Measurements of 230 6-meter and 136 4-meter dipoles constructed for the Fermilab Main Injector were carried out as part of the magnet production effort. An automated measurement system provided data on magnetic field strength and shape using several partially redundant systems. Results of these measurements are available for each individual magnet for use in accelerator modelling. In this report we will summarise the results on all of the magnets to characterise the properties which will govern accelerator operation

Brown, B C

Di Marco, J

Glass, H D

Harding, D J

Martin, P S

Mazur, P O

Mishra, C S

Orris, D

Sim, J W

Tompkins, J C

Trombly-Freytag, K

Walbridge, D G C

Harding, D. J.

Brown, B. C.

Dimarco, J.

Glass, H. D.

Martin, P. S.

Mazur, P. O.

Mishra, C. S.

Orris, D. F.

Sim, J. W.

Tompkins, J. C.

Trombly-Freytag, Kelley

Walbridge, D. G. C.

UNT (University of North Texas) Digital Library

d& Fermi National Accelerator Laboratory FERMILAB-Conf-99/075 Strength and Shape of the Magnetic Field of the Fermilab Main Injector Dipoles D.J. Harding et al. Fermi National Accelerator Laboratory P.O. Box 500, Batavia, Illinois 60510 March 1999 Published Proceedings of the 1999 Particle Accelerator Conference, New York, New York, March 29-Apri12, 1999 Operated by Universities Research Association Inc. under Contract No. DE-ACCl2-76CH03000 with the United States Depaltment of Energy 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, expressed 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. Copyright Notification This manuscript has been authored by Universities Research Association, Inc. under con- tract No. DE-ACO%76CHO3000 with the U.S. Department of Energy. The United States Government and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government Purposes. STRENGTH AND SHAPE OF THE MAGNETIC FIELD OF THE FERMILAB MAIN INJECTOR DIPOLES * D.J. Hardinn’, B.C. Brown, J. Dimarco, H.D. Glass, P.S. Martin, P.O. Mazur, C.S. Mishra, D.F. Orris, J.W. Sim, J.C. Tompkins, K. Trombley-Freytag, D.G.C. Walbridge, Fermi National Accelerator Laboratory, P.O. Box 500, Batavia, IL 605 10 USA Abstract 2 MAGNET STRENGTH Measurements of 230 6-meter and 136 4-meter dipoles constructed for the Fermilab Main Injector were carried out as part of the magnet production effort. An automated measurement system provided data on magnetic field strength and shape using several partially redundant systems. Results of these measurements are available for each individual magnet for use in accelerator modelling. In this report we will summarise the results on all of the magnets to characterise the properties which will govern accelerator operation. Groups 4 and 5 define our nominal magnet strength at each current. The mean strength, including me 4-m magnets weighted at 2/3 of the 6-m magnets, was calculated for each current. Deviations from that strength (for the 6-m magnets) or from 2/3 of that strength (for the 4-m magnets) are normalized to the nominal strength of the 6-m magnets. These deviations are quoted here in “units” of parts in 104. 1 INTRODUCTION Over the last decade the Fermilab Main Injector and its magnets have been planned [1,2], designed [3,4,5,6] prototyped [7,8,9,10,11,12], produced [13,14], measured [15,16,17,18,19,20,21], installed [22], and commissioned [23,24]. Every dipole has been measured thoroughly, providing a rich set of data that is used for magnet assignments and beam modeling. Here we present an overview to give a flavor of the Main Injector dipoles. Figure 1 shows the distribution of deviations of magnet strength from nominal for all magnets as a function of magnetic field. The profile is dominated by a narrow peak around the nominal strength composed primarily of Groups 4 and 5. The standard deviation of the distribution, due to variations in magnet length, magnet gap, steel properties, and random measurement errors, is in the range of 2 to 4 units. Maln Injector Dipole Strength Distribution vs Curent In all, 230 6-meter and 136 4-meter dipoles were built and measured, including spares. These may be divided into several groups whose behavior differs for well- understood reasons: 1) Six 6-m R&D dipoles, 2) Six 4-m R&D dipoles, 3) the first 46 6-m dipoles, 4) the balance of the 6-m dipoles, and 5) the balance of the 4-m dipoles. Groups 1 and 2 were built with steel from Vendor A. Group 2 was built too long by 2.5mm. Group 3 was built all or in part from steel from Vendor B’s first production run. Groups 4 and 5 were built entirely with steel from Vendor B’s later runs. Field l-0 Fklonal devlatlon from nominal x1o’ The integrated strength and the harmonic composition of the magnetic field was measured at multiple currents using a rotating tangential probe that extended through the magnet following the path of the beam. Field strength and shape were also measured using an integrating coil that could be held on center as the current ramped or moved transversely at a fixed current. A sample of magnets was further measured with an NMR and Hall probe package that scanned the magnet longitudinally. Figure 1: Main Injector dipole magnet strength distribution as a function of field. The field ranges from the injection value of 0.1 T to its peak of 1.75 T. * Work supported by the United States Department of Energy under contract No. DE-AC02-76CH03000. # Email: harding@fnal.gov A second, lower ridge branches from the main stem at about 0.3 T and diverges to lower strength roughly linearly. These are Group 3 magnets with early steel from vendor B. [25] A handful of magnets appear below the nominal peak at 0.1 T, and the same magnets appear above the peak around 1.5 to 1.6 T. These are Groups 1 and 2 showing first a lower remanent field and then slower saturation. A modification to the back leg has allowed us to match the nominal field at 1.4 T and at 1.7 T, though it runs high in between.[26] The identity of InJectIon (WOA, 0.10 1) 120 100 Nu a’ ,“,,” 60 40 20 0 -44 -36 -26 -20 -12 -4 4 12 20 El R&D 6-m q  R&D 4-m ’ lFirst 46 6-m IENormal 6-m lNormal4-m Near Transition (1500A. 0.30 T) 60 60 1 40 20 0 0 R&D 6-m 0 R&D 4-m H First 46 6-n q  Normal 6-m 1mNormal4~ 120 &V/c (7000A, 1.37 T) W First 46 6-m Is Normal 6-m ,tP 9 g? Jl? ,?rr *b b 2! rL0 ___. 150 QeVlc (QBOOA, 1.75 1) 120 I 100 60 60 I 40 20 0 ,tP ,$P j-p ,rLo ,?!! ,b b + ?? n First 46 6-m Figure 2: Distribution of magnet strength at four key Figure3: Multipole components of the dipole magnets as a excitations. function of magnetic field. The ordinate scales vary. these groups of magnets is clear in the histograms of Figure 2 which represent slices though the Figure 1 mountain range. The hysteresis in the dipoles has been studied and is included as an operational factor 3 HARMONICS We characterize the variation of the magnet field across Sextupole Component of the Dipole Field .,2,00 _.............................  . Field (r) Octupole Component of the Dipole Field 0.50 0.40 I 0.30 B 0.20 * 0.10 ld 8 0.00 i ;::$ 0 Field t-l) Decapole Component ot the Dlpole Field o.so 0.40 a 0.20 5 2 0 E -0.40 5 1:::: 8 :::i -1.40 -1 .so 12-pole Component of the Dlpole Field Flald ,T) the aperture by the coefficients of its harmonic decomposition. The coefficient we quote is the fraction of the field due to the component in question at 25.4mm (typical of the maximum beam size) relative to the dipole component in “units” or parts in 104. Figure 3 shows the distribution of the normal sextupole, octupole, decapole, and 12-pole as a function of magnetic field. The error bars represent one standard deviation. Note that the plots extend below the injection field of 0.10 T. As expected, we see some contribution of even terms as the steel saturates, reflecting the symmetry of the magnet, but the design and fabrication process minimizes the antisymmetric terms. In operation, a significant sextupole field is also generated by eddy curents in the beam tube.[27,28] 4 CONCLUSION Although the variation in steel properties prevented the overall Main Injector dipole strength variation from meeting expectations, within a steel run the uniformity was excellent. The field shapes meet the project requirements.[3] The non-standard magnets have been assigned locations in the ring where they produce small, local two-bumps, minimizing their impact on the closed orbit. [29]. Care has been taken to reserve a suitable collection of spare magnets to allow replacement of any magnet with a like magnet. Purchasing all the steel before the project was funded would have alleviated the strength variation by reducing the increasing the uniformity of the steel and permitting homogenization of the magnet cores. In the end, the cost and schedule savings enabled by the phased steel purchases justify the extra effort required. 5 REFERENCES [l] S. Holmes, “The Fermilab Upgrade”, In Proceedings of the 1989 Particle Accelerator Conference,Chicago, (1989). [2] S. Holmes, “Tevatron Performance Goals for the Coming Decade”, In Proceedings this Conference, (1999). [3] The Fermilab Main Injecvtor Technical Design Handbook, (Fermilab, Batavia, 1997). [4] D. Harding et al., “Design Considerations and Prototype Performance of the Fermilab Main Injector Dipole”, In Proceedings of the 1991 Particle Accelerator Conference, San Francisco, (1991). [5] M. Bleadon et al., “The Fermilab Main Injector Dipole Construction Techniques and Prototype Magnet Measurements”, Presented at the 12th International Conference on Magnet Technology, Leningrad, (1991). [6] B. Brown et al., “The Design and Manufacture of the Fermilab Main Injector Dipole Magnet”, Presented at the EPAC Conference, Berlin, (1992). [7] D. Harding et al., “Design Considerations and Prototype Performance of the Fermilab Main Injector Dipole”, In Proceedings of the 1993 Particle Acceleraror Conference, Washington, (1993). [8] J. Ostiguy, “Magnet End Design: The Main Injector Dipoles”, In Proceedings of rhe 1991 Particle Accelerator Conference, San Francisco, (1991). [9] J. Ostiguy, “Magnet End Design: The Main Injector Dipoles”, In Proceedings of the 1993 Particle Accelerator Conference, Washington, (1995). [lo] J. Ostiguy, “Longitudinal Profile and Effective Length of a Conventional Dipole Magnet”, In Proceedings of the 1993 Particle Accelerator Conference, Washington, (1993). [ 1 l] H. Glass, ‘Techniques for Measurement of Dipole Endfields with a Rigid Integrating Coil”, In Proceedings of the 1993 Particle Accelerator Conference, Washington, (1993). [12] D. Harding et al., “Design and Measurements of Prototype Fermilab Main Injector Dipole Endpacks”, In Proceedings of the 1993 Particle Accelerator Conference, Washington, (1993). [13] D. Harding et al., “Experience with the Source Evaluation Board Method of Procuring Technical Components for the Fermilab Main Injector”, In Proceedings of the 1993 Particle Accelerator Conference, Washington, (1993). [14] A. Russell et al., “Selecting Magnet Laminations Recipes Using the Method of Simulated Annealing”, Proceedings of Ihe 1997 Particle Accelerator Conference,Vancouver, (1997). [15] H. Glass et al., “Flatcoil Systems for Measurements of Fermilab Magnets”, Presented at the Fourteenth International Conference on Magnet Technology, Tampere, Finland, (1995). [16] B. Brown er al., “Software Design for a Database Driven System for Accelerator Magnet Systems”, In Proceedings of rhe 1991 Particle Accelerator Conference, San Francisco, (1991). [17] B. Brown et al., “Software Design for a Database Driven System for Accelerator Magnet Measurements”, In Proceedings of rhe 1993 Particle Accelerator Conference, Washington, (1993). [18] J. Sim et al.. ” Software for a Database-Controlled Measurement System at the Fermilab Magnet Test Facility”, In Proceedings of the 1995 Particle Accelerator Conference, Dallas, (1995). [19] J. Sim et al., “A Relational Database for Magnets and Measurement Systems at the Fermilab Magnet Test Facility”, In Proceedings of the 1995 Particle Accelerator Conference, Dallas, (1995). [20] D. Harding et al., “Magnetic Field Measurements of the Initial Fermilab Main Injector Production Dipoles”, In Proceedings of rhe 1995 Particle Accelerator Conference, Dallas, (1995). [21] B. Brown et al., “Results on Fermilab Main Injector Dipole Measurements”, Presented at the Fourteenth Inrernarional Conference on Magnet Technology, Tampere, (1995). [22] J. Satti, “The Fermilab Main Injector Dipole and Quadrupole Cooling Design and Bus Connections”, In Proceedings of rhe 1995 Particle Accelerator Conference, Dallas, (1995) [23] P. Martin et al., “Fermilab Main Injector Commissioning Status”, In Proceedings this Conference, (1999). [24] C. Mishra, “Simulation and Measurements of the Fermilab Main Injector Dynamic Aperture”, In Proceedings this Conference, (1999). [25] P. Martin et al., “Variations in the Steel Properties and the Excitation Characteristics of Fermilab Main Injector Dipoles, “, Proceedings of the 1997 Particle Accelerator Conference,Vancouver, (1997). [26] P. Martin et al., “Modifications to the Excitation Characteristics of Fermilab Main Injector Dipoles by Machining”, Proceedings of the 1997 Particle Accelerator Conference,Vancouver, (1997). [27] D. Walbridge et al., “Measurements of Beam Pipe Eddy Current Effects in Main Injector Dipole Magnets”, Presented at the XVth International Conference on High Energy Accelerators, Hamburg, (1992). [28] D. Walbridge et al., “Field Errors Introduced by Eddy Currents in Fermilab Main Injector Magnets”, Proceedings of rhe 15th International Conference on Magnet Technology, Beijing, (1997). [29] P. Martin er al., ‘Excitation Characteristics of Fermilab Main Injector Dipoles and Magnet Assignment to Reduce Closed Orbit Errors”, Proceedings of the 1997 Particle Accelerator Co$erence,Vancouver, (1997). 

Strength and shape of the magnetic field of the Fermilab Main Injector dipoles

CERN Document Server

STRENGTH AND SHAPE OF THE MAGNETIC FIELD OF THE FERMILABMAIN INJECTOR DIPOLES *D.J. Harding#, B.C. Brown, J. Dimarco, H.D. Glass, P.S. Martin, P.O. Mazur, C.S. Mishra,D.F. Orris, J.W. Sim, J.C. Tompkins, K. Trombley-Freytag, D.G.C. Walbridge, Fermi NationalAccelerator Laboratory, P.O. Box 500, Batavia, IL 60510 USAAbstractMeasurements of 230 6-meter and 136 4-meter dipolesconstructed for the Fermilab Main Injector were carriedout as part of the magnet production effort.  An automatedmeasurement system provided data on magnetic fieldstrength and shape using several partially redundantsystems.  Results of these measurements are available foreach individual magnet for use in accelerator modelling.In this report we will summarise the results on all of themagnets to characterise the properties which will governaccelerator operation.1  INTRODUCTIONOver the last decade the Fermilab Main Injector and itsmagnets have been planned [1,2], designed [3,4,5,6]prototyped [7,8,9,10], produced [11,12], measured[13,14,15,16,17,18], installed [19], and commissioned[20,21].  Every dipole has been measured thoroughly,providing a rich set of data that is used for magnetassignments and beam modeling.  Here we present anoverview to give a flavor of the Main Injector dipoles. In all, 230 6-meter and 136 4-meter dipoles were builtand measured, including spares.  These may be dividedinto several groups whose behavior differs for well-understood reasons:  1) Six 6-m R&D dipoles, 2) Six 4-mR&D dipoles, 3) the first 46 6-m dipoles, 4) the balance ofthe 6-m dipoles, and 5) the balance of the 4-m dipoles.Groups 1 and 2 were built with steel from Vendor A.Group 2 was built too long by 2.5-mm.  Group 3 was builtall or in part from steel from Vendor B’s first productionrun.  Groups 4 and 5 were built entirely with steel fromVendor B’s later runs. The integrated strength and the harmonic compositionof the magnetic field was measured at multiple currentsusing a rotating tangential probe that extended through themagnet following the path of the beam.  Field strength andshape were also measured using an integrating coil thatcould be held on center as the current ramped or movedtransversely at a fixed current.  A sample of magnets wasfurther measured with an NMR and Hall probe packagethat scanned the magnet longitudinally. _______________________ * Work supported by the United States Department of Energy undercontract No. DE-AC02-76CH03000. # Email: harding@fnal.gov2  MAGNET STRENGTHGroups 4 and 5  define  our nominal magnet strength ateach current.  The mean strength, including the 4-mmagnets weighted at 2/3 of the 6-m magnets, wascalculated for each current.  Deviations from that strength(for the 6-m magnets) or from 2/3 of that strength (for the4-m magnets) are normalized to the nominal strength ofthe 6-m magnets.  These deviations are quoted here in"units" of parts in 104. Figure 1 shows the distribution of deviations of magnetstrength from nominal for all magnets as a function ofmagnetic field.  The profile is dominated by a narrowpeak around the nominal strength composed primarily ofGroups 4 and 5.  The standard deviation of thedistribution, due to variations in magnet length, magnetgap, steel properties, and random measurement errors, isin the range of  2 to 4 units.  Figure 1: Main Injector dipole magnet strengthdistribution as a function of field.  The field ranges fromthe injection value of 0.1 T to its peak of 1.75 T.  A second, lower ridge branches from the main stem atabout 0.3 T and diverges to lower strength roughlylinearly.  These are Group 3  magnets with early steelfrom vendor B. [22]  A handful of magnets appear belowthe nominal peak at 0.1 T, and the same magnets appearabove the peak around 1.5 to 1.6 T.  These are Groups 1and 2 showing first a lower remanent field and thenslower saturation.  A modification to the back leg hasallowed us to match the nominal field at 1.4 T and at1.7 T, though  it runs high in between.[23]  The identity of-44 -36-28 -20-12 -4 4 12 20020406080100120140Main Injector Dipole Strength Distribution vs FieldField(T) Fractional deviation from nominal x1040.11.750-7803-5573-3/99/$10.00@1999 IEEE. 3318Proceedings of the 1999 Particle Accelerator Conference, New York, 1999Figure 2:  Distribution of magnet strength at four keyexcitations. these groups of magnets is clear in the histograms ofFigure 2 which represent slices though the Figure 1mountain range. The hysteresis in the dipoles has also been studied.  Thevariety of operational modes requires that it be included incontrol systems calculations.[24,25]   Figure 3: Multipole components of the dipole magnets asa function of magnetic field.  The ordinate scales vary.3  HARMONICS We characterize the variation of the magnet field acrossthe    aperture    by   the   coefficients    of    its    harmonicdecomposition.  The coefficient we quote is the fraction ofthe field due to the component in question at 25.4 mm(typical of the maximum beam size) relative to the dipolecomponent in "units" or parts in 104.Octupole Component of the Dipole Field-0.30-0.20-0.100.000.100.200.300.400.500.00 0.50 1.00 1.50 2.00Field (T)8-pole at 25.4 mm (units)Decapole Component of the Dipole Field-1.60-1.40-1.20-1.00-0.80-0.60-0.40-0.200.000.200.400.600.00 0.50 1.00 1.50 2.00Field (T)10-pole at 25.4 mm (units)12-pole Component of the Dipole Field-0.40-0.30-0.20-0.100.000.100.200.300.400.00 0.50 1.00 1.50 2.00Field (T)12-pole at 25.4 mm (units)Sextupole Component of the Dipole Field-12.00-10.00-8.00-6.00-4.00-2.000.000.00 0.50 1.00 1.50 2.00Fie ld (T)6-pole at 25.4 mm (units)Near Transition (1500A, 0.30 T)020406080100120-44-36-28-20-12 -4 4 12 20NumberR&D 6-mR&D 4-mFirst 46 6-mNormal 6-mNormal 4-m120 GeV/c (7000A, 1.37 T)020406080100120-44-36-28-20-12 -4 4 12 20NumberR&D 6-mR&D 4-mFirst 46 6-mNormal 6-mNormal 4-m150 GeV/c (9500A, 1.75 T)020406080100120-44-36-28-20-12 -4 4 12 20NumberR&D 6-mR&D 4-mFirst 46 6-mNormal 6-mNormal 4-mDistribution of Dipole  strengths at Injection Fie ld(500A, 0.10 T)0102030405060708090100-44-38-32-26-20-14 -8 -2 4 10 16 22Deviation from nominal (x1e4 of 6-m)NumberR&D 6-mR&D 4-mFirs t 46 6-mNormal 6-mNormal 4-m3319Proceedings of the 1999 Particle Accelerator Conference, New York, 1999 Figure 3 shows the distribution of the normal sextupole,octupole, decapole, and 12-pole as a function of magneticfield.  The error bars represent one standard deviation.Note that the plots extend below the injection field of0.10 T.  As expected, we see some contribution of eventerms as the steel saturates, reflecting the symmetry of themagnet, but the design and fabrication process minimizesthe antisymmetric terms. In operation, a significant sextupole field is alsogenerated by eddy currents in the beam tube.[26,27]4  CONCLUSION Although the variation in steel properties prevented theoverall Main Injector dipole strength variation frommeeting expectations, within a steel run the uniformitywas excellent. The field shapes meet the projectrequirements.[28]  The non-standard magnets have beenassigned locations in the ring where they produce small,local two-bumps, minimizing their impact on the closedorbit.[29].  Care has been taken to reserve a suitablecollection of spare magnets to allow replacement of anymagnet with a like magnet. Purchasing all the steel before the project was fundedwould have alleviated the strength variation by increasingthe uniformity of the steel and permitting homogenizationof the magnet cores.  In the end, the cost and schedulesavings enabled by the phased steel purchases justify theextra effort required.5  REFERENCES[1] S.D. Holmes et al., "The Fermilab Upgrade", In Proceedings of the1989 Particle Accelerator Conference, Chicago, (1989).[2] S.D. Holmes, "Tevatron Performance Goals for the ComingDecade", In  Proceedings this Conference, (1999).[3] The  Fermilab Main Injector  Technical  Design  Handbook,(Fermilab, Batavia, 1997).[4] D.J. Harding et al., "Design Considerations and PrototypePerformance of the Fermilab Main Injector Dipole", In Proceedings ofthe 1991 Particle Accelerator Conference, San Francisco, (1991).[5] M. Bleadon et al., "The Fermilab Main Injector Dipole ConstructionTechniques and Prototype Magnet Measurements", Presented at the12th International Conference on Magnet Technology, Leningrad,(1991).[6] B.C. Brown et al., "The Design and Manufacture of the FermilabMain Injector Dipole Magnet", Presented at the EPAC Conference,Berlin, (1992).[7] J. Ostiguy, "Magnet End Design:  The Main Injector Dipoles", InProceedings of the 1991 Particle Accelerator Conference, SanFrancisco, (1991).[8] J. Ostiguy, "Longitudinal Profile and Effective Length of aConventional Dipole Magnet",  In Proceedings of the 1993 ParticleAccelerator Conference, Washington, (1993).[9] H. D. Glass, "Techniques for Measurement of Dipole Endfields witha Rigid Integrating Coil",  In Proceedings of the 1993 ParticleAccelerator Conference, Washington, (1993).[10] D.J. Harding et al., "Design and Measurements of PrototypeFermilab Main Injector Dipole Endpacks",  In Proceedings of the 1993Particle Accelerator Conference, Washington, (1993).                                                                                             [11] D.J. Harding et al., "Experience with the Source Evaluation BoardMethod of Procuring Technical Components for the Fermilab MainInjector",  In Proceedings of the 1993 Particle Accelerator Conference,Washington, (1993).[12] A.D. Russell et al., "Selecting Magnet Laminations Recipes Usingthe Method of Simulated Annealing", In Proceedings of the 1997Particle Accelerator Conference, Vancouver, (1997).[13] H. D. Glass et al., "Flatcoil Systems for Measurements of FermilabMagnets", Presented at the Fourteenth International Conference onMagnet Technology, Tampere, Finland, (1995).[14] B.C. Brown et al., "Software Design for a Database Driven Systemfor Accelerator Magnet Systems", In Proceedings of the 1991 ParticleAccelerator Conference, San Francisco, (1991).[15] J.W. Sim et al., "A Relational Database for Magnets andMeasurement Systems at the Fermilab Magnet Test Facility",  InProceedings of the 1995 Particle Accelerator Conference, Dallas,(1995).[16] J.W. Sim et al., "Software for a Database-Controlled MeasurementSystem at the Fermilab Magnet Test Facility",  In Proceedings of the1995 Particle Accelerator Conference, Dallas, (1995).[17] D.J. Harding et al., "Magnetic Field Measurements of the InitialFermilab Main Injector Production Dipoles",  In Proceedings of the1995 Particle Accelerator Conference, Dallas, (1995).[18] B.C. Brown et al., "Results on Fermilab Main Injector DipoleMeasurements", Presented at the Fourteenth International Conferenceon Magnet Technology, Tampere, (1995).[19] J.A. Satti, "The Fermilab Main Injector Dipole and QuadrupoleCooling Design and Bus Connections", In Proceedings of the 1995Particle Accelerator Conference, Dallas, (1995)[20]  P.S. Martin et al., "Fermilab Main Injector CommissioningStatus", In Proceedings this Conference, (1999).[21] C.S. Mishra, "Simulation and Measurements of the Fermilab MainInjector Dynamic Aperture", In  Proceedings this Conference, (1999).[22] P.S. Martin et al., "Variations in the Steel Properties and theExcitation Characteristics of Fermilab Main Injector Dipoles",  InProceedings of the 1997 Particle Accelerator Conference, Vancouver,(1997).[23] P.S. Martin et al., "Modifications to the Excitation Characteristicsof Fermilab Main Injector Dipoles by Machining", Proceedings of the1997 Particle Accelerator Conference, Vancouver, (1997).[24] B.C. Brown et al., "Design for Fermilab Main Injector MagnetRamps which Account for Hysteresis", In Proceedings of the 1997Particle Accelerator Conference, Vancouver, (1997).[25] B.C. Brown et al., "Analytic Fits to Hysteretic Fields in MainInjector Dipoles, Quadrupoles and Sextupoles", In Proceedings thisConference, (1999).[26] D.G.C. Walbridge et al., "Measurements of Beam Pipe EddyCurrent Effects in Main Injector Dipole Magnets", Presented at theXVth International Conference on High Energy Accelerators,Hamburg, (1992).[27] D.G.C. Walbridge et al., "Field Errors Introduced by EddyCurrents in Fermilab Main Injector Magnets", In Proceedings of the15th International Conference on Magnet Technology, Beijing, (1997).[28] F.A. Harfoush et al., "Defining the Systematic and RandomMultipoles Errors for Main Injector Tracking," In Proceedings of the1993 Particle Accelerator Conference, Washington, (1993).[29] P.S. Martin et al., "Excitation Characteristics of Fermilab MainInjector Dipoles and Magnet Assignment to Reduce Closed OrbitErrors", In Proceedings of the 1997 Particle Accelerator Conference,Vancouver, (1997).3320Proceedings of the 1999 Particle Accelerator Conference, New York, 1999

Strength and shape of the magnetic field of the Fermilab main injector dipoles

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Strength and shape of the magnetic field of the Fermilab main injector dipoles

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