Engines of Discovery

R.S. Orr

Department of Physics

University of Toronto

Berkley 1930

1 MeV

Geneva

14 TeV 20089

Birth of Particle Physics and Accelerators

• 1909 Geiger/Marsden MeV a backscattering - Manchester

• 1919 Rutherford disintegrates Nitrogen - Manchester

• 1927 Rutherford demands accelerator development

Particle accelerator studies - Cavendish

• 1929 Cockcroft and Walton start high voltage experiments

• 1932 The goal achieved: Cockcroft + Walton split Li nucleus

Cockcroft-Walton Generator

665 kV

Ising – 1924

Resonant Accelerator Concept

• The acceleration occurs in the electric field between cylindrical drift tubes.

• The RF power must be synchronised with the motion of the electrons, so that acceleration occurs in every gap.

Wideroe - 1928

Linear Accelerator = LINAC

Alternating (radio frequency) fields allow higher voltages

Recirculation Concept - Cyclotron

Radio frequency alternating voltage

Hollow metal drift tubes

time t =0

time t =½ RF period

D-shaped RF cavities

• Orbit radius increases with momentum

• Orbital Frequency independent of momentum

• Particle motion and RF in phase

Lawrence:

4” – 80 keV

11” - 1.2 MeV

B mv

ep

ef rev

v

2v

2

eB

mveB

2m

Magnetic rigidity Constant revolution frequency

Equilibrium Orbit

Orbit Stability

Slight Displacement from Equilibrium Orbit Particle Lost

Vertical and Horizontal Focusing

Vertical Orbit Stability in Lawrence’s Cyclotron

Cross Section Thru Ds Electrostatic Focusing Lens

Orbital Stability in a Cyclotron

qF v B

c

SHIMS

Horizontal Vertical

0z

n

zR

B Br

0

2

0zmv e

vBR c

2

x zmv e

F vBr c

2

1xmv x

FR R

n

1x nv

R

1n

2

2 xd y e

m vBcdt

0x zB B

z x

2

2z

znBd y e

m v FR cdt

2 2

2 20n

d y vm m

dt R

2

2zR

nv

0n

Field Index

Equilibrium Orbit

Centrifugal = Lorentz on equilibrium orbit

Restoring Force

Simple Harmonic

Stable Oscillations around Equilibrium orbit

Weak Focusing

Betatron Oscillations

This machine is just a model for a bigger

one, of course

This machine is just a model for a bigger

one, of course

This machine is just a model for a bigger

one, of course

1931 410 Volts

1932

1953

610 Volts

910 Volts

1960 1010 Volts

Marcus Oliphant

– later to become

Governor of South Australia

Invention of the Synchrotron

Synchrotron Ring Schematic

Focusing magnets

Vacuum

tube

Accelerating

cavity

Bending magnets

• Increase magnetic field

during acceleration.

• Constant orbital radius

1 0 1 01

1 11 10 1

L

f f

2

1

1

LL

f

L L

f f

2

1 0

1L

f

L f Net Focusing

• FODO Lattice

• Strong Focusing

Strong Focusing

• Field Index set by Pole Face Shape

• Weak, n = 0.5

• Strong, n = 3500

• Strong Focusing = Alternating Gradient

• “Combined Function” Magnet

Weak Focusing Magnet

Strong Focusing Magnet

Enormous Cost Saving

• Strong Focusing = Alternating Gradient

• Reduce amplitude of betatron oscillations

• Reduce diameter of vacuum pipe

• Reduce Aperture of Magnets

• 35 GeV (CERN PS, AGS) costs same as 7 GeV (NIMROD)

2

20

d YK s Y

ds

cosY s A s s

cosY s s s

2

2 3

1dK s

ds

2s s

TRAJECTORY

BEAM ENVELOPE

Amplitude of betatron oscillations

• Single Particle Phase Space

• Beam Envelope

position

angle

Shape of phase space changes along accelerator lattice

Area constant -> Liouville

• Real Accelerator

• Non-linear

2 2

1 1

A B C

1

sins s sn nE E eV

Successive turns around accelerator lattice

• B is synchronous with RF phase

• A too energetic to be in phase

• B not energetic enough to be in phase

Closed Oscillations in Phase

(non relativistic)

Change in transit time around lattice

Synchronous particle

1 1

1

1

2

2

s

s

in sin

ins s s

n n n

n

n n

s

n s

E E eV

c

vE

E E eV

E

• Symplectic Mapping

• Preserves Phase Space

Synchronous Particle

Non-Synchronous Particle

Transformed “s” into “Φ” position around lattice

Particle orbits in energy-phase

separatrix Stable oscillations

Trapped by RF

Unconfined motion = “lost” particles

Synchronous particle

1

2

2

sin si

sin

n

s n

s

s

s snE E eV

cdE

dn

d EeV

dn

v E

Non-linear equations

Describing deviation in phase and energy from synchronous orbit

2 2

2cos s

1constant = Η in=

2s

s

c

v

d

dn E

RF Bucket

separatrix

cos sin s

H

Initial condition

CERN Seen from the Air

• Tunnels of CERN accelerator complex superimposed on a map of Geneva.

• Accelerator is 50 m underground

• 25 km in circumference

Superconducting Magnet

8 Tesla

•In order to accelerate protons to high energy, must bend them in circular accelerator

•7 TeV momentum needs intense magnetic field

LHC 2002

LHC 2003

Dipole Cold Masses

Ph. Lebrun ATLAS Plenary Meeting

18 February 2005

Infrastructure completed in 2003

Underground

Dipole-dipole interconnect

March 2006

Descent of the Last Magnet, 26 April 2007

300 m underground at 2 km/h!

RF Modules

Sector 7-8 Sector 8-1

Point 8

Su

rfa

ceC

ave

rn

QSCA QSCB

QSRB

QURC

QUIC

QURA

Sh

aft

QSCC QSCC

Tu

nn

el

Storage

QURC

QSRA

IHI Linde Air Liquide

Refrigeration Units at 1.8 K

Sector 7-8 Sector 8-1

Point 8

Su

rfa

ceC

ave

rn

QSCA QSCB

QSRB

QURC

QUIC

QURA

Sh

aft

QSCC QSCC

Tu

nn

el

Storage

QURC

QSRA

Cryogenic Distribution

DFBA Electrical Feed Box

Low current module 6kA & 600A leads

High current module 13kA & 6kA leads

Shuffling module

Vacuum equipment VAA

Connection to

magnets

Jumper cryo

connection to QRLSHM/HCM

interconnect

HCM/LCM

interconnect

Supporting beam

600A leads

6kA leads

6kA leads

13kA leads

Current lead chimneys

Removable door

x 16

2 per LHC Point

1.9K

4.5K

13 kA HTS Current Leads

6 kA current leads with water-cooled cables

Lyn Evans – EDMS docment no. 970483 45

Beam 2 first beam – D-Day

46

Beam on turns 1 and 2

47 Courtesy R. Bailey

No RF, debunching in ~ 25*10 turns, i.e.

roughly 25 mS

48 Courtesy E. Ciapala

First attempt at capture, at exactly the wrong

injection phase…

49 Courtesy E. Ciapala

Capture with corrected injection phasing

50 Courtesy E. Ciapala

Capture with optimum injection phasing,

correct reference

51 Courtesy E. Ciapala

LHC longitudinal bunch profile Beam 2

52

Lyn Evans – EDMS document no. 970483

H wire scan

53

Kick response compared with

theoretical optics

54

Alors, c’est fini!

Et maintenant?

• Storage Ring

• Stable phase =

• No acceleration

0

2 2

2 2

2

2

cos 0

2 0

s

s

s

d c eV

dn v E

d

dn

0 ; ; cos 0

0 ; ; cos 0

t s

t s

Synchrotron (phase) oscillations