ILC Accelerator Physics

2008.09.

Kiyoshi Kubo (KEK)

Note

• We concentrate on electron - positron Linear Colliders, especially ILC.

• There is nothing about proton machines, or LHC.

ContentsIntroductionBeam collision• Luminosity and emittance• Beam-beam force• crossing angle• Beam Delivery System (Final focus)Acceleration• Basics• Beam parameter and power efficiency• For high gradientLow emittance• Creation of low emittance - Damping Ring• (Preservation of low emittance)Other system in ILC• Bunch compression• Spin rotationMajor test facilities for ILC• ATF and ATF2

1/1

Two important parameters of colliders

• Center of mass energy– Circular e+e- collider will be too expensive for higher

energy than LEP (energy loss due to synchrotron radiation) Linear Collider

• Luminosity (Compare with circular colliders)

– Each particle bunch has only one collision chance. • Collision rate is very low.

– Do not have to care beams after collision.

Very strong focus and small beam size at collision.

2/3

ILC

e- source Damping ring long transfer line turn around bunch compressor Main linac (undulator for e+) final focus system collision dump

photons e+ sourcee+ system is similar to e- system, except for the undulator

1/4

Beam Collision

Instantaneous Luminosity

What is Luminosity ?

21213 )()( vvxxdxL

beams. 2nd and1st of s velositiealLongitudin : and

beams 2nd and1st of Densities :)( and )(

21

21

vv

xx

section Cross :

unit timein events ofnumber

L

Luminosity determines event rate.

1.5/5.5

(Average) luminosity of beams of “rigid” Gaussian bunches

size beam RMS (vertical) Horizontal :

rate)n (repetitio unit timein pulsesNumber :

pulseper bunches ofNumber :

bunchper particles ofNumber :

*)( yx

rep

b

f

n

N

**

2

4 yx

repb fnNL

**1

yx

L

Luminosity is proportional to transverse density, inverse of cross section of the beam

1.5/7

Usually, x: horizontal, y: vertical coordinate

Limit of beam size at collision

High luminosity needs small transverse beam size. But it is limited.

• Hourglass effect

• Oide limit

Both effects require small emittance beam for high luminosity.

1/8

Beam Focusing

Lens: Quadrupole magnet

Focal point

Stronger focus shorter focal depth

.5/8.5

Basics of (one dimensional) beam optics -1: quadrupole field gradient g

dsskK

dsskK

sysksy

sxsksx

y

x

)(

)(

:strength Integrated

0)()()(''

0)()()(''

field quadrupolein motion ofEquation

gxB

gyB

y

x

s : distance along beam line

ecgyF

ecgxF

y

x

xxz vvcv ,

)/( zpegk

2/10.5

entrance

entrance

entrance

exit

'

1

01

)0('

]cosh[]sinh[)/1(

]sinh[]cosh[

)0('

]cos[]sin[)/1(

]sin[]cos[

'

:relation haveexit and entranceat ' and

),strength integrated ,(lenght magnet quadrupoleFor thin

x

x

K

Kx

x

LKLKL

LKLLK

Kx

x

LKLKL

LKLLK

x

x

xx

KL

direction beam along distance :

/' position, Transverse :

s

dsdxxx

These are called “transfer matrix”.1/11.5

)('

)(

10

1

)('

)(

:relation have , and locations, at two and space,drift In

1

112

2

2

21

sx

sxss

sx

sx

ssx'x

222 '' xxxxx

Emittance is invariant in quadrupole field and drift space(Determinant of the transfer matrix is 1.)

<> denotes average over particles in the beam

Basics of (one dimensional) beam optics -2: drift space

emittance ~ (beam size) x (angular divergence)

1/12.5

Beam size near focal point(focal point is in drift space)

*2*2222

22222

/)0(/)0(

)0(')0()()(

sxsx

xsxsxs

xx

x

RMS beam size at distance s from the focal point:

)0( and ,function"-beta" called iswhich

,)( )(*

2

xx

xx sxs

xx x )0(2*

)(sx

hyperbola a is

emittance toalproportion is)( 2

(s)σ

s

x

x

1.5/14

Small beam size at s=0 rapid increase of beam size. (hourglass)Bunch length is finite and collisions at finite s contribute to luminosity.There should be optimum beam size for given emittance.

ε toalproportion is

lengthbunch tocomparable is Optimum*

*

* Small

* Large

We need small emittance beam for high luminosity.

s

lengthbunch ~

place takeCollisions

s

2/16

*2*2*222* //)( sss xxxxx

In Phase Space, x-x’x-x’ (y-y’ ) 　 plane is called “phase space”.Gaussian distribution can be expressed as an ellipse.Emittance can be regarded as the area of the ellipse.

x

x’

weakquad

Strongquad

longdrift

shortdrift

2/18

Another limit of Minimum beam sizeQuantum effect - Oide limit

Quad magnet

Radiation in the focusing magnet

Uncertain energy loss uncertain orbit downstream

Stronger focus More uncertainty

1.5/19.5

Quantum effect - Oide limit Ref.: K. Oide, PRL vol. 61, p1713 (1988)

• Supposing the bunch length is very small, * should be as small as possible for high luminosity.

• In classical electro-magnetic dynamics, * can be very small using very strong focusing magnetic field. But,

• Particles emit radiation in the strong magnetic field. – The energy loss is uncertain in quantum dynamics.– Inducing uncertain change of trajectory after the radiation.

(Lower energy particles change angle in magnetic field more.)– This uncertainty affects the beam size at the focal point.

7/5*

min*

2/5**2*

, choosing

A

The minimum beam size depends on emittance, AGAIN.1.5/21

In Phase SpaceFor small beam size, with a certain emittance, strong focus is required.

x’

x stronger focus

weak

beam size at focal pointfrom classicaldynamics

1/22

SKIP

Beam-beam force

Particles feel electro-magnetic field induced by the opposite beam

• Particles emit radiation (beamstrahlung) and lose energy. Energy spread is increased

• Particles are focused. Luminosity is enhanced.• Particles are deflected and/or oscillate. Luminosi

ty is reduced.

.

1/23

beamstrahlung

Particles feel strong electro-magnetic field induced by the opposite beam and emit radiation and lose energy

e+

e-

.5/23.5

• beamstrahlung Induces energy spread during collisions (not only after collisions) and affect quality of experimental data.

• beamstrahlung parameter

lengthbunch : factor, Lorentz: ,

energy beamdesign torelative lossenergy Average

2**

23

z

yxz

e

BS

Nr

This should be several percent or less (depends on aimed physics)

1/24.5

2**

23

yxz

eBS

Nr

For large luminosity and small beamstrahlung, FLAT BEAM

2*

23**** then,,)(or

xz

eBSyxyx

Nr

**4 yxave

NnL

time)particles/ ofnumber average :( aven

On collision parameters

Vertical beam size should be much smaller than horizontal.(Usually, Vertical emittance can be smaller than horizontal because: Vertical alignment is easier than horizontal. Damping ring is in a horizontal plane.)

Horizontal beam size should not be so small for small BS .

2/26.5

y

BSave

e nr

L

4

2/3

, , ***yzyyyzy

Limit of vertical beam size

Luminosity per one bunch collision as function of vertical emittance and beamstrahlung

On collision parameters (continued)

Keeping beamstrahlung small, the only two ways to increase luminosity are• Increase number of particles (increase beam power)• Reduce the vertical emittance.

Hour-glass

Directly increase cost

1.5/28

Charges of two beams are opposite. In head on collision, particles are focused and luminosity increase.

Luminosity enhancement due to beam-beam force

factort enhancemen Luminosity :

4 **

2

D

Dyx

repb

H

HfNn

L

Collisions with offset/angle error, Bunch oscillates during collision and Bunch is deflected.

1/29

ILCin 10

, largeFor

1

2

)( ere, wh

:force beam-beam ofstrength Expressing

collision.in particleeach of periodsn oscillatio ofNumber

force. beamby length focal is ),( If

)()(

)()(

D

D

D

D

nrf

fD

fzf

e

yxyxyx

yxzyx

1/30

SKIP ?Disruption parameter

Head on, 1

By computer code CAIN (developed by K.Yokoya)

3/33

Head on, 2

Head on, 3

Head on, 4

Head on, 5

Head on, 6

Head on, 7

Head on, 8

Head on, 9

2- Offset, 1

2- Offset, 2

2- Offset, 3

2- Offset, 4

2- Offset, 5

2- Offset, 6

2- Offset, 7

2- Offset, 8

2- Offset, 9

Crossing angle

Large crossing angle is desirable:• Beam should be dumped safely after collision• It is necessary to measure property of beam after collision for monit

oring beam conditionBut, reduce luminosity

ILC design has crossing angle 14 mrad.

.5/34.5

Crossing angle and crab crossing

kick kick

Crab crossing

zx

if reduction, luminositycrossing angle

(2 mrad in ILC)

l. position

h. k

ick

2.5/37

Luminosity vs. Crossing anglewithout crab

0

0.2

0.4

0.6

0.8

1

1.2

0 0.002 0.004 0.006 0.008 0.01

L/L

0

crossing angle (rad)

ILC nominal parameter, by CAIN.5/37.5

Parameters at IPNumber of particles/bunch 2E10

Normalized emittance, h 1E-5 m-rad

Normalized emittance, v 4E-8 m-rad

*x 21 mm

*y 0.4 mm

*x 655 nm

*y 5.7 nm

z 0.3 mm

Dx 0.16

Dy 19

BS 0.022

crossing angle 14 mrad

Luminosity 2E34 /cm^2/s

1/38.5

Beamstrahlung and Luminosity vs. bunch population

0

2

4

6

8

10

0 1 2 3 4

TotalECM > 495 GeV

L (

1034

cm-2

s-1)

N (1010)

Total luminosity and luminosity ECM energy reduction <1%

0

0.02

0.04

0.06

0.08

0.1

0 1 2 3 4

BC

N (1010)

1.5/40

Luminosity vs. offset error at collision

Normalized bygeometrical luminosity

0

0.5

1

1.5

2

0 0.5 1 1.5 2 2.5 3 3.5 4

N=2E10

N=0

N=4E10

L

/col

lisi

on

(4N

2 /x*

y*)

y/y*

2/42

SUMMARY of Beam Collision• High luminosity need small beam size at IP• Beam size is limited by emittance (Hourglass, Oide-limit)• Beam-beam force focuses opposite charge beams.

Enhance luminosity.• Beam-beam force induce radiation and energy loss durin

g collision. (beamstrahlung)• Suppression of beamstrahlung requires flat beam.• Luminosity is roughly proportional to

• Crossing angle and crab-crossing

emittance) icallung/(VertBeamsstrah charge) (Total

2/44

Beam Delivery System

Last part of Linear Collider • Final Focus

luminosity • Collimation reduce back ground machine protection

1/45

Final focus system optics design

• Quadrupole fields must be very strong for small beam size

• Beam has momentum spread Different angle changes in magnetic fields different trajectories in crease beam size at IP (chromatic aberration)– Need to be compensated by sextupole magnetic field– This compensation induce higher order optics in additi

on to the linear optics. (geometric aberration)• Imperfection of the magnetic field, misalignment, etc. cau

se additional geometric aberrations.• ILC final focus method will be tested in ATF2 at KEK

2/47

Schematic view of simple (first order) chromatic aberration

quadrupole

/' Eyy

Because horizontal beam size >> vertical beam size, we can concentrate on vertical direction.

low energy particle

high energy particle

1/48

Schematic view of correction of first order chromatic aberration

sextupole quadrupole

/' Eyy /' Exyy

energydesign : ),(

sextupoleat dispersion horizontal Introduce

00 EEEx

But this induces higher order aberrations.1/49

00

*

/)(

''),',,',(

EEE

yyxxayyxxfy nmlkjjklmn

)necessary.not and eliminate to(difficult

.eliminated benot may sorder termHigher

design.in eliminated be should

3 of most terms and

2 of termsAll

nmlkj

nmlkj

SKIPAppendix: Expansion of vertical position at IP

Tuning and Control of collision

• Designing the system (what is the optimum beam optics, etc.) is one big issue.

• Make a real machine close to the design is another big issue.

• In actual operation, various errors will affect the design optics.

• Tuning (reducing errors or mitigating effects of errors) procedures have been studied, mainly by simulations.– if we do not have a machine

• Maintaining luminosity for reasonably long time will also need a lot of efforts.– Luminosity is affected by small fluctuations, movements of many

parameters of the machine.– Need continuous feed back control. etc.

1/50

Tuning and feedback loops in Final focus

Monitoring is essentially important. IF we can measure anything, we can control them.

Final focus system

IP Orbit feedback

LuminosityMonitor

deflector

Luminosity tuning

IP

tuning/feedback control

Monitorscorrectors

Deflectedbeam positionmonitor

2/52

IP beam position feedback• Measure deflected beam position after collision • feedback to steering magnet (deflector) for the next bunch of the opposite beam

– Feedback signal processing within bunch spacing (~300 ns)

.

-300

-250

-200

-150

-100

-50

0

0 10 20 30 40 50 60 70

<y'>

(r

ad)

y/y

Deflection angle vs. offset at IP

feedback works if offset error < 30

1/53

0

0.5

1

1.5

2

2.5

0 1 2 3 4 5 6 7 8L

(10

34 c

m-2

s-1)

y/y

luminosity vs. offset at IP

CollimationHallo, particles far from the core of the beam

(energy and transverse position/angle), may hit materials near IP, (near the detector).– background

• Population and distribution of hallo cannot be well estimated. May be formed in the main linac.

• Post-linac collimation is necessary to prevent large hallo which induces detector background.

Some failure may cause big orbit distortions• If the beam hit a machine component, it will be

broken.• Failed beam must hit collimators.

– Collimators may be broken in rare failures.

1/54

SUMMARY of BDS

• Beam optics design of final focus: suppression of (chromatic and geometrical) aberrations.

• Tuning and feedback– IP position feedback: relying on beam-beam

deflection

• ILC final focus method will be tested in ATF2 at KEK (see later slides)

1/55

Acceleration

Basics of Acceleration

Standing wave, mode,

Electro-magnetic power of Radio Frequency (RF) is fed to resonator (RF Cavity).The power is accumulated in the cavity.

Lcell

fvLcell

cell / change Phase particles pass all cells on the same phase

Superconducting cavity is used in this mode.

1.5/56.5

RF unit of ILC Main Linac

from ILC RDR

1/57.5

DESY

.5/58

Super Conducting Cavity

From ILC RDR

Tuner: change length of cavity for adjusting resonance frequency Slow and large stroke : motor, Fast and small stroke : piezo

Input coupler: feed RF power

HOM coupler: Extract HOM

HOM coupler:

Le. He

1.5/59.5

Two parameters expressing Performance of Cavity

• Field Gradient

• Quality factor (Q0)

ILC RDR

cavity.in energy field EM :

power, loss Wall: frequency, :

0

0

0

W

P

PWQ

Specification of ILC beforeinstalling in cryomodule.

Necessary cooling capacity depends onQuality factor.

Quality factor strongly depends on smoothness and purity of cavity’s inner surface.

2/61.5

For high gradient of superconducting cavities (1)

Smoothness and Cleanness of cavity inner surface.– Any defect may cause heating (reduction of Q0),

breakdown of superconductivity.

• Fabrication – Electron beam welding

• Treatment of surface– Chemical polishing– Electric polishing– Cleaning

• Avoid contaminations

1/62.5

Construction of Superconducting cavitiesin clean environment

RDR

.5/63

For high gradient of superconducting cavities (2)

Design of cavity shape.• High magnetic field causes breakdown of superconductivity. (Fund

amental limit of gradient) [Saito’s hypothesis]Eacc (gradient felt by beam) / Hpeak (peak magnetic field)should be large.

Three different designs

1/65

from Kenji Saito

History of highest gradients achieved in single cell cavities.

1/65.5

Beam parameter of ILC (superconducting LC) in Main Linac, compare with normal conducting LC

Super (rough) Normal (very rough)

Particles/bunch 2E10 1E10

Bunches/pulse 3000 100

Charge/pulse 10 C 160 nC

Bunch spacing 300 ns 3 ns

Pulse length 0.9 ms 300 ns

Beam current in pulse 10 mA 500 mA

Rep. rate 5 Hz 100 Hz

Average beam current 50 A 16 A

1/66.5

Time structure of ILC beam

Bunch length: RMS 0.3 mm (1 ps)

Bunch to bunch spacing ~ 300 nsBunch number ~3000Pulse length ~ 0.9 ms (270 km)

Bunch

pulse

200 ms

0.9 ms

Repetition rate: 5 Hz

Note: In damping rings, bunch space is compressed to ~6 ns circumference ~ 6 km.

1.5/68

Transient behavior of cavity voltage

0

5

10

15

20

25

30

35

-0.001 0 0.001 0.002 0.003 0.004 0.005 0.006

Vc

(MV

)

time (s)

31.48

31.49

31.5

31.51

31.52

0 2 10-7 4 10-7 6 10-7 8 10-7 1 10-6 1.2 10-6 1.4 10-6beam

Power on

Bunches Assuming matched condition.

Beam loading = input powervoltage = constant

2/70

Accelerating field from short time range view(single bunch)

3.125 107

3.13 107

3.135 107

3.14 107

3.145 107

0

5 104

1 105

1.5 105

2 105

-0.001 -0.0005 0 0.0005 0.001

RF fieldTotal acceleration

wakefield Acc

eler

atin

g fi

eld

(V

/m)

wak

efield (V

/m)

z (m)

Total field is field induced by input power + field induced by beam (beam loading, or, wakefiled) (deceleration)

bunch tail

put bunch centerslightly off-crest minimize energy spread

1/71

Transient behavior of power to/from cavity

-50

0

50

100

150

200

250

300

-0.0005 0 0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035

Input PowerReflection Power

Pow

er/C

avit

y (k

W)

time (s)

InputReflection

beam

power on

hpulselengt Beam timeFill

hpulselengt Beam

powerinput total

beam power to total efficiencyPower RF

fill time

2/73

RF Power efficiency

• RF power during beam pulse is given to beam, almost all.

• RF power during “fill time” is lost.

beam) Energy to( cavity)in filled(Energy beam) Energy to(

Efficiency

V charge) Total(beam) Energy to(

2cavity)in filled(Energy V

For high efficiency, total charge/pulse should be large.

1/74

Roughly,

This is the reason why Superconducting LC has a long beam pulse and large number of bunches per pulse.

current) (Beamltage)(cavity vo power peak RF

large. be should

length) pulse (Beam)current Beam( :secharge/pul Total

For high efficiency,

High beam current increase RF peak power, then number of klystrons or power of klystrons. It increase construction cost.

So, beam current is limited. For increasing charge/pulse, increase pulse length.

2/76

Damping ring limits number of bunches/pulse

• Damping ring circumference

= [Number of bunches] x [Bunch spacing]

Bunch spacing is limited by extraction/injection kicker speed and

instabilities.

See later discussions.

1/77

Cryogenics limit pulse length

• Pulse length is limited by Power for Cryogenics– Cavity wall loss is negligible for RF power efficiency,

But, cannot be ignored considering total power efficiency. Cooling cavity needs power.

QHeat from cavity at T1

Need to be dumped to environment,

at T2

From fundamental law (total entropy cannot be reduces), dumped heat > Q x (T2/T1)Entropy has to be dumped, not only heat.

Need to add energy from outside

(Power to cryogenics)

Cryogenics

1.5/78.5

Q=q x Nb = Ib x T : Total charge

Simple Summary of Beam Parameter Choice

T: Pulse length

Ib: Average beam current

q: Bunch charge

Nb: Number of bunches

Determined by luminosity/beam-beam force

Limited by Cryogenics

Limited by RF system

Limited by Damping Ring

The larger the better for RF power efficiency

There must be some compromise.

Three independent parameters out of four:

1.5/80

In the case of normal conducting LCinput power

Power is rapidly lost Longer the beam pulse, larger the power loss. High beam current, short pulse.

length and voltagesame for the

gradient field same for the energy field Stored

2

3

f

f

High RF frequency (most designs choose > 10 GHz)

Power loss

(not so simple though )

2/82

Lorentz Detuning Electromagnetic field pull the surface of cavity (Lorenz force).Cavity is a mechanical spring.The force reforms the cavity change resonance frequency: Detuning

0

5

10

15

20

25

30

35

-0.001 0 0.001 0.002 0.003 0.004 0.005 0.006

Vc

(MV

)

time (s)

Time dependent field strength + cavity’s mechanical property Determine resonance frequency as function of time.

Keeping acc. voltage with detuning need too large input RF power in high gradient operation

2force Lorentz cV

1.5/83.5

Cure of Lorentz Detuning

Tuner: change length of cavity for adjusting resonance frequency Slow and large stroke : motor, Fast and small stroke : piezo

• Control piezo tuner to compensate Lorentz detuning. (can be pre-program since the behavior is the same for every pulse.)• Residual small detuning can be cured by RF feedback.

1/84.5

Dynamic Lorentz DetuningResults at TTF　

Pkly < 10 % →　 Detuning angle < 12 deg. , f < 46Hz

S.Nogichi, ILC School 2006, Hayama

Mechanical oscillation, long time range compensation by piezo tuner

1.5/86

END of Saturday’s session

Continue to Monday evening