1. SuperB Meeting, May 2008 Status of the magnetic design of the first quadrupole (QD0) for the SuperB interaction region S. Bettoni on behalf of the whole team (S. Bettoni, M.E. Biagini, E. Paoloni, P. Raimondi)

2.  Introduction  The SuperB interaction region  Why the siamese twins QD0 are auspicious for the SuperB IR  The conceptual design (2D) of the siamese twins QD0  How to generate a perfect multipole  Quadrupoles cross talk: how to compensate it  The 3D magnetic models  At a fixed wire properties (J, dimensions): Winding shape optimization (gradient and field quality) Winding shape optimization (gradient and field quality) Determination of the working point Determination of the working point  Study of the configuration with the 7/4 gradients ratio  Conclusions Outline

3. The IP region in the SuperB IP  SuperB strategy to reach high luminosity (10 36 cm -2 s -1 ) relies on:  Strong final focusing  Large crossing angle ( ~2 x 25 mrad )  Final doublet (QD0 + QF1)  Close to the IP to minimize chromaticity  Excellent field quality IP QD0 QF1

4. Possible options Option 1 QD0 shared among both HER and LER Option 2 Twin quadrupoles: both beams on axis QD0 IP QD0

5. Option 1: QD0 shared among HER and LER Very thick (expensive) tungsten shielding needed (~300 k€)! Tungsten shielding Courtesy Giovanni Marchiori Courtesy Mike Sullivan

6. Option 2: twin Siamese quads  Beams very closed @ QD0 entrance (2 cm)  60 σ ( σ x ~ 110 μm ) beam envelope leaves space for a very thin double quadrupole (3-4 mm allowable space)  Cross talk among the two magnets not negligible Novel QD0 design based on SC helical-type windings

7. Field in & out Source: infinite wire parallel to z Field point outside circle Field point inside circle E. Paoloni For a single infinite wire (unitary radius and ) Integrating over the circumference for infinitesimal  r wire

8. Quads cross talk compensation E. Paoloni Imposing the target functions

9. How to generate an ideal multipole *AML ideal multipolar magnet (dipole and quadrupole) To generate an ideal dipole Dipole + Solenoid Dipole - Solenoid Dipole Winding Parametrization Pure solenoidal field Current Density *

10. The ideal quadrupole Relative intensity @ x = ±5 mm B 2 /B 1 B 3 /B 1 z center 1.40E-02 -4.10E-02

11. The winding shape AML-like single Perfect Quadrupole Siamese Twin Quadrupole J (  )  z   Starting from the principle of the AML ideal multipolar magnet optimize the winding shape to produce an ideal quadrupolar field centered on each of the beams Two counter rotating windings to cancel out the inner solenoidal field and the outer field generated by the magnet centered on the close beam. →

12. How the analysis is performed For each winding the field quality at several z and the maximum field in the conductor are determined

13. The winding shape optimization SCAN NUMBER  Varied  The radius of curvature of the windings  The step of the windings  To maximize  The field quality at the beginning/end of the windings  The ratio gradient/maximum field on the conductor

14. The winding shape: the field quality

16. The winding shape: |B| MAX in the conductor

17. The winding shape: the conclusion Relative intensity @ x = ±5 mm B 2 /B 1 B 3 /B 1 |B| MAX (T) Scan 7 z centerz start -2.72E-05-1.36E-05 1.33E-051.52E-05 0.517 Scan 4 z centerz start -7.74E-05-6.28E-05 -1.09E-05-9.25E-06 0.502  Scan 7 more advantageous than scan 4:  Better field quality in the majority of the winding along the z-axis and acceptable at the end  Larger radius of curvature (better for degradation and mechanics)  Scan 4 more advantageous than scan 7:  Maximum field in the conductor slightly lower

18. The generated field

19. The NbTi critical surface parameterization *L. Bottura, A practical fit for the critical surface of NbTi, IEEE Transactions on Applied Superconductivity, Vol. 10, no. 1, March 2000. * Field (T) Temperature (K) Current density (A.mm -2 ) JcJc cc BcBc Parameters B c20 (T)14.5 T C0 (K)9.2 C 0 (AT/mm 2 )23.8  0.57  0.9  1.9

20. The working point At a FIXED current density and wire dimensions (1 mm x 1 mm): A.Determine the gradient → calculate the gradient as a function of J B.Determine the maximum field on the conductor → calculate the maximum field as a function of J C.Impose the target gradient and determine the necessary J D.Use B. to determine the maximum field in the conductor E.Compare the found (Bmax,J) with the critical curve of NbTi at a fixed temperature Target gradient = 1.66 T/cm Corresponding J = 2580 A/mm 2 Corresponding field in the conductor: 2.656 T C D A B

21. The possible configuration: By = f(x) Relative intensity @ x = ±5 mm B 2 /B 1 B 3 /B 1 |B| MAX (T) z centerz start -2.72E-05-1.36E-05 1.32E-051.52E-05 2.7

22. The working point The margin to quench has been calculated as a function of the copper over superconductor ratio (Cu/SC) for different temperatures B CC → B at the intersection between the load line and the critical curve at a fixed temperature B WP → B at the working point

23. The possible gradient at 4.2 K

24. High gradient coil Low gradient coil The 7/4 gradients ratio configuration (first try) Relative intensity @ x = ±5 mm B 2 /B 1 B 3 /B 1 z centerz start 2.92E-053.00E-05 4.68E-054.71E-04 z centerz start 1.02E-051.22E-05 -1.10E-05-7.43E-06 Two different gradients for HER and LER → gradients ratio equal to HER and LER energy ratio E. Paoloni

25. QD0: the possible scenarios HER LER HERLER Option 2 Winding shape different along z-axis Option 1 Configuration like the presented one HER Option 3 Winding shape in such a way that the magnetic axis moves along z-axis Applicable if the integrated dipole is tolerable (to be investigated) Finding the solution seems to be challenging E. Paoloni recently proposed a solution (to be checked) LER

26. Conclusions  QD0 shared by HER and LER would produce backgrounds (synchrotron radiation and off- energy leptons over-bending)  One QD0 for each ring would allow to reduce/solve the problem  Up to now:  A good field quality has been obtained both in the central part of the coil and at the end  The winding shape has been optimized to maximize the gradient and improve the field quality  For the future:  Dimensioning of the coil according to the SuperB IR requests and maximization of the gradient  A first try to produce a configuration with the gradients in ratio 7/4 is under optimization  Recently proposed a method to move the magnetic axis of the quads along z axis (work in progress)  Mechanical feasibility  Cryogenic system

27. Extra slides

28. Last presented coil (BINP Meeting-April 2008) @ j = 500 A/mm 2 B max < 0.56T E. Paoloni Relative intensity @ x = ±5 mm B 2 /B 1 B 3 /B 1 z center 4.44E-05 7.26E-05

29. The possible dimensions of the coils x ENTR = 1 cm  ENTR = 110  m x EXIT = 2 cm  EXIT = 0.23 mm  x for the beam → Fixed J

30. The end

32. Field in & out For unitary radius and imposing  0 /2  = 1 Source: infinite wire parallel to z Field point outside circle Field point inside circle E. Paoloni

33. COIL L COIL R  Inside R + Outside L Inside L + Outside R