1. 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

2. 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

3. 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

4. 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

5. 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)

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

7. The cross talk compensation algorithm
More in the spare slide

8. 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

9. 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

10. 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 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

11. 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.

12. 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

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

14. 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

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

16. 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 = cm …
* Already rescaled for the Cu/SC ratio (assumed = 1)

17. 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?

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

19. 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

20. 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

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

22. 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.

23. 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, …)

24. Thanks! 24

25. Spare slides

26. The cross talk compensation algorithm

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

28. 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.

29. 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

30. 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

31. The end … now it’s true 31