Interaction Region Magnets. Eugenio Paoloni INFN & Università di Pisa

Transcription

1 Interaction Region Magnets Eugenio Paoloni INFN & Università di Pisa 1

2 Forewords & Talk Outline Caveat: my experience comes from SuperB (i.e. 4 GeV on 7 GeV) which is a quite different regime w.r.t. a Higgs factory (shorter magnets, ~ smaller gradients, softer and weaker synchrotron radiation, etc.)! I will present some general consideration about scaling laws worked out by L. Todesco, P.Ferracin and others.! I will present some of the peculiar features of the SuperKEKB I.R. and of the SuperB I.R. that are of main interest for a two rings collider. Eugenio Paoloni!2

3 Why I.R. Quadrupoles Are Not Easy Pieces Usually:! they are the strongest quadrupoles of the lattice! the β y ( β x )function reaches her maxima at the QD0 (QF1): the mechanical aperture is large! their field quality must be excellent to preserve dynamic aperture! their thickness is limited by the detector acceptance (single ring), nearby beam line (two rings): they are thin Eugenio Paoloni!3

4 Super Conductors Limit: B J The superconductor current density must be below the critical surface.! The highest the gradient and the larger the aperture the larger the field on the superconductor and the lower the current thicker coil pancake! e.g.: Niobium Titanium critical surface approximate expression J J c C 0 B b (1 b) (1 t 1.7 ) Temperature (K) J c Field (T) b B B c2 t T T c20 B c2 B c20 (1 t 1.7 ) NbTi Parameters B c T C0 9.2 C α 0.57 β 0.9 Τ c B c Current density (ka/mm 2 ) γ 1.9 *L. Bottura, A practical fit for the critical surface of NbTi, IEEE Transactions on Applied Superconductivity, Vol. 10, no. 1, March Eugenio Paoloni!4

5 S.C. Quadrupole Thickness Scaling Law G q j o log 1 w is ~ coil width w r (2) where r is the aperture radius and q =0.69 in the horrible but very practical units (T/m)/ (A/mm 2 ) [11]. These equations can be generalized to include the influence of the iron, but we use j 0 = 600 A/mm 2 current density j o (A/mm 2 ) HQ TQ RHIC Tevatron RHIC MQY HERA LHC MQM LHC MQXB LHC MQY SSC Nb-Ti Nb3Sn LHC MQ LHC MQXA w eq /r (-) Fig. 7: Overall current density versus coil width quadrupoles (80% of short sample at 1.9 K for Nb 3 Sn models). Operational gradient (T/m) RHIC MQ HERA Tevatron RHIC MQY HQ TQ LHC MQXB LHC MQM LHC MQY LHC MQXA LHC MQ SSC Nb-Ti Nb3Sn ln(1+w eq /r) (-) Fig. 6: Operational gradient versus coil width quadrupoles (80% of short sample at 1.9 K for Nb 3 Sn models). Eugenio Paoloni!5

6 Warm Bore: Cold To Warm Transition r is larger than the bare beam stay clear. A first order assumption can be: r = b.s.c.+ 10mm for a cold bore magnet For large forces, Andy M. wants at least a 3 mm thick support tube. Superconducting Magnets for the NLC: A Design Odyssey Brett Parker will be your guide today... If coil starts at 15 mm inner radius... For helium flow Lin says, less than 1 mm thickness does not make sense. Space for insulating vacuum and superinsulation is needed. 0.5 mm for LHe containment wall Double wall beam tube; must leave space for cooling. Eugenio Paoloni!6

7 Double Ring Extra Complication Early design of SuperB IR (Courtesy Mike Sullivan) B0H QF1 B00H QD0H QD0 QD0 B00L QF1 B0L cm QD0H B0L -2 QF1-1 QF1 B0H m M.Sullivan! Nov. 13, 2006! SB_IT_ILC_G3_300 Geant 4 simulation High luminosity e + e - collider suffers from beamstrahlung backgrounds. A QD0 shared by both beams behaves like an obnoxious spectrometer. Eugenio Paoloni!7

8 E.g.: SuperKEKB (Ohuchi-san talk NA-PAC13) LER! e + HER! e - Eugenio Paoloni!8

9 S.C. magnets in SuperKEKB IR (Ohuchi-san) Eugenio Paoloni!9

10 QC1RP main dimensions R 35.5 Collar outer radius R Collar inner radius R 25.0 Coil inner radius R 21.0 Corrector inner radius R 14.5 Beam pipe outer radius S R 18.0 Support bobbin inner radius R 10.5 Beam pipe inner radius Eugenio Paoloni!10

11 QC1RP main dimensions R 35.5 Collar outer radius R Collar inner radius R 25.0 Coil inner radius R 21.0 Corrector inner radius R 18.0 Support bobbin inner radius Operational gradient (T/m) RHIC MQ HERA Tevatron RHIC MQY HQ TQ ln(1+w eq /r) (-) Fig. 6: Operational gradient versus coil width quadrupoles (80% of short sample at 1.9 K for Nb 3 Sn models). R 14.5 Beam pipe outer radius R 10.5 Beam pipe inner radius j 0 = 600 A/mm 2 LHC MQXB LHC MQM LHC MQY Nb-Ti Nb3Sn S LHC MQXA LHC MQ SSC Eugenio Paoloni!11

12 Leaking Field Compensation 2D Simulation ( Poisson )! J z = 0 quadrupolar field B y x Cross talk B y 1/x 3! J z cos 2φ Idea: exploit the superposition principle to design the coil shape in such a way that the integrated beam kick is a linear function of the displacement from the reference orbit Eugenio Paoloni!12

13 E.g.: SuperKEKB (Ohuchi-san talk NA-PAC13) LER! e + HER! e - Eugenio Paoloni!13

14 SuperKEKB approach Canceling coils to null the terms B 3,B 4,B 5 and B 6 of the field leaking from the QC1RP: B 1 and B 2 are retained. SUPERCONDUCTING CORRECTOR IR MAGNET PRODUCTION FOR SUPERKEKB* B. Parker #, M. Anerella, J. Escallier, A. Ghosh, H. Hocker, A. Jain, A. Marone, P. Wanderer, BNL, Upton, NY 11973, USA Y. Arimoto, M. Iwasaki, N. Ohuchi, M. Tawada, K. Tsuchiya, H. Yamaoka, Z. Zong, same length wound on top of it [6]. KEK, Tsukuba, Ibaraki Japan Abstract Table 1: Corrector Integral Field Strength Requirements. Figure 3: Decomposition into magnetic multipoles for QC1P external field plotted as a function of distance to the IP, for 10 mm reference radius, at the HER beam line. Figure 6: The b5 and a5 field multipole distributions generated by the b5 cancel coil with an applied twist transformation are compared here to the target goals set for perfect QC1P external field cancellation. Eugenio Paoloni!14

15 How To Produce Such A Field? Direct winding technique + Biot Savart + F.E.M. simulation + inspiration (and lot of perspiration) BNL Direct Winding Machine at work 10/4 NA-PAC 2013 Eugenio Paoloni!15

16 SuperB Approach In SuperB we tried to reduce l* at the very minimum to ease the chromatic correction! We designed a pair of combined function magnets able at same time to null the leaking field of the nearby quad and to generate a pure quadrupolar field. By(x) generated by: the right coil, the left coil,their sum B y Right coil x Left coil Total field Eugenio Paoloni!16

17 How We Did It? Double Helix Coils MOPAS055 Proceedings of PAC07, Albuquerque, New Mexico, USA COMBINED FUNCTION MAGNETS USING DOUBLE-HELIX COILS * C. Goodzeit, R. Meinke, M. Ball, Advanced Magnet Lab, Inc., Melbourne, FL 32901, U.S.A. Figure 1. (Left) Layout of double helix winding. The axial field components of the 2 layers cancel each other and the total transverse field is enhanced. (Right) For the case of a dipole, the z coordinate of the conductor path is given by z(θ) = h θ / 2π + A sin θ with A = a / tan α where a The double helix winding concept can be readily extended to produce pure higher order multipole magnets, and as we shall show, combinations of superimposed multipole fields. This can be seen from the general expression for the conductor path of a double-helix coil given by: N hθ! " z( θ) = + A0 sinθ εnsin ( nθ φn) 2π # + ' + $ (1) % n= 2 & where the geometric variables are described in Figure 1. The variable ε is the fraction of the dipole sinusoidal Eugenio Paoloni!17

18 F IRST P ROTOTYPE OF THE S UPER B QD0 Magnetic length 510 mm, inner bore diameter 50 mm! With 60 turns/layer the quadrupole gradient is 50 T/m at 2600 A! 28 m m The stored energy is 1.1 kj (twice the QD0 one)! 1. The current density in the wire is the same of the QD0 CMS strand kindly gifted by Luvata Min. thickness Ou ter Inn er win din g win din g Typical cross section of the Quadrupole prototype E.Paoloni for the SuperB QD0 group MT-22 Marseille, Sept. 2011

19 SuperB I.R. Eugenio Paoloni!19

20 SuperB I.R. j 0 = 600 A/mm 2 Operational gradient (T/m) RHIC MQ HERA Tevatron RHIC MQY HQ TQ LHC MQXB LHC MQM LHC MQY LHC MQXA LHC MQ SSC Nb-Ti Nb3Sn ln(1+w eq /r) (-) Fig. 6: Operational gradient versus coil width quadrupoles (80% of short sample at 1.9 K for Nb 3 Sn models). Eugenio Paoloni!20

21 Second Prototype Of A Single Qd0 Completed in June 2014! We are planning to cold test it by mid Eugenio Paoloni!21

22 Answers To Some Questions Is a 300 T/m quadrupole feasible? Yes, probably, but some R/D is needed, perhaps a baseline design should consider a 200 T/m quad.! Is a 100T/m double bore quad feasible? Yes, probably, but some R/D is needed to asses the feasibility of a 7x scaled version of the SuperB QD0. Eugenio Paoloni!22

23 Conclusions B factories made very fancy super conducting quads for final focus! Very compact and strong with leaking field compensation! I.R. designer and magnet makers should interact from the early stage of the project not to waste time! The R/D time needed to realize the first SuperB QD0 prototype from the I.R. designer requests was couple of years (without the test of the cross talk compensation): plan well in advance what you do need. Eugenio Paoloni!23

24 Thank you for your attention 24