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SuperB Meeting, May 2008

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

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SuperB Meeting, May 2008

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  1. Statusof 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) SuperB Meeting, May 2008

  2. Outline • 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) • Determination of the working point • Study of the configuration with the 7/4 gradients ratio • Conclusions

  3. The IP region in the SuperB QF1 IP IP QD0 • SuperB strategy to reach high luminosity (1036 cm-2s-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

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

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

  6. Option 2: twin Siamese quads • Beams very closed @ QD0 entrance (2 cm) • 60 σ ( σx ~ 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 For a single infinite wire (unitary radius and ) Integrating over the circumference for infinitesimal Dr wire E. Paoloni

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

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

  10. The ideal quadrupole

  11. The winding shape J (j) 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 j → Two counter rotating windings to cancel out the inner solenoidal field and the outer field generated by the magnet centered on the close beam. z(j) j AML-like single Perfect Quadrupole Siamese Twin Quadrupole

  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 • 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 SCAN NUMBER

  14. The winding shape: the field quality

  15. The winding shape: the field quality

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

  17. The winding shape: the conclusion • 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 * Temperature (K) Jc Field (T) Current density (A.mm-2) Tc Bc *L. Bottura, A practical fit for the critical surface of NbTi, IEEE Transactions on Applied Superconductivity, Vol. 10, no. 1, March 2000.

  20. The working point • At a FIXED current density and wire dimensions (1 mm x 1 mm): • Determine the gradient → calculate the gradient as a function of J • Determine the maximum field on the conductor → calculate the maximum field as a function of J • Impose the target gradient and determine the necessary J • Use B. to determine the maximum field in the conductor • Compare the found (Bmax,J) with the critical curve of NbTi at a fixed temperature B Target gradient = 1.66 T/cm Corresponding J = 2580 A/mm2 Corresponding field in the conductor: 2.656 T A D C

  21. The possible configuration: By = f(x)

  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 BCC → B at the intersection between the load line and the critical curve at a fixed temperature BWP → B at the working point

  23. The possible gradient at 4.2 K

  24. The 7/4 gradients ratio configuration (first try) Two different gradients for HER and LER → gradients ratio equal to HER and LER energy ratio E. Paoloni

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

  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/mm2 Bmax< 0.56T E. Paoloni

  29. The possible dimensions of the coils xENTR = 1 cm sENTR = 110 mm xEXIT = 2 cm sEXIT = 0.23 mm 60 sx for the beam → Fixed J

  30. The end

  31. Field in & out Source: infinite wire parallel to z Field point outside circle Field point inside circle For unitary radius and imposing m0/2p = 1 E. Paoloni

  32. COIL L COIL R Inside L + Outside R Inside R + Outside L D

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