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