1

Winni DeckingDESY

DESY Summer Student Lecture

16th July 2003

(based on last years lecture by Nick Walker)

The TESLA Linear Collider

Energy Frontier e+e- Colliders

LEP at CERN, CHEcm = 180 GeVPRF = 30 MW

LEP at CERN, CHEcm = 180 GeVPRF = 30 MW

TESLA

SPEAR, DORIS (charm quark, τ lepton)

CESR, DORIS II

2

Why a Linear Collider?

B

Synchrotron Radiation froman electron in a magnetic field:

Energy loss per turn of a machine with an average bending radius ρ:

ρ=∆ γ

4

/EC

revE

Energy loss must be replaced by RF system

2222

2BEC

ceP γγ π

=

( ) 420

−∝ cmCγ

Cost Scaling

• LINAC: optimised cost ($lin+$RF) ∝ E

•Linear Costs (tunnel, magnets etc): $ lin ∝ ρ

•RF costs: $RF ∝ ∆E ∝ E4/ρ

•Optimum at $lin = $RF

•optimised cost ($lin+$RF) ∝ E2

3

Linear ColliderNo Bends, but lots of RF!

e+ e-

10 km

For a Ecm = 500 GeV:

Effective gradient: 25 MV/m

Ez

z

c

bunch sees field:Ez =E0 sin(kz+f )sin(kz)(standing wave cavity)

c2ct λ=

A Little HistoryA Possible Apparatus for Electron-Clashing Experiments (*).

M. Tigner

Laboratory of Nuclear Studies. Cornell University - Ithaca, N.Y.

•SLC (SLAC, 1988-98)•NLCTA (SLAC, 1991-)•TTF (DESY, 1994-)•ATF (KEK, 1991-)•FFTB (SLAC, 1992-1995)•SBTF (DESY, 1994-1998)•CLIC CTF1,2,3 (CERN, 1994-)

Nuovo Cimento 37 (1965) 1228

Over 15 Years of Linear Collider

R&D

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The Luminosity Issue

Dyx

repb HfNn

L ×= **

2

4 σπσ

particles per bunch

No. bunches in bunch trainrepetition rate

LEP frep = 40 kHz

LC frep = 5 - 200 Hz!

beam cross-section at Interaction Point (IP)

LEP: 130×6 µm2

LC: 550×5 nm2

Beam-beam enhancement factor(typically º 2

The Luminosity Issue

( ) Dyx

brepcmcm

HN

NnfEE

L ×

= **

14

1σσπ

Requirements for Next Generation LC:L ≥ 1034 cm−2 s−1

Ecm = 0.5 - 1 TeV

Pbeam typically 5-8 MW

5

The Luminosity Issue

( )

= D

yxAC

cm

HN

PE

L **41

σση

π

Beam-Beam effects:beamstrahlung, disruptionStrong focusing:optical aberrations, stability issues

Efficiency RF→beam: 20-60%Wall plug →RF: 28-40%

Beam Beam Effects

e+

e−γγ

γ

2

*

σσ

∝δxz

cmBS

NERMS Energy Loss for a flat beam(σx >> σy)

hard γs radiated by intense electric field= Beamstrahlung

leads to pair-production => backgroundstrong focussing:

enhancement HD

6

Limit on β*

-2000 -1000 0 1000 2000 3000

-40

-20

0

20

40

IP (s = 0)

y

s

)0(,)( **

2* =β=β

β+β=β s

ss

σz

β* = “depth of focus”

reasonable lower limit for β* is bunch length σz

Thus set β* = σz

=> zyy σεσ =

Beam-Beam Simulation (‘Banana’ Effect)

Nominal TESLA Beam Parameters +

y-z correlation (equivalent to few % projected emittance growth)

Beam centroids head on

• Instability driven by vertical beam profile distortion

• Strong for high disruption

• Distortion caused by transverse wakefields and quad offset – only a few percent emittance growth

• Tuning can remove static part

7

Final Luminosity Scaling Law

21

εδ

η∝

y

BS

cm

RF

EP

L

0.5 – 1.0 TeV

as high as possible ≈ 100 MWbackground

as small as possible

The Luminosity Issue

• High Beam Power

• Small IP verticalbeam size

• High current (nb N)• High efficiency

(PRF →Pbeam)

• Small emittance εy

• strong focusing(small β*y)

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The Luminosity Issue

• High current (nb N)• High efficiency

(PRF →Pbeam)

• Small emittance εy

• strong focusing(small β*y)

Superconducting RFTechnology

The Superconducting Advantage

• Low RF losses in resonator walls(Q0 ≈ 1010 compared to Cu ≈ 104)

– high efficiency ηAC →beam

– long beam pulses (many bunches) → low RF peak power

– large bunch spacing allowing feedback correction within bunch train.

9

The Superconducting Advantage

• Low-frequency accelerating structures(1.3 GHz, for Cu 6-30 GHz)

– very small wakefields

– relaxed alignment tolerances

– high beam stability

t

Wake Fields•Electromagnetic fields produced by charge and changes in the surrounding environment

•Act back on the same bunch ==> transverse and longitudinal deformation

•Interact with subsequent bunches ==> position and energy variation along train

•

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Wakefields (alignment tolerances)

bunch

0 km 5 km 10 km

head

head

headtailtail

tail

accelerator axis

cavities

∆y

tail performsoscillation

Misplaced cavity “Banana”

TESLA superconducting (T=2K) 9-cell Niobium cavity

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The TESLA Test Facility (TTF)

Cavity strings are prepared and assembled in ultra-clean room environment at TTF

lecture on sc in accelerators

The TESLA Test Facility (TTF)

TTF Test Linac constructed from completed Cryomodules

12

The TESLA Linac

Cryomodule

Cavities

Damping Ring

BEAM

The TESLA Linac

Klystrons mounted inside tunnel

13

The TESLA Linac

1 9-cell 1.3GHz Niobium Cavity

~1m

The TESLA Linac

12 9-cell 1.3GHz Niobium Cavity1 Cryomodule

~16m

14

The TESLA Linac

36 9-cell 1.3GHz Niobium Cavity3 Cryomodule

K

1 10MW Multi-Beam Klystron

The TESLA Linac

• 10,296 Cavities• 858 Cryomodules• 286 Klystrons• Gradient: 23.4 MV/m

(inc. 2% overhead)

• LENGTH 14.4km(fill factor: 74%)

Per Linac (Ecm = 500 GeV):

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Cryoplants

• Each linac divided into 6 Cryo-units(~140 cryomodules)

• 7 refrigeration (liquid He) plants housed in 7 surface halls (~5km)

Cryohalls

LINAC tunnelRefrigerators

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The LINAC is only one part of a linear collider!

• Efficiently accelerate a high charge to high energies(high RF→beam power transfer efficiency)

• Preserve the required small bunch volumes (small emittance) because of low wakefields

• Has relatively relaxed tolerances

The SC linac can:

The LINAC is only one part of a linear collider!

• Produce the electron charge?

• Produce the positron charge?

• Make small emittance beams?

• Focus the beam down to 5nm at the IP?

BUT how do we:

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The LINAC is only one part of a linear collider!

main linacbunchcompressor

dampingring

source

pre-accelerator

collimation

final focus

IP

extraction& dump

KeV

few GeV

few GeVfew GeV

250-500 GeV

Machine Overview

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e− Source• laser-driven photo injector• circ. polarised photons on

GaAs cathode → long. polarised e−

• laser pulse modulated to give required time structure

• very high vacuum requirements for GaAs(<10−11 mbar)

• beam quality is dominated by space charge(note v ~ 0.2c)

120 kV

electrons

laser photons

GaAscathode

λ = 840 nm

20 mm

510n mε −≈

factor 10 in x plane

factor ~500 in y plane

e− Source: pre-acceleration

KKK

E = 12 MeV E = 76 MeV

SHB

laser

to DR inector linac

solenoids

to DR injector linac

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e+ Source

γ

e+

e−

Photon conversion to e±

pairs in target material

Standard method is e-

beam on ‘thick’ target (em-shower)

e−

e+

e− e−

ie− γ

N

N

N

N

N

N

N

N

N

N

S

S

S

S

S

S

S

S

S

S ~30MeV photons

0.4X target

undulator (~100m)

250GeV e to IP−

frome- linac

e+e- pairs

e+ Source :undulator-based

ε=10-2 m

PT= 5kW

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Damping Rings• beam is damped

down due to synchrotron radiation effects

γεx = 10−5 mγεy = 3×10−8 m

γε = 10−2 m

How β-damping works

δp

δp

γdipole RF cavity

y’ not changed by photon

δp replaced by RF such that ∆pz = δp.

since

y’ = dy/ds = py/pz,

we have a reduction in amplitude:

δy’ = −δp y’

DTeqieqf e τεεεε /2)( −−+=

final emittance equilibriumemittance

initial emittance(~0.01m for e+)

damping time~ 28 ms

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TESLA Damping Rings• Long pulse: 950ms × c = 285km!!• Compress bunch train into 18km “ring”• Minimum circumference set by speed of

ejection/injection kicker (~20ns)• Unique “dog-bone” design: 90% of

‘circumference’ in linac tunnel.

Bunch Compression

RF

z

∆E/E

z

∆E/E

z

∆E/E

z

∆E/E

z

∆E/E

long.phasespace

dispersive section

bunch length:after DR 6 mm at IP 300 µm

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Bunch Compression

Bunch length

After compression(300 µm)

Damping ring

6 mm

Damping ring(~ppm)

After compression

2.8%

5 GeV: 2.8%250 GeV: 0.6‰

∆E/E

Final Focus System for small β*

• Optical telescope required to strongly demagnify the beam(Mx ≈ 1/100, My ≈ 1/500)

• Strong focusing leads to unacceptable chromatic aberrations [non-linear optics]

• Require 2nd-order optical correction

nmy 50* ≈σ nmy 5* ≈σ

uses non-linear elements (sextupoles )

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Positron Production System

Beam Delivery System

σy = 3 µmσy = 3 µm

σy = 5 nmσy = 5 nm

Demagnification: ×636Demagnification: ×636

Collimation System

Final Focus System

Stability

• Tiny (emittance) beams• Tight component tolerances

– Field quality– Alignment

• Vibration and Ground Motion issues• Active stabilisation• Feedback systems

Linear Collider will be “Fly By Wire”

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Stability: some numbers

• Cavity alignment (RMS): 500 µm• Linac magnets: 100 nm• BDS magnets: 10-100 nm• Final “lens”: ~ nm !!!

Parallel-to-Point focusing

IP Fast (orbit) Feedback

Beam-beam kick

Long bunch train:

2820 bunches

tb = 337 ns

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IP Fast (orbit) Feedback

Systems successfully tested at TTF

Long Term Stability

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.1 1 10 100 1000 10000 100000 1000000

time /s

rela

tive

lum

ino

sity

1 hour 1 day1 minute 10 days

No FeedbackNo Feedback

IP FeedbackIP Feedback

IP Feedback & slow orbit feedback

IP Feedback & slow orbit feedback

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Proposed Site

Ellerhoop (16.5 km)

Westerhorn (32.8 km)

DESYHERA

Experimental Area (Ellerhoop)

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DESY Site and Cryo-Hall

Thanks for listening and have a lot of fun here at DESY

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The Linear Accelerator (LINAC)

• Gradient given by shunt impedance:– PRF RF power /unit length– RS shunt impedance /unit length

• The cavity Q defines the fill time:– vg = group velocity, ls = structure length

• For TW, τ is the structureattenuation constant:

• RF power lost along structure (TW):

z RF sE P R=

2 / SW

2 Q/ / TWfills g

Qt

l v

ω

τ ω

= =

2, ,RF out RFinP P e τ−=

2RF z

b zs

dP E i Edz R

= − −

power lost to structure beam loading

ηRF

would like RS to be as high as possible

sR ω∝

Basic Optics 1: Phase Space and Emittance

angle y’=dy/dz ( )

y

y’

y

y’

y

Electron optics analogous to light optics(quadrupole magnets instead of lenses)

phase space

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Basic Optics 1: Phase Space and Emittance

'ydyε = ∫Ñangle y’=dy/dz ( )

y

y’

y

y’

y

particle trajectories map out an area in the phase plane.Integral over y-y’ space is the emittance, which is a constant

y’

y

Basic Optics 2: RMS Emittance

y yε β

y yε γ

2

22 (1 ) /y y

yy y y

y yy

yy y

β αε

α α β

′ − = − + ′ ′

Take statistical 2nd-order moments of phase space coordinates

2det yε= det 1=

22 2(1 )

2yy y y

y

y yy yα

α β εβ+

′ ′+ + =equation of an ellipse which bounds one standard deviation of the bivariate distribution

22 2y y y yyε ′ ′= −define

RMS emittance is conserved by linear optics.

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The parameters β= β(s) and α= α(s) are functions of the magnetic lattice (optics). s is the distance along the system (magnetic axis).

At any point s=s1, we can transform the phase space ellipse into a circle (floquet transformation)

Basic Optics 3: Phase Advance

y’

y

y

yuβ

=

( )yy

y

v y yα

ββ

′= +

1s s=

1 2s s s s= +∆ =

φ∆

2

1

1 2( , )( )

s

ys

dss ss

φβ

∆ = ∫

phase advance

( ) ( )y ys sα β ′= −note also:

( )( ) ( ) cos ( ) (0)y y y yy s a s sβ φ φ= + ‘betatron’ oscillation

Basic Optics 4: Emittance and Acceleration

py

pz

P

py

pz+∆Vacc

P P+∆P

high-energy (relativistic) optics is based on very small angle approximations.

Hence we assumeand thus

z

y y

z

p

p pdyy

dz p

≈

′ = ≈ ≈

P

P

z yp p?

1

.

.y

y

y constconst

γγγε

′ ∝

′ =⇒ =

hence for ultra-relativistic beams /E mγ =

≡ normalised emittance

adiabaticdamping

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Beam-Beam

( ),,

2 e z zx y

beamx y x y

r ND

fσ σ

γ σ σ σ= ≈

+

beam-beam characterised by Disruption Parameter:

σz = bunch length, fbeam = focal length of beam-lens

( )3, ,1 / 4

, , ,3,

0.81 ln 1 2ln

1x y x y

Dx y x y x yx y z

DH D D

D

β

σ

= + + + +

Enhancement factor (typically HD ~ 2):

‘hour glass’ effect

for storage rings, and zbeamf σ? , 1x yD =

In a LC, hence zbeamf σ<10 20yD ≈ −

Beamstrahlung

3 2

2 20

0.862 ( )

e cmBS

z x y

er E Nm c

δσ σ σ

≈ +

RMS relative energy loss

we would like to make σxσy small to maximise luminosity

BUT keep (σx+σy) large to reduce δSB.

Trick: use “flat beams” with x yσ σ?2

2cm

BSz x

E Nδσ σ

∝

Now we set σx to fix δSB, and make σy as small as possible to achieve high luminosity.

For most LC designs, δSB ~ 3-10%

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Beamstrahlung

1RF RF

cm x y

P NL

Eη

σ σ

∝

Returning to our L scaling law, and ignoring HD

z BS

x cm

NE

σ δσ

∝From flat-beam beamstrahlung

3 / 2BS zRF RF

cm y

PL

Eδ σησ

∝hence