CERN, 7th October 2015
Italian teachers program
LHC: PRESENT STATUS
AND FUTURE PROJECTS
E. Todesco
HL-LHC IR magnets WP leader
Magnet, Superconductors and Cryostats Group
Technology Department
CERN, Geneva, Switzerland
E. Todesco
CONTENTS
The present: LHC in the 10’s
LHC energy
The race towards luminosity
Unknowns and suprises
The 20’s: the HL-LHC project
Beam optics and beam intensity
The 30’s: FCC studies
Aiming at 100 TeV centre of mass
A digression on power expansions
E. Todesco
LHC in the 10’s - 2
LHC IN the 10’s:
ENERGY
In run I, LHC energy has been 3.5 TeV and 4 TeV
Unforeseen limitation, due to weakness in the interconnections
This caused the 2008 incident
In 2008 one sector was pushed to 6.6 TeV showing a training longer
than expected – only in 3000 series magnets
Major consolidation in LS1
Shunt being added to cure interconnection the problem [J. P. Tock, F. Bordry,
et al., EUCAS conference, to be published on IEEE Trans. Appl. Supercond.]
12
7 TeV
Current (kA)
11
6.5 TeV
Firm2 HC
10
Firm3 HC
9
8
0
Cross-section of the intreconnection and
radiography showing missing continuity
[F. Bordry, J. P. Tock and LS1 team]
E. Todesco
20
40
Quench number
60
80
The training of sector 56
[HC and MP3 team]
LHC in the 10’s - 3
LHC IN the 10’s:
ENERGY
2014: decision to train LHC at 6.5 TeV
Compromise between time, risk and energy for physics reach
1-2 week to train one sector, in the shadow of hardware commissioning
Expected 100 quenches, we went to 6.5 TeV with 174 quenches
A bit worse then expected, but we got there
First data about the whole LHC
3000 series confirmed to be weaker (~1/3 of the magnets quenched)
First data about the whole LHC: magnet production not uniform
Effort sto understand what happened are ongoing
sector
12
23
34
45
56
67
78
81
LHC
E. Todesco
quenches per sector 2015
1000
2000
3000
2
1
4
0
2
15
1
7
7
0
3
46
0
0
17
0
1
19
2
10
9
0
3
25
5
27
142
total
7
17
15
49
17
20
21
28
174
sector
12
23
34
45
56
67
78
81
LHC
quenches per magnet 2015
1000
2000
3000
0.04
0.01
0.44
0.00
0.03
0.38
0.02
0.09
0.24
0.00
0.07
0.74
0.00
0.00
0.20
0.00
0.03
0.31
0.04
0.25
0.15
0.00
0.13
0.38
0.01
0.06
0.34
The training to 6.5 TeV [HC and MP3 team, A. Verweij, S. Le Naour et al.]
total
0.14
LHC in the 10’s - 4
LHC IN the 10’s:
ENERGY
Possibilities of further increasing to 7 TeV?
LHC designed to reach 7 TeV, all LHC magnets reached >7 TeV on
the test bench during the production
But loss of memory in 3000 series
At the moment, without any sector pushed to 7 TeV, one has to rely on
extrapolation of unknown phenomena, so hard to say how long it takes
If physics requires, energies higher than 6.5 TeV could be reached
More info before LS2
Understanding of this limit is important for future projects
LHC magnets at 7 TeV work at 86% of short sample limit
At 6.5 TeV we are at 80%, usually considered as a good margin
The first Nb3Sn triplet (for HL-LHC) will work at 75%
LHC operating at 7 TeV  one could design FCC with lower margin
i.e. the 16 T magnet need a short sample of 18-19 T and not 20 T (and
these additional tesla(s) of margin is very expensive)
E. Todesco
LHC in the 10’s - 5
CONTENTS
The present: LHC in the 10’s
LHC Energy
The race towards luminosity
The 20’s: the HL-LHC project
Optics and intensity
The 30’s: FCC studies
Aiming at 100 TeV centre of mass
E. Todesco
LHC in the 10’s - 6
LHC IN the 10’s:
THE RACE TOWARDS LUMINOSITY
Equation for the luminosity
N b2 nb f rev
c  2
1
L
F

N
n
F
b b
4en b *
4 l
enb *
Accelerator features
Energy of the machine 7 TeV
Length of the machine 27 km
Beam intensity features
Nb Number of particles per bunch 1.151011
nb Number of bunches ~2808
Beam geometry features
Nominal luminosity: 1034 cm-2 s-1
(considered very challenging in the 90’s,
pushed up to compete with SSC)
E. Todesco
en Size of the beam from injectors: 3.75 mm mrad
b* Squeeze of the beam in IP (LHC optics): 55 cm
F: geometry reduction factor: 0.84
LHC in the 10’s - 7
LHC IN the 10’s:
THE RACE TOWARDS LUMINOSITY
Equation for the luminosity
N b2 nb f rev
c  2
1
L
F

N
n
F
b b
4en b *
4 l
enb *
We will outline some of the luminosity limits
Beam beam (limit on Nb/en)
Electron cloud (limit on nb)
Squeeze (limit on b* en)
Injectors (limit on Nb, nb, en)
E. Todesco
LHC in the 10’s - 8
LHC IN THE 10’S:
THE RACE TOWARDS LUMINOSITY
The beam-beam limit (Coulomb)
  nIP
N b2 nb f rev 
Nb
f rev
L
F

N
n
F
b b
en
4e n b *
4b *
rp N b
 0.01?
4 e n
Nb Number of particles per bunch
en transverse size of beam
One cannot put too many particles in a “small space” (brightness)
Otherwise the Coulomb interaction seen by a single particle when
collides against the other bunch creates instabilities (tune-shift)
This is an empirical limit, also related to nonlinearities in the lattice
Very low nonlinearities  larger limits
LHC behaves better than expected – boost to 50 ns operation in RunI
E. Todesco
Nb
en
(adim)
(m rad)
Nominal
1.15E+11
3.75E-06
Ultimate September 2012 2012 MD*
1.70E+11
1.55E+11
2.20E+11
3.75E-06
2.50E-06
1.70E-06
 IP
(adim)
0.0034
0.0050
0.0068
0.0142
NIP
(adim)
2
2
2
2

(adim)
0.007
0.010
0.014
0.028
* No long range interactions, W. Herr et al, CERN-ATS-Note-2011-029-MD
LHC in the 10’s - 9
LHC IN THE 10’S:
THE RACE TOWARDS LUMINOSITY
The electron cloud
L
N b2 nb f rev 
4e n b *
c 1 2
1
F
 N b nb
F
4 L
enb *
Mechanism of electron cloud formation [F. Ruggiero]
This is related to the extraction of electrons in the vacuum chamber
from the beam
A critical parameter is the spacing of the bunches: smaller spacing
larger electron cloud – threshold effect
So this effect pushes for 50 ns w.r.t. 25 ns
Spacing (length)  spacing (time)  number of bunches nb
7.5 m

25 ns
 3560 free bunches (2808 used)
E. Todesco
LHC in the 10’s - 10
LHC IN THE 10’S:
THE RACE TOWARDS LUMINOSITY
Electron cloud has been observed where expected in RunI
during 50 ns ramp up
Was cured by scrubbing of surface with intense beam
In runI we operated in a reliable way with 1300 bunches at 50 ns
RunII has 25 ns as baseline
After initial run at 50 ns, scrubbing has just finished and ramp up of
bunch number is going on
At the moment we are at 458 bunches, we have to reach 2800
Scrubbing run effective, but many instabilities -50 ns looks much easier
Reduction of beam losses during the scrubbing run
[G. Rumolo, et al., LMC August 2015]
E. Todesco
LHC in the 10’s - 11
LHC IN THE 10’S:
THE RACE TOWARDS LUMINOSITY
Optics: squeezing the beam
L
N b2 nb f rev 
4e n b *
Size of the beam in a magnetic lattice
Luminosity is inverse prop to e and b*
F
c 1 2
1
 N b nb
F
*
4 L
enb
x( s ) 
eb ( s)
r
In the free path (no accelerator magnets) around the
experiment, the b* has a
6000
Q2
l*
5000
nasty dependence
Q1
Q3
4000
with s distance to IP
3000
b (m)
Betax
Betay
2000
b (s)  b * 
s2
b
*

s2
b
*
1000
0
0
50
100
Distance from IP (m)
150
200
The limit to the squeeze is the magnet aperture
Key word for magnets in HL LHC: not stronger but larger
E. Todesco
LHC in the 10’s - 12
LHC IN THE 10’S:
THE RACE TOWARDS LUMINOSITY
Optics: squeezing the beam
L
N b2 nb f rev 
4e n b *
Size of the beam in a magnetic lattice
c 1 2
1
F
 N b nb
F
4 L
enb *
x( s ) 
eb ( s)
r
LHC was designed to reach b* = 50 cm with 70 mm
aperture IR quads
This aperture had no margin - when beam screen was added, one
had to lower the target b* = 55 cm (and recover L=1034 cm-2 s-1 by slightly
increasing bunch intensity from 1011 to 1.15  1011)
In RunI, less energy  larger beam  higher b*
But lower emittance, so at the end we manage to run at 60 cm
In RunII, we started at 80 cm
E
en
40 cm reachable, debate if going now to 60 cm
E. Todesco
Nominal
2012 Gain b*
(TeV)
7.0
4.0
0.57
(m rad) 3.75E-06 2.50E-06 1.50
0.86
LHC in the 10’s - 13
LHC IN THE 10’S:
THE RACE TOWARDS LUMINOSITY
The injector chain limits
N b2 nb f rev 
4.0
4.0
c 1 2
1
L
F
 N b nb
F
Emittance en vs intensity Nb
4 L
4e n b *
enb *
This relation also depends on the bunch spacing nb
SPS 450 GeV 25 ns
3.5
3.5
3.0
3.0
0.5
0.0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Bunch Intensity [e11]
3.5
4.0
2.5
HL-LHC
2.0
1.5
1.0
0.5
PS RF power
Longitudinal insabilities
1.0
SPS Longitudinal insabilities
1.5
SPS TMCI limit
2.0
Emittance (x+y)/2 [um]
HL-LHC
2.5
nominal
SPS RF power
Longitudinal insabilities
2012
PS Longitudinal insabilities
Emittance (x+y)/2 [um]
SPS 450 GeV 50 ns
0.0
4.5
5.0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Bunch Intensity [e11]
Limits imposed by the injectors to the LHC beam [R. Garoby, IPAC 2012]
50 ns allow larger intensities and smaller emittances
Pushing up these limits is the aim of the injector upgrade
E. Todesco
LHC in the 10’s - 14
LHC IN THE 10’S:
THE RACE TOWARDS LUMINOSITY
In RunI, we reached at 4 TeV 70% of nominal luminosity at 50 ns
operation
Nb
en
nb
b*
E
F
L
protons per bunch (adim)
emittance
(m)
number of bunches (adim)
beta*
bunch spacing
Energy
Geometric factor
2012 sept
50 ns: 2015 june
25 ns: 2015 aug 24
Nominal
w.r.t. nom
w.r.t. nom
w.r.t. nom
1.15E+11 1.55E+11
1.82
1.30E+11
1.28
1.10E+11
0.91
3.75E-06 2.50E-06
1.50
2.50E-06
1.50
3.50E-06
1.07
2808
1380
0.49
476
0.17
458
0.16
(m)
0.55
0.6
(ns)
25
50
(TeV)
7.0
4
(adim)
0.86
-2 -1
Peak luminosity (cm s ) 1.00E+34 7.0E+33
pile up
26
37
0.92
0.57
0.70
0.8
50
6.5
0.69
2.1E+33
32
0.21
0.93
0.8
25
6.5
0.69
1.0E+33
16
0.10
0.93
In 2015, we reached at 6.5 TeV 20% of nominal luminosity at 50 ns
operation
We did not push more the number of bunches to go for 25 ns operation
Today (August 25, 2015) we are in the middle of the ramp up of
number of bunches at 25 ns operation, 10% of nominal reached
For the moment, no bottlenecks in magnet operation due to 6.5 TeV
E. Todesco
LHC in the 10’s - 15
CONTENTS
The present: LHC in the 10’s
LHC Energy
The race towards luminosity
The 20’s: the HL-LHC project
Optics and intensity
The 30’s: FCC studies
Aiming at 100 TeV centre of mass
E. Todesco
LHC in the 10’s - 16
HL-LHC
tHE PATH TOWARDS 3000 FB-1
CERN Project, EU funds for the design study, preliminary
design report done www.cern.ch/hilumi [L. Rossi]
The target: after reaching 300 fb-1 in 2022, we need 3000 fb-1 in 20242035
We need to gain a factor four-five (250-300 fb-1 per year,
HL-LHC
from the beginning of HL-LHC)
Nominal
Peak lumi 1035 cm-2 s-1 is not acceptable
for the experiments (pile up)
A levelling is proposed at
51034 cm-2 s-1
To have this the LHC must be able to reach
a peak lumi 21035cm-2 s-1
20 larger than nominal:
Factor ~5 from the beam
Factor ~4 from optics (reducing b*)
E. Todesco
Nb
en
nb
(adim)
(m)
(adim)
b*
spacing
E
F
(m)
(ns)
(TeV)
(adim)
Lmax
Llev
pile up
1.15E+11 2.20E+11
3.75E-06 2.50E-06
2808
2808
0.55
25
7.0
0.86
0.15
25
7.0
1
(cm-2 s-1) 1.00E+34 2.0E+35
-2
3.7
1.5
1.0
3.7
1.0
20.1
-1
(cm s ) 1.00E+34 5.0E+34
26
132
N b2 nb f rev
L
F
*
4e n b
The 20’s: High Lumi LHC - 17
HL-LHC
luminosity levelling
The luminosity levelling aims at compensating the faster
decay in luminosity induced by higher peak lumi
With crossing angle ?
With separation ?
With b* ?
35- no level
1035
Luminosity (cm-2 s-1)
That’s why we need
a factor 20 but we use
only a factor 5
How to do leveling
Level at 5 10
34
1.E+35
8.E+34
6.E+34
4.E+34
Average
no level
Average level
2.E+34
0.E+00
0
5
10
15
20
25
time (hours)
Luminosity levelling principle (with a factor 10 shown)
Main result: similar integrated lumi but lower pile up
That’s the desiderata of experiments
E. Todesco
The 20’s: High Lumi LHC - 18
HL-LHC:
LOWER BETA*
How to get a factor four from the optics ?
To reduce b* to 15 cm (factor four from 55 cm nominal) one
needs larger aperture quadrupoles
b in the quads is  1/b*
Scaling with square root: a factor two in aperture,
i.e. 150 mm aperture quadrupoles
x( s ) 
eb ( s)
r
First upgrades aimed b*=25 cm [F. Ruggiero, et al, LHC PR 626 (2002)]
The quadrupole will rely on Nb3Sn technology
Collaboration CERN-US-Hilumi
Based on US-LARP (LHC accelerator research program) efforts
during the past 10 years
Important leap in technology, with huge impact on CERN future
(FCC)
E. Todesco
The 20’s: High Lumi LHC - 19
HL-LHC: MAGNET TECHNOLOGY
FOR LOWER BETA*
Superconductivity takes place in some materials below
thresholds values for magnetic field, current density and
temperature
Thresholds called critical surface
Phenomena known since 100 years, applications since 50 years
In a SC electromagnet, the coil must
tolerate field and current density
to produce that field
This sets a limit of ~8 T for Nb-Ti
LHC is built on this limit
4000
Superconductor current density (A/mm2)
Related to quantum mechanics
3500
3000
2500
2000
1500
1000
HL-LHC IR
500
0
0
Nb3Sn has a wider critical surface,
with possibility of increasing up to ~16 T
For HL-LHC we will operate at 11.5 T peak field
E. Todesco
LHC dipoles
5
10
Field (T)
15
20
The 20’s: High Lumi LHC - 20
HL-LHC:
not only magnets and crabs
HL LHC is not only new magnets in ~1 km of the the main
ring, but also
Cryogenics upgrade
Collimation upgrade
“Cold” powering
Crab cavities
E. Todesco
The 20’s: High Lumi LHC - 21
HL-LHC:
CRAB CAVITIES
When going to very low b*, (below 25 cm) the geometric
factor considerably reduces the gain
Crab cavity allows to set this factor to one by turning the bunches in
the longitudinal space [R. Calaga, Chamonix 2012]
qc
Crab crossing
One possible option for the design of crab cavity
Hardware being built, successful test in some electron machines
[WP4, E. Jensen, collaboration with many institutes]
First compact crab cavities with good performance have been built
E. Todesco
The 20’s: High Lumi LHC - 22
HL-LHC
As LHC, HL-LHC is an international collaboration
Hardware assigned to several labs for design and model
D1
Q4
Cor
Q3
Q2b
Q2a
Q1
ATLAS
CMS
CC
D2
First baseline from Q1 to Q4, and contributions [F. Bordry, Washington FCC week]
E. Todesco
The 20’s: High Lumi LHC - 23
HL-LHC:
INTENSITY
How to get the factor five from the beam ?
25 ns option
LIU: LHC Injector Upgrade project [M. Meddahi]
4.0
SPS 450 GeV 25 ns
HL-LHC
3.5
Nominal
2.5
1.5
1.0
0.5
PS RF power
Longitudinal insabilities
HL-LHC
2.0
SPS RF power
Longitudinal insabilities
Emittance (x+y)/2 [um]
3.0
Nb
en
nb
(adim)
(m)
(adim)
b*
spacing
E
F
(m)
(ns)
(TeV)
(adim)
Lmax
Llev
pile up
Nominal
1.15E+11 2.20E+11
3.75E-06 2.50E-06
2808
2808
0.55
25
7.0
0.86
0.15
25
7.0
1
(cm-2 s-1) 1.00E+34 2.0E+35
-2
3.7
1.5
1.0
3.7
1.0
20.1
-1
(cm s ) 1.00E+34 5.0E+34
26
132
0.0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Bunch Intensity [e11]
E. Todesco
Emittance vs intensity at 25 ns [R. Garoby, IPAC 2012]
The 20’s: High Lumi LHC - 24
CONTENTS
The present: LHC in the 10’s
LHC Energy
The race towards luminosity
The 20’s: the HL-LHC project
Optics and intensity
The 30’s: FCC studies
Aiming at 100 TeV centre of mass
E. Todesco
The 30’s: FCC study - 25
THE HIGH ENERGY FRONTIER
First ideas
Installing a 16.5+16.5 TeV proton Collision energy (TeV)
Dipole field
(T)
accelerator in the LEP tunnel
Main ingredient: 20 T operational field dipoles
LHC
7.0
8.3
HE LHC
16.5
20
ratio
2.4
2.4
Proposal in 2005 for an LHC tripler, with 24 T magnets [P. McIntyre, A.
Sattarov, “On the feasibility of a tripler upgrade for the LHC”, PAC (2005) 634].
CERN study in 2010 www.cern.ch/he-lhc
R. Assmann, R. Bailey, O. Bruning, O. Dominguez Sanchez, G. De Rijk, M. Jimenez, S. Myers, L. Rossi, L. Tavian,
E. Todesco, F. Zimmermann, « First thoughts on a Higher Energy LHC » CERN ATS-2010-177
E. Todesco, F. Zimmermann, Eds. « The High Energy LHC » CERN 2011-003 (Malta conference proceedings)
Motivations [J. Wells, CERN 2011-3]
“The results of the LHC will change everything, one way or another. There
will be a new “theory of the day” at each major discovery, and the
arguments will sharpen in some ways and become more divergent in other
ways. Yet, the need to explore the high energy frontier will remain.”
The energy frontier is always extremely interesting and for many
processes cannot be traded with more luminosity at lower energy
E. Todesco
The 30’s: FCC study - 26
THE FUTURE CIRCULAR COLLIDER
The FCC study
Tunnel of 80-100 km with 16-20 T magnets to reach 50+50 TeV with
proton collisions – plus possibility of e-e, e-h machine
Study group Future Circular Collider (FCC) established in
2013 [M. Benedikt, F. Zimmermann]
Opening event of the collaboration in Washington, March 2015
http://indico.cern.ch/event/340703/
E. Todesco
A new tunnel in the CERN area
The 30’s: FCC study - 27
THE FUTURE CIRCULAR COLLIDER
A baseline is being established [D. Schulte, Washington FCC week]
Luminosity as in HL LHC
Emittance as in HL LHC
Moderate bunch charge
25 ns operation
b* of 1 m
Pile up 50% larger than HL LHC
No leveling
Looks reasonable
LHC
Nb
en
nb
b*
frev
spacing
F
E
lenght
HL-LHC
FCC
w.r.t. LHC
w.r.t. LHC
(adim) 1.15E+11 2.20E+11
3.66
1.00E+11
0.76
(m) 3.75E-06 2.50E-06
1.50
2.20E-06
1.70
(adim) 2808
2808
1.00
10000
3.56
(m)
0.55
0.15
3.67
1.1
0.50
(s-1) 1.12E+04 1.12E+04
(ns)
25
25
(adim)
0.86
(TeV)
7
7
(km)
26.7
26.7
-2 -1
Lmax (cm s )1.00E+34 2.0E+35
Lave
5.0E+34
pile up
25
127
1.00
0.27
1.00
1.00
3.00E+03
25
1
50
100
20
5.1E+34
5
1.16
7.14
3.75
176
Goal of 250 fb-1 per year
There is also an ultimate scenario
a kind of HL FCC , very challenging parameters, especially for
radiation dose
There is also an option for 5 ns operation
E. Todesco
The 30’s: FCC study - 28
THE FUTURE CIRCULAR COLLIDER
A baseline is being established [D. Schulte WG]
16 T magnets with Nb3Sn technology (about 5000 dipoles)
Aperture of 50 mm
Double cell length from 100 to 200 m
5 MW of synchrotron radiation on beam screen
It was 7 kW in the LHC
50 K beam screen
Electrical consumption critical
100 MW only of synchrotron
Shielding the magnet is essential
Tungsten insert of 1-2 cm
Reason for larger aperture
Radiation dose OK
Becomes very critical for the ultimate
Layout baseline [D. Schulte]
E. Todesco
The 30’s: FCC study - 29
THE FUTURE CIRCULAR COLLIDER
First thoughts about a very challenging beam screen
Vacuum quality [R. Kersevan]
Beam screen geometry [R. Kersevan, C. Garion]
E. Todesco
Heat transfer [L. Tavian]
The 30’s: FCC study - 30
THE FUTURE CIRCULAR COLLIDER:
MAGNETS
One of the main challenge are the magnets
First choice: current density – keep the same as the LHC
w
B [T] ~ 0.0007 × coil width [mm] × current density
LHC:
[A/mm2]
-
8 [T]~ 0.0007 × 30 × 380
+
a
r
-
+
Accelerators used current density of the order of 350400 A/mm2
This provides ~2.5 T for 10 mm thickness
Present record is 13.5 T
Short model of acc magnet
CERN is building FrescaII
13 T with potential of going to 15 T
E. Todesco
[G. De Rjik]
FCC
20
HTS
Operational field (T)
80 mm needed for reaching 20 T
60 mm needed for reaching 16 T
Coil size is still manageable
HE-LHC
15
Nb3Sn
HD2
D20
(max. reached)
(max. reached)
10
LHC
Nb-Ti
SSC
Hera
Tevatron
RHIC
5
0
0
20
40
Coil width (mm)
60
80
Operational field versus coil width in accelerator magnets
The 30’s: FCC study - 31
THE FUTURE CIRCULAR COLLIDER:
MAGNETS
What material can tolerate 400 A/mm2 and at what field ?
For Nb-Ti: LHC performances - up to 8 T
For Nb3Sn: possibly reach 16 T with grading
Studies led by D. Tommasini and L. Bottura - international collab.
Cost is an issue with present prices
If we want to reach 20 T, last 4 T made by HTS
Today in Bi-2212 and YBCO we have not so far from there
Eng. current density (A/mm2)
800
Nb-Ti
Bi-2212
600
400
200
Nb3Sn
0
0
5
10
15
20
25
Field (T)
Engineering current density versus field for Nb-Ti and Nb3Sn (lines) and operational current (markers)
E. Todesco
The 30’s: FCC study - 32
THE LHC TUNNEL IN THE 30’s:
DIPOLE PARAMETERS
Design is driven by the cost – grade as much as possible
One critical parameter: how much margin?
FCC Units of Magnet Cost (-)
Using 80% rule, we should design for 25 T – 5 T margin – is it
too much?
LHC at 6.5 TeV (80% rule ) would have 2 T margin
… we go back to the 6.5-7 TeV issue
4.50
4.00
4.2 K
3.50
1.9 K
3.00
2.50
2.00
1.50
1.00
0.50
0.00
0
A 15 T dipole: coil grading (one quarter of coil shown)
and sketch of double aperture (coils in blue)
[E. Todesco, et al., IEEE Trans Appl Supercond (2014)]
E. Todesco
0.1
0.2
Margin (-)
0.3
Estimate of cost versus margin for 16 T
[D. Schoerling, Wshington FCC week 2015]
The 30’s: FCC study - 33
CONCLUSIONS
The Fathers of the LHC designed a wise machine with the
potential of reaching ultimate performance
At full performance one can expect 60 fb-1 per year (four times 2012),
and 300 fb-1 at the horizon of the 20’s
These 300 fb-1 are the lower estimate for the life of the inner triplet
magnets
The aperture of the triplet is a bottleneck to performance
So in any case better to replace with larger aperture. This will come
in ~2024
Coupled with crab cavities, larger triplet can give a factor
four boost to luminosity
Together with the injector upgrade, one can get another factor five
from beam intensity
HL LHC can provide 3000 fb-1 at the horizon of the 30’s
E. Todesco
34
CONCLUSIONS
HL-LHC can provide 3000 fb-1 at the horizon of the 30’s
Enabling technologies: large aperture magnets and crab cavities
The could be the first application of Nb3Sn to accelerators, pushing
the operational field from 8 to 12 T
With another jump of 4 T, we can go to 16 T, the ultimate of Nb3Sn
A 100 km tunnel would allow reaching 50+50 TeV
With 100 km ne would need 16 T magnet, which is not so far from
our capabilities
No bottlenecks have been identified from the point of view of beam
dynamics
The same magnets in the LHC tunnel would make an LHC doubler
E. Todesco
35
A DIGRESSION ON MAGNETIC FIELD, ANALYTIC
FUNCTIONS AND PERTURBATIVE EXPANSIONS
Maxwell equations for magnetic field
B x B y B z
B 


0
x
y
z
  B   0 J   0e 0
E
t
In absence of charge and magnetized material
 B y B z B z B x B x B y 
0
  B  

,

,

y x
z y
x 
 z
If
James Clerk Maxwell,
Scottish
(13 June 1831 – 5 November 1879)
B z
 0 (constant longitudinal field), then
z
Bx By

0
x
y
E. Todesco
Bx By

0
y
x
Unit 5: Field harmonics – 5.36
A DIGRESSION ON MAGNETIC FIELD, ANALYTIC
FUNCTIONS AND PERTURBATIVE EXPANSIONS
A complex function of complex variables is analytic if it
coincides with its power series

f ( z )   Cn z
n 1
n 1

f x ( x, y )  if y ( x, y )   Cn ( x  iy ) n 1
on a domain D !
( x, y )  D
n 1
Note: domains are usually a painful part, we talk about it later
A necessary and sufficient condition to be analytic is that
 f x f y
 x  y  0

f
 f x  y  0
 y x
called the Cauchy-Riemann conditions
E. Todesco
Augustin Louis Cauchy
French
(August 21, 1789 – May 23, 1857)
Unit 5: Field harmonics – 5.37
A DIGRESSION ON MAGNETIC FIELD, ANALYTIC
FUNCTIONS AND PERTURBATIVE EXPANSIONS
If
B z
0
z
 f x f y
 x  y  0

f
 f x  y  0
 y x
By
Bx

0
x
y
Maxwell gives
By
y

Bx
0
x
and therefore the function By+iBx is analytic

n1
By ( x, y )  iBx ( x, y )   Cn x  iy 
n1
( x, y )  D
Georg Friedrich Bernhard Riemann,
German
(November 17, 1826 - July 20, 1866)
where Cn are complex coefficients
Advantage: we reduce the description of a function from R2
to R2 to a (simple) series of complex coefficients
Attention !! We lose something (the function outside D)
E. Todesco
Unit 5: Field harmonics – 5.38
A DIGRESSION ON MAGNETIC FIELD, ANALYTIC
FUNCTIONS AND PERTURBATIVE EXPANSIONS

n 1
By ( x, y )  iBx ( x, y )   Cn x  iy 
n 1
 C0  C1 ( x  iy )  ...
( x, y )  D
Each coefficient corresponds to a “pure” multipolar field
A dipole
A quadrupole
[from P. Schmuser et al, pg. 50]
A sextupole
Magnets usually aim at generating a single multipole
Dipole, quadrupole, sextupole, octupole, decapole, dodecapole …
Combined magnets: provide more components at the same time (for
instance dipole and quadrupole) – more common in low energy
rings, resistive magnets – one sc example: JPARC (Japan)
E. Todesco
Unit 5: Field harmonics – 5.39
A DIGRESSION ON MAGNETIC FIELD, ANALYTIC
FUNCTIONS AND PERTURBATIVE EXPANSIONS
n1

By ( x, y )  iBx ( x, y )   Cn x  iy 
n 1
n 1

  Bn  iAn x  iy 
n1
The field harmonics are rewritten as
 x  iy 

B y  iB x  10 B1  (bn  ia n )
 R 
n 1
 ref 
4

n 1
We factorize the main component (B1 for dipoles, B2 for quadrupoles)
We introduce a reference radius Rref to have dimensionless
coefficients
We factorize 10-4 since the deviations from ideal field are 0.01%
The coefficients bn, an are called normalized multipoles
bn are the normal, an are the skew (adimensional)
E. Todesco
Unit 5: Field harmonics – 5.40
A DIGRESSION ON MAGNETIC FIELD, ANALYTIC
FUNCTIONS AND PERTURBATIVE EXPANSIONS
Field given by a current line (Biot-Savart law)
y
B( z )  B y ( z )  iB x ( z )
I 0
I
1
B( z ) 
 0
2 ( z  z0 )
2z0 1  z
z0
using
40
z 0 =x 0 +iy 0
B=B y +iB x
0
-4 0
x
0
40
z=x+iy
-4 0

1
2
3
 1  t  t  t  ...   t n1
1 t
n 1
t  1 !!!
Félix Savart,
French
(June 30, 1791-March 16, 1841)
we get
I 0
B( z )  
2z0
E. Todesco
 z
 

n 1  z 0 

n 1
I 0

2z0
 Rref


n 1  z 0




n 1
 x  iy 


 R 
 ref 
n 1
Jean-Baptiste Biot,
French
(April 21, 1774 – February 3, 1862)
Unit 5: Field harmonics – 5.41
A DIGRESSION ON MAGNETIC FIELD, ANALYTIC
FUNCTIONS AND PERTURBATIVE EXPANSIONS
Now we can compute the multipoles of a current line at z0
I 0
B( z )  
2z0
 z
 

n 1  z 0 

n 1
I 0

2z0
 Rref


n 1  z 0

 x  iy 

B y  iB x  10 B1  (bn  ia n )
 R 
n 1
 ref 
4

 x  iy 


 R 
 ref 
I 010  Rref

bn  ia n  
2z0 B1  z0
4



n 1
x  iy  z0
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0
E. Todesco
n 1
n 1
¦bn+ian¦
I0  1 
B1  
Re 
2
 z0 



n 1
5
10
Multipole order n
15
Unit 5: Field harmonics – 5.42
A DIGRESSION ON MAGNETIC FIELD, ANALYTIC
FUNCTIONS AND PERTURBATIVE EXPANSIONS
Multipoles given by a current line decay with the order
10



n 1
 I  010 
 Rref


ln  bn  ia n   ln
 n ln 
 2R B 
ref 1 
 z0

4
1
¦bn+ian¦
I 010  Rref

bn  ia n  
2z0 B1  z0
4

  p  nq


0.1
0.01
0.001
0
5
10
Multipole order n
15
The slope of the decay is the logarithm of (Rref/|z0|)
At each order, the multipole decreases by a factor Rref /|z0|
The decay of the multipoles tells you the ratio Rref /|z0|, i.e. where
is the coil w.r.t. the reference radius –
like a radar … used to detect the location of assembly errors in the
magnets
E. Todesco
Unit 5: Field harmonics – 5.43
A DIGRESSION ON MAGNETIC FIELD, ANALYTIC
FUNCTIONS AND PERTURBATIVE EXPANSIONS
Case of measurements anomalies during the production of the LHC
dipole
We plot the absolute values of the field anomaly in the semilogarithmic scale
The slope of decay fits very well with a defect at ~28 mm (inner radius
of the inner layer coil)
Normal
Skew
Slope of defect at 28 mm
Slope of defect at 43 mm
Field anomaly (units)
10.00
1.00
0.10
Measurement precison
0.01
0
E. Todesco
5
10
Multipole order n
15
Unit 21: Magnetic measurements and production control – 21.44
A DIGRESSION ON MAGNETIC FIELD, ANALYTIC
FUNCTIONS AND PERTURBATIVE EXPANSIONS
We tried our library of defects
15
15
Normal
Skew
(Field anomaly-simulated
error)/sigma (adim)
Field anomaly/sigma (adim)
Subtracting from the anomaly an inward
movement of ~0.8 mm of block6 in one
quadrant we go within three sigma in all
multipoles (almost a miracle …)
10
5
3 sigma
0
10
5
3 sigma
0
0
5
10
Multipole order n
Field anomalies expressed in units of sigma
in the LHC main dipole 2032
E. Todesco
Normal
Skew
15
0
5
10
15
Multipole order n
Field anomalies minus 0.75 mm block6 displacement
expressed in units of sigma in the LHC main dipole 2032
Unit 21: Magnetic measurements and production control – 21.45
A DIGRESSION ON MAGNETIC FIELD, ANALYTIC
FUNCTIONS AND PERTURBATIVE EXPANSIONS
We convinced the firm to open the magnet
It has been found that the coil was not glued and that block6 was
detached from the inner layer
A more careful control of curing has been implemented
Picture from here, collars removed
Block6 inward displacement in the LHC main dipole 2032
E. Todesco
Expected displacement in the LHC main dipole 2032
Unit 21: Magnetic measurements and production control – 21.46
A DIGRESSION ON MAGNETIC FIELD, ANALYTIC
FUNCTIONS AND PERTURBATIVE EXPANSIONS
When we expand a function in a power series we lose
something

1
 1  t  t 2  t 3  ...   t n1
1 t
n 1
y
t 1
Example 1. In t=1/2, the function is
1
1

2
1 1/ 2 1/ 2
40
0
-4 0
0
x
40
and using the series one has
-4 0
2
3
1 1 1
1         ...  1  0.5  0.25  0.125  1.875  ...
2 2 2
not bad … with 4 terms we compute the function within 7%
E. Todesco
Unit 5: Field harmonics – 5.47
A DIGRESSION ON MAGNETIC FIELD, ANALYTIC
FUNCTIONS AND PERTURBATIVE EXPANSIONS
When we expand a function in a power series we lose
something

1
2
3
 1  t  t  t  ...   t n1
1 t
n 1
y
40
t 1
Ex. 2. In t=1, the function is infinite
1
1
 
11 0
and using the series one has
1  1  1  1  ...  1  1  1  1  ...
2
0
-4 0
0
x
40
-4 0
3
which diverges … this makes sense
E. Todesco
Unit 5: Field harmonics – 5.48
A DIGRESSION ON MAGNETIC FIELD, ANALYTIC
FUNCTIONS AND PERTURBATIVE EXPANSIONS
When we expand a function in a power series we lose
something

1
2
3
 1  t  t  t  ...   t n1
1 t
n 1
y
40
t 1
Ex. 3. In t=-1, the function is well defined
1
1

11 2
0
-4 0
0
x
40
BUT using the series one has
-4 0
1  (1)   1   1  ...  1  1  1  1  ...
2
3
even if the function is well defined, the series does not work: we are
outside the convergence radius
E. Todesco
Unit 5: Field harmonics – 5.49