Twin aperture D2 magnets are one of the several types of dipoles to be built by BNL for the interaction regions of LHC. To minimize the number of dipole correctors required in the interaction regions, D2 will also be used as part of the steering system. Consequently, the operating fields in the two apertures may differ by up to ~10at 7 TeV operation and ~33at injection in order to compensate for the strengths of the correctors that would otherwise be required. Such asymmetric excitation of the two apertures may induce undesirable field harmonics. The saturation behavior of various harmonics is studied using POISSON and OPERA-2D. It is shown that the changes in harmonics resulting from the anticipated asymmetry are within tolerable limits. (2 refs)

Jain, A

Wanderer, P J

Willen, E

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FIELD  QUALITY  IN  THE  TWIN  APERTURE  D2  DIPOLES  FOR  LHCUNDER  ASYMMETRIC  EXCITATION*,A. Jain#, P. Wanderer and E. Willen,  BNL, Upton, NY 11973-5000AbstractTwin aperture D2 magnets are one of the several types ofdipoles to be built by BNL for the interaction regions ofLHC. To minimize the number of dipole correctorsrequired in the interaction regions, D2 will also be used aspart of the steering system. Consequently, the operatingfields in the two apertures may differ by up to ~10% at7 TeV operation and ~33% at injection in order tocompensate for the strengths of the correctors that wouldotherwise be required. Such asymmetric excitation of thetwo apertures may induce undesirable field harmonics.The saturation behavior of various harmonics is studiedusing POISSON and OPERA-2D. It is shown that thechanges in harmonics resulting from the anticipatedasymmetry are within tolerable limits.1   INTRODUCTIONAs part of the US-CERN collaboration for the LargeHadron Collider (LHC), Brookhaven National Laboratory(BNL) will build a number of superconducting insertionmagnets. There are six different styles of dipoles, all witha magnetic length of 9.45 m. Also, all dipoles will use thesame 80 mm aperture coil design that was used for theRHIC arc dipoles. In the twin aperture D2 and D4magnets, the dipole field points in the same direction inthe two apertures. This presents design challenges,particularly for the D2/D4B magnets where the separationbetween the two apertures is only 194 mm. Preliminarymagnetic designs of all the dipoles to be built by BNL canbe found in reference [1].In order to minimize the number of dipole correctorsrequired in the interaction regions, it was decided to useD2 as part of the steering system also. Consequently, theoperating fields in the two apertures may differ by up to~10% at 7 TeV operation and ~33% at injection in orderto compensate for the strengths of the correctors thatwould otherwise be required. Such asymmetric excitationof the two apertures may induce undesirable fieldharmonics. The saturation behavior of various harmonicsunder asymmetric excitation is studied in this paper.2   MAGNETIC DESIGN OF D2 DIPOLESA preliminary design [1] of D2 dipoles minimizedsaturation induced harmonics, but was based on tentativelocations and sizes of bus slots and other cut outs neededin the iron yoke. It was assumed in this optimization thatthe two apertures will be operated at the same dipole field.Subsequently, the locations of bus slots and various cutouts were changed significantly from the original designdue to engineering reasons. This required a newoptimization of the yoke for the twin aperture magnets.The current design for the D2/D4B magnets is shownschematically in Fig. 1. In particular, the saturationcontrol holes near the center of the yoke had to beenlarged to compensate for the proximity of the bus slots.Instead of rectangular holes of the original design, holeswith semicircular ends were used in order to maintainsufficient distance from the collars. This design wasobtained by minimizing current dependence of variousharmonics, calculated using POISSON. Only one fourthof the magnet was modeled to obtain maximum precision.This implied equal currents for the coils in the twoapertures.3   ASYMMETRIC EXCITATION OF D2As mentioned before, it is planned to use D2 as part of thesteering system in order to minimize the number of dipolecorrectors required in the interaction regions. Therequired correction strength is 0.55 T.m at injection and2.5 T.m at 7 TeV operation. Assuming a magnetic lengthof 9.45 m, these strengths correspond to 0.0582 T in theD2 magnet at injection and 0.265 T at 7 TeV. The lowestoperating fields for D2 (at regions IR1 and IR5) are0.176 T at injection and 2.74 T at 7 TeV. Thus, thecorrection strength amounts to ~33% of the field atinjection and ~10% of the field at 7 TeV.Since the iron in the yoke is far from saturation at thevery low fields at injection, even an asymmetry of 33%_________________________________* Work supported by the US Department of Energy under contractno. DE-AC02-98CH10886.# jain@bnl.govHELIUM  VENTBUS  SLOTSSATURATIONCONTROLHOLESFig. 1: Design of the D2 cold mass with the relocatedbus slots and other cut outs.0-7803-5573-3/99/$10.00@1999 IEEE. 3173Proceedings of the 1999 Particle Accelerator Conference, New York, 1999in the excitation of the two apertures is not expected toproduce any undesired harmonics. However, at highfields, the iron is saturated and an asymmetric powering islikely to produce a different current dependence invarious harmonics.In order to study the effect of asymmetric excitation, itis necessary to model at least one half of both theapertures, thus doubling the problem size. This made itdifficult to obtain precise results at all values of excitationwith the currently implemented problem size limits in theBNL version of POISSON. Consequently, the problemwas also analyzed using the program OPERA-2D, whichpermitted a finer mesh. Good agreement was foundbetween the results of OPERA-2D and POISSON for thecases where the POISSON solution converged.In order to obtain a conservative estimate, a currentasymmetry of 15% was studied. This is 50% over themaximum asymmetry expected at 7 TeV operation. Threecases were studied – (a) equal currents in both theapertures, (b) current in the left aperture higher than thatin the right aperture by 15% and (c) current in the leftaperture lower than that in the right aperture by 15%.Fig. 2 shows a sample output from OPERA-2D.4   RESULTSFor each of the three cases studied, the harmonics werecalculated with the center of the right aperture as theorigin. The harmonics, in “units”, are defined according tothe expansionB iB B b ia x iyRy x n n refn+ = × ++−∞−∑10 4 011( ) (1)where B0 is the strength of the dipole field, Rref is asuitable reference radius, chosen to be 17 mm [2], and xand y are the horizontal and the vertical displacementsfrom the chosen origin (center of the right aperture). Inpractice, the normal and skew coefficients, bn and an, wereobtained by a Fourier analysis of the Bθ component at aradius of 35 mm, and then scaled to 17 mm. Due to a top-bottom symmetry in the model, the skew coefficientswere zero.The low field transfer function is 0.6345 T/kA for allthe three cases. Fig. 3 shows the change in transferfunction (from the low field value) in the right aperture asa function of the dipole field in this aperture. For a givendipole field, there is a bigger drop in transfer functionwhen the other aperture is powered with a higher current,as compared to the case of a symmetric powering. A±15% asymmetry in excitation gives rise to a ±0.4%change in transfer function at ~6 kA. This implies that thecurrent required to achieve the same field in a givenaperture may vary by up to ±23 A at 3.8 T depending onthe excitation level of the other aperture.The saturation behaviors of various harmonics rangingfrom quadrupole to 14-pole are shown in Figs. 4 through9. For each harmonic, any systematic value at low fieldsis subtracted out to obtain the contribution from ironsaturation alone. As can be seen from these figures, thesaturation induced harmonics are well below 1 unit in thecase of symmetric excitation (solid lines) up to themaximum operating field of 3.83 T for these dipoles(7 TeV operation). In the case of asymmetric excitation,the lowest order quadrupole and sextupole harmonics arethe most affected. Even for these harmonics, it is seenfrom Figs. 4 and 5 that the saturation induced harmonics-2.4-2.0-1.6-1.2-0.8-0.40.00.40.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0Dipole Field in right aperture (T)Change in T.F. (%)I(L) = I(R)I(L) = 1.15 I(R)I(L) = 0.85 I(R)0.6345 T/kAFig. 3: Changes in transfer function from the low fieldvalue as a function of dipole field for variousasymmetries in excitation of the two apertures.Fig. 2: Field lines calculated using OPERA-2D at3.77 T (6kA) in the right aperture, with 15%more current in the left aperture-0.50.00.51.01.52.02.50.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0Dipole Field in right aperture (T)Change in Normal Quadrupole (units)I(L) = I(R)I(L) = 1.15 I(R)I(L) = 0.85 I(R)Fig. 4:   Saturation behavior of the quadrupole term3174Proceedings of the 1999 Particle Accelerator Conference, New York, 1999are still below 1 unit at the highest operating point. Sincethe actual asymmetry needed in operation is expected tobe less than 10%, and that too at a lower field, the smalldeterioration in the saturation behaviour should be quiteacceptable. For the higher order terms, octupole throughthe 14-pole, the changes are at the level of 0.02 unit orless. These changes also are not expected to limit theperformance of the D2 dipoles.ACKNOWLEDGEMENTSWe thank S. Kahn and B. Parker for their help with theOPERA-2D calculations.REFERENCES[1] A. Jain, et al., “Magnetic Design of Dipoles for LHC InsertionRegions", Proc. EPAC98, pp. 1993-5.[2] R. Wolf, “Field Error Naming Conventions for LHC Magnets”,CERN report LHC-MMS/ES/01-2.0-1.5-1.0-0.50.00.51.01.52.02.50.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0Dipole Field in right aperture (T)Change in Normal Sextupole (units)I(L) = I(R)I(L) = 1.15 I(R)I(L) = 0.85 I(R)Fig. 5:   Saturation behavior of the sextupole term-0.18-0.16-0.14-0.12-0.10-0.08-0.06-0.04-0.020.000.020.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0Dipole Field in right aperture (T)Change in Normal Octupole (units)I(L) = I(R)I(L) = 1.15 I(R)I(L) = 0.85 I(R)Fig. 6:   Saturation behavior of the octupole term-0.20-0.16-0.12-0.08-0.040.000.040.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0Dipole Field in right aperture (T)Change in Normal Decapole (units)I(L) = I(R)I(L) = 1.15 I(R)I(L) = 0.85 I(R)Fig. 7:   Saturation behavior of the decapole term-0.05-0.04-0.03-0.02-0.010.000.010.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0Dipole Field in right aperture (T)Change in Normal 12-pole (units)I(L) = I(R)I(L) = 1.15 I(R)I(L) = 0.85 I(R)Fig. 8:   Saturation behavior of the 12-pole term0.0000.0020.0040.0060.0080.0100.0120.0140.0160.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0Dipole Field in right aperture (T)Change in Normal 14-pole (units)I(L) = I(R)I(L) = 1.15 I(R)I(L) = 0.85 I(R)Fig. 9:   Saturation behavior of the 14-pole term3175Proceedings of the 1999 Particle Accelerator Conference, New York, 1999

Field quality in the twin aperture D2 dipoles for LHC under asymmetric excitation

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