In order to help assess the usable dynamic range of iron-dominated dipoles, field shape data at low field on several Fermi-lab accelerator dipole designs are presented. Emphasis is placed on the systematic and random values of the low field sextupole since it is the first ``allowed`` field error. The Main Injector dipoles provide four times smaller sextupole and more than 20 times less sextupole hysteresis than earlier designs for the Main Ring

Brown, B.C.

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Fermi National Accelerator Laboratory FERMIIAB-Cord-96/369 Field Quality Issues in Iron-Dominated Dipoles at Low Fields Bruce C. Brown Fermi National Accelerator Laboratory P.O. Box 500, Batavia, Illinois 60510 October 1996 Presented at Snowmass 96: New Directions for High Energy Physics, Snowmass, Colorado, June 25-July 12,1996. 15 Opembd by Uriversilies Flemah Asaodim Inc. under Cmtrd No. DE-AC02-76CH03000 nriKtheUnitedStatesDep&rmntdEnergy Disclaimer This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied. or assumes any legal liability or responsibility for the accuracy, completeness or usefulness of any information, apparatus, product or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process or service by trade name, trademark, manufacturer or otherwise, does not necessarily constitute or imply its endorsement, recommendation or favoring by the United States Government or any agency thereof The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof Distribution Approved for public release: further dissemination unlimited. Field Quality Issues in Iron-dominated Dipoles at Low Fields Bruce C. Brown Accelerator Division/Main Injector Department Fermi National Accelerator Laboratory * P.0. Box 500, Batavia, Illinois 605 10 ABSTRACT In order to help assess the usable dynamic range of iron- dominated dipoles, field shape data at low field on several Fermi- lab accelerator dipole designs are presented. Emphasis is placed on the systematic and random values of the low field sexupole since it is the first “allowed’ field error. The Main Injector dipoles provide four times smaller sextupole and more than 20 times less sextupole hysteresis than earlier designs for the Main Ring. I. INTRODUCTION The Fermilab Main Ring, when utilized at 400 GeV, explored a dynamic range of about 45 from its 400 gauss injection field (for 8.9 GeV/c) to 1.8 Tat 400 GeV. The Fermilab Main Injector is designed to operate from 8.9 GeVlc to 150 GeV for a dynamic range of 17, using an injection field of 0.1 T and a field of 1.7 T for 150 GeV. When considering future accelerators, one must al- locate an field error budget (lattice dependent) and choose a suit- able dynamic range. Magnet design requires an understanding of the sources of systematic and random errors which determine the field shape at low, intermediate, and high fields. The field shape errors due to hysteretic effects in iron at low fields are not well understood. We will explore here some data available from the measurement of several series of magnet designs for the Main Ring and one series from the Main Injector to illustrate the large differences which are experienced in existing designs. At this time, calcu- lations which include hysteretic effects have not been available for these magnet designs. A. Design Perspectives and Fermilab Experience For accelerator design, one must answer the question: For a specified normalized field error budget, what dynamic range can be used for a given magnet technology? For magnet design one must answer the questions: For specified magnet technology, what design features control the systematic and random errors in the field shape? Which tools permit one to design such fea- tures? Frequently, the answer given for both superconducting (coil dominated) and iron dominated magnets has been that a field range of 20: 1 was a nominal upper limit. The Fermilab Main Ring, when injecting 8.9 GeV protons into a 400 Gauss field experiences poor storage lifetimes during in- jection and significant losses at the beginning of acceleration. This is due in large part to the field shape at low fields in the Main Ring dipoles. The Fermilab Main Injector will replace the Main Ring as a Tevatron injector (at 150 GeV) and also provide beams l Operated by the Universities Research Association under contract with the U. S. Department of Energy Magnet Accel Aperture Remanent Remanent HxV Sextupole Dipole Bl(ADM) MR 1.5” x 5” -.0196 17 G B2(BDM) MR 2” x 4” -.0188 13 G B3(0DM) MR 3” x Y -.0122 20 G IDC MI 2” x 6” -.00069 20 G Table I: Summary of apertures and fields of dipoles considered in the report. For Main Ring dipoles, there are coils on the mid-plane which define an aperture edge. For the Main Injector dipoles, no copper is placed on the mid-plane, and the aperture reported is the nominal pole width. Transverse cross sections are the same for all four MI Dipoles (IDA, IDB, IDC, and IDD). Sextupole is the normalized sextupole harmonic with a reference radius of 1”. ODM Dipoles are made with a variety of steel types and exhibit a wide variation in remanent dipole. (at 120 GeV) for anti-proton production and external beam ex- periments. The injection field was raised for this accelerator to 0.1 T so that effects due to remanent fields would be smaller. Fields at extraction will be 1.35 T and 1.7 T, so the maximum dynamic range is only 17. But the design of the Main Injec- tor dipoles has achieved fields which are very good even at 400 gauss. What controls the field shape? For most high quality magnets, there is an intermediate field range where effects due to finite permeability of iron are negligible and the observed field shape is due to the mechanical shape of the iron. At high fields, iron saturation may affect both magnet strength and shape. At low fields, the hysteretic contribution of the iron to the field may af- fect both strength and shape of the magnetic fields. The strength (dipole field) change due to iron hysteresis is related simply to s H dl along the relevant flux lines which pass through the beam aperture of the dipole. The quality of the iron is the signifi- cant parameter which can be controlled to impact this magnet property. The field shape changes due to iron hysteresis (differ- ences from the intermediate field shape) are governed by both iron quality and geometry. Neither design strategies nor analytic tools are widely known which guide this design problem. Com- puter codes for magnet design have provided good descriptions of the fields at intermediate and high fields. Currently, no code conveniently describes the hysteretic field contributions. II. DATA We will present data from several fairly comparable accelera- tor dipoles. Table I lists the names and nominal transverse aper- tures of the magnets which we will consider. The important field errors of the respective accelerators are dominated by these mag- O.OWO - -0.ooo5 B i d a E P -0.0010 Sextupole Hysteresis Magnet ALM580 B 0 0 -0.0015 L 0.0 500.0 1000.0 .___ _ 1500.” _. ZI Magnet currant (Amperes) loo. 0 0 -2 -4 -6 -8 -10 -12 Figure 1: Normalized sextupole harmonics for a portion of the body of a Main Ring Bl dipole at transverse center. Injection field is about 400 Gauss at a current of about 97 A. All mea- surements are on an up ramp except for the more positive values shown at 97 A which are measured on a down ramp after a ramp to full field. nets. We will present the sextupole fields for these magnets since they are the first field error which respects the dipole symme- try of the design. Since we are examining errors which come from the design rather than from fabrication errors, sextupole will raise the issue which is of interest. Figures 1 and 2 plot the normalized sextupole fields as a func- tion of current for some representative dipoles.’ Characteristi- cally, beginning with no excitation current and some sextupole, the sextupole vs. current traces out a hysteretic curve with lower values when the current is increasing and higher values when the current is decreasing. Only a minimal set of measurements is available for an example Main Ring dipole, whereas, with a full length probe and more automated data acquisition, we have ac- quired more complete data on Main Injector dipoles[3][4]. The Main Ring magnets were measured only up to a field of about 0.7 T, so saturation effects were not explored. The full 1.7 T is explored in the Main Injector measurements so the high field sat- uration sextupole is shown. The hysteretic sextupole (down ramp minus up ramp) is quite large for Main Ring dipoles. Routine measurements were only ‘Measurements of Main Ring dipoles with harmonic coils were carried out since 1986 using a VAX-CAMAC-based measurement system derived from the one used for measurements of anti-proton source magnets[ I]. A bucked tangen- tial coil[Z] of radius selected for each magnet series (ADM, BDM, ODM), was used for all of these measurements. Either three or four longitudinal positions were required to measured the full length of these 6 m dipoles. Results of these measurement are available in permanent databases, but no formal reports of this measurement effort are available. current, A : #igTi!&lD ---- up ramp tlC lev 2 ------- UD mmD QC lev 1 , I I . t I I It I I III I I, t t I I I, b 2ObO 4000 BQOO 8QOb current, A Figure 2: Normalized sextupole harmonics x lo4 at 1” reference radius integrated throughMain Injector dipole IDC028-0. Injec- tion is at 1000 Gauss at a current of 500 A. Measurements with a full length probe are taken at the fixed currents plotted with both up ramp and down ramp measurements shown. At most currents, the hysteretic fields produce a slightly more positive sextupole on the down ramp. Solid and dashed line are limits on the magnet-to-magnet variability expected based on previously measured dipoles. made, however, at a few currents including 97 A on the up ramp and 0 A on the down ramp. From the variability of these as well as the difference in average value, we will demonstrate the mag- nitude of these fields. Figure 3 provides histograms of the nor- malized sextupole harmonics at 400 Gauss on the up ramp for a sample of Main Ring dipoles. Figure 4 provides histograms of the same quantity at a current of 0 A (remanent field). The reference dipole field for these measurements are given in Ta- ble I. Both sets of histograms are for fields averaged over the full length (including end fields) of the magnets. The more extensive data on the Main Injector dipoles provides a direct measurement of the magnitude and variability of the (very small) sextupole hysteresis in those magnet. Figures 5, 6 and 7 histogram the sextupole on the up ramp, on the down ramp, and the magnet by magnet difference for the IDC series dipoles of the Main Injector but not at the Main Injector injection field of 0.1 T but at 0.04 T (400 Gauss) to be directly comparable to the Main Ring data. Figure 8 is a histogram of the distribution of integrated remanent sextupole for these magnets. Summaries of the magnitudes of these sextupole field at 0.04 T are provided in Table II. The dipole and sextupole remanent Magnet 1 Sext 1 Sext 1 Sext Series 1 Uv 1 Down 1 diff Table II: Summary of mean values of the normalized sextupole harmonics at 0.04 T for a various series of accelerator dipole de- signs. are summarized with the apertures in Table I. III. DISCUSSION AND CONCLUSIONS Accelerator magnets require high field quality to allow high intensity, high quality beams to be injected, accelerated and stored. While it is possible to provide correction magnet sys- tems which reduce the need for precise fields in the main mag- nets, such systems add complexity and cost, so one seeks clean designs which minimize the need for correction. Since field er- rors due to hysteretic iron properties usually change with exci- tation level, their correction is particularly cumbersome. This makes the discovery that their magnitude is greatly reduced in the Main Injector Dipole design of some general interest. The data above provides a remarkable contrast between the Main Injector dipoles and the Main Ring dipoles. When com- paring the B2 dipoles with the Main Injector dipoles, we find that the normalized sextupole at 0.04 T is improved by x4 in the newer design (comparing magnets of comparable aperture). The hysteretic component of the sextupole is x 20 smaller. Com- paring the variability of these quantities (e.g. RMS values) con- firms the improved rejection of hysteretic iron influences in the Main Injector design. Other hysteretic non-uniformities are also significantly improved, providing a very uniform dipole field at all excitation levels until iron saturation begins to influence the field at about 1.3 T. To reduce the overall iron cost, the Main In- jector dipoles were designed with a large saturation sextupole at high fields. The pole shape was optimized to minimize the field errors due to saturation and a sextupole correction system was built to control the beam effects of the high field sextupole. A comparable magnet was designed for the SSC Medium Energy Booster. It utilized more steel to carry the flux at high fields and the saturation sextupole was about x 3 smaller than for the Main Injector. Examining the field quality achieved in these magnets suggests that a dynamic range of greater than 40 is demonstra- bly achievable. Further examination of the low field properties of the Main Injector dipoles would be a worthwhile way to learn more about the low field possibilities for iron dominated mag- nets for accelerators. We have not understood what effects permit the low hysteretic field errors in the Main Injector dipole design. The larger hori- zontal aperture will have some effect. We suspect that the over- all transverse profile of the pole may have a significant im- pact. That shape is quite similar to the end shape which has been designed so that the field in the iron will be vertical at all excitations[!I& Such a pole shape may assist in reducing vari- able field errors by controlling the effects of iron magnetization. Contemplation of very large accelerators with iron dominated magnets makes such considerations quite important in the op- timization of such magnets. IV. ACKNOWLEDGMENTS I would like to thank Peter Mazur for his leadership in the effort which remeasured the Main Ring dipoles with harmonic coils. My colleagues who assisted in the Main Injector measure- ments are gratefully acknowledged. Discussions with Fran9ois Ostiguy were the source of the suggestion that the improved hys- teretic behavior was due to the pole shape. PI PI [31 [41 ISI V. REFERENCES B. C. Brown, D. J. Harding, M. F. Gormley, M. E. Johnson, A. J. Lennox, K. J. McGuire, J. E. Pachnik, J. K. Plymale, R. A. Shenk, and A. A. Wehmami. Data Acquisition System Design for Pro- duction Measurements of Magnets for the Fermilab Anti-Proton Source. IEEE Trans. on Nut. Sci, NS-32:2050,1985. B. C. Brown. Fundamentals of Magnetic Measurements with Il- lustrations from Fermilab Experience. In P. E Dahl, editor, Pro- ceedings of the ICFA Workshop on Superconducting Magnets and Cryogenics, page 297. Brookhaven National Lab, May 1986. Also available as Fermilab TM-1403. D.J. Harding, R. Baiod, B.C. Brown, J.A. Carson, N.S. Chester, E. Desavouret, J. Dimarco, J.D. Garvey, H.D. Glass, PJ. Hall, P.S. Martin, PO. Mazur, C.S. Mishra, A. Mokbtarani, J.M. Nogiec, D.F. On-is, J.E. Pachnik, A.D. Russell, S.A. Sharonov, J.W. Sim, J.C. Tompkins, K. Trombly-Freytag, D.G.C. Walbridge, and V.A. Yarba. Magnetic Field Measurements of the Initial Production Main Injector Dipoles. In Proceedings of the 1995 IEEE Particle Accelerator Conference, Dallas, May I-5, 1995, page 1340. huti- tute of Electrical and Electronic Engineers, 1995. J.W. Sim, R. Baiod, B.C. Brown, E. Desavouret, H.D. Glass, P.J. HalI, D.J. Harding, C.S. Mishra, J.M. Nogiec, J.E. Pachnik, A.D. Russell, K Trombley-Freytag, and D.G.C. Walbridge. Software for a Database-ControlIed Measurement System at the Fermilab Mag- net Test Facility. In Proceedings of the 1995 IEEE Particle Accel- erator Conference, Dallas, May I-5, 1995, page 2285. Institute of Electrical and Electronic Engineers, 1995. J. F. Ostiguy. Longitudinal Profile and Effective Length of a Con- ventional Dipole Magnet. In Proceeding of the 1993 IEEE Parti- cle Accelerator Conference, page 2901. Institute of Electrical and Electronic Engineers, 1993. FERMILAB-Conf-93/220. adm Sextupole Harmonics Main Ring Dipole - Sextupole Harmonics 10 [ 1 ID 2 ID 2 EIlbleS 33 Mean 0.1961E-01 91 8 7: 61 5’ 41 7: 6: 5 : 4: 3: 2: 1 : r r Lf 1 RMS 0.2559Ed2 .03 -0.025 -0.02 -0.015 -0.01 -0.005 OASext adm Normal Sexi at 97 A x10 -I Main Ring Dipole - Sextupole Harmonics bdm Sextupole Harmonics 1 ID 2 1 ID 2 L 12 - 10 - 8- 6- 14 12 10 8 6 4 2 Entrles 33 Mean -0.1675Eal I itties 47 fan -0.462OEd3 IS 0.1161 E-03 1 RMS 0.1732E-02 1 .12 -0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 bdm Normal Sext at 97 A x10 -2 8’ ’ ’ I ’ ’ ’ ’ c .03 -0.025 -0.02 -0.015 -0.01 -0.005 OASext odm Sextupole Harmonics Main Ring Dipole - Sextupole Harmonics t ’ ID 6 5 Entrler L Mean RMS -0. 0. : 2 26 -03 -03 - 1: I 1 i I 02 L L 0.021; x10 12 1 1 ID 2 33 -0.1125E-01 0.4642E-02 10 - 8 - Entrle: L Mean RMS 6- 4- 2 1 n r-l4 1 r...N...j.,.j..Il.I 8.12 -0.1 -0.08 -0.06 -0.04 - odm Normal Sext at 194 A t %!oi ‘-0%” -idi ’ ‘-6.615’ ’ -0:oi ‘-O&s’ 0ASex-t Figure 3: Histogram of normalized sextupole field at 400 Gauss Figure 4: Histogram of normalized sextupole field at 0 A exci- for Main Ring B 1, B2, and B3 (ADM, BDM, and ODM) dipoles. tation for Main Ring B 1, B2, and B3 dipoles. Magnets prepared Magnets prepared with 3 ramps to full field followed by a reset at with 3 ramps to full field before down ramp to 0 A for this mea- 0 A before ramp to 97 A (194 A for ODM) for this measurement. surement. IDC Sextupole Harmonics IDC Sextupole Harmonics 25 t 1 ID 2 4 66 0.6016E-06 0.3274E-05 ID 20 i Fntrler &2 an RM - t !S 66 -0.1152E-03 0.8071 EO5 10 - 8- 6- 4- 2- 15 - 10 - 5- r r o”“““““‘.“““‘l”..‘...‘.I -0.2 -0.18 -0.16 -0.14 -0.12 -0.1 -0.08 JJM3 2OOASextUp x10 L In 01 -0.1 -0.08-0.06-0.04XL02 0 0.02 0.04 0.06 0.08 0 1 I. 2OOASext(Down-Up) x10 4 Figure 5: Histogram of normalized sextupole field at 200 A ex- citation for Main Injector IDC dipoles. Magnets prepared with 3 ramps to full field with resets to 0 A before ramp to 200 A for this measurement. Figure 7: Histogram of normalized sextupole field difference of down ramp value minus up ramp value at 200 A excitation for Main Injector IDC dipoles. IDC Sextupole Harmonics IDC Sextupole Harmonics E 1 ID 3 14 12 10 8 6 4 2 0 ’ ID 2 ntrtes ean M +! 67 -0.6668E03 0.1547E-03 2o t -0.1151 E-03 15 12.5 10 7.5 5 1 J 2.5 t r O”“““‘.““““‘.‘..‘.‘...‘. -0.2 -0.18 -0.16 -0.14 -0.12 -0.1 -0.08 -0.06_ I. I. I ,I.. I... I ,.. I ..,,l... I ,,. 0.14 -0.12 -0.1 -0.08 -0.06 -0.04 -0.02 OASext 2OOASext Dn x10 -a Figure 6: Histogram of normalized sextupole field at 200 A exci- Figure 8: Histogram of normalized sextupole field at 0 A exci- tation for Main Injector IDC dipoles. Following 200 A up ramp tation for Main Injector IDC dipoles. Magnets prepared with 3 measurement, magnets ramped to full field before down ramp to ramps to full field before down ramp to 0 A for this measure- 200 A for this measurement. ment. 

Field quality issues in iron-dominated dipoles at low fields

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Field quality issues in iron-dominated dipoles at low fields

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