Energy Particle Beams, LBL -19285, 1985

2. K. Halbach, Permanent Magnezt Undtulators, Journal dePhysique44, I21C1, 1983

3. PANDIRA is an improved version of POISSON whichallows solution of permnanent magnet and residual

field problems. POISSON is an improved version ofTRIM (A.M. Winslow, J. Computer Phys. 1, 149, 1967)that was developed by K. Halbach, et al

4. D. Plate, D. Shuman, Magnetic Measurement Data forPrototype Pole Assemblies, LBL Engineering NoteM6341, 1985

5. E. Iioyer, et al, The Beam L-ine VI REC -Steel HybridWiggler for SSRL, IE.EFE: 1ransactions, Nuclear Science.NS-30, 3118 1983

6. E. Hoyer, et al, The Beam Line VIII Wiggler ConceptualDesign Report, LBID-990, 1985.

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FIELD QUALITY AS A FUNCTION OF POLE OVERHANG FOR8.5 cm WIDE POLE CSEM-STEEL HYBRID CONFIGURATIONS

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