Accelerators LISHEP Lecture I Oliver Brning CERN - - PDF document

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Accelerators

Oliver Brüning CERN LISHEP Lecture I

electro dynamics, computer science classical and quantum mechanics,

Particle Accelerators

Magnet design + construction Vacuum

Physics of Particle Beams:

computer science

High power RF waves Cryogenics Super conductivity

surface science, solid state physics, electro dynamics, engeneering,

Single particle dynamics Collective effects Two beam effects

non-linear dynamics, relativity,

Physics of Accelerators:

Projects & Applications

)

I

Overview

Motivation & Sources

+

II)

Circular Accelerators Linear Accelerators

+

main limitations

IV) III )

Challanges for the LHC Other Accelerator

Overview and History:

• S. Weinberg, ’The Discovery of Subatomic Particles’, Scientific American Library, 1983.

(ISBN 0-7167-1488-4 or 0-7167-1489-2 [pbk]) (539.12 WEI)

• C. Pellegrini, ’The Development of Colliders’, AIP Press, 1995. (ISBN 1-56396-349-3)

(93:621.384 PEL)

• P. Waloschek, ’The Infancy of Particle Accelerators’, DESY 94-039, 1994.
• R. Carrigan and W.P. Trower, ’Particles and Forces - At the Heart of the Matter’, Read-

ings from Scientific American, W.H. Freeman and Company, 1990.

• Leon Lederman, ’The God Particle’, Delta books 1994
• Lillian Hoddeson (editor), ’The rise of the standard model: particle physics in the 1960s

and 1970s’, Cambridge University Press, 1997

• S. Weinberg, ’Reflections on Big Science’, MIT Press, 1967 (5(04) WEI)

Introduction to Particle Accelerator Physics:

• Mario Conte and William McKay, ’An Introduction to the Physics of Particle Accelera-

tors’, Word Scientific, 1991

• H.Wiedemann, ’Particle Accelerator Physics’, Springer Verlag, 1993.
• CERN Accelerator School, General Accelerator Physics Course, CERN Report 85-19,

1985.

• CERN Accelerator School, Second General Accelerator Physics Course, CERN Report

87-10, 1987.

• CERN Accelerator School, Fourth General Accelerator Physics Course, CERN Report

91-04, 1991.

• M. Sands, ’The Physics of Electron Storage Rings’, SLAC-121, 1970.
• E.D. Courant and H.S. Snyder, ’Theory of the Alternating-Gradient Synchrotron’, Annals
• f Physics 3, 1-48 (1958).
• CERN Accelerator School, RF Engeneering for Particle Accelerators, CERN Report 92-

03, 1992.

• CERN Accelerator School, 50 Years of Synchrotrons, CERN Report 97-04, 1997.
• E.J.N. Wilson, Accelerators for the Twenty-First Century - A Review, CERN Report

90-05, 1990.

Special Topics and Detailed Information:

• J.D. Jackson, ’Calssical Electrodynamics’, Wiley, New York, 1975.
• Lichtenberg and Lieberman, ’Regular and Stochastic Motion’, Applied Mathematical Sci-

ences 38, Springer Verlag.

• A.W. Chao, ’Physics of Collective Beam Instabilities in High Energy Accelerators’, Wiley,

New York 1993.

• M. Diens, M. Month and S. Turner, ’Frontiers of Particle Beams: Intensity Limitations’,

Springer-Verlag 1992, (ISBN 3-540-55250-2 or 0-387-55250-2) (Hilton Head Island 1990) ’Physics of Collective Beam Instabilities in High Energy Accelerators’, Wiley, New York 1993.

• R.A. Carrigan, F.R. Huson and M. Month, ’The State of Particle Accelerators and High

Energy Physics’, American Institute of Physics New Yorkm 1982, (ISBN 0-88318-191-6) (AIP 92 1981) ’Physics of Collective Beam Instabilities in High Energy Accelerators’, Wiley, New York 1993.

Linear Accelerators

Electro−Magnetic Waves & Boundary Conditions DC Acceleration Equations and Units RF Acceleration Motivation Particle Sources Acceleration Concepts: Summary

I) Motivation & Sources

Search for Elementary Particles

1803: 1896: 1896: 1906: Dalton Thomson Rutherford Electron Atom 1911: Rutherford α+ N O + H+

Chronology:

Electron Nucleus + M & P Curie Atoms can decay

Stage I: Nuclear Physics

Particle Accelerators Disintegration of Nuclei!

NP 1906: discovery of the electron

Rutherford experimental evidence of atom structure NP for N. Bohr in 1922 1906 − 1911:

Stage II:

Particle Physics

Chronology (Theory):

2

E = mc Einstein (Cosmic Rays) Antimatter

• Meson

π

Dirac Yukawa 1905: 1930: 1935:

Chronology (Experiments):

Anderson

e µ

+ Anderson 1937: 1932:

p-

π }

Accelerators

?

ionizing particle

+ (NP 1936: cosmic rays) 1932: Anderson

e

particle Κ

bubble chamber

−

e :

−

− +

Particle Sources:

e

Cathode Rays

H + e H + e 2 e H + H H + e + H + e H + 2 e

2 2 2 + + + + − − − − − −

Pair Production Antimatter: Particle Sources:

ions

Example:

p+

φ -

A

e

t

e

c 1

• grad

E = B = rot A

Time varying fields ( = 0)

Acceleration Concepts

φ

)

v x B + E

(

* = Q dp dt

Lorentz Force: Scalar and Vector Potential:

Energy gain only due to E field! Electrostatic fields (A = 0)

−19

Units

Energy Gain:

e−

E

(1.6 * 10 J)

1 eV

−27

Total Particle Energy: Common Units: keV, MeV, GeV, TeV

3

10 , 10 , 10 , 10

6 12 )

(

2

E = mc ; m = * m

γ

Relativity: Electron:

−31

m = 9.11*10 kg; 0.51 MeV 0.94 GeV m = 1.67*10 kg; Proton:

1 Volt

9

γ = 1/ 1 − ; β

2

β = v/c

high voltage unit

Electrostatic Fields

V = 200 kV

max

1928: 1932: Cockroft + Walton p + Li 2 He (Nobel Prize 1951)

capacitors U = U sin t

ω

• 2U

4U 6U

• diodes

Cascade Generator: High Voltage Unit:

+

• 700kV (p)

800kV

target tube acceleration ion source

High Voltage Unit at CERN:

Cascade Generator at CERN:

Van de Graaf Generator

source

Single Unit: V = 10 MVolt

max channel acceleration 50 kV dc + + + + + + + + + + + + + + + + + + + + + + + 10 MV conveyor belt top terminal evacuated experiment spectrometer magnet spraycomb charge charge collector ion

Van de Graaf Generator

Tuve 1935:

• max
• +

+ + + + + + + + + + dc 50 kV

• r gas

experiment pressure tank high voltage terminal negative ion Source spraycomb striping foil charge conveyor belt

Van de Graaf Generator

Tandem generator: V = 25 MVolt

42 m high 20 MVolt

Van de Graaf Generator

2 * Tandem Van de Graaf in BNL 1970 Daresbury:

Time Varying Fields

beam

E

beam

E E E−Field in the wrong direction!

Linear Acceleration: requires energy to move charges on capacitor plates! timing between ´v´ and freq! requires shielding and bunched beam long accelerator structure

1928:

BEAM

+ + − − + + + − − + + + − 1.3MV mercury ions with 48kV Lawrance: 50kV potassium ions 1MHz, 25kV oscillator demonstrated by Wideroe V t AC Voltage: 1924: Ising

part

l = v T/2

Drift Tubes

Symmetric line:

find a structure with passive supports f < 7MHz

• peration limited to low frequencies

implies large structures for v = c! f = 7MHz −> l = 21 meter (for v = c)!

• nly efficient for low energetic particles

high energetic particles require higher frequencies But:

part

l = v T/2

BEAM

+ + − − + + + − − + + + − support tubes have capacitive impedance

Drift Tubes

Resonator:

capacitor AC generator capacitor coil beam cavity beam cavity beam

E E

e e

t c rot B = µε

L = l µ N A

2

C = ε A d

E = − 1

A

e e

c

E B

t f; Q; R

Resonance Structures

TM mode with 352 MHz; 1.5 MV/m

010

LEP Cavity

LEP Cavity

E H axis beam

efficient use of energy exact dimensions determined by Maxwell Equations with boundary conditions

Cavity Resonator:

Resonance Structures

d) b) and plus: Rotation on

Time Varying Fields

= E E

2

e

2

t

e

c2

µε

Δ

2

B

e

2

e

t2 = B µε

c 2

Δ

2

d) c)

Δ

* B = 0

Δ

c

e

t

x B − = 0

µε

e

E a)

Δ

* E = 0

b)

Δ

c

e

t

x E + = 0 1

e

B x ( x V ) = ( V ) − V Δ Δ Δ Δ Δ

Maxwell Equations without Sources

Wave equation:

ω ω

B = B e

ik n x − t ik n x − t

k = 2 π

λ

µε B = n x E No acceleration in the direction of propagation! E = E e

Plane Electro Magnetic Wave:

Time Varying Fields

n s

Boundary condition: E = 0

e

n

e

B

s

2 λ

H E

wall currents displacement currents

B = 0 everywhere;

z

E = 0 everywhere;

z

Boundary condition: = 0

2 λ

immage charges

E H H

Wave Guide Boundary Conditions

Transverse Electric Waves (TE): Transverse Magnetic Waves (TM):

• ption of two field configurations

B = 0 everywhere;

z

Boundary condition: E = 0

n s z

E = 0 everywhere;

e

n

e

B

s

Boundary condition: = 0

I

TM

01

Transverse Electric Waves (TE):

Boundary Conditions

Transverse Magnetic Waves (TM):

Example TM−mode: mode frequency: Maxwell Equations:

(Chapter 8 in Jackson: Classical Electrodynamics)

Solutions for TM Waves

Cylindrical Coordinates:

lowest TE−mode:

(0,1,0)

E does not depend on ´z´

(0,1,0)

−long cavity −> significant change of E during passage −short cavity implies small voltage: becomes small

gap z (1,1,1)

TE

z max

the Electro−Magnetic wave is characterized by: TM or TE b) the number of ´zero´ crossings: a) the field pattern on the metallic surface: (m,n,p) mode characteristics: cavity radius inversly proportional to frequency Cavity with TM mode: lowest TM−mode: TM ω V = E exp( z / v) dz V = E dz

Modes of the EM Waves

010

Vgap Vmax h Vgap Vmax short cavity and low RF frequency minimize: h ω large cavity structure minimize: h / r for TM 200MHz parabolic efficent acceleration requires maximum (transit time factor) not efficient for low energetic particles

Efficient Cavity Design

PS 19MHz Cavity

II

displacement currents

install shielding where the E−field has the wrong sign

beam

the shielding is passive! we can use high frequencies! low energetic particles! use higher order modes for

2 λ

H mode

01

E − E

wall currents

Boundary Conditions

acceleration using TM mode

we can use high frequencies! Alvarez: (f = 200 MHz gives good tube size) Tubes are passive Posts

gr

Pre−accelerator for most acclelerators proton v = vparticle

BEAM support posts part

l = v / c − − + − + − + − + +

λ

Resonance Tank

e.g. at CERN most accelerators: Pre−accelerator for

Resonance Tank

− Pre−accelerator for ion beam at CERN

BEAM

− −

posts part

IH Structure: Posts are connected to tubes TE Modes allow short structures better efficiency for slow particles + + + longitudinal E field for TE mode! charge can flow between tubes l = v / 2c

support

− + − +

λ

Resonance Tank with TE Mode

used for the Pb ion acceleration at CERN

Interdigital H Structure (TE−Modes)

Acceleration Using TE Modes

III

B = 0 everywhere;

z

Boundary condition: E = 0

n s

Problem:

ph

v

ph

v > v particle

Shielding changes

2 λ

H mode

01

E − E

wall currents displacement currents

v

Boundary Conditions

Transverse Magnetic Waves (TM): Acceleration using travelling waves:

But: Concept of linear acceleration is limited by power of RF generator! Not feasible before World War II

particle beam path iris

v = v

ph

Acceleration using Travelling Waves Loaded Wave Guide:

SPS at CERN Cu linac structure:

Travelling Wave Structures