physics of particle accelerators - in2p3 events directory ... · physics of particle accelerators...
TRANSCRIPT
1
Physics of particle accelerators
IDPASC School LPNHE, Paris, 8-21 February, 2015
Patrick Puzo Laboratoire de l’Accélérateur Linéaire, Université Paris-Sud
P. Puzo IDPASC School, February 2015
Outline
1. Basic principles of particle accelerators 2. Several ways of accelerating particles 3. Accelerator zoology 4. Colliders 5. Some more complex topics 6. Conclusions
2
I assume you have prerequisite on classical electrodynamics and special relativity
We will always deal with ultra-relativistic particles
So:
P. Puzo IDPASC School, February 2015 3
Energie totale (MeV)1 10 210 310 410 510 610 710
Fact
eur d
e Lo
rent
z
1
10
210
310
410
510
610
710
ElectronsProtons
€
Total Energy = γ m c2
€
Kinetic Energy = (γ −1) m c2
€
Momentum = γ m β c ≈ γ m cTotal energy (MeV)
Lore
ntz
fact
or
References
Particle Accelerator Physics, Springer, H. Wiedemann
An introduction to the Physics of Particle Accelerators, World Scientific Publishing, M. Konte & W. Mackay
Accelerator Physics, World Scientific Publishing, S. Lee
Cern Accelerator Schools (specialized) and Cern Summer Student Lectures (introduction)
Some pictures will be taken from a book on Accelerators I am currently writing with André Tkatchenko (in French)
P. Puzo IDPASC School, February 2015 4
A bit of vocabulary
Accelerators/colliders Past • CERN (Geneva): Sp S (p, ), LEP (e+, e-) • SLAC (Stanford): PEP (e+, e-), SLC (e+, e-), PEP II (e+, e-) • DESY (Hamburg): HERA (e, p) • Fermilab (Chicago): Tevatron (p, ) • KEK (Tsukuba): KEK-B (e+, e-)
Present • BNL (New York): RHIC (Au, Au) • GANIL (Caen): SPIRAL (ions) • CERN: LHC (p, p)
(Far) future • ILC (e+, e-)
P. Puzo IDPASC School, February 2015 5
€
p
€
p €
p
P. Puzo IDPASC School, February 2015
Outline
1. Basic principles of particle accelerators
2. Several ways of accelerating particles 3. Accelerator zoology 4. Colliders 5. Some more complex topics 6. Conclusions
6
2
Driving equations in accelerator physics
Particle accelerators use electromagnetism and special relativity Maxwell equations
Lorentz: Action of E(t) and B(t) on a charge q (moving at speed v):
To produce high energy photons or neutrons, one needs first to accelerate charged particles and create neutral particles via nuclear reaction. For instance: Neutral beam cannot be well collimated
P. Puzo IDPASC School, February 2015 7
€
∇ . E = ρ
ε0
∇ . B = 0
∇ × E = − ∂
B ∂t
∇ × B = µ0
J + 1
c2∂ E ∂t
€
F = q (
E + v ×
B )
Lorentz force
Electric force Magnetic force
€
9Be(d,n)10B or e+ + e− → q + q +γ
Lorentz force : action of E field
The momentum variation of a charge under the Lorentz force is:
The kinetic energy gain is:
Accelerating a charged particle is always done by an electric field
P. Puzo IDPASC School, February 2015 8
€
Δ p =
F .∫ dt
€
ΔEkin = F .∫ d s with d s = v dt and
F = q
E + v ×
B ( )
€
⇒ ΔEkin = q E .∫ d s ⇒
dEkin
dt= q E . v
€
⇒ Ekin = Cste if E = 0 or
E ⊥ v
Lorentz force: action of B field
Trajectory is curved in B field: Projecting: (ρ: local radius)
Numerically (for a quantum charge):
Particles turn around B field at cyclotron frequency
P. Puzo IDPASC School, February 2015 9
€
d p dt
=d(γ m v )
dt= q v ×
B
€
dvdt
= 0
€
γ m v2
ρ= q v B ⇒ B ρ =
pq
€
ωc =q Bm
or ωc =q Bγ m
€
pGeV/c = 0,3 BT ρm
Relativistic case Classical case
No speed variation
Magnetic rigidity
Relative effects of E and B
Limits: Emin ≈ 0 and Bmin ≈ BEarth Emax in vacuum: ≈ 100 kV/cm or 107 V/m Bmax ≈ 2 T (classical magnet) or ≈ 10 T (superconducting
magnet)
If B and v are perpendicular:
If E = 107 V/m, then the B field to have the same force is 3 T if β = 0,01 and 0,03 T if β = 1
At high energy, guiding of high energy particles will only be done by B fields. E fields are only used at low energy
P. Puzo IDPASC School, February 2015 10
€
Fe
Fm=
E v × B
=E
β c B
Charged particle optics
Optics is guiding of charged particles. To 1st order (as in geometrical optics), it is linear
An element is a region where B ≠ 0. For one element:
For two elements:
P. Puzo IDPASC School, February 2015 11
€
xʹ′ x
⎛
⎝ ⎜ ⎞
⎠ ⎟ =
a bc d⎛
⎝ ⎜
⎞
⎠ ⎟
x0ʹ′ x 0
⎛
⎝ ⎜
⎞
⎠ ⎟
€
xʹ′ x
⎛
⎝ ⎜ ⎞
⎠ ⎟ =
e fg h⎛
⎝ ⎜
⎞
⎠ ⎟
a bc d⎛
⎝ ⎜
⎞
⎠ ⎟
x0ʹ′ x 0
⎛
⎝ ⎜
⎞
⎠ ⎟
€
A =a bc d⎛
⎝ ⎜
⎞
⎠ ⎟
€
B =e fg h⎛
⎝ ⎜
⎞
⎠ ⎟
x : position x’ : angle
A B
€
⇒xʹ′ x
⎛
⎝ ⎜ ⎞
⎠ ⎟ = B A
x0ʹ′ x 0
⎛
⎝ ⎜
⎞
⎠ ⎟
Between elements, we have drift spaces:
An accelerator merges drift spaces and elements where B field guides charged particles: Usually dipoles, quadrupoles and sextupoles
P. Puzo IDPASC School, February 2015 12
€
C =1 L0 1⎛
⎝ ⎜
⎞
⎠ ⎟
L
A B
€
⇒xʹ′ x
⎛
⎝ ⎜ ⎞
⎠ ⎟ = B C A
x0ʹ′ x 0
⎛
⎝ ⎜
⎞
⎠ ⎟
3
Dipoles
Orthogonal B field usually is uniform if pole geometry is under control
A charged particle is bent on a circular trajectory with radius ρ:
A particle with another momentum will be more or less deviated: Particles with Δp will not be kept
on magnetic axis
For an angle θ and a radius of curvature ρ :
P. Puzo IDPASC School, February 2015 13
€
1ρ
=q Bp≈q B cγ m c2
€
A =1 ρ θ
0 1⎛
⎝ ⎜
⎞
⎠ ⎟
Fringe field
p
p - Δp
p + Δp
Matrix for a dipole
In a ring, all particles come back to the same longitudinal position s after one turn (but not necessary at the same transverse position)
If all dipoles have the same B field value (or the same radius of curvature ρ), the ring is isomagnetic
Be careful of the difference between the dipole radius of curvature ρ and the ring circumference R
P. Puzo IDPASC School, February 2015 14
Classical dipoles are usually in iron to keep magnetic field lines g is the gap
Several types: C-shape magnets H-shape magnets Window magnets
P. Puzo IDPASC School, February 2015 15
!r >> 1
Chambre à vide
g
Culasse
Bobine d’excitationparcourues par le
courant NI/2
Chambre à vide
Culasse
Yoke
Vacuum chamber
Yoke
Vacuum chamber
Each coil circulates
NI/2
For a C-shape magnet iron to 1st order
Real example:
P. Puzo IDPASC School, February 2015 16
!r
2000
8000
6000
4000
B (T)1.61.20.80.40
!rmax
Be
NI (Ampères-tours)
µ = f(B) Be = f(μ)
LEP dipole
!r >> 1
Chambre à vide
g
Culasse
Bobine d’excitationparcourues par le
courant NI/2
From theory to practice
Quadrupoles
B field proportional to the axis: the further away from the axis, the higher deviation
Geometry of the poles matters a lot for the field homogeneity
Each quadrupole is focusing in one plan and defocusing in the other but …
P. Puzo IDPASC School, February 2015 17
€
Bx = k y and By = k x with k =∂Bx∂y
=∂By∂x
A set of two orthogonal quadrupoles focusing in each plane is globally focusing:
Matrices are:
Convention: a focusing quadrupole is focusing in horizontal (and defocusing in vertical) and a defocusing quadrupole is defocusing in horizontal (and focusing in vertical)
P. Puzo IDPASC School, February 2015 18
€
1f
=1fF
+1fD
−L
fF fD
€
AFoc =1 0
−1/ fF 1⎛
⎝ ⎜
⎞
⎠ ⎟ et ADéfoc =
1 01/ fD 1⎛
⎝ ⎜
⎞
⎠ ⎟
4
Sextupoles
Field is non linear:
B field on horizontal axis:
B field on vertical axis:
A sextupole is equivalent to a dipole combined with a quadrupole. It creates some coupling between horizontal and vertical planes
P. Puzo IDPASC School, February 2015 19
€
Bx =∂2By∂x2
x y et By =∂2By∂x2
x2 − y2( )
€
Bx =∂2By∂x2
x0 Δy and By =∂2By∂x2
x02
2− x0 Δx
⎛
⎝ ⎜
⎞
⎠ ⎟
€
Bx =∂2By∂x2
y0 Δx and By = −∂2By∂x2
y02
2− y0 Δy
⎛
⎝ ⎜
⎞
⎠ ⎟
Classical dipole schematics:
Classical sextupole schematics:
P. Puzo IDPASC School, February 2015 20
x
z
S
N
N N
S
S
Bobine
x
z
N
N
S
SFrom theory to practice
From theory to practice
Combined function magnets
No longer used nowadays on purpose, but can be created by misalignment .. To correct for the coupling, one uses sextupoles or squew
quadrupoles
P. Puzo IDPASC School, February 2015 21
Combine focusing and deviation
Squew quadrupole: combines H and V
focusing
Chambre à vide
X, x
Z z
dN
N
SSx
z
Vacuum chamber
Superconducting magnets
P. Puzo IDPASC School, February 2015 22
12,5 kA
Dipôle
I(!) = I0 cos(!)
Quadrupôle Sextupôle
I(!) = I0 cos(2!) I(!) = I0 cos(3!)
I(!)
Superconducting magnets
High field limits:
Limits: Joule effect or high B threshold for Sc phase
Differences: Classical: conductor position does not matter. Quality of the
B field is given by the geometry of the polar pieces Superconducting: conductor position gives quality of the field.
The yoke purpose is only to channel the B lines outside and has no influence on the field in the center
P. Puzo IDPASC School, February 2015 23
Dipole (T) Quadrupole (Tm) Classical magnet ≈ 2 ≈ 20 Superconducting magnet ≈ 8 ≅ 100
Large Hadron Collider (LHC)
p-p collider (E = 7 TeV) built in the LEP tunnel (2πR = 27 km)
Superconducting magnets (dipoles: 8,4 T) 90 tons of liquid helium II
« The largest refrigerator in the world »
P. Puzo IDPASC School, February 2015 24
T (K)
p (bar)
10
20
30
00 1 2 3 4 5
C
(V)
(S)
s
gHe II(L)
He I(L)Helium
phase diagram
(no field)
5
P. Puzo IDPASC School, February 2015 25
LHC dipole magnets
P. Puzo IDPASC School, February 2015 26
P. Puzo IDPASC School, February 2015 27
Source
1st part of an accelerator is always a source delivering stable particles (electrons, protons, ions)
Simplest electron source
Anode
H+
Plasma (obtained by heating)
Simplest proton source
P. Puzo IDPASC School, February 2015 28
Best performances are obtained with more sophisticated sources using: Plasmas Chemistry for surfaces
(breakdowns, ..) Vacuum technology Lasers (photocathodes)
Ion and p beam properties are fixed after the source
Simplest ion source
More realistic example
Vacuum chambers
Vacuum is needed to limit interactions with residual gas (elastic or inelastic collisions) and allow perfect running of specific systems (sources, accelerating cavities, ..) In practice: from 10-5 to 10-13 mbar (lower than on the Moon)
New technology since LEP: distributed pumping using NEG pumps (Non Evaporable Getter)
P. Puzo IDPASC School, February 2015 29
LEP vacuum chamber
Cooling Al
Lead shield
NEG coating
LHC vacuum chamber
Cooling
Proton
Synchrotron radiation
Photons emitted by ultra-relativistic electrons in a cone centered on the trajectory with opening angle θ = 1/γ
First evidence in 1947 on an electron synchrotron from GE built by Langmuir
Energy loss on one turn by ultra-relativistic electrons:
P. Puzo IDPASC School, February 2015 30
€
θ =1γ
€
ΔE( ) keV[ ] = 88,5E [GeV ]4
ρ [m] Radius of curvature
6
For e± and protons of the same Momentum on the same orbit, one has:
Synchrotron radiation is only visible on electron machines, and barely on proton machines
Synchrotron power can be very damaging
P. Puzo IDPASC School, February 2015 31
€
PRSp
PRSe =
memp
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟
4=
11836⎛ ⎝ ⎜
⎞ ⎠ ⎟ 4≈10 −13
e ±
protons
E (GeV) PSR (MW) LEP 1 50 1,1 LEP 2 108 15,6 LHC 7000 0,0073
Example of the lead shielding of the LEP
polarimeter
Synchrotron radiation is a limit if the energy is the key point HEP accelerators will be large
Synchrotron radiation is looked forward in some cases Dedicated accelerators to produce synchrotron radiation will
be compact
Obviously, the synchrotron radiation limitation vanishes (quite completely) for a linear accelerator
P. Puzo IDPASC School, February 2015 32
Beam power
Power stored in the beam is enormous
Safety aspects are crucial
P. Puzo IDPASC School, February 2015 33
€
P(MW) = E(GeV) × I(mA)
Energy (GeV) Total current (mA) Power (GW)
Tevatron 1000 60 60 HERA p 920 60 55 HERA e 27,5 20 0,55 RHIC 250 0,013 0,003 LHC 7000 500 3500 SOLEIL 2,75 400 1,1
P. Puzo IDPASC School, February 2015
Outline
1. Basic principles of particle accelerators
2. Several ways of accelerating particles
3. Accelerator zoology 4. Colliders 5. Some more complex topics 6. Conclusions
34
Static electric field
Bertozzi experiment (1964) ΔL = 8 m Evidence of relativistic effects
in the electron gun of a microscope
Classical theory:
Relativistic theory:
P. Puzo IDPASC School, February 2015 35 €
γ =1+Ecm c2
2/mccE0 1 2 3 4 5 6 7 8 9 10
2/c2 v
0
0.2
0.4
0.6
0.8
1
1.2
Description relativisteDescription classique
rimentalesees expeDonnClassical theory
Experimental data
Relativistic theory
Static electric field
Practical limitation due to breakdowns (order of MV/m) Can push limit up to 10 MV/m using SF6, but not more
How to reach higher energies ? Would it be possible to chain these accelerating cells ?
P. Puzo IDPASC School, February 2015 36
7
Time varying electric field
VRF is the accelerating voltage (time dependant) across the gap
A particle crossing the gap will receive:
What matters only in the field when the particle goes through the cavity (10 cm ≈ 300 ps)
P. Puzo IDPASC School, February 2015 37
€
ΔE = q Ez(z, t) dz−g /2+g /2∫
Accelerating cavity
Half accelerating cell
Time varying magnetic field
Acceleration via the induced electric field
Neglecting B variation on one turn, total force F and accelerating force Facc are:
Sparsely used
P. Puzo IDPASC School, February 2015 38
€
⇒ Facc =e r2dBdt
Plasma based acceleration
1979: first proposal (Tajima and Dawson) 1983: first acceleration (UCLA and LULI laboratories) 2004: first bunches (RAL and LOA laboratories)
An intense laser beam creates a plasma wave: some electrons can experience very high gradients
One can reach in principle 10 GV/m (compared to < 50 MV/m in a classical structure)
P. Puzo IDPASC School, February 2015 39
Electric field Electron density
Laser wake field accelerator Plasma created by laser pulse
Plasma wake field accelerator Plasma created by ultra-relativistic
electron beam
P. Puzo IDPASC School, February 2015 40
Particule au repos = 1.2
v
= 3
v
= 10
vFiled line for fast moving charge
LWFA example:
Next step: 40 J / 40 fs 10 GeV
PWFA example (FFTB) 42 GeV electrons in
plasma cell
P. Puzo IDPASC School, February 2015 41
Some electrons double their
energy in 84 cm
Nature 445 741 15-Feb-2007
Plasma is probably (part of) the future of high energy accelerators Timescale ?
P. Puzo IDPASC School, February 2015 42
Conv
entio
nal a
ccele
rato
rs
8
More exotic scheme
CLIC project: energy transfer from low energy high intensity beam through high energy low intensity beam
Concept tested since several years. 80 MV/m achieved, but with damages in the transfer structure. Will it be operational one day ?
P. Puzo IDPASC School, February 2015 43 P. Puzo IDPASC School, February 2015
Outline
1. Basic principles of particle accelerators 2. Several ways of accelerating particles
3. Accelerator zoology
4. Colliders 5. Some more complex topics 6. Conclusions
44
P. Puzo IDPASC School, February 2015 45
Repetition rate can be much higher on a circular machines than on a linear one (50 kHz versus 100 Hz typically) Consequences for a collider on beam size
Is synchrotron radiation a concern ?
P. Puzo IDPASC School, February 2015
Outline
1. Basic principles of particle accelerators 2. Several ways of accelerating particles
3. Accelerator zoology 1. Circular accelerators 2. Linear accelerators
4. Colliders 5. Some more complex topics 6. Conclusions
46
Cyclotron
Principle due to Ernest Lawrence (1929) Beam is curved by B field in
« Ds » produced by classical magnets
Alternative E field in the gap Time to travel in one D is
independent of the radius
One could show that:
Used for ions and protons, not for electrons
P. Puzo IDPASC School, February 2015 47
€
ω =q Bγ m
1st cyclotron (80 keV)
A modern one: the 590 MeV from PSI (Zurich)
P. Puzo IDPASC School, February 2015 48
Cavities
Magnets
9
For years, cyclotrons were the most popular accelerators in the world (simplicity, cost, compactness, ..)
To go higher than the GeV, something else is needed
P. Puzo IDPASC School, February 2015 49
TRIUMPH cyclotron (used for heavy ion
research)
Synchrotron
On the opposite to the cyclotron, B field is applied on the circumference only
Principle: Particles are running on a circular path and gain energy by
going through accelerating cavities The higher the energy, the higher the cavity frequency B field has to increased simultaneously to keep the particle on
the circular orbit
P. Puzo IDPASC School, February 2015 50
€
1ρ
=q BpCyclotron
Synchrotron
Guiding and focusing are done by different elements
Dynamical range of a classical mgnet is limited (≈ Bmax/20, Bmax) Examples:
• LEP: from 20 tp 110 GeV • LHC: from 0,45 to 7 TeV
Synchrotron concept requires the use of an injector
P. Puzo IDPASC School, February 2015 51
Acceleration chain at DESY (920 GeV protons and 27,5
GeV e+/e-)
Example with an injector
Two types of synchrotrons: Proton synchrotrons
• The 1st one discovered the antiproton (Bevatron, Berkeley, 1954)
• SppS (CERN) discovered W± and Z0 • LHC discovered Higgs boson
Electron synchrotrons • LEP was a Z0 and W± factory. Determined the number of
neutrino families and 10s of precise standard model measurements
Most of the HEP discoveries since 1955 were done on synchrotrons
P. Puzo IDPASC School, February 2015 52
Betatron
Principle is to used time varying B field to accelerate particles vie induced E field (formerly only with protons)
One has:
Modern use: X ray production (with electrons)
P. Puzo IDPASC School, February 2015 53
€
Fem =e r2dBdt
B field
€
F
€
F
Particle trajectory
Radiography Tumor treatment