Status of the QD0 design S. Bettoni on behalf of the whole team (S. Bettoni, M.E. Biagini, E. Paoloni, P. Raimondi, M. Sullivan) SuperB Workshop, Paris, February 2009

Outline Introduction The conceptual design (2D) of the twins QD0s The requests for the final focus quadrupoles The twin quadrupoles solution The conceptual design (2D) of the twins QD0s Perfect multipoles magnets (AML-like) Quadrupoles cross talk: the compensation algorithm The 3D magnetic models: field quality and margin to quench Basic configuration Nested quadrupoles set-up Conclusions

Possible options for the final focus quadrupoles Ideally the beam particles should pass on-axis of the FF quadrupoles Backgrounds: The dipolar component bends the low energy particles into the detector Optics: Higher order components reduce the dynamic aperture Option 1 QD0 shared among HER and LER Option 2 Twin quadrupoles: both beams on axis

The challenging constraints Maximum required gradient in the range of 1.5 T/cm Mechanical aperture of the quadrupoles in the range of 2 cm Distance between the beams in the range of 2 cm: Only few millimeters space for the conductors Cross talk between the quadrupoles LER HER

AML found a new way to build ideal multipoles/combined magnets AML magnets AML found a new way to build ideal multipoles/combined magnets SOLENOID+QUADRUPOLE -SOLENOID+QUADRUPOLE QUADRUPOLE QUADRUPOLE DIPOLE Wire wound in such a way that the angular distribution of Jz is proportional to cos(nf) http://www.magnetlab.com/

The cross talk compensation By generated by: the right coil, the left coil, their sum

The cross talk compensation algorithm More in the spare slide

The winding shape Jz (j) j Starting from the principle of the AML ideal multipolar magnet optimize the winding shape to produce an ideal quadrupolar field on each of the beam lines z(j) j AML-like single Perfect Quadrupole Compensated Quadrupole

3D finite difference models (Tosca) For each winding the field quality at several z and the maximum field in the conductor are determined BCC → B at the intersection between the load line and the critical curve at a fixed temperature BWP → B at the working point

The winding shape optimization Field quality 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 Relative intensity @ x = ±5 mm B2/B1 B3/B1 Scan 4 z center z start -7.74E-05 -6.28E-05 -1.09E-05 -9.25E-06 Scan 7 z center z start -2.72E-05 -1.36E-05 1.33E-05 1.52E-05

The NbTi critical surface parameterization * Field (T) Temperature (K) Current density (A.mm-2) Jc Tc0 Bc20 Parameters Bc20 (T) 14.5 TC0 (K) 9.2 C0 (AT/mm2) 23.8 a 0.57 b 0.9 g 1.9 *L. Bottura, A practical fit for the critical surface of NbTi, IEEE Transactions on Applied Superconductivity, Vol. 10, no. 1, March 2000.

The working point (qq configuration) At a FIXED current density and wire dimensions and properties (Cu/SC = 1): 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 NOT feasible 1.66 T/cm

The new idea: the nested quadrupoles configuration Use also an external quadrupole to produce the target gradient Q q

The advantage of the nested quadrupoles configuration Starting working point (qq) Gradient shared between the external and the internal quadrupole Bz = f(J, geometry) New working point (Q&qq) Margin to quench increased

The “but” of the nested quadrupoles configuration The advantage: margin to quench increased The price to pay: magnetic axis shifted

The nested quadrupole configuration Margin to quench at 4.2 K (%) Margin to quench at 1.9 K (%) J design* (A/mm2) B design (T) Q&qq (R = 1 cm, 1 mm wire) 35.7 48.6 1383 2.57 Q&qq (R = 1.75 cm, 1 mm wire) -23 0.98 2305 5.75 Q&qq (R = 1.75 cm, 1.5 mm wire) -1.6 18.8 1730 5.05 qq (R = 1 cm, 1 mm wire) 8.7 26.88 2580 2.656 qq (R = 1.75 cm, 1 mm wire) -74 -39 4611 5.53 qq (R = 1.75 cm, 1.5 mm wire) -32 -6 3458 4.256 G = 166 T/m Achievable gradients for the Q&qq configuration (R = 1.75 cm, 1.5 mm wire)* G (T/m) Margin to quench at 4.2 K (%) Margin to quench at 1.9 K (%) J design* (A/mm2) B design (T) 100 38.8 51.1 1041 3.04 125 23.5 38.9 1302 3.80 150 8.2 26.7 1562 4.56 *Assuming axis at x = 1.125 cm … * Already rescaled for the Cu/SC ratio (assumed = 1)

qq & Q: the optimization We have several parameters to optimize: The external quadrupole axis The external quadrupole gradient Internal and external winding of each quadrupole ratio (not used yet) Hybrid configuration?

P4 SuperB Interaction Region Layout (M. Sullivan) HER LER Gradient (T/cm) -1.191338 -0.5223842 Magnetic axis position (mm) 22.0 -20.0 Aperture (mm) 23.5 Mechanical axis position (mm) 27.5

qq vs Q&qq Q&qq configuration qq configuration GEXT = 0.622 T/cm External quad x-axis = 6 mm Internal/external contribution to the gradient not optimized yet JOverall = 1520 A/mm2 max|B| = 5.5 T qq configuration

QD0 for the P4 configuration Cold mass space = 4 mm+4 mm Used space (supports) = 2.6 mm+2.6 mm Fwire (Bare) = 1.3 mm Field quality around 10-4 (Scan not performed yet) Only internal quads on Complete configuration Gauss Gauss

QD0 for the P4 configuration: margin to quench (NbTi) Margin to quench = 20 % @ 1.9 K Typical NbTi properties and Cu/SC ratio = 1 assumed. More in spare slides.

Margin to quench ~ 30 %, BUT … QD0 for the P4 configuration: margin to quench (Nb3Sn) With this new design J is lower → we are moving away from the instability T = 4.4 K * Working point Rescaled for our design** 763 A Margin to quench ~ 30 %, BUT … T = 1.9 K Working point Rescaled for our design** 763 A *MANUFACTURE AND TEST OF A SMALL CERAMIC-INSULATED Nb3Sn SPLIT SOLENOID, B. Bordini et al., EPAC’08 Proceedings. ** Insulation not considered.

Conclusions Twins quadrupoles scheme necessary Cross-talk compensation algorithm 3D model check and optimization Excellent field quality achievable (in the simulations) Margin to quench No possible to satisfy the requests with the qq configuration with a safe margin A promising configuration has been found for the P4 layout (safe margin with NbTi at 4.2 K and more comfortable for Nb3Sn wire) For the next days, weeks, months, … Find out the “optimum” for the QD0 positions, gradients and magnetic axes shift All the more “practical” studies (mechanics, cryogenics, …)

Thanks! 24

Spare slides

The cross talk compensation algorithm

Which wire? NbTi Oxford Instruments NbTi (APC) Supercon inc. Link Link

Lower Jc than the RRP, but also more stable. Which wire? Nb3Sn? Restacked Rod Process (Internal Tin) Bronze or PIT process Link Bare= 0.8 mm Insulated = 0.93 mm 4.2 K 1.9 K * Lower Jc than the RRP, but also more stable. * MANUFACTURE AND TEST OF A SMALL CERAMIC-INSULATED Nb3Sn SPLIT SOLENOID, B. Bordini et al., EPAC’08 Proceedings.

Superconducting Magnets for Accelerators JUAS Feb 2003 Flux jumping: why it happens Unstable behaviour is shown by all type 2 and HT superconductors when subjected to a magnetic field It arises because:- magnetic field induces screening currents, flowing at critical density Jc B * change in screening currents allows flux to move into the superconductor B flux motion dissipates energy thermal diffusivity in superconductors is low, so energy dissipation causes local temperature rise DQ critical current density falls with increasing temperature Df Dq go to * One of the criterion for stability a = half width of filament Jc Martin Wilson Lecture 2 slide29 Superconducting Magnets for Accelerators JUAS Feb 2003

QD0 for the P4 configuration: margin to quench (Nb3Sn) With this new design J is lower, then we are moving away from the instability T = 4.4 K * Rescaled for our design** 1032 A T = 1.9 K Rescaled for our design** 1032 A *MANUFACTURE AND TEST OF A SMALL CERAMIC-INSULATED Nb3Sn SPLIT SOLENOID, B. Bordini et al., EPAC’08 Proceedings. ** Also the insulation considered

The end … now it’s true 31