collider concept synchrotron radiation vacuum requirements trajectory stabilitystorage rings acceleration conceptsdesign parameters for the LHCBasic Accelerator Principles :units and equations Overview

http://bruening.home.cern.ch/bruening/summer−school/HST−Lecture.pdf

trajectory stability storage rings

acceleration concepts

design parameters for the LHC Basic Accelerator Principles :

units and equations

Overview

collider concept

synchrotron radiation vacuum requirements

Overview and History:

• M.S. Livingston and E.M. McMillan, ’History of the Cyclotron’, Physics Today, 1959

• S. Weinberg, ’The Discovery of Subatomic Particles’, Scientific Ameri- can 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’, Readings 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:

• J.J. Livingood, ’Principles of Cyclic Particle Accelerators’, D. Van Nos- trand Company, 1961

• M.S. Livingston and J.P. Blewett, ’Partticle Accelerators’, McGraw- Hill, 1962

• Mario Conte and William McKay, ’An Introduction to the Physics of Particle Accelerators’, 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 of 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 Sciences 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: In- tensity 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 Accel- erators and High Energy Physics’, American Institute of Physics New Yorkm 1982, (ISBN 0-88318-191-6) (AIP 92 1981) ’Physics of Collec- tive Beam Instabilities in High Energy Accelerators’, Wiley, New York 1993.

super conducting magnet technology R = 2784 meter

FODO lattice proton collider

2 in 1 magnet design

2835 bunche with 10 particles per bunch B = 8.38 T

high luminosity insertions beam screen

super conducting RF

cryo pump at 2K

11

Choices for the LHC

max earth: 0.3 * 10 Tesla

iron sarturation: 2 Tesla

−4

Stage I:

Nuclear Physics

1803:

+ 1896:

1896:

1906:

Dalton

M & P Currie Thomson

Rutherford

Electron Atom

Search for Elementary Particles

Particle Accelerators

Disintegration of Nuclei!

1911: Rutherford α+ N O + H+ Atoms can decay

Chronology:

Electron Nucleus

Stage II:

Particle Physics

Chronology (Theory):

E = mc2

Einstein

(Cosmic Rays)

Antimatter - Meson

π

Dirac Yukawa 1905:

1930:

1935:

Chronology (Experiments):

Anderson e

µ

+ Anderson

1937:

1932:

p^-

π } ?

magnetic fields:

F

v

)

v x B E +

(

= Q * dp

dt

Acceleration Concepts

Lorentz Force:

Energy gain only due to E field!

Trajectory curvature due to B field!

B

1 Volt

0.51 MeV proton: 0.94 GeV

γ = 1/ 1 − ;β² β ^{= v/c}

Total Particle Energy:

E = mc ; m = * m2 γ ₀

Relativity:

keV, MeV, GeV, TeV 10 , 10 , 10 , 103 ^{6 12} )

( ⁹

Units

Energy Gain:

e⁻ E

(1.6 * 10 J)⁻¹⁹

1 eV

Common Units:

electron:

- +

e

e :

p

:

Antimatter:

H + e H + e

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

2 2

2 +

+ +

+ -

- -

- - -

Particle Sources:

Cathode Rays Cathode Tube with H

Pair Production

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_o ω

0 2U_o 4U_o 6U_o

diodes

Cascade Generator:

High Voltage Unit:

+

−

700kV (p) 800kV

target tube

acceleration ion source

source

Van de Graaf Generator

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

Circular Accelerator:

Time Varying Fields

E

beam

E beam

beam

E

Linear Acceleration:

bunched beam

long accelerator!

Resonator:

capacitor

AC generator

capacitor

coil

beam

cavity beam

cavity

f; Q; R

beam

E

e E

e t rot B = µεc

L = l

µ N A₀ ²

C = ε A d

0

Time Varying Fields

E = - ^{1 A}

e e

c

E B

t

Q m

Bγ ω =

Q r = m

B γ ω

v

=

00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000

11111111 11111111 11111111 11111111 11111111 11111111 11111111 11111111 11111111 11111111 11111111 11111111

B

injection

magnet

vacuum chamber

extraction / target RF cavity

0

0 0 0

Circular Accelerators

Synchrotron: R = const.

B = const.

(LHC/LEP: 11.3kHz)

Q r = m

B

γ v

R[meter]

p[GeV/c]

B[T] = 1 0.3

B = 8.38 T

L = 27000 meter arcs: L = 22200 meter R = 3500 meter

p = 7000 GeV/c

Bending and Focusing: R = 2784 meter

Why 8.4 Tesla?

LEP tunel:

Physics:

max earth: 0.3 * 10 Tesla

iron sarturation: 2 Tesla

−4

0

R = const.

B γ

Synchrotron:

P = R I

P = 78 MW / magnet B = 8.38 T

2

B I

8.4 T is at the limit of available technology!

I = 4500A; R = 1m ca. 500 magnets

LHC:

max I = 280000 A

superconducting technology!

ca. 500 magnets P > 39 GW

Power Consumption

B = 0.135 Tesla LEP:

Ω P = 20 kW / magnet P = 10 MW

gravitation:

g = 10 m s⁻²

∆ s = 18 mm ∆ t = 60 msec

660 Turns!

B

v F

v

B

x F

y

particle trajectory ideal orbit

B (y)x

Vertical Plane:

2

∆ s = g t1 ∆ ²

requires focusing!

Trajectory Stability

1

small vacuum chamber

high oscillation frequency

for a fixed energy F = −g y

efficient magnets

2 g

A g

small amplitudes

000000 000 111111 111

000000000000000 000000000000000 000000000000000 000000000000000 111111111111111 111111111111111 111111111111111 111111111111111

Strong Focusing

oscillator (spring):

Ω

strong focusing:

Quadrupole Focusing

Quadrupole Magnet B = −g y_x

B = −g xy

R

N S

S N

Alternate Gradient Focusing

00000000 00000000 00000000 0000

11111111 11111111 11111111 1111

00000 00000 00000 00000 00000 00000

11111 11111 11111 11111 11111 11111

ω > ωβ 0

Idea: cut the arc sections in

elements defocusing

focusing and

defocusing in horizontal plane!

x

y

F = g x F = −g y

Q ; Q ; Q

y(s) = A sin( Q s + ) number of oscillations Q = turn

β( ) = β( )s + L s

β( )s Q = 1

2π

1 ds

2π

β L φ₀

amplitude term due to injector

amplitude term due to focusing

sorage ring circumference

Tune:

Envelope Function:

Storage Ring

x y s

B L Q 2π

p = m

Q

0

B

0

γ

Q c 2π

r = v

E / c

−drift space for installation

−different types of magnets

−space for experiments etc for E >> E

B−field is not uniform:

−high magnetic field

−large packing factor ’F’

high beam energy requires:

Circular Accelerators

R = const.

uniform B−field:

B d l E =

realistic synchrotron:

D B F B

B

D

x = x + x₀

dipole component

quadrupole

y

B = -g yx

B = -g x - g x

orbit error

y

B = -g yx

0

B = -g x

B F B D B

F

Closed Orbit

Orbit Offset in Quadrupole:

slow drift

moon seasons

civil engineering

power supplies calibration

civilisation

Sources for Orbit Errors

Alignment: +/− 0.1 mm

Ground motion

Energy error of particles Error in dipole strength

b)

π γ

t V

a)

f = h fRF rev

f = 1 2

q

m B

rev

E depends on orbit and magnetic field!

assume: L > design orbit

the orbit determines the particle energy!

Synchrotron:

energy increase

Equilibrium:

momentum increase

1 Q² α

R

∆ = α ∆pR p α = 1γ_t²

momentum compaction factor:

increase particle energy

transition energy

E error depends on transition energy!

longer revolution time shorter revolution time velocity increase

Orbit Correction

place orbit corrector and BPM next to the main quadrupoles

vertical BPM and corrector next to QD

QF MB QD

BPM

HX

BPM

HV

aim at a local correction of the dipole error due to the quadrupole alignment errors

relative alignment of BPM and quadrupole?

horizontal BPM and corrector next to QF

minimise field errors

Orbit Stability

dipole error and Q = N:

Kick

watch out for fractional tunes!

watch out for integer tunes!

the perturbation adds up

field errors:

the perturbations add up for Q = 1/n

and avoid strong resonances!

changes

y s

avoid low order resonances!

x

h A^n+m+s strength:

and tune

00000000 00000000 00000000 11111111 11111111 11111111

n Q + m Q + r Q = p

limits for b

Q

Tune Diagram

resonances:

n x

Q y

0 0.2 0.4 0.6 0.8 1

0 0.2 0.4 0.6 0.8 1

Q _x

Q y

0.2 0.22 0.24 0.26 0.28 0.3

0.2 0.22 0.24 0.26 0.28 0.3

particle energy

200 400 600 800 1000 500

1000 1500 2000

fixed target collider

ISR

Tevatron

Tevatron

GeV GeV

center of mass energy

SPS SppS

But:

CM p

+ +

−

1970 : −

e / e collider p / p collider

Collider Rings

fixed target physics 1960:

(bubble chamber)

0 2

cm 2

E

0

Collider: E = 2 E

E = 2 m c 1 + − 1 2 m c

1960 :

collision regions

collision point

anti−particles

long storage times

requires beam separation anti−particles hard to produce

two rings

beam−beam interaction

−

Features ( )

not all particles collide in one crossing

+

requires 2 beams:

/

ALICE

injection b1 collimation

machine protection

extraction

injection b2 LHCb

CMS TOTEM

ATLAS RF

beam2 beam1

IP3

IP8 IP5

IP4 IP6

IP2

IP1

LHC Layout

2 Ring Layout:

2−in−1 magnet design

beam cross−over in 4 IR’s

4 proton experiments + 1 ion experiment

IP7

−

e e^{+ −}

Z

+

1990 LEP

Lepton versus Hadron Collider

+ −

( p / p )

elementary particles

multi particle collisions energy spread

well defined energy precision experiments

discovery potential

Example:

Leptons:

Hadrons:

( e / e )+ −

−2

00000 00000 00000 11111 11111 11111

N N

1 2

area A

interaction region

n N N f A

b 1 2 rev

00000 00000 00000 11111 11111 11111

[ L ] = cm s−1

σ

many bunches

small beam size

coupling; dispersion; hardware

Luminosity

N / sec = Lev

L =

high bunch current

beam−beam; collective effects

total current (RF); collective effects

00000000 0000 11111111 1111

b 1 2 rev

00000000 0000 11111111 1111

N N

1 2

area A

interaction region

n N N f A

Beam Size

Luminosity:

Limit:

aperture

magnet strength

β

x = sin( )A φ

L =

LHC:

<β>_arc= 80 meter = 0.5 meter

βIP

β

x = A sin( )φ

γ = 7000

accelerated charge emits electro−magnetic waves

bending plane

radiation fan in bending plane

<E > _γ γ ³ ρ

γ ⁴ P ρ²

Electro−Magnetic Waves :

particle trajectory light cone

synchrotron

radio signal X−rays

Synchrotron Radiation

opening angle γ1

LEP: γ = 200000

LHC:

0.04

[km]

u

[keV]

c

[MW]

P

LEP 1

LHC LEP 2

X−rays

γ

UV light

−rays

Examples

LEP 2 LEP 1

[GeV]

E

45 100

3.1

[10 ]

N

12

4.7

U

[MeV]

260 3.1

90

LHC 7000 3.1 312

LEP2+ 312

4.7 3.1

110

30 1.2 2900

3900 44

715 952 0.007 0.005

ρ

equipment damage!

Bremsstrahlung + Coulomb Scattering

Vacuum

beam blow−up

particle loss

background in experiments

loss in luminosity!

LHC − Beam Parameter

Beam−Beam Interaction:

+

magnet quality aperture

∆

ε

quadrupole strength aperture+

β:

Synchrotron Radiation Beam Power

E = 300 MJ

= 120 kg TnT

P = 0.5 W/m n = 2835_b

N

n

L = ε β

f 2

rev

π L = 10 cm s

Beam Size:

< 5 10⁻³

ε

N = 10

p

11

β

beam

Circular Accelerator:

Time Varying Fields

E

beam

E beam

beam

E

Linear Acceleration:

bunched beam

long accelerator!

BEAM + ++ − − + + − − + + +

−

1MHz, 25kV oscillator

But: f < 7MHz (l = 21 meter)!

l = v T/2part

1.3MV mercury ions with 48kV Lawrance:

V

t AC Voltage:

50kV potassium ions 1924: Ising

1928: demonstrated by Wideroe

Drift Tubes

Symmetric line:

b) and d)

plus:

Rotation on

Time Varying Fields

= E

2

e

e

2

µε

∆

^e

e

∆

c)

∆

∆

c

e

x B − = 0^µε t

e

a)

∆

∆

c

e

x E + = 01

e

x ( x V ) = ( V ) − V∆ ∆ ∆ ∆ ∆

Maxwell Equations without Sources

Wave equation:

ω ω

B = B e0

ik n x − t ik n x − t

k = ^{2 π} µε λ

B = n x E_{0 0}

No acceleration in the

direction of propagation!

E = E e0

Time Varying Fields

Plane Electro Magnetic Wave:

s

Problem:

v > c

v

Shielding or change

I

E = 0 everywhere;z

e

e

s

Boundary condition: = 0

B = 0 everywhere;_z

Boundary condition: E = 0

n

λ 2

H mode⁰¹

E − E

wall currents displacement currents

Transverse Electric Waves (TE):

Transverse Magnetic Waves (TM):

Boundary Conditions

proton

BEAM + − − + + − − + + −

support

posts

l = v T_part

(f = 200 MHz gives good tube size) Tubes are passive

Posts v = 0_gr

Pre−accelerator for most acclelerators

Alvarez:

higher frequencies!

Resonance Tank

E axis H

beam

Short Section:

multi−cell

multi−passage

II

TM mode with longitudinal boundary;

Cavity Resonator:

Boundary Conditions

iris

But:

Concept of linear acceleration is limited by power of RF generator!

Not feasible before World War II

particle

beam path

III

v = v_ph

Boundary Conditions

Loaded Wave Guide: