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J.P. Koutchouk, L. Rossi, E. Todesco
A phase-one LHC luminosity upgrade based on Nb-Ti
J.P. Koutchouk, L. Rossi, E. TodescoMagnets, Cryostats and Superconductors Group
Accelerator Technology Department, CERN
Fermilab, 12th June 2007
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 2J.P. Koutchouk, L. Rossi, E. Todesco
CONTENTS
Goals of a phase one luminosity upgrade
A flow-chart for determining triplet parameters
Limits to long (and large) triplets
Geometric aberrations
Issues in magnet design
Most of the presented material has been published in LHC Project Report 1000 (2007)A paper with issues related to magnet design will be presented in PAC07 (F. Borgnolutti, E. Todesco)A paper about the accelerator physics issues for the phase-two upgrade will be presented in PAC07 (J.P.
Koutchouk et al)
15 m
1.9 Km
41° 49’ 55” N – 88 ° 15’ 07” W
1 Km
40° 53’ 02” N – 72 ° 52’ 32” W
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 3J.P. Koutchouk, L. Rossi, E. Todesco
GOALS OF A PHASE-ONE UPGRADE
Staging the LHC luminosity upgrade in two phasesPhase one (asap – for ultimate or recovery)
Aim: not more than ultimate luminosity (~2.5×1034 cm-2 s-1), or ways to recover nominal (~1×1034 cm-2 s-1) in case that some parameters are not met
No modification of detectors – minimal lay-out modifications (D1)
Larger aperture triplet to reduce part of the limit on intensity due to collimators(presently 40% of nominal, or β*~0.9 m instead of 0.55 m)
Larger aperture to have stronger focusing with some margin (β*~0.25 m, L~1.5×1034 cm-2 s-1 )
Fast: use Nb-Ti quadrupoles with available cable
Phase two (the ‘real’ upgrade)Aim at 10×1034 cm-2 s-1
Upgrade of detectors to tolerate it (6-12 months shut-down ?)
Use Nb3Sn to better manage energy deposition and have shorter triplet allowing reaching a 30% lower β*
Crab cavities or D0 to reduce effect of crossing angle
… all other possibilities analysed up to now in CARE-HHH and LARP
15 m
41° 49’ 55” N – 88 ° 15’ 07” W
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 4J.P. Koutchouk, L. Rossi, E. Todesco
GOALS OF A PHASE-ONE UPGRADE: METHODS AND TOOLS
Several works have been carried out since 2002 both on the optics and on the magnets
A large effort to have parametric analysis (“scaling laws”) has been done since 2004
In the spirit of the work on the dipoles carried out in LARP [S. Caspi, P.
Ferracin, S. Gourlay, in PAC05 and ASC06] , and in the 90’s by Rossi et al. in LASA
This allows having a global view on the parameter space to find the optimum – what we did:
Technological limit: gradient vs aperture in Nb-Ti and Nb3Sn quadrupoles [L. Rossi, E. Todesco, Phys. Rev. STAB 9 (2006) 102401]
Field quality: multipoles versus quadrupole aperture [B. Bellesia, J. P. Koutchouk,
E Todesco, Phys. Rev. STAB 10 (2007) 062401]
Forces: stresses versus quadrupole aperture and coil width [P. Fessia, F. Regis,
E. Todesco, ASC06, IEEE Trans. Appl. Supercond. in press]
Optics: Quadrupole aperture versus triplet length, β* , distance to IP, sc material [E. Todesco, J. P. Koutchouk, Valencia06 proceedings ]
15 m
41° 49’ 55” N – 88 ° 15’ 07” W
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 5J.P. Koutchouk, L. Rossi, E. Todesco
GOALS OF A PHASE-ONE UPGRADE
Tentative summary of previous optics lay-outs to go to β* = 0.25 m
Nb-Ti: black baseline Nb3Sn: red
15 m
1.9 Km
41° 49’ 55” N – 88 ° 15’ 07” W
40° 53’ 02” N – 72 ° 52’ 32” W
0
100
200
300
400
0 50 100 150 200 250
Magnet aperture φ (mm)
Gra
die
nt (
T/m
)
80% of Nb-Ti at 1.9 K
80% of Nb3Sn
LARP TQ
Ostojic Pac05
De Maria Arci05, EPAC06 (dipole first)
Bruning Vale06 De Maria EPAC06
Strait PAC03
Ruggiero Epac04
T. Sen, Arci05
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 6J.P. Koutchouk, L. Rossi, E. Todesco
GOALS OF A PHASE-ONE UPGRADE
We will explore the region between 100 and 150 mm, at the limit of Nb-Ti
15 m
1.9 Km
41° 49’ 55” N – 88 ° 15’ 07” W
40° 53’ 02” N – 72 ° 52’ 32” W
0
100
200
300
400
0 50 100 150 200 250
Magnet aperture φ (mm)
Gra
die
nt (
T/m
)
80% of Nb-Ti at 1.9 K
80% of Nb3Sn
LARP TQ
Ostojic Pac05
De Maria Arci05, EPAC06 (dipole first)
Bruning Vale06 De Maria EPAC06
Strait PAC03
Ruggiero Epac04
T. Sen, Arci05
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 7J.P. Koutchouk, L. Rossi, E. Todesco
GOALS OF A PHASE-ONE UPGRADE:MAIN RESULTS
The analysis of the aperture requirements for β*=0.25 m shows that
90 mm are not enough
this comes from several factors (collimation, optics, beam dynamics …)
130 mm is a reasonable choice
130 mm allow to ease the beam dynamics (lower aberrations)
One can obtain a β*=0.25 m with Nb-Ti by making a triplet 10 m longer
This involves moving the separation dipole (D1) 10 m further away from the IP
This changes the goal of 200 T/m, which was related to the triplet length
In the followings, I will outline the main motivations behind these choices
15 m
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 8J.P. Koutchouk, L. Rossi, E. Todesco
CONTENTS
Goals
A flow-chart for determining triplet parameters
Limits to long (and large) triplets
Geometric aberrations
Issues in magnet design
15 m
1.9 Km
41° 49’ 55” N – 88 ° 15’ 07” W
1 Km
40° 53’ 02” N – 72 ° 52’ 32” W
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 9J.P. Koutchouk, L. Rossi, E. Todesco
A FLOWCHART FOR TRIPLET PARAMETERS
15 m
1.9 Km
41° 49’ 55” N – 88 ° 15’ 07” W
1 Km
40° 53’ 02” N – 72 ° 52’ 32” W
46° 14’ 15” N – 6 ° 02’ 51” E
Matching condition in Q4
Equal beta max in the triplet
Limit of the technology,design choices
1. Relative lengths of Q1-3/Q2
2. Gradient vs Lt
Aperture vs Gradient 3. Possible aperture vs Lt
Triplet length Lt
Beta funct. in IP
4. Beta function in triplet
5. Required aperture vs Lt
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 10J.P. Koutchouk, L. Rossi, E. Todesco
A FLOWCHART FOR TRIPLET PARAMETERS
1 Km
40° 53’ 02” N – 72 ° 52’ 32” W
[F. Zimmermann, HB2006]
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 11J.P. Koutchouk, L. Rossi, E. Todesco
A FLOWCHART: OPTICS REQUIREMENTS
15 m
1.9 Km
41° 49’ 55” N – 88 ° 15’ 07” W
1 Km
40° 53’ 02” N – 72 ° 52’ 32” W
46° 14’ 15” N – 6 ° 02’ 51” E
Matching condition in Q4
Equal beta max in the triplet
Limit of the technology,design choices
1. Relative lengths of Q1-3/Q2
2. Gradient vs Lt
Aperture vs Gradient 3. Possible aperture vs Lt
Triplet length Lt
Beta funct. in IP
4. Beta function in triplet
5. Required aperture vs Lt
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 12J.P. Koutchouk, L. Rossi, E. Todesco
A FLOWCHART: OPTICS REQUIREMENTS
Triplet structureWe fix the distance to the IP to the 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
1.9 Km
41° 49’ 55” N – 88 ° 15’ 07” W
1 Km
40° 53’ 02” N – 72 ° 52’ 32” W
0 25 50Distance from IP (m)
Q1
Q2A Q2B
Q3l *
l 1
l 2
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 13J.P. Koutchouk, L. Rossi, E. Todesco
A FLOWCHART: OPTICS REQUIREMENTS
How to fix the relative lengths of Q1-Q3 and Q2For each total quadrupole length there is a combination of lengths that gives equal beta function in the two planes
We compute four cases,
and then we fit
[E. Todesco, J. P. Koutchouk, Valencia06]
15 m
1.9 Km
41° 49’ 55” N – 88 ° 15’ 07” W
1 Km
40° 53’ 02” N – 72 ° 52’ 32” W
5
6
7
8
9
10
20 25 30 35 40Total quadrupole length (m)
Qu
ad
rupo
le le
ngt
h (
m)
Q1-Q3
Q2
Baseline
0
2000
4000
6000
8000
10000
12000
14000
0 50 100 150 200Distance from IP (m)
β (
m)
0
0
0
0
0
0
0
Betax
Betay
Q1Q2
Q3l *
0
2000
4000
6000
8000
10000
12000
14000
0 50 100 150 200Distance from IP (m)
β (
m)
0
0
0
0
0
0
0
Betax
Betay
Q1Q2
Q3l *
Nominal triplet l1=5.50 m l2=6.37 m
Triplet l1=5.64 m l2=6.22 m
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 14J.P. Koutchouk, L. Rossi, E. Todesco
A FLOWCHART: OPTICS REQUIREMENTS
How to fix the gradientThis depends on matching conditions
We require to have in Q4 “similar” beta functions to the nominal
We find an empirical fit of the four cases 15 m
1.9 Km
41° 49’ 55” N – 88 ° 15’ 07” W
1 Km
40° 53’ 02” N – 72 ° 52’ 32” W
50
100
150
200
250
20 25 30 35 40Total quadrupole length (m)
Gra
die
nt (
T/m
)
Baseline
qq hlflG
+=
2
1
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 15J.P. Koutchouk, L. Rossi, E. Todesco
A FLOWCHART: TECHNOLOGY LIMITS
15 m
1.9 Km
41° 49’ 55” N – 88 ° 15’ 07” W
1 Km
40° 53’ 02” N – 72 ° 52’ 32” W
46° 14’ 15” N – 6 ° 02’ 51” E
Matching condition in Q4
Equal beta max in the triplet
Limit of the technology,design choices
1. Relative lengths of Q1-3/Q2
2. Gradient vs Lt
Aperture vs Gradient 3. Possible aperture vs Lt
Triplet length Lt
Beta funct. in IP
4. Beta function in triplet
5. Required aperture vs Lt
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 16J.P. Koutchouk, L. Rossi, E. Todesco
A FLOWCHART: TECHNOLOGY LIMITS
The technology imposes a relation gradient-apertureValues for some LHC quadrupoles
15 m
1.9 Km
41° 49’ 55” N – 88 ° 15’ 07” W
1 Km
40° 53’ 02” N – 72 ° 52’ 32” W
0
100
200
300
400
0 50 100 150 200 250
Magnet aperture φ (mm)
Gra
die
nt (
T/m
)
LHC MQ, operational
LHC MQX, operational
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 17J.P. Koutchouk, L. Rossi, E. Todesco
A FLOWCHART: TECHNOLOGY LIMITS
Nb-Ti lay-outs for apertures 90 to 110 mm (MQY cable)[R. Ostojic, et al, PAC05]
15 m
1.9 Km
41° 49’ 55” N – 88 ° 15’ 07” W
1 Km
40° 53’ 02” N – 72 ° 52’ 32” W
0
100
200
300
400
0 50 100 150 200 250
Magnet aperture φ (mm)
Gra
die
nt (
T/m
)
LHC MQ, operational
LHC MQX, operational
Ostojic,et al PAC05 - MQY
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 18J.P. Koutchouk, L. Rossi, E. Todesco
A FLOWCHART: TECHNOLOGY LIMITS
First scaling laws estimates date back to the 90’s[L. Rossi, et al, INFN-TC 112 (1994)]
15 m
1.9 Km
41° 49’ 55” N – 88 ° 15’ 07” W
1 Km
40° 53’ 02” N – 72 ° 52’ 32” W
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 19J.P. Koutchouk, L. Rossi, E. Todesco
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]
15 m
1.9 Km
41° 49’ 55” N – 88 ° 15’ 07” W
1 Km
40° 53’ 02” N – 72 ° 52’ 32” W
0
100
200
300
400
0 50 100 150 200 250
Magnet aperture φ (mm)
Gra
die
nt (
T/m
)
LHC MQ, operational
LHC MQX, operational
Ostojic,et al PAC05 - MQY
Rossi Todesco, Wamdo06
80% of Nb-Ti at 1.9 K
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 20J.P. Koutchouk, L. Rossi, E. Todesco
A FLOWCHART: TECHNOLOGY LIMITS
Assumption for low gradient, very long triplet [O. Bruning, R. De Maria, Valencia workshop 2006]
15 m
1.9 Km
41° 49’ 55” N – 88 ° 15’ 07” W
1 Km
40° 53’ 02” N – 72 ° 52’ 32” W
0
100
200
300
400
0 50 100 150 200 250
Magnet aperture φ (mm)
Gra
die
nt (
T/m
)
LHC MQ, operational
LHC MQX, operational
Ostojic,et al PAC05 - MQY
Rossi Todesco, Wamdo06
(Bruning, Vale06)
80% of Nb-Ti at 1.9 K
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 21J.P. Koutchouk, L. Rossi, E. Todesco
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
15 m
1.9 Km
41° 49’ 55” N – 88 ° 15’ 07” W
1 Km
40° 53’ 02” N – 72 ° 52’ 32” W
0
100
200
300
400
0 50 100 150 200 250
Magnet aperture φ (mm)
Gra
die
nt (
T/m
)
LHC MQ, operational
LHC MQX, operational
Ostojic,et al PAC05 - MQY
Rossi Todesco, Wamdo06
(Bruning, Vale06)
LHC cable, 2 layers
80% of Nb-Ti at 1.9 K
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 22J.P. Koutchouk, L. Rossi, E. Todesco
A FLOWCHART: TECHNOLOGY LIMITS
We can now have aperture vs quadrupole lengthWith two layers Nb-Ti we can build focusing triplet of 30 m, 110 mm aperture – or 34 m, 130 mm aperture
15 m
1.9 Km
41° 49’ 55” N – 88 ° 15’ 07” W
1 Km
40° 53’ 02” N – 72 ° 52’ 32” W
50
100
150
200
250
20 25 30 35 40Total quadrupole length (m)
Gra
die
nt (
T/m
)
Baseline
0
100
200
300
400
0 50 100 150 200 250
Magnet aperture φ (mm)
Gra
die
nt (
T/m
)
LHC MQ, operational
LHC MQX, operational
Ostojic,et al PAC05 - MQY
Rossi Todesco, Wamdo06
(Bruning, Vale06)
LHC cable, 2 layers
80% of Nb-Ti at 1.9 K
0.050
0.100
0.150
0.200
20 25 30 35 40 45 50Total quadrupole length (m)
Ap
ert
ure
(m
)
Baseline
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 23J.P. Koutchouk, L. Rossi, E. Todesco
A FLOWCHART: APERTURE REQUIREMENTS
15 m
1.9 Km
41° 49’ 55” N – 88 ° 15’ 07” W
1 Km
40° 53’ 02” N – 72 ° 52’ 32” W
46° 14’ 15” N – 6 ° 02’ 51” E
Matching condition in Q4
Equal beta max in the triplet
Limit of the technology,design choices
1. Relative lengths of Q1-3/Q2
2. Gradient vs Lt
Aperture vs Gradient 3. Possible aperture vs Lt
Triplet length Lt
Beta funct. in IP
4. Beta function in triplet
5. Required aperture vs Lt
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 24J.P. Koutchouk, L. Rossi, E. Todesco
A FLOWCHART: APERTURE REQUIREMENTS
Longer triplet will give larger beta functions !Larger, but not terribly larger … we find a fit as
a~77.5 m (where β* is the beta in the IP)[E. Todesco, J. P. Koutchouk, Valencia06] 15 m
1.9 Km
41° 49’ 55” N – 88 ° 15’ 07” W
1 Km
40° 53’ 02” N – 72 ° 52’ 32” W
*
2*
max ββ qall +
=
0
5000
10000
15000
20000
20 25 30 35 40Total quadrupole length (m)
Max
imu
m b
eta
fun
ctio
n (
m)
beta*=55 cm beta*=37 cm
beta*=25 cm beta*=20 cm
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 25J.P. Koutchouk, L. Rossi, E. Todesco
A FLOWCHART: APERTURE REQUIREMENTS
15 m
1.9 Km
41° 49’ 55” N – 88 ° 15’ 07” W
1 Km
40° 53’ 02” N – 72 ° 52’ 32” W
46° 14’ 15” N – 6 ° 02’ 51” E
Matching condition in Q4
Equal beta max in the triplet
Limit of the technology,design choices
1. Relative lengths of Q1-3/Q2
2. Gradient vs Lt
Aperture vs Gradient 3. Possible aperture vs Lt
Triplet length Lt
Beta funct. in IP
4. Beta function in triplet
5. Required aperture vs Lt
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 26J.P. Koutchouk, L. Rossi, E. Todesco
A FLOWCHART: APERTURE REQUIREMENTS
β*, βmax and the triplet length determine the aperture needs10 σ: the nominal
13 σ : reduces the collimator impedance, and allowing a nominal beam intensity [E. Metral, ‘07] – 16 σ gives additional clearance
Example: a 28 m triplet with 95 mm aperture would leave 6 σ for collimation at β*=0.55 m
15 m
1.9 Km
41° 49’ 55” N – 88 ° 15’ 07” W
1 Km
40° 53’ 02” N – 72 ° 52’ 32” W
β *=0.55 m
0.050
0.100
0.150
0.200
20 25 30 35 40 45 50Total quadrupole length (m)
Ape
rtur
e (
m)
Nb-Ti, 2 layers
10 sigma13 sigma
16 sigma
bbtt kN
llll*
2/3*
3*
*
2max10
)(
βφ
βφβχφφφ
++
+++=
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 27J.P. Koutchouk, L. Rossi, E. Todesco
A FLOWCHART: APERTURE REQUIREMENTS
Going at β*=0.25 m the aperture needs become largerExample: a 34 m triplet with 130 mm aperture would leave 3 σ for collimation at β*=0.25 m
Nice game … where to stop ? 15 m
1.9 Km
41° 49’ 55” N – 88 ° 15’ 07” W
1 Km
40° 53’ 02” N – 72 ° 52’ 32” W
β *=0.25 m
0.050
0.100
0.150
0.200
20 25 30 35 40 45 50Total quadrupole length (m)
Ape
rtur
e (
m)
Nb-Ti, 2 layers10 sigma13 sigma16 sigma
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 28J.P. Koutchouk, L. Rossi, E. Todesco
CONTENTS
Goals
A flow-chart for determining triplet parameters
Limits to long (and large) triplets
Geometric aberrations
Issues in magnet design
15 m
1.9 Km
41° 49’ 55” N – 88 ° 15’ 07” W
1 Km
40° 53’ 02” N – 72 ° 52’ 32” W
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 29J.P. Koutchouk, L. Rossi, E. Todesco
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 is 6 modules of warm magnets working at 1.28 T, with a marginof 18% - could be pushed away from IP of 15
is aperture enough ?
Otherwise, change D1 – in general, easy to recover space
15 m
1.9 Km
41° 49’ 55” N – 88 ° 15’ 07” W
1 Km
40° 53’ 02” N – 72 ° 52’ 32” W
0 50 100 150 200distance to the IP (m)
D1 D2
Q1 Q3
Q2 Q4
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 30J.P. Koutchouk, L. Rossi, E. Todesco
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 β*∼0.20-0.18 mlimit of 90 per IP deduced from [S. Fartoukh, LHC Project Report 308] 15 m
1.9 Km
41° 49’ 55” N – 88 ° 15’ 07” W
1 Km
40° 53’ 02” N – 72 ° 52’ 32” W
20
40
60
80
100
120
20 25 30 35 40Total quadrupole length (m)
Q'
beta*=0.55 m beta*=0.37 mbeta*=0.25 m beta*=0.20 mbeta*=0.18 m
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 31J.P. Koutchouk, L. Rossi, E. Todesco
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
1.9 Km
41° 49’ 55” N – 88 ° 15’ 07” W
1 Km
40° 53’ 02” N – 72 ° 52’ 32” W
0
50
100
150
200
0 100 200 300 400 500Critical gradient [T/m]
Str
ess
[M
Pa
]
2r=40 mm 2r=80 mm
2r=120 mm 2r=160 mm
2r=200 mm 2r=240 mm
Nb-Ti 1.9 K - 80% margin
φ φ
φ φ
φ φ
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 32J.P. Koutchouk, L. Rossi, E. Todesco
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
1.9 Km
41° 49’ 55” N – 88 ° 15’ 07” W
1 Km
40° 53’ 02” N – 72 ° 52’ 32” W
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 33J.P. Koutchouk, L. Rossi, E. Todesco
LIMITS TO LONG TRIPLETS
We propose aperture for β*=0.25 m with 3 σ for collimationThis would go up to β*∼0.18 m without collimation clearance
This would give the following parametersTotal 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 β* =0.25 m
15 m
1.9 Km1 Km
40° 53’ 02” N – 72 ° 52’ 32” W
0
100
200
300
400
0 50 100 150 200 250
Magnet aperture φ (mm)
Gra
die
nt (
T/m
)
80% of Nb-Ti at 1.9 K
80% of Nb3Sn
LARP TQ
Ostojic Pac05
De Maria Arci05, EPAC06 (dipole first)
Bruning Vale06 De Maria EPAC06
Strait PAC03
Ruggiero Epac04
This proposal
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 34J.P. Koutchouk, L. Rossi, E. Todesco
CONTENTS
Goals
A flow-chart for determining triplet parameters
Limits to long (and large) triplets
Geometric aberrations
Issues in magnet design
15 m
1.9 Km
41° 49’ 55” N – 88 ° 15’ 07” W
1 Km
40° 53’ 02” N – 72 ° 52’ 32” W
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 35J.P. Koutchouk, L. Rossi, E. Todesco
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 βmax=20000 m
The large β in the triplet is the cause of this effect – for instance first order terms in multipoles scale as
and larger beta functions are amplified by the exponent …
A crucial ingredient is the estimate of the field errors bn
∫ −∝ dsR
ssGsbT
nref
nn
n 2
2/ )()()( β2
2/max
−∝nref
nIn
nR
GbT
β
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 36J.P. Koutchouk, L. Rossi, E. Todesco
GEOMETRIC ABERRATIONS AND LARGE APERTURES
Scaling law for field errors [B. Bellesia, et al, Phys. Rev. STAB 10 (2007) 062401]
The hypothesis: field errors only due to cable positioning
Cable positioning independent of the aperture, based on LHC and RHIC data
15 m
1.9 Km
41° 49’ 55” N – 88 ° 15’ 07” W
1 Km
αn
nn
bbb =→
refrefref RRR α=→αφφφ =→
0.00
0.01
0.02
0.03
0.04
0.05
0 50 100 150 200
Aperture (mm)
d 0 (
mm
)
RHIC MQ RHIC Q1-Q3
LHC MQ LHC MQM-C-L
LHC MQY LHC MQXA
LHC MQXB
Precision in coil positioning reconstructed from measurements
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 37J.P. Koutchouk, L. Rossi, E. Todesco
GEOMETRIC ABERRATIONS AND LARGE APERTURES
Using the scaling for field errors, we evaluated the aberrations at β*=0.25 m as a function of the triplet aperture
We normalized them to the values of the baseline at β*=0.55 m
A triplet of 90 mm aperture has significantly larger aberrations
A triplet of 130 mm has only 30% more
Cross-check: solution of [R. De Maria, O. Bruning, EPAC06] would give a factor 3-7 larger aberrations
0
1
2
3
4
5
6
70 90 110 130 150 170
Magnet aperture φ (mm)
Non
line
ar
term
s w
.r.t
. no
min
al
at
β* =
0.55
m (
adi
m)
b3 b4
b5 b6
b3^2
β *=0.25 m
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 38J.P. Koutchouk, L. Rossi, E. Todesco
CONTENTS
Goals
A flow-chart for determining triplet parameters
Limits to long (and large) triplets
Geometric aberrations
Issues in magnet design
15 m
1.9 Km
41° 49’ 55” N – 88 ° 15’ 07” W
1 Km
40° 53’ 02” N – 72 ° 52’ 32” W
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 39J.P. Koutchouk, L. Rossi, E. Todesco
ISSUES IN MAGNET DESIGNMAIN FEATURES
Main parameters compared to other LHC quadrupoles
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
Margin GradingMagnet Aperture Length Coil Gradient Current Peak field (%)
(mm) (m) (mm2) (T/m) (A) (T)MQ 56 3.10 5014 223 11870 6.9 0.80 0
MQY 56 3.40 5674 160 3610 6.1 0.82 43MQXA 70 6.37 8496 215 7149 8.6 0.80 10MQXB 70 5.50 5395 215 11950 7.7 0.84 24MQXC 130 7.8/9.2 10145 121 11400 8.4 0.79 27
Operational
length n turns pole length n turns length(m) (per pole) (m) (per pole) (m)
MQXC 9.2 18 331 26 478MQXC 7.8 18 281 26 406
MB 14.3 15 429 25 715
Inner layer Outer layer0
20
40
0 20 40 60 80x (mm)
y (m
m)
RHIC large aperture quadrupole
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 40J.P. Koutchouk, L. Rossi, E. Todesco
ISSUES IN MAGNET DESIGN – FIELD QUALITY
Field quality is critical at nominal field – optimization includes iron saturation, persistent currents not an issue
Coil designed on the [24°,30°,36°] lay-out – 25 mm thick collars
Probably, a first iteration will be needed to fine tune field quality
Thick mid-plane shims have been 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
Are critical !!
0
20
40
60
0 20 40 60 80 100 120x (mm)
y (m
m)
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 41J.P. Koutchouk, L. Rossi, E. Todesco
ISSUES IN MAGNET DESIGN – PROTECTION
This MQXC is longer and larger than the previous onesInductance 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
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
Magnet Current Inductance Energy
(A) (mH) (MJ)
LHC MB 11850 99 6.93LHC MQ 11870 6 0.39
LHC MQY 3610 74 0.48
LHC MQXA 7150 90 2.30LHC MQXB 11950 19 1.36LHC MQXC 11400 76 4.93
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 42J.P. Koutchouk, L. Rossi, E. Todesco
ISSUES IN MAGNET DESIGN – FORCES
According to analytical modelLorentz 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
0
50
100
150
0 100 200 300Critical gradient [T/m]
Str
ess
[M
Pa
]
2r=70 mm
2r=130 mm
Nb-Ti 1.9 K
φ
φMQXC
MQXA-B
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 43J.P. Koutchouk, L. Rossi, E. Todesco
ISSUES IN MAGNET DESIGN – FORCES
Computations using FEM model [F. Borgnolutti, E. Todesco PAC07]
MQXC: ∼80 MPa
MQXA: ∼ 70 MPa, MQXB: ∼ 50 MPA
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 44J.P. Koutchouk, L. Rossi, E. Todesco
CONCLUSIONS
Proposed lay-out aims atβ*=0.25 m with 3 σ clearance for collimation
β*∼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 βmax =12600 m)
The lay-out is simpleOne 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)
30th March 2007 – LHC phase-one upgrade based on Nb-Ti - 45J.P. Koutchouk, L. Rossi, E. Todesco
CONCLUSIONS
Implications of phase-one upgrade on 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
Two main implicationsMoving D1 → the goal of 200 T/m disappears
200 T/m is the force needed for a 25 m triplet at 23 m from IP
The optimal aperture will be 130 mm (at least)
130 mm corresponds to the aperture of the outer layer of TQ
Stresses for these large aperture magnets can be critical
Studies are ongoing and will be presented in PAC and MT-20