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Transcript of USPAS June 2007, Superconducting accelerator magnets Unit 2 Magnet specifications in circular...
USPAS June 2007, Superconducting accelerator magnets
Unit 2Magnet specifications in circular accelerators
Soren Prestemon and Paolo FerracinLawrence Berkeley National Laboratory (LBNL)
Ezio TodescoEuropean Organization for Nuclear Research (CERN)
Unit 2 – Magnet specifications in particle accelerators 2.2
USPAS June 2007, Superconducting accelerator magnets
QUESTIONS
Order of magnitudes of the size of our objects: why ?High energy circular accelerators
Length of an accelerator: Km15 m
1.9 Km
Main ring at Fermilab, Chicago, US
41° 49’ 55” N – 88 ° 15’ 07” W
1 Km
40° 53’ 02” N – 72 ° 52’ 32” W
RHIC ring at BNL, Long Island, US
46° 14’ 15” N – 6 ° 02’ 51” E
Unit 2 – Magnet specifications in particle accelerators 2.3
USPAS June 2007, Superconducting accelerator magnets
QUESTIONS
Order of magnitudes of the size of our objects: why ?High energy linear accelerators
Length of a linear accelerator: Km - but we will not deal with them 15 m
Linear accelerator at Stanford, US
46° 14’ 15” N – 6 ° 02’ 51” E
3.5 Km
37° 24’ 52” N – 122° 13’ 07” W
Unit 2 – Magnet specifications in particle accelerators 2.4
USPAS June 2007, Superconducting accelerator magnets
QUESTIONS
Order of magnitudes of the size of our objects: why ?High energy circular accelerators
Length of an accelerator magnet: 10 mDiameter of an accelerator magnet: mBeam pipe size of an accelerator magnet: cm
15 m
A stack of LHC dipoles, CERN, Geneva, CH
46° 14’ 15” N – 6 ° 02’ 51” E
Dipole in the LHC tunnel, Geneva, CH
0.6 m 6 cm
Unit 2 – Magnet specifications in particle accelerators 2.5
USPAS June 2007, Superconducting accelerator magnets
CONTENTS
1. Principles of synchrotron2. The arc: how to keep particles on a circular orbit
Relation between energy, dipolar field, machine length
3. The arc: size of the beam and focusing Aperture requirements for arc quads and dipoles (size of the beam)Gradient requirements (focusing force) for arc quadrupoles
4. The arc: a flow chart for computing magnet parametersExample: the LHC
5. The interaction regions: low-beta magnet specificationsHow to squeeze the beamGradient and aperture requirements for low-beta quadrupoles
6. The interaction regions: detector specifications
Unit 2 – Magnet specifications in particle accelerators 2.6
USPAS June 2007, Superconducting accelerator magnets
1. PRINCIPLES OF A SYNCHROTRON
Electro-magnetic field accelerates particlesMagnetic field steers the particles in a closed (circular) orbit
To drive particles through the same accelerating structure several timesAs the particle is accelerated, its energy increases and the magnetic field is increased (“synchro”) to keep the particles on the same orbit
Limits to the increase in energyThe maximum field of the dipoles (proton machines)The synchrotron radiation due to bending trajectories (electron machines)
Colliders: two beams with opposite momentum collideThis doubles the energy !One pipe if particles collide their antiparticles (LEP, Tevatron)Otherwise, two pipes (ISR, RHIC, HERA, LHC)
Unit 2 – Magnet specifications in particle accelerators 2.7
USPAS June 2007, Superconducting accelerator magnets
1. PRINCIPLES OF A SYNCHROTRON
The arcs: region where the beam is bentDipoles for bendingQuadrupoles for focusingCorrectors
Long straight sections (LSS)Interaction regions (IR) where the experiments are housed
Quadrupoles for strong focusing in interaction pointDipoles for beam crossing in two-ring machines
Regions for other servicesBeam injection (dipole kickers)Accelerating structure (RF cavities)Beam dump (dipole kickers)Beam cleaning (collimators)
ArcArc
ArcArc
LSS
LSS
LSS
LSS
A schematic view of a synchrotron
The lay-out of the LHC
Unit 2 – Magnet specifications in particle accelerators 2.8
USPAS June 2007, Superconducting accelerator magnets
CONTENTS
1. Principles of synchrotron2. The arc: how to keep particles on a circular orbit
Relation between energy, dipolar field, machine length
3. The arc: size of the beam and focusing Aperture requirements for arc quads and dipoles (size of the beam)Gradient requirements (focusing force) for arc quadrupoles
4. The arc: a flow chart for computing magnet parametersExample: the LHC
5. The interaction regions: low-beta magnet specificationsHow to squeeze the beamGradient and aperture requirements for low-beta quadrupoles
6. The interaction regions: detector specifications
Unit 2 – Magnet specifications in particle accelerators 2.9
USPAS June 2007, Superconducting accelerator magnets
2. THE ARC:HOW TO KEEP PARTICLES ON A CIRCLE
Kinematics of circular motionRelativistic dynamics
Lorentz (?) force
Putting all togetherHyp. 1 - longitudinal acceleration<<transverse acceleration
vmp
2
2
1
1
c
v
vdt
dv
dt
d
2v
dt
vd
vdt
dmv
dt
dmp
dt
dF
Hendrik Antoon Lorentz, Dutch
(18 July 1853 – 4 February 1928), painted by Menso Kamerlingh
Onnes, brother of Heinke
vdt
dmp
dt
dF
2vm
dt
vdmF
BveF
evBF pvmeB
eBp
Unit 2 – Magnet specifications in particle accelerators 2.10
USPAS June 2007, Superconducting accelerator magnets
2. THE ARC:HOW TO KEEP PARTICLES ON A CIRCLE
Relation momentum-magnetic field-orbit radiusPreservation of 4-momentum
Hyp. 2 Ultra-relativistic regime
Using practical units for particle with charge 1, one has
magnetic field in Tesla …Remember 1 eV=1.60210-19 JRemember 1 e= 1.60210-19 C
2242 cpcmE 42222 cmcpE
2mcpc pcE
][][3.0][ mTBGeVE r [m] B [T] E [TeV]FNAL Tevatron 758 4.40 1.000DESY HERA 569 4.80 0.820IHEP UNK 2000 5.00 3.000SSCL SSC 9818 6.79 20.000BNL RHIC 98 3.40 0.100
CERN LHC 2801 8.33 7.000CERN LEP 2801 0.12 0.100
eBp
ceBE
Unit 2 – Magnet specifications in particle accelerators 2.11
USPAS June 2007, Superconducting accelerator magnets
2. THE ARC:HOW TO KEEP PARTICLES ON A CIRCLE
Nikolai Tesla (10 July 1856 - 7 January 1943)Born at midnight during an electrical storm in Smiljan near Gospić (now Croatia)Son of an orthodox priestA national hero in Serbia
CareerPolytechnic in Gratz (Austria) and PragueEmigrated in the States in 1884Electrical engineerInventor of the alternating current induction motor (1887)Author of 250 patents
MiscellaneousStrongly against marriage [brochure of Nikolai Tesla Museum in Belgrade (2000)]
Considered sex as a waste of vital energy [guardian of Nikolai Tesla Museum in Belgrade, private communication (2002)]
Tesla, man of the year
Unit 2 – Magnet specifications in particle accelerators 2.12
USPAS June 2007, Superconducting accelerator magnets
2. THE ARC:HOW TO KEEP PARTICLES ON A CIRCLE
Relation momentum-magnetic field-orbit radius
][][3.0][ mTBGeVE
0.01
0.10
1.00
10.00
100.00
0 5 10 15
Dipole field (T)
Ene
rgy
(TeV
)
Tevatron HERASSC RHICUNK LEPLHC
=10 km
=3 km
=1 km
=0.3 km
Unit 2 – Magnet specifications in particle accelerators 2.13
USPAS June 2007, Superconducting accelerator magnets
2. THE ARC:HOW TO KEEP PARTICLES ON A CIRCLE
The magnet that we need should provide a constant (over the space) magnetic field, to be varied with time to follow the particle acceleration
This is done by dipoles
As the particle can deviate from the orbit, one needs a linear force to bring it back
We will show in the next section that this is given by quadrupoles
01
x
y
B
BB
GyB
GxB
x
y
Unit 2 – Magnet specifications in particle accelerators 2.14
USPAS June 2007, Superconducting accelerator magnets
CONTENTS
1. Principles of synchrotron2. The arc: how to keep particles on a circular orbit
Relation between energy, dipolar field, machine length
3. The arc: size of the beam and focusing Aperture requirements for arc quads and dipoles (size of the beam)Gradient requirements (focusing force) for arc quadrupoles
4. The arc: a flow chart for computing magnet parametersExample: the LHC
5. The interaction regions: low-beta magnet specificationsHow to squeeze the beamGradient and aperture requirements for low-beta quadrupoles
6. The interaction regions: detector specifications
Unit 2 – Magnet specifications in particle accelerators 2.15
USPAS June 2007, Superconducting accelerator magnets
3. THE ARC:SIZE OF THE BEAM AND FOCUSING
The force necessary to stabilize linear motion is provided by the quadrupoles
Quadrupoles provide a field which is proportional to the transverse deviation from the orbit, acting like a spring
One can prove that the motion equation in transverse space (with some approximations) is
where
yysxx BBsByc
eBv
c
eF )(
B
G
x
B
BK
y
11
0)(12
2
xsKds
xd
GyB
GxB
x
y
Unit 2 – Magnet specifications in particle accelerators 2.16
USPAS June 2007, Superconducting accelerator magnets
3. THE ARC:SIZE OF THE BEAM AND FOCUSING
A sequence of focusing and defocusing quadrupoles with the same (opposite) strength and spaced by L is a providing linear stability to the beam – this is called a FODO cell
Let L be the distance between two consecutive quadrupoles
The equations of transverse motion areWhere the term K is zero in dipoles, and
in focusing quadrupoles, in defocusing quadrupoles
0)(12
2
xsKds
xd
0)(12
2
ysKds
yd
BG
K 1 BG
K 1
Unit 2 – Magnet specifications in particle accelerators 2.17
USPAS June 2007, Superconducting accelerator magnets
3. THE ARC:SIZE OF THE BEAM AND FOCUSING
The motion equation in the transverse space is similar to a harmonic oscillator
where the force depends on time …
Solution: a oscillator whose amplitude and frequency are modulated
and give the beam size
x y are the invariants (emittances) [m rad]
x and y are the beta functions [m]
is the phase advance, related to the beta function
The beta functions oscillate
along the ring, reaching
maxima and minima
in the quadrupoles
s
t
dts
0 )()(
0)(12
2
ysKds
yd
))(cos()()( sssy yyy
))(cos()()( sssx xxx
0
50
100
150
200
0 50 100 150 200 250 300Length (m)
fun
ctio
n (m
)
Betax
Betay
QF QF QFQD QD QD
L
0)(12
2
xsKds
xd
Unit 2 – Magnet specifications in particle accelerators 2.18
USPAS June 2007, Superconducting accelerator magnets
3. THE ARC:SIZE OF THE BEAM AND FOCUSING
Relations for a FODO cell: beam size vs cell lengthLet 2L be the cell length – we consider it for the moment as an independent variableWe define (2L) as the phase advance per cell
A typical cell has (2L)=/2 (90° phase advance) – for this cell one has
LLf 4.3)22(
LLd 6.0)22(
0
50
100
150
200
250
300
350
400
0 50 100 150 200 250 300Length (m)
f
unct
ion
(m)
Betax
Betay
QF QD QD
L
Beta functions in a FODO cell with L=50 m
Beta functions in a FODO cell with L=100 m
0
50
100
150
200
250
300
350
400
0 50 100 150 200 250 300Length (m)
fu
ncti
on (
m)
Betax
Betay
QF QF QFQD QD QD
L
Unit 2 – Magnet specifications in particle accelerators 2.19
USPAS June 2007, Superconducting accelerator magnets
3. THE ARC:SIZE OF THE BEAM AND FOCUSING
Example of the LHC: L=50 m, f =170 m, d =30 m
The beta functions are in metersthey are related, but not equal to the beam size
Pay attention ! f =170 m does not mean that the beam size is 170 m !!It is not easy to “feel” the dimension of a beta function
Radius of the beam in the arc (1 sigma)LHC: n =3.75 10-6 m rad
High field E=7 TeV, =7460 - =0.29 mmInjection E=450 GeV, =480 - =1.2 mm
Beam size depends on cell length, energy and normalized emittance
nn L
0
50
100
150
200
0 50 100 150 200 250 300Length (m)
fun
ctio
n (m
)
Betax
Betay
QF QF QFQD QD QD
L
Unit 2 – Magnet specifications in particle accelerators 2.20
USPAS June 2007, Superconducting accelerator magnets
3. THE ARC:SIZE OF THE BEAM AND FOCUSING
Focusing in a FODO cellThin lens approximation: focusing strength in a 90° FODO cell is
The focusing strength is related to K1
and to the quadrupole length ℓq
and the quadrupole gradient is
LHC: at high field B=8.33 T, =2801 m, L=50 m, G ℓq=660 T
For a 60° phase advance the same linear dependence on L, with different constants
It looks worse: same beam size, 50% more focusing required
L
Lf 7.0
2
LLf 2.133
2 LLd 4.332 Lf
qq G
B
Kf
1
1
L
B
f
BG q
2
Unit 2 – Magnet specifications in particle accelerators 2.21
USPAS June 2007, Superconducting accelerator magnets
CONTENTS
1. Principles of synchrotron2. The arc: how to keep particles on a circular orbit
Relation between energy, dipolar field, machine length
3. The arc: size of the beam and focusing Aperture requirements for arc quads and dipoles (size of the beam)Gradient requirements (focusing force) for arc quadrupoles
4. The arc: a flow chart for computing magnet parametersExample: the LHC
5. The interaction regions: low-beta magnet specificationsHow to squeeze the beamGradient and aperture requirements for low-beta quadrupoles
6. The interaction regions: detector specifications
Unit 2 – Magnet specifications in particle accelerators 2.22
USPAS June 2007, Superconducting accelerator magnets
4. THE ARC:FLOWCHART FOR MAGNET PARAMETERS
Arc magnets aperture
Collision energy
Total length of the dipoles Ld
Injection energy Emittance(injectors)
Cell length (free)
Maximum field (technology)
Integrated gradient in
quadrupoles
Maximum gradient in
quadrupolesQuadrupole length
Number of quadrupoles, and total length of the arc
Field errors,beam stability
Unit 2 – Magnet specifications in particle accelerators 2.23
USPAS June 2007, Superconducting accelerator magnets
Arc magnets aperture
Collision energy
Total length of the dipoles Ld
Injection energy Emittance(injectors)
Cell length (free)
Maximum field (technology)
Integrated gradient in
quadrupoles
Maximum gradient in
quadrupolesQuadrupole length
Number of quadrupoles, and total length of the arc
Field errors,beam stability
4. THE ARC:FLOWCHART FOR MAGNET PARAMETERS
Unit 2 – Magnet specifications in particle accelerators 2.24
USPAS June 2007, Superconducting accelerator magnets
4. THE ARC:FLOWCHART FOR MAGNET PARAMETERS
Input 1. Collision energy Ec
Gives a relation between the dipole magnetic field B and the total length of the dipoles Ld
Technology constraint 1. Dipole magnetic field BDoes not depend on magnet apertureBt <2 T for iron magnets
Bt <13 T for Nb-Ti superconducting magnets (10 T in practice)
Bt <25 T for Nb3Sn superconducting magnets (16-17 T in practice)
Output 1. Length of the dipole part
Length in m, B in T, energy in GeV
][][3.0][ mTBGeVE
tBB
B
ELd 3.0
22
Unit 2 – Magnet specifications in particle accelerators 2.25
USPAS June 2007, Superconducting accelerator magnets
Arc magnets aperture
Collision energy
Total length of the dipoles Ld
Injection energy Emittance(injectors)
Cell length (free)
Maximum field (technology)
Integrated gradient in
quadrupoles
Maximum gradient in
quadrupolesQuadrupole length
Number of quadrupoles, and total length of the arc
Field errors,beam stability
4. THE ARC:FLOWCHART FOR MAGNET PARAMETERS
Unit 2 – Magnet specifications in particle accelerators 2.26
USPAS June 2007, Superconducting accelerator magnets
4. THE ARC:FLOWCHART FOR MAGNET PARAMETERS
Input 2. Injection energy Ei
Determines the relativistic factor, that affect the beam size
Constraint 2. Normalized beam emittance n
Determined by the beam properties of the injectors
Semi-cell length LThis is a free parameter that can be used to optimizeDetermines the beta functions
Output 2. Aperture of the arc magnets (also determined by field errors and beam stability)
Size of the beam at injection
Magnet aperture
LLf 4.3)22(
fn
i
n
i
fna
Lbababa
22
Unit 2 – Magnet specifications in particle accelerators 2.27
USPAS June 2007, Superconducting accelerator magnets
Arc magnets aperture
Collision energy
Total length of the dipoles Ld
Injection energy Emittance(injectors)
Cell length (free)
Maximum field (technology)
Integrated gradient in
quadrupoles
Maximum gradient in
quadrupolesQuadrupole length
Number of quadrupoles, and total length of the arc
Field errors,beam stability
4. THE ARC:FLOWCHART FOR MAGNET PARAMETERS
Unit 2 – Magnet specifications in particle accelerators 2.28
USPAS June 2007, Superconducting accelerator magnets
4. THE ARC:FLOWCHART FOR MAGNET PARAMETERS
Technology constraint 1. Quadrupole magnetic field vs aperture
Output 3. Gradient of the quadrupoles
Semi-cell length LAlso determines the focusing, i.e. the integrated gradient
Output 4. Length of the quadrupoles
L
E
L
BL
L
BG d
q 3.0
2
2
22
ta B
G
2
a
tat
BBGG
2
),(
GL
E
GL
BL
GL
B dq 3.0
2
2
22
Unit 2 – Magnet specifications in particle accelerators 2.29
USPAS June 2007, Superconducting accelerator magnets
Arc magnets aperture
Collision energy
Total length of the dipoles Ld
Injection energy Emittance(injectors)
Cell length (free)
Maximum field (technology)
Integrated gradient in
quadrupoles
Maximum gradient in
quadrupolesQuadrupole length
Number of quadrupoles, and total length of the arc
Field errors,beam stability
4. THE ARC:FLOWCHART FOR MAGNET PARAMETERS
Output 5. Number of semi-cells and arc lengthEqual to the number of quadrupoles
q
dq L
Ln
LnL qa
Unit 2 – Magnet specifications in particle accelerators 2.30
USPAS June 2007, Superconducting accelerator magnets
4. THE ARC:FLOWCHART FOR MAGNET PARAMETERS
Example: Large Hadron ColliderE=7000 GeVNb-Ti magnets, dipole field B=8.3 T
Ld=17600 m
Cell length L=50 mf =170 m
n=3.7510-6m rad
Injection energy 450 GeV, =480Beam size =0.0012 m (at injection)
2*10=0.024 m, i.e., much less than the available aperture of 0.056 m Aperture is larger then needed to have the beam at injection in the zone of “good field”
B
ELd 3.0
22
LLf 4.3)22(
fn
Unit 2 – Magnet specifications in particle accelerators 2.31
USPAS June 2007, Superconducting accelerator magnets
4. THE ARC:FLOWCHART FOR MAGNET PARAMETERS
Example: Large Hadron ColliderArc magnets aperture and technology constraint determine quadrupole gradient:8.3 T at 28 mm radius gives 300 T/m for Nb-Ti at 1.9 K – large safety margin taken, operational gradient chosen at 220 T/m
Cell length determines focusing strength, i.e. quadrupole length
Quadrupole length → length in the cell available for dipolestogether with total length of dipoles → number of quadrupoles400
is the space for correctors, instrumentation, interconnections
2
Lf
fB
G q 1
mLG
B
fG
Bq 3
2
LnL qa icicq
dq L
Ln
,,
icic ,,
Unit 2 – Magnet specifications in particle accelerators 2.32
USPAS June 2007, Superconducting accelerator magnets
CONTENTS
1. Principles of synchrotron2. The arc: how to keep particles on a circular orbit
Relation between energy, dipolar field, machine length
3. The arc: size of the beam and focusing Aperture requirements for arc quads and dipoles (size of the beam)Gradient requirements (focusing force) for arc quadrupoles
4. The arc: a flow chart for computing magnet parametersExample: the LHC
5. The interaction regions: low-beta magnet specificationsHow to squeeze the beamGradient and aperture requirements for low-beta quadrupoles
6. The interaction regions: detector specifications
ArcArc
ArcArc
LSS
LSS
LSS
LSS
Unit 2 – Magnet specifications in particle accelerators 2.33
USPAS June 2007, Superconducting accelerator magnets
5. THE INTERACTION REGIONS:LOW-BETA MAGNET SPECIFICATIONS
We are now in the straight sections of the machineThere are no dipolesOnly quadrupoles to keep the beam focused
In the middle of the straight section one has a free space for the experiment, with the interaction point (IP) where beams collide
Around the experiment the optics must keep two distinct aimsKeep the beam focusedReduce the size of the beam in the interaction point (IP) to increase the rate of collisions (luminosity)
Beam size proportional to () – but is invariant, so act on
n
Unit 2 – Magnet specifications in particle accelerators 2.34
USPAS June 2007, Superconducting accelerator magnets
5. THE INTERACTION REGIONS:LOW-BETA MAGNET SPECIFICATIONS
A system of quadrupoles is used to reach a very low beta function, called *, in the IP (LHC: 0.55 m instead of the 30-200 m in the arcs)Physical constraint: empty space around the IP – distance of the first magnet to the IP, called l*, (LHC: 23 m) – needed for the detectors !
0
1000
2000
3000
4000
5000
6000
0 50 100 150 200Distance from IP (m)
(
m)
-1
0
0
0
0
0
0
Betax
Betay
Q1
Q2
Q3l *
The lay-out of quadrupoles close to the interaction point in the LHC, and the beta functions
Unit 2 – Magnet specifications in particle accelerators 2.35
USPAS June 2007, Superconducting accelerator magnets
5. THE INTERACTION REGIONS:LOW-BETA MAGNET SPECIFICATIONS
Drawback: beta function gets huge in the quadrupoles !But this happens only in collision, where the beam is smaller
In free space around IP (s=0), one has
At the entrance of the triplet one has
In reality, the situation is even worse: the maximum beta function in the LHC triplet is much larger than at the entrance
at the entrance we have
whereas in the triplet we have m =4400 m
*
2*)(
s
s
*
2*
*
2***)(
ll
l
m96055.0
23)(
2
*
2**
ll
*
* ),(
tm
llF
Unit 2 – Magnet specifications in particle accelerators 2.36
USPAS June 2007, Superconducting accelerator magnets
5. THE INTERACTION REGIONS:LOW-BETA MAGNET SPECIFICATIONS
Aperture requirement: a+c/* and dependent on l*, lt
Given the aperture, the technology limits the maximal gradientAt first order, G1/
We will show the limits of the approximation, and a more precise estimate, in Unit 8
The triplet has to focus the beam in the interaction pointThe focusing strength is a function of l*, lt, and is not related to * This gives a requirement on the integrated gradient …… that together with the maximum gradient gives the triplet length
The 4 equations are coupled
*
* ),(
t
c
n
c
mn llFbaba
2)( tBGG
Unit 2 – Magnet specifications in particle accelerators 2.37
USPAS June 2007, Superconducting accelerator magnets
5. THE INTERACTION REGIONS:LOW-BETA MAGNET SPECIFICATIONS
The 4 equations are coupled
For the LHC, one has *=0.55 mm=4400 m
With respect to the arc, m is ~22 times larger, but the is ~16 times larger in collision the aperture is not so different from the cell magnets
= 0.070 m instead of = 0.056 m in the arcsWith a triplet length of 24 m the required integrated gradient of 4800 TThis requires a quadrupole gradient of 200 T/mWith Nb-Ti one can get up to 300 T/m quadrupoles of = 0.070 m – one has a good safety margin
)(GG ),( *tII llGG
),,( ** tll
GlG tI
c
mnba
Unit 2 – Magnet specifications in particle accelerators 2.38
USPAS June 2007, Superconducting accelerator magnets
5. THE INTERACTION REGIONS:LOW-BETA MAGNET SPECIFICATIONS
Example: the LHC interaction regionsBaseline: Nb-Ti quadrupoles, 200 T/m, 70 mm aperture, *
=0.55 mLARP : Nb3Sn quadrupoles, 200 T/m, 90 mm aperture, *
=0.25 m
0
100
200
300
400
0 25 50 75 100 125 150 175 200 225Aperture (mm)
Gra
dien
t (T
/m)
Baseline
LARP program
Nb-Ti 1.9 K
Nb3Sn 1.9 K
l*=23 m
*=55 cm *=14 cm *=7 cm*=28 cm
lq=20 m
lq=25 mlq=30 m
lq=40 mlq=50 m
Unit 2 – Magnet specifications in particle accelerators 2.39
USPAS June 2007, Superconducting accelerator magnets
CONTENTS
1. Principles of synchrotron2. The arc: how to keep particles on a circular orbit
Relation between energy, dipolar field, machine length
3. The arc: size of the beam and focusing Aperture requirements for arc quads and dipoles (size of the beam)Gradient requirements (focusing force) for arc quadrupoles
4. The arc: a flow chart for computing magnet parametersExample: the LHC
5. The interaction regions: low-beta magnet specificationsHow to squeeze the beamGradient and aperture requirements for low-beta quadrupoles
6. The interaction regions: detector specifications
Unit 2 – Magnet specifications in particle accelerators 2.40
USPAS June 2007, Superconducting accelerator magnets
6. THE INTERACTION REGIONS:DETECTOR SPECIFICATIONS
Detector magnets provide a field to bend the particlesThe measurement of the bending radius gives an estimate of the charge and energy of the particle
Different lay-outsA solenoid providing a field parallel to the beam direction (example: LHC CMS, LEP ALEPH, Tevatron CDF)
Field lines perpendicular to (x,y)
A series of toroidal coils to provide a circular field around the beam (example: LHC ATLAS)
Field lines of circular shape in the (x,y) plane
Sketch of a detector based on a solenoidSketch of the CMS detector in the LHC
Unit 2 – Magnet specifications in particle accelerators 2.41
USPAS June 2007, Superconducting accelerator magnets
6. THE INTERACTION REGIONS:DETECTOR SPECIFICATIONS
Detector transverse sizeThe particle is bent with a curvature radius
B is the field in the detector magnetRt is the transverse radius of the detector
magnetThe precision in the measurements is related to the parameter bA bit of trigonometry gives
The magnetic field is limited by the technologyIf we double the energy of the machine, keeping the same magnetic field, we must make a 1.4 times larger detector …
R t
b
eBE
E
BReRb tt
22
22
Unit 2 – Magnet specifications in particle accelerators 2.42
USPAS June 2007, Superconducting accelerator magnets
6. THE INTERACTION REGIONS:DETECTOR SPECIFICATIONS
Detector transverse sizeB is the field in the detector magnetRt is the transverse radius of the detector magnetThe precision in the measurements is 1/b
ExamplesLHC CMS: E=2300 GeV, B=4 T, Rl=12.9 m, Rt=5.9 m, b=9 mm
LEP ALEPH: E=100 GeV, B=1.5 T, Rl=6.5 m, Rt=2.65 m, b=16 mmthat’s why we need sizes of meters and not centimeters !
The magnetic field is limited by technologyBut fields are not so high as for accelerator dipoles (4T instead of 8 T)Note that the precision with BRt
2 – better large than high field …
Detector longitudinal sizeseveral issues are involved – not easy to give simple scaling laws
E
BReRb tt
22
22
GeV15.0
2
E
BRb t
Unit 2 – Magnet specifications in particle accelerators 2.43
USPAS June 2007, Superconducting accelerator magnets
SUMMARY
We gave the principles of a synchrotronThe problem is not only accelerating …but also keeping on a circle !Magnets are needed for keeping particle on the orbit
Arcs: dipoles for bending and quadrupoles for focusingHow to determine apertures, fields and gradientsInput: machine energy and beam emittance (injectors)Free parameter: cell lengthOutput: dipole field, quadrupole gradient, magnet lengths and numbers (i.e. machine length, excluding IR regions)
Interaction regionsHow to squeeze the beam sizeDetermination of the aperture, gradient and length of the IR quads
Unit 2 – Magnet specifications in particle accelerators 2.44
USPAS June 2007, Superconducting accelerator magnets
COMING SOON
During the next days: How these technological limits are determined ? What is the physics and the engineering behind?
0
100
200
300
400
0 25 50 75 100 125 150 175 200 225Aperture (mm)
Gra
dien
t (T
/m)
Baseline
LARP program
Nb-Ti 1.9 K
Nb3Sn 1.9 K
l*=23 m
*=55 cm *=14 cm *=7 cm*=28 cm
lq=20 m
lq=25 mlq=30 m
lq=40 mlq=50 m
Unit 2 – Magnet specifications in particle accelerators 2.45
USPAS June 2007, Superconducting accelerator magnets
REFERENCES
Beam dynamics - arcsP. Schmuser, et al, Ch. 9.F. Asner, Ch. 8.K. Steffen, “Basic course of accelerator optics”, CERN 85-19, pg 25-63.J. Rossbach, P. Schmuser, “Basic course of accelerator optics”, CERN 94-01, pg 17-79.
Beam dynamics - insertionsP. Bryant, “Insertions”, CERN 94-01, pg 159-187.
Beam dynamics - detectorsT. Taylor, “Detector magnet design”, CERN 2004-08, pg 152-165.
Unit 2 – Magnet specifications in particle accelerators 2.46
USPAS June 2007, Superconducting accelerator magnets
ACKNOWLEDGEMENTS
J. P. Kouthcouk, M. Giovannozzi, W. Scandale for discussions on beam dynamics and opticswww.wikipedia.org for most of the picturesThe Nikolai Tesla museum of Belgrade, for brochures, images, and information, and the anonymous guard I met in August 2002F. Borgnolutti for listening all my dry talksB. Bellesia for providing the slides template
Unit 2 – Magnet specifications in particle accelerators 2.47
USPAS June 2007, Superconducting accelerator magnets
APPENDIX A: DEPENDENCE ON THE CELL LENGTH
Example: Large Hadron ColliderLarger L → larger beta function → larger beam size → larger magnet aperture, butLarger L → small number of cells → smaller focusing strength
→ smaller number of quadrupoles
0.045
0.050
0.055
0.060
0.065
0 20 40 60 80Cell length (m)
Ape
rtur
e (m
m)
0100200300400500600700800
Num
ber
of q
uads
Magnet aperture (mm)Number of quads
Unit 2 – Magnet specifications in particle accelerators 2.48
USPAS June 2007, Superconducting accelerator magnets
APPENDIX A: DEPENDENCE ON THE CELL LENGTH
Example: Large Hadron ColliderDipoles contribute for around 17.5 KmWith a cell length of 30 m quads are 3.5 Km long (20%), with 70 m quads are 1 Km long (6%) – baseline is 50 m, giving 1.3 Km
17000
18000
19000
20000
21000
22000
0 20 40 60 80Cell length (m)
Arc
leng
th (
m)
dipoles
dipoles+quadrupoles
Unit 2 – Magnet specifications in particle accelerators 2.49
USPAS June 2007, Superconducting accelerator magnets
APPENDIX A: DEPENDENCE ON THE CELL LENGTH
Example: Large Hadron ColliderThe amount of the cable needed for dipoles and quadrupoles can also be estimated – equations will be derived in Unit 8The quantity of cable is roughly independent of the cell length, with a minimum around 50 m (but this was not the criteria used to select L!)
0
5
10
15
20
0 20 40 60 80Cell length (m)
Supe
rcon
duct
or v
olum
e (m
3 )
total
dipoles
quadrupoles