Beam DeliveryAndrei Seryi

SLAC

International Accelerator School for Linear Colliders19-27 May 2006, Sokendai, Hayama, Japan

2

• Energy – need to reach at least 500 GeV CM as a start

• Luminosity – need to reach 10^34 level

Linear Collider – two main challenges

3

The Luminosity Challenge

• Must jump by a Factor of 10000 in Luminosity !!! (from what is achieved in the only so far linear collider SLC)

• Many improvements, to ensure this : generation of smaller emittances, their better preservation, …

• Including better focusing, dealing with beam-beam, safely removing beams after collision and better stability

at SLC

4

How to get Luminosity

• To increase probability of direct e+e- collisions (luminosity) and birth of new particles, beam sizes at IP must be very small

• E.g., ILC beam sizes just before collision (500GeV CM): 500 * 5 * 300000 nanometers (x y z) Vertical size

is smallest

Dyx

brep HNnf

L

2

4

5

300000500

5

BDS

BDS: from end of linac to IP, to dumps

6

BDS subsystems

• As we go through the lecture, the purpose of each subsystem should become clear

7

Beam Delivery System challenges

• Focus the beam to size of about 500 * 5 nm at IP • Provide acceptable detector backgrounds

– collimate beam halo

• Monitor the luminosity spectrum and polarization– diagnostics both upstream and downstream of IP is desired

• Measure incoming beam properties to allow tuning of the machine

• Keep the beams in collision & maintain small beam sizes – fast intra-train and slow inter-train feedback

• Protect detector and beamline components against errant beams

• Extract disrupted beams and safely transport to beam dumps• Minimize cost & ensure Conventional Facilities constructability

8

How to focus the beam to a smallest spot?

• If you ever played with a lens trying to burn a picture on a wood under bright sun, then you know that one needs a strong and big lens

• It is very similar for electron or positron beams

• But one have to use magnets

(The emittance is constant, so, to make the IP beam size ( )1/2 small, you need large beam divergence at the IP ( / )1/2 i.e. short-focusing lens.)

9

• Beta function characterize optics

• Emittance is phase space volume of the beam

• Beam size: ( )1/2

• Divergence: (/)1/2

• Focusing makes the beam ellipse rotate with “betatron frequency”

• Phase of ellipse is called “betatron phase”

Recall couple of definitions

10

Etc…

Just bend the trajectory

Focus in one plane,defocus in another:

x’ = x’ + G xy’ = y’– G y

Second ordereffect:

x’ = x’ + S (x2-y2)y’ = y’ – S 2xy

Here x is transverse coordinate, x’ is angle

What we use to handle the beam

11

f1 f2 (=L*)

f1 f2 f2

IP

final doublet

(FD)

Optics building block: telescope

Use telescope optics to demagnify beam by factor m = f1/f2= f1/L*

Essential part of final focus is final telescope. It “demagnify” the incoming beam ellipse to a smaller size. Matrix transformation of such telescope is diagonal:

YX,

YX,YX, M0

01/MR

A minimal number of quadrupoles, to construct a telescope with arbitrary demagnification factors, is four.

If there would be no energy spread in the beam, a telescope could serve as your final focus (or two telescopes chained together).

δ

Δl

y'

y

x'

x

x iinjji

outi xRx

Matrix formalism for beam transport:

12

Why nonlinear elements

• As sun light contains different colors, electron beam has energy spread and get dispersed and distorted => chromatic aberrations

• For light, one uses lenses made from different materials to compensate chromatic aberrations

• Chromatic compensation for particle beams is done with nonlinear magnets– Problem: Nonlinear elements create

geometric aberrations

• The task of Final Focus system (FF) is to focus the beam to required size and compensate aberrations

13

How to focus to a smallest size and how big is chromaticity in FF?

• The final lens need to be the strongest• ( two lenses for both x and y => “Final Doublet” or FD )

• FD determines chromaticity of FF • Chromatic dilution of the beam

size is / ~ E L*/*

• For typical parameters, / ~ 15-500 too big !

• => Chromaticity of FF need to be compensated

E -- energy spread in the beam ~ 0.002-0.01L* -- distance from FD to IP ~ 3 - 5 m* -- beta function in IP ~ 0.4 - 0.1 mm

Typical:

Size: ( )1/2

Angles: (/)1/2

L*IP

Size at IP: L* (/)1/2

+ ( )1/2 E

Beta at IP: L* (/)1/2 = ( *)1/2

=> * = L*2/

Chromatic dilution: ( )1/2 E

/ ( *)1/2

= E L*/*

14

Sequence of elements in ~100m long Final Focus Test Beam

beam

Focal point

Dipoles. They bend trajectory,but also disperse the beamso that x depend on energy offset

Sextupoles. Their kick will containenergy dependent focusing x’ => S (x+ )2 => 2S x + .. y’ => – S 2(x+ )y => -2S y + ..that can be used to arrange chromatic correction

Terms x2 are geometric aberrationsand need to be compensated also

Necessity to compensate chromaticity is a major driving factor of FF design

Example of traditional Final Focus

15

Final Focus Test Beam

Achieved ~70nm vertical beam size

16

Synchrotron Radiation in FF magnets

Energy spread caused by SR in bends and quads is also a major driving factor of FF design

• Bends are needed for compensation of chromaticity

• SR causes increase of energy spread which may perturb compensation of chromaticity

• Bends need to be long and weak, especially at high energy

• SR in FD quads is also harmful (Oide effect) and may limit the achievable beam size

Field lines

Field left behind

v <

c

v =

c

17

Beam-beam (Dy, E , ) affect choice of IP parameters and are important for FF

design also

• Luminosity per bunch crossing

• “Disruption” – characterize focusing strength of the field of the bunch (Dy ~ z/fbeam)

• Energy loss during beam-beam collision due to synchrotron radiation

• Ratio of critical photon energy to beam energy (classic or quantum regime)

yx

2

σσ

N~Lumi

yx

zy σσ

σN~D

zxσσ

N~

z2x

2

E σσ

N~δ

18

Beam-beam effectsHD and instability

yx

zey

NrD

2

Dy~12

Nx2Dy~24

19

Factor driving BDS design

• Chromaticity

• Beam-beam effects

• Synchrotron radiation– let’s consider it in more details

20

Let’s estimate SR power

dVEW 2Energy in the field left behind (radiated !):

The field the volume2r

eΕ dSrV 2

22

222 r

r

erE

dS

dW

Energy loss per unit length:

Compare with exact formula: 2

42

R

γe

3

2

dS

dW

Substitute and get an estimate:22γ

Rr

2

42

R

γe

dS

dW22γ

R1

v

cRr

R + rR

Field left behind

Field lines

v <

c

v =

c

21

Let’s estimate typical frequency of SR photons

During what time t the observer will see the photons?

Observerv e <

c

1/γ

2

v = c

R Photons emitted during travel along the 2R/ arc will be observed.

For >>1 the emitted photons goes into 1/ cone.

c

v1

γ

2RdS

Photons travel with speed c, while particles with v. At point B, separation between photons and particles is

A B

Therefore, observer will see photons during 3γc

Rβ1

γc

2R

c

dSΔt

R

γc

2

3ω

3

c Compare with exact formula:Estimation of characteristic frequencyR

γc

Δt

1ω

3

c

22

Let’s estimate energy spread growth due to SR

We estimated the rate of energy loss : And the characteristic frequencyR

γcω

3

c 2

42

R

γe

dS

dW

The photon energy 2e

33

cc mcλR

γ

R

cγωε

2

2

e mc

er

c

eα

2

α

rλ e

e where

Compare with exact formula:

3

5ee

2

R

γλr

324

55

dS

ΔE/Ed

Number of photons emitted per unit length R

γ

dS

dW1

dS

dN

c

(per angle )θγαN

3

5ee

2

R

γλr

dS

ΔE/EdWhich gives:

The energy spread E/E will grow due to statistical fluctuations ( ) of the number of emitted photons :

22

2c

2

γmc

1

dS

dNε

dS

ΔE/Ed

N

23

Let’s estimate emittance growth rate due to SR

Dispersion function shows how equilibrium orbit shifts when energy changes

Equi

libriu

m

orbi

t for

EEqui

libriu

m o

rbit

for E

+E

E/E

When a photon is emitted, the particle starts to oscillate around new equilibrium orbit

Emit photon

ΔE/EηΔx Amplitude of oscillation is

1/2xxx βεσ Compare this with betatron beam size:

And write emittance growth: β

Δx Δε

2

x

Resulting estimation for emittance growth:

3

5ee

x

22

x

2x

R

γλr

β

η

dS

ΔE/Ed

β

η

dS

dε

Compare with exact formula (which also takes into account the derivatives):

3

5ee

x

2'x

'x

2x

R

γλr

324

55

β

/2ηβηβη

dS

dε

H

24

Let’s apply SR formulae to estimate Oide effect (SR in FD)

Final quad

** ε/βθ

** β εσ

IP divergence:

IP size:R

L L*

*θ / L R Radius of curvature of the trajectory:

Energy spread obtained in the quad:

3

5ee

2

R

Lγλr

E

ΔE

Growth of the IP beam size: 2

2**20

2

E

ΔEθLσσ

This achieve minimum possible value:

5/71/7ee

2/7*1/71min γελr

L

LC35.1σ

When beta* is:

3/72/7ee

4/7*2/71optimal γεγλr

L

LC29.1β

5/2

*5

ee

2*

1*2

β

εγλr

L

LCβεσ

Which gives ( where C1 is ~ 7 (depend on FD params.))

Note that beam distribution at IP will be non-Gaussian. Usually need to use tracking to estimate impact on luminosity. Note also that optimal may be smaller than the z (i.e cannot be used).

25

Concept and problems of traditional FF

0 200 400 600 800 1000 1200 1400 1600 18000

100

200

300

400

500

1 / 2

(

m1

/ 2 )

s (m)

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

y

x

y

1/2

x

1/2

(

m)

Traditional FF

• Chromaticity is compensated by sextupoles in dedicated sections

• Geometrical aberrations are canceled by using sextupoles in pairs with M= -I

FinalDoublet

X-Sextupoles Y-Sextupoles

• Chromaticity not locally compensated– Compensation of aberrations is

not ideal since M = -I for off energy particles

– Large aberrations for beam tails– …

Problems:

/

Chromaticity arise at FD but pre-compensated 1000m upstream

26

FF with local chromatic correction

• Chromaticity is cancelled locally by two sextupoles interleaved with FD, a bend upstream generates dispersion across FD

• Geometric aberrations of the FD sextupoles are cancelled by two more sextupoles placed in phase with them and upstream of the bend

27

Local chromatic correction

• The value of dispersion in FD is usually chosen so that it does not increase the beam size in FD by more than 10-20% for typical beam energy spread

IP

FD

Dx

sextupoles

dipole

0 0 0

0 1/ 0 0

0 0 0

0 0 0 1/

m

m

m

m

R

L*

28

Chromatic correction in FD

x +

IP

quadsextup.

KS KF

Quad: )ηδδx(Kηδ)(xδ)(1

Kx' 2

FF

)2

ηδxδ(ηKηδ)(x

2

K x'

2

S2S Sextupole:

• Straightforward in Y plane

• a bit tricky in X plane:

Second order dispersion

chromaticityIf we require KS= KF to cancel FD chromaticity, then half of the second order dispersion remains.

Solution: The -matching section produces as much X chromaticity as the FD, so the X sextupoles run twice stronger and cancel the second order dispersion as well.

η

K2KKK

)2

ηδδx(K2x

δ)(1

Kηδ)(x

δ)(1

Kx'

FSFmatch-

2

Fmatch-F

29

Traditional and new FF

A new FF with the same performance can be ~300m long, i.e. 6 times

shorter

Traditional FF, L* =2m

New FF, L* =2m

new FF

30

New Final Focus

• One third the length - many fewer components!

• Can operate with 2.5 TeV beams (for 3 5 TeV cms)

• 4.3 meter L* (twice 1999 design)

0 200 400 600 800 1000 1200 1400 1600 18000

100

200

300

400

500

1 / 2

(

m1

/ 2 )

s (m)

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

y

x

y

1/2

x

1/2

(

m)

0 100 200 300 4000

100

200

300

400

500

1 / 2

(

m1

/ 2 )

s (m)

-0.06

-0.04

-0.02

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

y

x

y

1/2

x

1/2

(

m)

1999 Design 2000 Design

31

IP bandwidth

Bandwidth is much better for New FF

32

Aberrations & halo generation

-100 -80 -60 -40 -20 0 20 40 60 80 100-100

-80

-60

-40

-20

0

20

40

60

80

100

Traditional FF New FF

Y (

mm

)X (mm)

Halo beam at the FD entrance. Incoming beam is ~ 100 times larger than nominal beam

• Traditional FF generate beam tails due to aberrations and it does not preserve betatron phase of halo particles

• New FF has much less aberrations and it does not mix phases particles

Incoming beam halo

Beam at FD

Traditional FF

New FF

33

Beam halo & collimation

• Halo must be collimated upstream in such a way that SR & halo e+- do not touch VX and FD• => VX aperture needs to be somewhat larger than FD aperture• Exit aperture is larger than FD or VX aperture• Beam convergence depend on parameters, the halo convergence is fixed for given geometry => halo/beam (collimation depth) becomes tighter with larger L* or smaller IP beam size • Tighter collimation => MPS issues, collimation wake-fields, higher muon flux from collimators, etc.

VertexDetector

FinalDoublet (FD)

L*

IP

SR

Beam

Halo

beam= / *

halo= AFD / L*

AFD

• Even if final focus does not generate beam halo itself, the halo may come from upstream and need to be collimated

34

More details on collimation

• Collimators has to be placed far from IP, to minimize background

• Ratio of beam/halo size at FD and collimator (placed in “FD phase”) remains

• Collimation depth (esp. in x) can be only ~10 or even less• It is not unlikely that not only halo (1e-3 – 1e-6 of the

beam) but full errant bunch(s) would hit the collimator

collimator

35

MPS and collimation design

• The beam is very small => single bunch can punch a hole => the need for MPS (machine protection system)

• Damage may be due to– electromagnetic shower damage

(need several radiation lengths to develop)

– direct ionization loss (~1.5MeV/g/cm2 for most materials)

• Mitigation of collimator damage– using spoiler-absorber pairs

• thin (0.5-1 rl) spoiler followed by thick (~20rl) absorber

– increase of beam size at spoilers– MPS divert the beam to emergency

extraction as soon as possible

Picture from beam damage experiment at FFTB. The beam was 30GeV, 3-20x109 e-, 1mm bunch length, s~45-200um2. Test sample is Cu, 1.4mm thick. Damage was observed for densities > 7x1014e-/cm2. Picture is for 6x1015e-/cm2

36

Spoiler-Absorber & spoiler design

Thin spoiler increases beam divergence and size at the thick absorber already sufficiently large. Absorber is away from the beam and contributes much less to wakefields.

Need the spoiler thickness increase rapidly, but need that surface to increase gradually, to minimize wakefields. The radiation length for Cu is 1.4cm and for Be is 35cm. So, Be is invisible to beam in terms of losses. Thin one micron coating over Be provides smooth surface for wakes.

37

Spoiler damage

Temperature rise for thin spoilers (ignoring shower buildup and increase of specific heat with temperature):

The stress limit based on tensile strength, modulus of elasticity and coefficient of thermal expansion. Sudden T rise create local stresses. When T exceed stress limit, micro-fractures can develop. If T exceeds 4Tstress, the shock wave may cause material to delaminate. Thus, allowed T is either the melting point or four time stress limit at which the material will fail catastrophically.

38

Survivable and consumable spoilers

• A critical parameter is number of bunches #N that MPS will let through to the spoiler before sending the rest of the train to emergency extraction

• If it is practical to increase the beam size at spoilers so that spoilers survive #N bunches, then they are survivable

• Otherwise, spoilers must be consumable or renewable

39

Renewable spoilers

This design was essential for NLC, where short inter-bunch spacing made it impractical to use survivable spoilers. This concept is now being applied to LHC collimator system.

40

BDS with renewable spoilers

• Beam Delivery System Optics, an earlier version with consumable spoilers

• Location of spoiler and absorbers is shown

• Collimators were placed both at FD betatron phase and at IP phase

• Two spoilers per FD and IP phase

• Energy collimator is placed in the region with large dispersion

• Secondary clean-up collimators located in FF part

• Tail folding octupoles (see below) are include

betatron

energy

41

ILC FF & Collimation

• Betatron spoilers survive up to two bunches

• E-spoiler survive several bunches

• One spoiler per FD or IP phase

betatron spoilers

E- spoiler

42

tune-up dump

MPS betatron collimators

skew correction

4-wire 2D diagnostics

Energy diag. chicane & MPS energy collimator

polarimeter chicane

betatron collimation

MPS in BSY

kicker, septum

sigma (m) in tune-up extraction line

43

Nonlinear handling of beam tails in ILC BDS

• Can we ameliorate the incoming beam tails to relax the required collimation depth?

• One wants to focus beam tails but not to change the core of the beam– use nonlinear elements

• Several nonlinear elements needs to be combined to provide focusing in all directions– (analogy with strong focusing by FODO)

• Octupole Doublets (OD) can be used for nonlinear tail folding in ILC FF

Single octupole focus in planes and defocus on diagonals.

An octupole doublet can focus in all directions !

44

Strong focusing by octupoles

Effect of octupole doublet (Oc,Drift,-Oc) on parallel beam, (x,y).

• Two octupoles of different sign separated by drift provide focusing in all directions for parallel beam:

Next nonlinear termfocusing – defocusingdepends on

Focusing in all directions

*3423333 1 iii eLrerer

527352 33 ii eLrer

ireiyx

• For this to work, the beam should have small angles, i.e. it should be parallel or diverging

45

Tail folding in ILC FF

Tail folding by means of two octupole doublets in the ILC final focus Input beam has (x,x’,y,y’) = (14m,1.2mrad,0.63m,5.2mrad) in IP units (flat distribution, half width) and 2% energy spread, that corresponds approximately to N=(65,65,230,230) sigmas

with respect to the nominal beam

QF1QD0QD6

Oct.

• Two octupole doublets give tail folding by ~ 4 times in terms of beam size in FD• This can lead to relaxing collimation requirements by ~ a factor of 4

46

Tail folding or Origami Zoo QD6

Oct.QF5B

QD2

QD2

QF5B

QD6QF1

QD0

IP

QF1

QD0

IP

47

Halo collimatio

n

Assuming 0.001 halo, beam losses along the beamline behave nicely, and SR photon losses occur only on dedicated masks

Smallest gaps are +-0.6mm with tail folding Octupoles and +-0.2mm without them.

Assumed halo sizes. Halo population is 0.001 of the main beam.

48

Dealing with muons in BDS

Assuming 0.001 of the beam is collimated, two tunnel-filling spoilers are needed to keep the number of muon/pulse train hitting detector below 10

Good performance achieved for both Octupoles OFF and ON

49

9 & 18 m Toroid Spoiler Walls

Long magnetized steel walls are needed to spray the muons out of the tunnel

2.2m

50

Example of a 2nd IR BDS optics for ILC; design history; location of design knobs

BDS design methods & examples

51

In a practical situation …

• While designing the FF, one has a total control

• When the system is built, one has just limited number of observable parameters (measured orbit position, beam size measured in several locations)

• The system, however, may initially have errors (errors of strength of the elements, transverse misalignments) and initial aberrations may be large

• Tuning of FF is done by optimization of “knobs” (strength, position of group of elements) chosen to affect some particular aberrations

• Experience in SLC FF and FFTB, and simulations with new FF give confidence that this is possible

Laser wire will be a tool for tuning and diagnostic of FF

Laser wire at ATF

52

Stability – tolerance to FD motion

• Displacement of FD by dY cause displacement of the beam at IP by the same amount

• Therefore, stability of FD need to be maintained with a fraction of nanometer accuracy

• How would we detect such small offsets of FD or beams?

• Using Beam- beam deflection !

• How misalignments and ground motion influence beam offset?

IP

53

Ground motion & cultural noises

• Periodic signals can be characterized by amplitude (e.g. m) and frequency

• Random signals described by PSD

• The way to make sense of PSD amplitude is to *by frequency range and take Power Spectral Density of absolute

positiondata from different labs 1989 - 2001

Cultural noise& geology

7sec hum

54

Detector complicates reaching FD stability

Cartoon from Ralph Assmann (CERN)

55

Beam-Beam orbit feedback

IP

BPM

bb

FDBK kicker

y

e

e

use strong beam-beam kick to keep beams colliding

56

Beam-beam deflection

Sub nm offsets at IP cause large well detectable offsets (micron scale) of the beam a few meters downstream

57

ILC intratrain simulation

Injection Error (RMS/y): 0.2, 0.5, 1.0

Luminosity for ~100 seeds / run

Luminosity through bunch train showing effects of position/angle scans (small). Noisy for first ~100 bunches (HOM’s).

1.0

0.2

0.5

[Glen White]

ILC intratrain feedback (IP position and angle optimization), simulated with realistic errors in the linac and “banana” bunches, show Lumi ~2e34 (2/3 of design). Studies continue.

Positionscan

Anglescan

58

x

x

RF kick

Crab crossing

2 2 2,

20mr 100μm 2μm

x projected x c z

c z

factor 10 reduction in L!

use transverse (crab) RF cavity to ‘tilt’ the bunch at IP

59

Crab cavity requirements

IP

~0.12m/cell ~15m

Crab Cavity

Slide from G. Burt & P. Goudket

Use a particular horizontal dipole mode which gives a phase-dependant transverse momentum kick to the beam

Actually, need one or two multi-cell cavity

60

Crab cavity requirements

Δx

Interaction point

electron bunch

positron bunch

Slide from G. Burt & P. Goudket

Phase error (degrees)

Crossing angle 1.3GHz 3.9GHz

2mrad 0.222 0.665

10mrad 0.044 0.133

20mrad 0.022 0.066

Phase jitter need to be sufficiently small

Static (during the train) phase error can be corrected by intra-train feedback

61

Crab cavity

Right: earlier prototype of 3.9GHz deflecting (crab) cavity designed and build by Fermilab. This cavity did not have all the needed high and low order mode couplers. Left: Cavity modeled in Omega3P, to optimize design of the LOM, HOM and input couplers.FNAL T. Khabibouline et al., SLAC K.Ko et al.

62

Anti-Solenoids in FD

When solenoid overlaps QD0, coupling between y & x’ and y & E causes y(Solenoid) / y(0) ~ 30 – 190 depending on solenoid field shape (green=no solenoid, red=solenoid)

Even though traditional use of skew quads could reduce the effect, the LOCAL COMPENSATION of the fringe field (with a little skew tuning) is the best way to ensure excellent correction over wide range of beam energies

without compensati

on y/

y(0)=32

with compensation by

antisolenoid

y/ y(0)<1.01

63

Preliminary Design of Anti-solenoid for SiD

456mm

316mm

70mm cryostat

1.7m long

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0 2 4 6 8 10

15T Force

Four 24cm individual powered 6mm coils, 1.22m total length, rmin=19cm

64

Detector Integrated Dipole

• With a crossing angle, when beams cross solenoid field, vertical orbit arise

• For e+e- the orbit is anti-symmetrical and beams still collide head-on

• If the vertical angle is undesirable (to preserve spin orientation or the e-e- luminosity), it can be compensated locally with DID

• Alternatively, negative polarity of DID may be useful to reduce angular spread of beam-beam pairs (anti-DID)

65

Use of DID or

anti-DID

Orbit in 5T SiD

SiD IP angle zeroed w.DID

DID field shape and scheme DID case

anti-DID case

66

14(20)mrad IR

67

QD0SD0 QF1

SF1 Q,S,QEXF1

Disrupted beam & Sync radiations

BeamstrahlungIncoming beam

60 m

Shared Large Aperture Magnets

Rutherford cable SC quad and sextupole

pocket coil quad

2mrad IR

68

IR design

• Design of IR for both small and large crossing angles and to handle either DID or anti-DID

• Optimization of IR, masking, instrumentations, background evaluation

• Design of detector solenoid compensation

80

60

40

20

0

Beam

Cal E

nerg

y (T

eV)

3.02.52.01.51.00.50.0

Beampipe Radius (cm)

2 mrad 20 mrad 14 mrad 14 mrad + DI D 14 mrad + Anti-DI D

Shown the forward region considered by LDC for 20mrad (K.Busser) and an earlier version of 2mrad IR

69

Collider hall

• Collider hall sizes and detector assembly procedure for GLD (earlier version)

70

Tentative tunnel layout

71

Collider hall shielding design

• Shielding is designed to give adequate protection both in normal operation, when beam losses are small, and for “maximum credible beam” when full beam is lost in undesired location (but switched off quickly, so only one or several trains can be lost)

• Limits are different for normal and incident cases, e.g. what is discussed as guidance for IR shielding design:– Normal operation: dose less than 0.05 mrem/hr

(integrated less than 0.1 rem in a year with 2000 hr/year) – For radiation workers, typically ten times more is allowed

– Accidents: dose less than 25rem/hr and integrated less than 0.1 rem for 36MW of maximum credible incident (MCI)

72

IR & rad. safety

• For 36MW MCI, the concrete wall at 10m from beamline should be ~3.1m

18MW loss on Cu target 9r.l \at s=-8m. No Pacman, no detector. Concrete wall at 10m.Dose rate in mrem/hr.

Wall

25 rem/hr10m

73

Self-shielding detector

18MW on Cu target 9r.l at s=-8mPacman 1.2m iron and 2.5m concrete

dose at pacman external wall dose at r=7m 0.65rem/hr (r=4.7m) 0.23rem/hr

Detector itself is well shielded except for incoming beamlines

A proper “pacman” can shield the incoming beamlines and remove the need for shielding wall

18MW lost at s=-8m. Packman has Fe: 1.2m, Concrete: 2.5m

74

Beam dump for 18MW beam

• Water vortex• Window, 1mm thin, ~30cm

diameter hemisphere• Raster beam with dipole

coils to avoid water boiling• Deal with H, O, catalytic

recombination• etc.

undisrupted or disrupted beam size does not destroy beam dump window without rastering. Rastering to avoid boiling of water

20mr extraction optics

75

Get real with magnets

• Things to care: – needed aperture, L– strength, field quality,

stability– losses of beam or SR in the area

• E.g., extraction line => need aperture r~0.2m and have beam losses => need warm magnets which may consume many MW => may cause to look to new hybrid solutions, such as high T SC magnets

76

Magnet current (Amp*turn) per coil

and total powerI(A)=B(Gs)*h(cm)*10/(4) P(W)=2*I(A)*j(A/m2)*(*m)*l(m)

I(A)=1/2*B(Gs)*h(cm)*10/(4)

P(W)=4*I(A)*j(A/m2)*(*m)*l(m)

I(A)=1/3*B(Gs)*h(cm)*10/(4)

P(W)=6*I(A)*j(A/m2)*(*m)*l(m)

For dipole h is half gap. For quad and sextupole h is aperture radius, and B is pole tip field. Typical bends may have B up to 18kGs, quads up to 10kGs. Length of turn l is approximately twice the magnet length. For copper ~2*10-8 *m.For water cooled magnets the conductor area chosen so that current density j is in the range 4 to 10 A/mm2

Bend

Quad

Sextupole

77

ATF and ATF2

78

Optics Design of ATF2

New Beamline

Beam

ATF2

(A) Small beam sizeObtain y ~ 35nmMaintain for long time

(B) Stabilization of beam center Down to < 2nm by nano-BPM Bunch-to-bunch feedback of

ILC-like train New final focus

New diagnosti

cs

existing extraction

Earlier version of layout and optics are shown

79

Advanced beam instrumentation at ATF2

• BSM to confirm 35nm beam size• nano-BPM at IP to see the nm stability• Laser-wire to tune the beam• Cavity BPMs to measure the orbit• Movers, active stabilization, alignment system• Intratrain feedback, Kickers to produce ILC-like

train

IP Beam-size monitor (BSM)(Tokyo U./KEK, SLAC, UK)

Laser-wire beam-size Monitor (UK group)

Cavity BPMs, for use with Q magnets with 100nm resolution (PAL, SLAC, KEK)

Cavity BPMs with 2nm resolution, for use at the IP (KEK)

Laser wire at ATF

80

• Many colleagues whose slides or results were used in this lecture, namely Tom Markiewicz, Nikolai Mokhov, Brett Parker, Nick Walker, Jack Tanabe, Timergali Khabibouline, Kwok Ko, Cherrill Spencer, Lew Keller, Sayed Rokni, Alberto Fasso, Joe Frisch, Yuri Nosochkov, Mark Woodley, Takashi Maruyama, Karsten Busser, Graeme Burt, Rob Appleby, Deepa Angal Kalinin, Glen White, Phil Burrows, Tochiaki Tauchi, Junji Urakawa, and many other colleagues. Thanks!

Many thanks to

81

Homework

• There are 7 tasks• Some of them sequential, some

independent• Very rough estimations would be ok

82

HW1

• For given FD:• Estimate beam

size growth due to Oide effect for nominal ILC parameters andother cases such as “low P” at 1TeV

• Note1: you may need to derive formula for Oide effect if x size in FD is larger than y size

• Note2: you need to rescale b for corresponding parameter set

83

HW2

• For the FD shown, and your favorite vertex detector radius, find the required collimation depth in x and y– take both nominal and other cases such as “low

P”

84

HW3

• For FD shown above, estimate effect on the beam size due to – second order dispersion – geometrical aberrations

• if they would not be compensated upstream

85

HW4

• For the FD shown above, and for the collimation depth that you determined,

• choose the material for thin spoiler• find the minimal beam size so that spoiler

survive N (choose between 1 and 100) bunches – (ignore thermal diffusion between bunches)

• find the gap opening for the spoiler

86

HW5

• For the FD considered above, find the min length of the bend that creates dispersion, to limit beam size growth caused by SR– see appendix for a similar example

87

HW6

• Estimate SR emittance growth at 1TeV in “big bend” that turns the beam to one of IRs

• Estimate SR emittance growth at 1TeV in the polarimeter chicane

to IR

to IR

to dump

big bend

polarimeter chicane

88

HW7

• Estimate allowable steady state beam loss in IR, from the radiation safety point of view, for– IR hall with shielding wall as shown above– for self-shielding detector assuming it is fenced

out at 7m

89

Appendix: • Couple of definitions of chromaticity,

suitable for single pass beamlines• Formulae connecting Twiss functions and

transfer matrices• Example of calculation of the min length of

the bend in FF system

90

Two more definitions of chromaticity1st : TRANSPORT

You are familiar now with chromaticity defined as a change of the betatron tunes versus energy. This definition is mostly useful for rings.

In single path beamlines, it is more convenient to use other definitions. Lets consider other two possibilities.

The first one is based on TRANSPORT notations, where the change of the coordinate vector

δ

Δl

y'

y

x'

x

x i

is driven by the first order transfer matrix R such that

injji

outi xRx

The second, third, and so on terms are included in a similar manner:

...xxxUxxTxRx inn

ink

injnkji

ink

injkji

injji

outi

In FF design, we usually call ‘chromaticity’ the second order elements T126 and T346. All other high order terms are just ‘aberrations’, purely chromatic (as T166, which is second order dispersion), or chromo-geometric (as U32446).

91

Two more definitions of chromaticity2nd : W functions

Let’s define chromatic function W (for each plane) as where

And where: and

2/BAiW 1i

βδ

Δβ

ββδ

ββB 1/2

12

12

δ

Δβ

β

α

δ

Δα

ββδ

βαβαA 1/2

12

2112

Lets assume that betatron motion without energy offset is described by twiss functions and and with energy offset by functions and

Using familiar formulae and where2αds

dβ

β

α1βK

ds

dα 2

dx

dB

pc

eK y

And introducing we obtain the equation for W evolution:Kδ

K(0)-K(δ(ΔK

ΔKβ2

iW

β

2i

ds

dW

can see that if K=0, then W rotates with double betatron frequency and stays constant in amplitude. In quadrupoles or sextupoles, only imaginary part changes.

Can you show this?

knowing that the betatron phase is

β

1

ds

d

Show that if T346 is zeroed at the IP, the Wy is also zero. Use approximation R34=T346* , use DR notes, page 12, to obtain R34=(0)1/2 sin(), and the twiss equation for d/d.

Show that if in a final defocusing lens =0, then it gives W=L*/(2*)

92

Several useful formulaeTRANSPORT Twiss

1) If you know the Twiss functions at point 1 and 2, the transfer matrix between them is given by

0

20

120111201201111 β

α1RαRRαRβRRβ

2) If you know the transfer matrix between two points, the Twiss functions transform in this way:

0

20

120112201101221 β

α1RαRRβRαRRα

16'012011 RηRηRη

26'022021

' RηRηRη

012011

120 αRβR

RarctgΦΦ

And similar for the other plane

93

Length required for the bends in

FF

bend

We know now that there should be nonzero horizontal chromaticity Wx upstream of FD (and created upstream of the bend). SR in the bend will create energy spread, and this chromaticity will be ‘spoiled’. Let’s estimate the required length of the bend, taking this effect into account.

Parameters: length of bend LB, assume total length of the telescope is 2*LB, the el-star L* , IP dispersion’ is ’

Can you show this ?Dispersion at the FD, created by bend, is approximatelyR

L

2

3η

2B

max

Recall that we typically have max~ 4 L* ’ , therefore, the bending radius is η'L

L

8

3R

*

2B

5B

33 *5ee

2

L

η'Lγλr19

E

ΔE

The SR generated

energy spread is then And the beam size growth

22x2

2

E

ΔEW

σ

Δσ

Example: 650GeV/beam, L*=3.5m, ’=0.005, Wx=2E3, and requesting <1% => LB > 110m

Energy scaling. Usually ’ ~ 1/1/2 then the required LB scales as 7/10 Estimate LB for telescope you created in Exercise 2-4.