Physics of particle accelerators - IN2P3 Events Directory ... · Physics of particle accelerators...

1

Physics of particle accelerators

IDPASC School LPNHE, Paris, 8-21 February, 2015

Patrick Puzo Laboratoire de l’Accélérateur Linéaire, Université Paris-Sud

[email protected]

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)


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

€

p €

p


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


€

∇ . 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


€

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


€

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


€

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:


€

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


€

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 :


€

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


  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


!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:


!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 …


€

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)


€

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


€

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:


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


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


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


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 »


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


LHC dipole magnets



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


  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)


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:


€

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


€

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


Beam power

  Power stored in the beam is enormous

  Safety aspects are crucial


€

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


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 ?


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)


€

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


€

⇒ 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)


Electric field Electron density

  Laser wake field accelerator   Plasma created by laser pulse

  Plasma wake field accelerator   Plasma created by ultra-relativistic

electron beam


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


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 ?


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


  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 ?


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


€

ω =q Bγ m

  1st cyclotron (80 keV)

  A modern one: the 590 MeV from PSI (Zurich)


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


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


€

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


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


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)


€

Fem =e r2dBdt

B field

€

F

€

F

Particle trajectory

Radiography Tumor treatment

Physics of particle accelerators - IN2P3 Events Directory ... · Physics of particle accelerators...

Documents

Transcript of Physics of particle accelerators - IN2P3 Events Directory ... · Physics of particle accelerators...