SuperB Meeting, May 2008SuperB Meeting, May 2008

StatusStatus

of the magnetic design of the of the magnetic design of the

first quadrupole (QD0) first quadrupole (QD0)

for the Superfor the SuperBB interaction interaction

regionregionS. Bettoni on behalf of the whole teamS. Bettoni on behalf of the whole team

(S. Bettoni, M.E. Biagini, E. Paoloni, P. Raimondi)(S. Bettoni, M.E. Biagini, E. Paoloni, P. Raimondi)

IntroductionIntroduction The SuperThe SuperBB interaction region interaction region

Why the siamese twins QD0 are auspicious for the SuperWhy the siamese twins QD0 are auspicious for the SuperBB IR IR

The conceptual design (2D) of the siamese twins QD0The conceptual design (2D) of the siamese twins QD0 How to generate a perfect multipoleHow to generate a perfect multipole

Quadrupoles cross talk: how to compensate itQuadrupoles cross talk: how to compensate it

The 3D magnetic modelsThe 3D magnetic models At a fixed wire properties (J, dimensions): 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 pointDetermination of the working point

Study of the configuration with the 7/4 gradients ratioStudy of the configuration with the 7/4 gradients ratio

ConclusionsConclusions

Outline

The IP region in the SuperB

IPIP

SuperSuperBB strategy to reach high luminosity (10 strategy to reach high luminosity (103636 cm cm-2-2ss-1-1) relies on:) relies on:

Strong final focusing Strong final focusing

Large crossing angle ( ~2 x 25 mrad )Large crossing angle ( ~2 x 25 mrad )

Final doublet (QD0 + QF1)Final doublet (QD0 + QF1)

Close to the IP to minimize chromaticityClose to the IP to minimize chromaticity

Excellent field qualityExcellent field quality

IPIP

QD0QD0

QF1QF1

Possible optionsOption 1Option 1

QD0 shared among QD0 shared among

both both

HER and LERHER and LER

Option 2Option 2

Twin quadrupoles:Twin quadrupoles:

both beams on axisboth beams on axis

QD0

IPQD0

-10

-8

-6

-4

-2

0

2

4

6

8

10

-5 -4 -3 -2 -1 0 1 2 3 4 5

x (cm)

By (T

)

-10

-8

-6

-4

-2

0

2

4

6

8

10

-5 -4 -3 -2 -1 0 1 2 3 4 5

x (cm)

By (T

)

Option 1: QD0 shared among HER and LER

Very thick (expensive) tungsten shielding needed Very thick (expensive) tungsten shielding needed

(~300 k€)! (~300 k€)!

-10

-8

-6

-4

-2

0

2

4

6

8

10

-5 -4 -3 -2 -1 0 1 2 3 4 5

x (cm)By (T

)

Tungsten shieldingTungsten shielding

CourtesyCourtesyGiovanni MarchioriGiovanni Marchiori

Courtesy Mike SullivanCourtesy Mike Sullivan

Option 2: twin Siamese quads

-10

-8

-6

-4

-2

0

2

4

6

8

10

-5 -4 -3 -2 -1 0 1 2 3 4 5

x (cm)By (T

)

-10

-8

-6

-4

-2

0

2

4

6

8

10

-5 -4 -3 -2 -1 0 1 2 3 4 5

x (cm)By (T

)

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 Novel QD0 design based on SC helical-typehelical-type windingswindings

Field in & outSource: infinite Source: infinite

wire parallel to zwire parallel to z

Field point outside Field point outside circlecircle

Field point Field point inside circleinside circle

E. Paoloni

For a single infinite wire (unitary radius and )

Integrating over the circumference for infinitesimal r wire

12

0

Quads cross talk compensation

E. Paoloni

Imposing the target functions

How to generate an ideal multipole

*AML ideal multipolar magnet (dipole and quadrupole)

To generate an To generate an idealideal dipole dipoleTo generate an To generate an idealideal dipole dipole

Dipole + SolenoidDipole + Solenoid Dipole - Solenoid Dipole - Solenoid DipoleDipole

Winding ParametrizationWinding ParametrizationWinding ParametrizationWinding Parametrization

Pure solenoidal fieldPure solenoidal field

Current DensityCurrent DensityCurrent DensityCurrent Density

*

-0.01-0.005

00.005

0.01

-0.01

-0.005

0

0.005

0.010

2

4

6

8

10

12

xy

z

-0.01-0.005

00.005

0.01

-0.01

-0.005

0

0.005

0.010

2

4

6

8

10

12

xy

z

-0.01-0.005

00.005

0.01

-0.01

-0.005

0

0.005

0.010

2

4

6

8

10

12

xy

z

-5 0 5

x 10-3

-0.1

-0.05

0

0.05

0.1

x (m)

By (

T)

y = - 0.51*x3 + 0.0068*x2 + 17*x - 2.6e-005

Simulated values cubic

The ideal quadrupole

-5 0 5

x 10-3

0

0.5

1

1.5

2

2.5x 10

-7

x-xC

(m)

By-b

1.x (

T)

-5 0 5

x 10-3

0.005

0.01

0.015

0.02

0.025

0.03

x (m)

By (

T)

y = 1e+004*x3 + 1.6e+002*x2 + 1.7*x + 0.014

Simulated values cubic

Relative intensity @ x = ±5 mm

B2/B1

B3/B1

z center

1.40E-02

-4.10E-02

The winding shape

AML-like single AML-like single Perfect QuadrupolePerfect Quadrupole

Siamese TwinSiamese TwinQuadrupoleQuadrupole

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.

→

How the analysis is performedFor each winding the field quality at several z and the maximum field in the conductor are For each winding the field quality at several z and the maximum field in the conductor are

determineddetermined

The winding shape optimization

SCAN NUMBER

VariedVaried The radius of curvature of the windingsThe radius of curvature of the windings The step of the windingsThe step of the windings

To maximizeTo maximize The field quality at the beginning/end of the windingsThe field quality at the beginning/end of the windings The ratio gradient/maximum field on the conductorThe ratio gradient/maximum field on the conductor

The winding shape: the field quality

0 1 2 3 4 5 6 7 8-0.5

0

0.5

1

1.5

2

2.5

3x 10

-4

Scan #

b0(T

)

Central z

Starting z

0 1 2 3 4 5 6 7 80

5

10

15

20

25

30

35

Scan #

b1(T

/m)

Central z

Starting z

0 1 2 3 4 5 6 7 8-20

-15

-10

-5

0

5

10

Scan #

b2(T

/m2 )

Central z

Starting z

0 1 2 3 4 5 6 7 8-250

-200

-150

-100

-50

0

50

100

150

200

250

Scan #

b3(T

/m3 )

Central z

Starting z

The winding shape: the field quality

0 1 2 3 4 5 6 7 8-0.5

0

0.5

1

1.5

2

2.5

3x 10

-4

Scan #

b0(T

)

Central z

Starting z

0 1 2 3 4 5 6 7 80

5

10

15

20

25

30

35

Scan #

b1(T

/m)

Central z

Starting z

0 1 2 3 4 5 6 7 8-20

-15

-10

-5

0

5

10

Scan #

b2(T

/m2 )

Central z

Starting z

0 1 2 3 4 5 6 7 8-250

-200

-150

-100

-50

0

50

100

150

200

250

Scan #

b3(T

/m3 )

Central z

Starting z

2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8-1.6

-1.4

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

Scan #

b2(T

/m2 )

Central z

Starting z

2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8-20

0

20

40

60

80

100

120

140

Scan #

b3(T

/m3 )

Central z

Starting z

The winding shape: |B|MAX in the conductor

1 2 3 4 5 6 70.44

0.46

0.48

0.5

0.52

0.54

Scan #

|B| M

AX (

T)

The winding shape: the conclusion

Relative intensity @ x = ±5 mm

B2/B1

B3/B1

|B|MAX (T)

Scan 7

z center z start

-2.72E-05 -1.36E-05

1.33E-05 1.52E-050.517

Scan 4

z center z start

-7.74E-05 -6.28E-05

-1.09E-05 -9.25E-060.502

Scan 7 more advantageous than scan 4:Scan 7 more advantageous than scan 4: Better field quality in the majority of the winding along the z-axis and acceptable Better field quality in the majority of the winding along the z-axis and acceptable

at the endat the end

Larger radius of curvature (better for degradation and mechanics)Larger radius of curvature (better for degradation and mechanics)

Scan 4 more advantageous than scan 7:Scan 4 more advantageous than scan 7: Maximum field in the conductor slightly lowerMaximum field in the conductor slightly lower

The generated field

-0.025 -0.02 -0.015 -0.01 -0.005 0 0.005 0.01 0.015 0.02 0.025-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

x (m)

By (

T)

z centerz start

The NbTi critical surface parameterization

)1()1(0 7.1tbbB

CJ c

2cB

Bb

)1( 7.1202 tBB cc

0cT

Tt

*L. Bottura, A practical fit for the critical surface of NbTi, IEEE Transactions on Applied Superconductivity, Vol. 10, no. 1, March 2000.

*

0 2 4 6 8 105

0

5

10

15

T (K)

Bc2

(T

)

Field (T)Temperature (K)

Curr

ent d

ensi

ty (A

.mm

-2)

Jc

c

Bc

Parameters

Bc20 (T) 14.5

TC0 (K) 9.2

C0 (AT/mm2) 23.8

0.57

0.9

1.9

The working pointAt 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

0 1 103 2 10

3 3 103 4 10

3 5 103

0

2

4

6

0

2

4

6

Gradient(J)Target gradient|B|max

J (A/mm2)

Gra

d (T

/cm

)

|B|m

ax (

T)

0 1 103 2 10

3 3 103 4 10

3 5 103

0

2

4

6

0

2

4

6

Gradient(J)Target gradient|B|max

J (A/mm2)

Gra

d (T

/cm

)

|B|m

ax (

T)

Target gradient = 1.66 T/cm

Corresponding J = 2580 A/mm2

Corresponding field in the conductor: 2.656 T

C D

A

B

The possible configuration: By = f(x)

-5 -4 -3 -2 -1 0 1 2 3 4 5

x 10-3

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

x-xC

(m)

By (

T)

y = 86*x3 - 0.88*x

2 + 1.6e+002*x + 0.00078

Simulated values cubic

Relative intensity @ x = ±5 mm

B2/B1

B3/B1

|B|MAX (T)

z center z start

-2.72E-05 -1.36E-05

1.32E-05 1.52E-05

2.7

-5 0 5

x 10-3

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0x 10

-5

x-xC

(m)

By-b

1.x (

T)

The working point

100(%)arg

CC

WPCC

B

BBquenchtoinm

0 1 2 3 40

4 109

8 109

1.2 1010

1.6 1010

2 1010

Jc (T = 4.2 K)Cu/SC = 0.0Cu/SC = 0.5Cu/SC = 1.0Cu/SC = 1.5Jc (T = 1.9 K)trace 7trace 8trace 9trace 10

B (T)

Jc (

A/m

2)

0 1 2 3 40

4 109

8 109

1.2 1010

1.6 1010

2 1010

Jc (T = 4.2 K)Cu/SC = 0.0Cu/SC = 0.5Cu/SC = 1.0Cu/SC = 1.5Jc (T = 1.9 K)

B (T)

Jc (

A/m

2)

0 0.5 1 1.5 20

10

20

30

40

T = 4.2 KT = 1.9 K

Cu/SC ratio

Mar

gin

to q

uenc

h (%

)

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

The possible gradient at 4.2 K

0 0.5 1 1.5 20

20

40

60

G = 1.66 T/cmG = 1.00 T/cmG = 1.25 T/cm

T = 4.2 K

Cu/SC ratio

Mar

gin

to q

uenc

h (%

)

0 0.5 1 1.5 20

20

40

60

G = 1.66 T/cmG = 1.00 T/cmG = 1.25 T/cm

T = 4.2 K

Cu/SC ratio

Mar

gin

to q

uenc

h (%

)

High gradient coilLow gradient coil

The 7/4 gradients ratio configuration (first try)

Relative intensity @ x = ±5 mm

B2/B1

B3/B1

z center z start

2.92E-05 3.00E-05

4.68E-05 4.71E-04

z center z start

1.02E-05 1.22E-05

-1.10E-05 -7.43E-06

Two different gradients for HER and LER → gradients ratio equal to HER and LER energy ratio

-0.02 -0.015 -0.01 -0.005 0 0.005 0.01 0.015 0.02-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

x (m)

By (

T)

HER quadLER quad

-5 0 5

x 10-3

-4

-2

0

2

4

6

8x 10

-6

xxC

(m)

By-b

1.x (

T)

LER quadHER quad

E. Paoloni

QD0: the possible scenarios

HERLER

HER

LER

Option 2Option 2

Winding shape Winding shape

different along z-axisdifferent along z-axis

Option 1Option 1

Configuration like the Configuration like the

presented onepresented one

HER

Option 3Option 3

Winding shape in such Winding shape in such

a way that the a way that the

magnetic axis moves magnetic axis moves

along z-axisalong z-axis

Applicable if the Applicable if the

integrated integrated

dipole is dipole is

tolerable tolerable

(to be (to be

investigated)investigated)

Finding the Finding the

solution seems solution seems

to be to be

challengingchallenging

E. Paoloni E. Paoloni

recently recently

proposed a proposed a

solution solution

(to be checked)(to be checked)

LER

Conclusions

QD0 shared by HER and LER would produce backgrounds (synchrotron radiation and off-QD0 shared by HER and LER would produce backgrounds (synchrotron radiation and off-

energy leptons over-bending)energy leptons over-bending)

One QD0 for each ring would allow to reduce/solve the problemOne QD0 for each ring would allow to reduce/solve the problem

Up to now:Up to now: A good field quality has been obtained both in the central part of the coil and at the endA 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 qualityThe winding shape has been optimized to maximize the gradient and improve the field quality

For the future:For the future: Dimensioning of the coil according to the SuperB IR requests and maximization of the gradientDimensioning 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 optimizationA 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 Recently proposed a method to move the magnetic axis of the quads along z axis (work in

progress)progress) Mechanical feasibilityMechanical feasibility Cryogenic systemCryogenic system

Extra slides

Last presented coil (BINP Meeting-April 2008)

• @ j = 500 A/mm2 Bmax< 0.56T

E. Paoloni

Relative intensity @ x = ±5 mm

B2/B1

B3/B1

z center

4.44E-05

7.26E-05

The possible dimensions of the coils

xENTR = 1 cm

ENTR = 110 m

xEXIT = 2 cm

EXIT = 0.23 mmx for the beam→

0 0.4 1.9 3.4

-3

-2

-1

0

1

2

3

x (cm)

y (c

m)

0

5

10

15

20

25

30

35

40

45

1 1.5 2 2.5

Gra

dien

t (T/

m)

Inner radius (cm)

Simulated points

R = 1.5 cm

Fixed J

The end

Field in & out

For unitary radius and imposing 0/2 = 1

Source: infinite Source: infinite wire parallel to zwire parallel to z

Field point outside Field point outside circlecircle

Field point Field point inside circleinside circle

E. Paoloni

COIL LCOIL L COIL RCOIL R

Inside R + Outside LInside R + Outside LInside L + Outside RInside L + Outside R