CERN, 30th March 2007
MCS Seminar
Parametric studies for a phase-one
LHC upgrade based on Nb-Ti
J.P. Koutchouk, L. Rossi, E. Todesco
Magnets, Cryostats and Superconductors Group
Accelerator Technology Department, CERN
J.P. Koutchouk, L. Rossi, E. Todesco
CONTENTS
Goals of a phase one
A flow-chart for determining triplet parameters
15 m
Limits to long (and large) triplets
Geometric aberrations
41° 49’ 55” N – 88 ° 15’ 07” W
Issues in magnet design
40° 53’ 02” N – 72 ° 52’ 32” W
1 Km
J.P. Koutchouk, L. Rossi, E. Todesco
1.9 Km
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 2
GOALS OF A PHASE-ONE UPGRADE
Staging the LHC luminosity upgrade in two phases
Phase one (asap)
Aim: not more than ultimate luminosity (~2.51034 cm-2 s-1), or ways to recover
nominal in case that some parameters are not met
15 m
No modification of detectors – minimal lay-out modifications
Larger aperture to reduce part of the limit on intensity due to collimators
(presently 40% of nominal)
Larger aperture to have stronger focusing (*~0.25 m, L~1.51034 cm-2 s-1 )
Fast: use Nb-Ti quadrupoles with available cable
Phase two (the ‘real’ upgrade)
41° 49’ 55” N – 88 ° 15’ 07” W
Aim at 101034 cm-2 s-1
Upgrade of detectors to tolerate it (6-12 months shut-down ?)
Use Nb3Sn if available to better manage energy deposition and have shorter
triplet
Crab cavities or D0 to reduce effect of crossing angle
… all other possibilities analysed up to now in CARE-HHH and LARP
J.P. Koutchouk, L. Rossi, E. Todesco
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 3
GOALS OF A PHASE-ONE UPGRADE
Tentative summary of previous optics lay-outs to go to * = 0.25 m
Nb-Ti: black
Nb3Sn: red
Gradient (T/m)
80% of Nb-Ti
400
at 1.9 K
80% of Nb3Sn
at 1.9 K
15 m
De Maria Arci05, EPAC06 (dipole first)
LARP TQ
300
T. Sen, Arci05
Strait PAC03
200
41° 49’ 55” N – 88 ° 15’ 07” W
40° 53’ 02” N – 72 ° 52’ 32” W
Ruggiero Epac04
100
Ostojic Pac05
De Maria EPAC06
Bruning Vale06
1.9 Km
0
0
J.P. Koutchouk, L. Rossi, E. Todesco
50
100
150
Magnet aperture f (mm)
200
250
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 4
GOALS OF A PHASE-ONE UPGRADE
We will explore the region between 100 and 150 mm, at the limit of
Nb-Ti
Gradient (T/m)
80% of Nb-Ti
400
at 1.9 K
80% of Nb3Sn
at 1.9 K
15 m
De Maria Arci05, EPAC06 (dipole first)
LARP TQ
300
T. Sen, Arci05
Strait PAC03
200
41° 49’ 55” N – 88 ° 15’ 07” W
40° 53’ 02” N – 72 ° 52’ 32” W
Ruggiero Epac04
100
Ostojic Pac05
De Maria EPAC06
Bruning Vale06
1.9 Km
0
0
J.P. Koutchouk, L. Rossi, E. Todesco
50
150
Magnet aperture f (mm)
100
200
250
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 5
CONTENTS
Goals
A flow-chart for determining triplet parameters
15 m
Limits to long (and large) triplets
Geometric aberrations
41° 49’ 55” N – 88 ° 15’ 07” W
Issues in magnet design
40° 53’ 02” N – 72 ° 52’ 32” W
1 Km
J.P. Koutchouk, L. Rossi, E. Todesco
1.9 Km
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 6
A flowchart for triplet parameters
46° 14’ 15” N – 6 ° 02’ 51” E
Triplet length Lt
15 m
Equal beta max
in the triplet
Matching condition
in Q4
1. Relative lengths
of Q1-3/Q2
Beta funct.
in IP
2. Gradient vs Lt
4. Beta function in triplet
41° 49’ 55” N – 88 ° 15’ 07” W
40° 53’ 02” N – 72 ° 52’ 32” W
Limit of the technology,
design choices
1.9 Km
1 Km
Aperture vs Gradient
J.P. Koutchouk, L. Rossi, E. Todesco
3. Possible aperture
vs Lt
5. Required
aperture vs Lt
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 7
A flowchart for triplet parameters
40° 53’ 02” N – 72 ° 52’ 32” W
1 Km
[F. Zimmermann, HB2006]
J.P. Koutchouk, L. Rossi, E. Todesco
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 8
A flowchart: optics requirements
46° 14’ 15” N – 6 ° 02’ 51” E
Triplet length Lt
15 m
Equal beta max
in the triplet
Matching condition
in Q4
1. Relative lengths
of Q1-3/Q2
Beta funct.
in IP
2. Gradient vs Lt
4. Beta function in triplet
41° 49’ 55” N – 88 ° 15’ 07” W
40° 53’ 02” N – 72 ° 52’ 32” W
Limit of the technology,
design choices
1.9 Km
1 Km
Aperture vs Gradient
J.P. Koutchouk, L. Rossi, E. Todesco
3. Possible aperture
vs Lt
5. Required
aperture vs Lt
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 9
A flowchart: optics requirements
Triplet structure
We fix the distance to the IP to nominal value of 23 m
We fix the gaps between magnets to nominal values
We keep the same gradient in all magnets
Two magnet lengths as free parameters: Q1-Q3 and Q2
We explore triplet lengths from 25 m to 40 m
15 m
41° 49’ 55” N – 88 ° 15’ 07” W
l
*
40° 53’ 02” N – 72 ° 52’ 32” W
Q1
l1
0
J.P. Koutchouk, L. Rossi, E. Todesco
Q2A
1 Km
25
Distance from IP (m)
l2
Q3
Q2B
1.9 Km
50
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 10
A flowchart: optics requirements
How to fix the relative lengths of Q1-Q3 and Q2
For each total quadrupole length there is a combination of lengths
that gives equal beta function in the two planes
15 m
We compute four cases,
14000
12000
and then we fit
10000
l*
Q2
 (m)
Q1
[E. Todesco, J. P. Koutchouk, Valencia06]
Q3
Betax
8000
6000
Betay
4000
2000
Q1-Q3
0
0
Q2
9
Baseline
50
100
Distance from IP (m)
150
200
41° 49’ 55”
N – 88
° 15’ 07”
W
Nominal
triplet
l1=5.50
m l2=6.37
m
40° 53’ 02” N – 72 ° 52’ 32” W
8
14000
l*
12000
10000
7
1 Km
6
 (m)
Quadrupole length (m)
10
Q2
Q1
Q3
Betax
1.9 Km
Betay
8000
6000
4000
2000
5
0
20
25
30
35
Total quadrupole length (m)
40
0
50
100
Distance from IP (m)
150
200
Triplet l1=5.64 m l2=6.22 m
J.P. Koutchouk, L. Rossi, E. Todesco
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 11
A flowchart: optics requirements
How to fix the gradient
This depends on matching conditions
We require to have in Q4 “similar” beta functions to the nominal
15 m
We find an empirical fit of the four cases
G
1
fl q  hl q
2
Gradient (T/m)
250
200
Baseline41° 49’ 55” N – 88 ° 15’ 07” W
40° 53’ 02” N – 72 ° 52’ 32” W
150
1.9 Km
1 Km
100
50
20
J.P. Koutchouk, L. Rossi, E. Todesco
25
35
30
Total quadrupole length (m)
40
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 12
A flowchart: optics requirements
How the integrated gradient depends on the triplet length
For larger lengths, the integrated gradient becomes smaller since the
triplet baricentre is moving away from the IP
15 m
Integrated gradient (T)
5000
Baseline
4500
41° 49’ 55” N – 88 ° 15’ 07” W
40° 53’ 02” N – 72 ° 52’ 32” W
4000
1 Km
1.9 Km
3500
20
J.P. Koutchouk, L. Rossi, E. Todesco
25
30
35
Total quadrupole length (m)
40
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 13
A flowchart: technology limits
46° 14’ 15” N – 6 ° 02’ 51” E
Triplet length Lt
15 m
Equal beta max
in the triplet
Matching condition
in Q4
1. Relative lengths
of Q1-3/Q2
Beta funct.
in IP
2. Gradient vs Lt
4. Beta function in triplet
41° 49’ 55” N – 88 ° 15’ 07” W
40° 53’ 02” N – 72 ° 52’ 32” W
Limit of the technology,
design choices
1.9 Km
1 Km
Aperture vs Gradient
J.P. Koutchouk, L. Rossi, E. Todesco
3. Possible aperture
vs Lt
5. Required
aperture vs Lt
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 14
A flowchart: technology limits
The technology imposes a relation gradient-aperture
Values for some LHC quadrupoles
Gradient (T/m)
400
LHC MQ, operational
15 m
300
LHC MQX, operational
200
41° 49’ 55” N – 88 ° 15’ 07” W
40° 53’ 02” N – 72 ° 52’ 32” W
100
1.9 Km
1 Km
0
0
J.P. Koutchouk, L. Rossi, E. Todesco
50
100
150
Magnet aperture f (mm)
200
250
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 15
A flowchart: technology limits
Nb-Ti lay-outs for apertures 90 to 110 mm (MQY cable)
[R. Ostojic, et al, PAC05]
LHC MQ, operational
400
15 m
Gradient (T/m)
LHC MQX, operational
300
Ostojic,et al PAC05 - MQY
200
41° 49’ 55” N – 88 ° 15’ 07” W
40° 53’ 02” N – 72 ° 52’ 32” W
100
1.9 Km
1 Km
0
0
J.P. Koutchouk, L. Rossi, E. Todesco
50
100
150
Magnet aperture f (mm)
200
250
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 16
A flowchart: technology limits
First scaling laws estimates date back to the 90’s
[L. Rossi, et al, INFN-TC 112 (1994)]
15 m
41° 49’ 55” N – 88 ° 15’ 07” W
40° 53’ 02” N – 72 ° 52’ 32” W
1 Km
J.P. Koutchouk, L. Rossi, E. Todesco
1.9 Km
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 17
A flowchart: technology limits
A semi-analytical formula has been proposed for Nb3Sn and Nb-Ti
[L. Rossi, E. Todesco, Phys. Rev. STAB 9 (2006) 102401]
LHC MQ, operational
15 m
400
Gradient (T/m)
LHC MQX, operational
Ostojic,et al PAC05 - MQY
300
Rossi Todesco, Wamdo06
200
41° 49’ 55” N – 88 ° 15’ 07” W
40° 53’ 02” N – 72 ° 52’ 32” W
100
80% of Nb-Ti
at 1.9 K
0
0
J.P. Koutchouk, L. Rossi, E. Todesco
50
1.9 Km
1 Km
100
150
Magnet aperture f (mm)
200
250
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 18
A flowchart: technology limits
Assumption for low gradient, very long triplet
[O. Bruning, R. De Maria, Valencia workshop 2006]
LHC MQ, operational
400
15 m
LHC MQX, operational
Gradient (T/m)
Ostojic,et al PAC05 - MQY
300
Rossi Todesco, Wamdo06
(Bruning, Vale06)
200
41° 49’ 55” N – 88 ° 15’ 07” W
40° 53’ 02” N – 72 ° 52’ 32” W
100
80% of Nb-Ti
at 1.9 K
0
0
J.P. Koutchouk, L. Rossi, E. Todesco
50
1.9 Km
1 Km
100
150
Magnet aperture f (mm)
200
250
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 19
A flowchart: technology limits
We computed three lay-outs with LHC MB cable, of apertures 100,
120, 140 mm – still at the max of what can be obtained
LHC MQ, operational
400
15 m
LHC MQX, operational
Gradient (T/m)
Ostojic,et al PAC05 - MQY
Rossi Todesco, Wamdo06
300
(Bruning, Vale06)
LHC cable, 2 layers
200
41° 49’ 55” N – 88 ° 15’ 07” W
40° 53’ 02” N – 72 ° 52’ 32” W
100
80% of Nb-Ti
at 1.9 K
0
0
J.P. Koutchouk, L. Rossi, E. Todesco
50
1.9 Km
1 Km
100
150
Magnet aperture f (mm)
200
250
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 20
A flowchart: technology limits
What can be done with the LHC cable beyond 110 mm ?
Simple 3 block design
60
b6 b10 less than 1 unit at Rref=f/3
80% of critical gradient
Iron at 25 mm from outer layer
y (mm)
based on the [24°,30°,36°] coil
40
15 m
20
0
20
40° 53’ 02” N – 72 ° 52’ 32” W
40
40
20
40
60
x (mm)
80
100
120
100
120
41° 49’ 55” N – 88 ° 15’ 07” W
60
60
y (mm)
y (mm)
0
1.9 Km
20
0
0
0
20
40
J.P. Koutchouk, L. Rossi, E. Todesco
60
x (mm)
80
100
120
0
20
40
60
x (mm)
80
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 21
A flowchart: technology limits
We give the detail of what can be obtained
a bit better than previous computations since we used the cable
measurements (better than specifications of around 10%)
15 m
Analytical estimate (no iron)
one layer
two layers
Ostojic et al., MQY
Ostojic et al., MB-MQ
Gradient (T/m)
200
150
41° 49’ 55” N – 88 ° 15’ 07” W
40° 53’ 02” N – 72 ° 52’ 32” W
100
1.9 Km
1 Km
50
90
J.P. Koutchouk, L. Rossi, E. Todesco
100
110
120
130
Magnet aperture f (mm)
140
150
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 22
A flowchart: technology limits
We can now have aperture vs quadrupole length
With two layers Nb-Ti we can build focusing triplet of 30 m, 110 mm
aperture – or 34 m, 130 mm aperture
With one layer (half cable), 15% longer … but cables are there
15 m
Gradient (T/m)
250
200
200
Baseline
150
100
20
150
25
30
35
40
41° 49’ 55” NTotal
– 88 quadrupole
° 15’ 07”length
W (m)
40° 53’ 02” N – 72 ° 52’ 32” W
two layers
100
one layer
1 Km
Baseline
50
20
25
J.P. Koutchouk, L. Rossi, E. Todesco
30
35
40
Total quadrupole length (m)
Linear (one
layer)
45
50
Analytical estimate (no iron)
one layer
two layers
Ostojic et al., MQY
Ostojic et al., MB-MQ
200
Gradient (T/m)
Aperture (m)
50
1.9 Km
150
100
50
90
100
110
120
130
Magnet aperture f (mm)
140
150
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 23
A flowchart: aperture requirements
46° 14’ 15” N – 6 ° 02’ 51” E
Triplet length Lt
15 m
Equal beta max
in the triplet
Matching condition
in Q4
1. Relative lengths
of Q1-3/Q2
Beta funct.
in IP
2. Gradient vs Lt
4. Beta function in triplet
41° 49’ 55” N – 88 ° 15’ 07” W
40° 53’ 02” N – 72 ° 52’ 32” W
Limit of the technology,
design choices
1.9 Km
1 Km
Aperture vs Gradient
J.P. Koutchouk, L. Rossi, E. Todesco
3. Possible aperture
vs Lt
5. Required
aperture vs Lt
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 24
A flowchart: aperture requirements
Longer triplet will give larger beta functions !
Larger, but not terribly larger … we find a fit as
(where * is the beta in the IP)
a~77.5 m
2
 max 
Maximum beta function (m)
[E. Todesco, J. P. Koutchouk, Valencia06]
20000
beta*=55 cm
beta*=25 cm
l *  al q
*
15 m
beta*=37 cm
beta*=20 cm
15000
10000
41° 49’ 55” N – 88 ° 15’ 07” W
40° 53’ 02” N – 72 ° 52’ 32” W
5000
1 Km
1.9 Km
0
20
J.P. Koutchouk, L. Rossi, E. Todesco
25
30
35
Total quadrupole length (m)
40
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 25
A flowchart: aperture requirements
46° 14’ 15” N – 6 ° 02’ 51” E
Triplet length Lt
15 m
Equal beta max
in the triplet
Matching condition
in Q4
1. Relative lengths
of Q1-3/Q2
Beta funct.
in IP
2. Gradient vs Lt
4. Beta function in triplet
41° 49’ 55” N – 88 ° 15’ 07” W
40° 53’ 02” N – 72 ° 52’ 32” W
Limit of the technology,
design choices
1.9 Km
1 Km
Aperture vs Gradient
J.P. Koutchouk, L. Rossi, E. Todesco
3. Possible aperture
vs Lt
5. Required
aperture vs Lt
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 26
A flowchart: aperture requirements
*, max and the triplet length determine the aperture needs
l *  lt
(l *  l t ) 3 / 2
N k
10 : the nominal


13  : reduces the collimator impedance, and allowing a nominal
15 m
beam intensity [E. Metral, ‘07] – 16  gives additional clearance
Example: a 28 m triplet with 95 mm aperture would leave 6  for
collimation at *=0.55 m
f  f 0  f1  max  f 2
*
 f3
b
*
b
 *=0.55 m
Aperture (m)
0.200
40° 53’ 02” N – 72 ° 52’ 32” W
0.150
Nb-Ti, 2 layers
41° 49’ 55”10
N –sigma
88 ° 15’ 07” W
13 sigma
16 sigma
1 Km
0.100
1.9 Km
0.050
20
J.P. Koutchouk, L. Rossi, E. Todesco
25
30
35
40
Total quadrupole length (m)
45
50
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 27
A flowchart: aperture requirements
Going at *=0.25 m the aperture needs become larger
Example: a 34 m triplet with 130 mm aperture would leave 3  for
collimation at *=0.25 m
15 m
Nice game … where to stop ?
 *=0.25 m
Aperture (m)
0.200
0.150
41° 49’ 55” N – 88 ° 15’ 07” W
40° 53’ 02” N – 72 ° 52’ 32” W
0.100
1 Km
Nb-Ti, 2 layers
10 sigma
13 sigma
16 sigma
1.9 Km
0.050
20
J.P. Koutchouk, L. Rossi, E. Todesco
25
30
35
40
Total quadrupole length (m)
45
50
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 28
CONTENTS
Goals
A flow-chart for determining triplet parameters
15 m
Limits to long (and large) triplets
Geometric aberrations
41° 49’ 55” N – 88 ° 15’ 07” W
Issues in magnet design
40° 53’ 02” N – 72 ° 52’ 32” W
1 Km
J.P. Koutchouk, L. Rossi, E. Todesco
1.9 Km
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 29
Limits to long triplets
Limits to long triplets: space ?
Present kicks in D1, D2  26 Tm
Separation dipole D2 is 9.45 m with 3.8 T – can go up to 36 Tm
D1 has a margin of 18% - could be pushed 15 m, if aperture is15 m
enough
Otherwise, change D1 – in general, easy to recover space
Q1
Q3
41° 49’ 55” N – 88 ° 15’ 07” W
40° 53’ 02” N – 72 ° 52’ 32” W
1.9 Km
1 Km
D1
D2
Q2
0
J.P. Koutchouk, L. Rossi, E. Todesco
Q4
50
100
distance to the IP (m)
150
200
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 30
Limits to long triplets
Limits to long triplets: chromaticity ?
Hypothesis: two IP strong focusing, one IP at 1 m, the other at 0.5 m
The linear correction is saturated for *0.20-0.18 m
15 m
limit of 90 per IP deduced from [S. Fartoukh, LHC Project Report 308]
beta*=0.55 m
beta*=0.25 m
beta*=0.18 m
120
Q'
100
beta*=0.37 m
beta*=0.20 m
80
41° 49’ 55” N – 88 ° 15’ 07” W
40° 53’ 02” N – 72 ° 52’ 32” W
60
40
1.9 Km
1 Km
20
20
J.P. Koutchouk, L. Rossi, E. Todesco
25
30
35
Total quadrupole length (m)
40
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 31
Limits to long triplets
Limits to long triplets: forces ?
Lorentz forces at operational field induce large stresses
Semi-analytical law [P. Fessia, F. Regis, E. Todesco, ASC 2006] gives values smaller
than 150 MPa for apertures up to 250 mm – should not be a problem
Nb-Ti 1.9 K - 80% margin
Stress [MPa]
200
150
100
mm
2r=40
f
mm
2r=80
f
mm
2r=120
f
mm
2r=160
f
mm
2r=200
f
41° 49’ 55” N – 88 ° 15’ 07” W
mm
2r=240
f
40° 53’ 02” N – 72 ° 52’ 32” W
50
1.9 Km
1 Km
0
0
J.P. Koutchouk, L. Rossi, E. Todesco
100
300
200
Critical gradient [T/m]
400
500
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 32
Limits to long triplets
Limits to long triplets: energy deposition ?
Larger and longer triplet could have a much higher energy
deposition, for the same luminosity
Preliminary comparison of the baseline with a 10 m longer and twice
larger triplet has been done [C. Hoa, F. Broggi, 2007]
The larger and longer triplet has a smaller (~-30%) impinging power in
W/m (energy per meter of triplet)
Longer triplets will not give additional energy deposition
Study on scaling laws for energy deposition is ongoing
41° 49’ 55” N – 88 ° 15’ 07” W
40° 53’ 02” N – 72 ° 52’ 32” W
1 Km
J.P. Koutchouk, L. Rossi, E. Todesco
1.9 Km
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 33
Limits to long triplets
We propose aperture for *=0.25 m with 3  for collimation
This would go up to *0.18 m without collimation clearance
This would give the following parameters
15 m
Total quadrupole length 34 m (+10 m w.r.t. baseline)
Triplet length (with gaps) 40.5 m
Operational gradient 122 T/m (20% safety factor on short sample)
Beta function in the triplet of 12600 m at * =0.25 m
Gradient (T/m)
80% of Nb-Ti
400
at 1.9 K
80% of Nb3Sn
at 1.9 K
DeNMaria
Arci05,
(dipole first)
40° 53’ 02”
– 72 °
52’ 32”EPAC06
W
300
LARP TQ
Strait PAC03
200
1 Km
1.9 Km
This proposal
Ruggiero Epac04
100
Ostojic Pac05
De Maria EPAC06
Bruning Vale06
0
0
J.P. Koutchouk, L. Rossi, E. Todesco
50
100
150
Magnet aperture f (mm)
200
250
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 34
CONTENTS
Goals
A flow-chart for determining triplet parameters
15 m
Limits to long (and large) triplets
Geometric aberrations
41° 49’ 55” N – 88 ° 15’ 07” W
Issues in magnet design
40° 53’ 02” N – 72 ° 52’ 32” W
1 Km
J.P. Koutchouk, L. Rossi, E. Todesco
1.9 Km
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 35
Geometric aberrations and large
apertures
In it has been observed that large beta functions in the
triplet may lead to insufficient dynamic aperture
[R. De Maria, O. Bruning, EPAC06]
Estimates based on tracking showed that there was a very strong
reduction for an extreme case with max=20000 m
The large  in the triplet is the cause of this effect – for instance first
order terms in multipoles scale as
Tn  
bn ( s)G( s)  n / 2 ( s)
R
n2
ref
ds
n/2
bn G I  max
Tn 
n2
Rref
and larger beta functions are amplified by the exponent …
A crucial ingredient is the estimate of the field errors bn
J.P. Koutchouk, L. Rossi, E. Todesco
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 36
Geometric aberrations and large
apertures
Scaling law for field errors [B. Bellesia, et al, submitted to Phys. Rev. STAB]
f  f  f
bn
bn  bn 
Rref  Rref  Rref

15 m
The hypothesis: field errors only due to cable positioning
Cable positioning independent of the aperture, based on LHC and
RHIC data
RHIC MQ
LHC MQ
LHC MQY
LHC MQXB
0.05
d0 (mm)
0.04
RHIC Q1-Q3
LHC MQM-C-L
LHC MQXA
41° 49’ 55” N – 88 ° 15’ 07” W
0.03
0.02
1.9 Km
1 Km
0.01
0.00
0
50
100
150
200
Aperture (mm)
Precision in coil positioning reconstructed from measurements
J.P. Koutchouk, L. Rossi, E. Todesco
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 37
Geometric aberrations and large
apertures
 *=0.25 m
6
*
 =0.55 m (adim)
Nonlinear terms w.r.t. nominal at
Using the scaling for field errors, we evaluated the aberrations at
*=0.25 m as a function of the triplet aperture
We normalized them to the values of the baseline at *=0.55 m
A triplet of 90 mm aperture has significantly larger aberrations
A triplet of 130 mm has only 30% more
5
4
b3
b4
b5
b6
b3^2
3
2
1
0
70
90
110
130
Magnet aperture f (mm)
150
170
Cross-check: solution of [R. De Maria, O. Bruning, EPAC06] would give a factor 3-7
larger aberrations
J.P. Koutchouk, L. Rossi, E. Todesco
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 38
CONTENTS
Goals
A flow-chart for determining triplet parameters
15 m
Limits to long (and large) triplets
Geometric aberrations
41° 49’ 55” N – 88 ° 15’ 07” W
Issues in magnet design
40° 53’ 02” N – 72 ° 52’ 32” W
1 Km
J.P. Koutchouk, L. Rossi, E. Todesco
1.9 Km
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 39
ISSUES IN MAGNET DESIGN – main features
Main parameters compared to other LHC quadrupoles
Magnet Aperture Length
Coil
(mm)
56
56
70
70
130
(mm2)
5014
5674
8496
5395
10145
MQ
MQY
MQXA
MQXB
MQXC
(m)
3.10
3.40
6.37
5.50
7.8/9.2
Operational
Margin
Gradient Current Peak field
(T/m)
223
160
215
215
121
(A)
11870
3610
7149
11950
11400
(T)
6.9
6.1
8.6
7.7
8.4
Grading
(%)
0.80
0.82
0.80
0.84
0.79
0
43
10
24
27
Large aperture ? RHIC MQX: 130 mm aperture, 50 T/m at 4.2 K, 12
mm width coil
Cable needed to wind
one dipole unit length is enough
y (mm)
40
20
0
MQXC
MQXC
MB
length
(m)
9.2
7.8
14.3
Inner layer
n turns
pole length
(per pole)
(m)
18
331
18
281
15
429
J.P. Koutchouk, L. Rossi, E. Todesco
Outer layer
n turns
length
(per pole)
(m)
26
478
26
406
25
715
0
20
40
x (mm)
60
80
RHIC large aperture quadrupole
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 40
ISSUES IN MAGNET DESIGN – field quality
Field quality is critical at nominal field – optimization should
include iron saturation, persistent currents not an issue
Coil designed on the [24°,30°,36°] lay-out – 25 mm thick collars
A first iteration will be needed to fine tune field quality
Mid-plane shims should be included from the beginning, so that can be
varied in both directions
At least three identical models should be built to assess the random
components
60
y (mm)
Are critical !!
40
20
0
0
J.P. Koutchouk, L. Rossi, E. Todesco
20
40
60
x (mm)
80
100
120
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 41
ISSUES IN MAGNET DESIGN – PROTECTION
This MQXC is longer and larger than the previous ones
Inductance similar to MQY, MB, MQXA
Operating current similar to MB, MQ, MQXB
Stored energy is 5 MJ: twice MQXA – 50% larger than one aperture
of an MB
Magnet
Current
Inductance
Energy
(A)
(mH)
(MJ)
LHC MB
LHC MQ
LHC MQY
11850
11870
3610
99
6
74
6.93
0.39
0.48
LHC MQXA
LHC MQXB
LHC MQXC
7150
11950
11400
90
19
76
2.30
1.36
4.93
Preliminary hot spot temperature evaluations show that the order of
magnitudes are similar to the MB
Time for firing quench heaters to avoid hot spot larger than 300 K must
be not larger than 0.1 s [M. Sorbi, Qlasa code] challenging, but feasible
J.P. Koutchouk, L. Rossi, E. Todesco
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 42
ISSUES IN MAGNET DESIGN – FORCES
According to analytical model
Lorentz forces induce a stress in the coil of 70 MPa, i.e. 40% more
than for the MQXA-B (50 MPa)
Does not look so critical, but mechanical structure should be
carefully designed
Nb-Ti 1.9 K
Stress [MPa]
150
2r=70
mm
f
100
2r=130
mm
f
MQXC
MQXA-B
50
0
0
J.P. Koutchouk, L. Rossi, E. Todesco
100
200
Critical gradient [T/m]
300
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 43
ISSUES IN MAGNET DESIGN – FORCES
Computations using FEM model [F. Borgnolutti]
MQXC: 80 MPa
MQXA:  70 MPa, MQXB:  50 MPA
J.P. Koutchouk, L. Rossi, E. Todesco
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 44
Other options
Shorter Q1 ?
The beta function in Q1 is half of max  one can have at most 30%
smaller aperture  30% shorter Q1  7% shorter triplet
The gain in length is marginal, but one has two different designs (lengths,
apertures, and cross-sections) – not a good bargain in my opinion
Same lengths for Q1-3 and Q2 ?
One can make an optics with same lengths – triplet must be 4 m longer, but
different gradients (up to 20%) – is it worth ?
4-plet ?
In absence of technology
constraints, it would be better
3-plet is more efficient
J.P. Koutchouk, L. Rossi, E. Todesco
l*
12000
10000
 (m)
A 4-plet allows 20% smaller max
But the gradient is 30% more
14000
betax
betay
8000
6000
4000
2000
0
0
50
100
Distance from IP (m)
150
200
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 45
CONCLUSIONS
Proposed lay-out aims at
*=0.25 m with 3  clearance for collimation
*0.18-0.20 m without clearance, reaching the linear chromaticity correction
limit
The clearance should allow keeping geometric aberrations under control
(we have a max =12600 m)
The lay-out is simple
One aperture: 130 mm
One gradient: 122 T/m
One power supply – operational current 11400 A
One cross-section: two layers with LHC MB cable
Two lengths: 7.8, 9.2 m – moderate increase of triplet length w.r.t. baseline
(+30%, i.e. from 30 to 40 m)
J.P. Koutchouk, L. Rossi, E. Todesco
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 46
CONCLUSIONS
Some issues to address
Having a matched solution, looking at Q4-Q11 strengths
Tracking to verify the scaling on aberrations
D1 displacement and/or upgrade
Design a simple and reliable a mechanical structure (vertical or horizontal
assembly) making use of existing tooling
Tolerances very important since we aim at very good field quality
Phase-one upgrade vs. LARP and Nb3Sn r&d
Phase two upgrade (the ‘real’ one) goals and schedule are not changed
Nb3Sn r&d should be pursued with all efforts
The proof of a long prototype is fundamental
If we had available Nb3Sn magnets today, we would use them
Moving D1  the goal of 200 T/m becomes less stringent
HQ should aim at apertures much larger than 90 mm
J.P. Koutchouk, L. Rossi, E. Todesco
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 47