Andrei Seryi
SLAC
International Accelerator School for Linear Colliders
19-27 May 2006, Sokendai, Hayama, Japan

• Energy – need to reach at least 500 GeV CM as a start
2
• Luminosity – need to reach 10^34 level

at SLC
• 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, …
3
• Including better focusing, dealing with beam-beam, safely removing beams after collision and better stability

4
• 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)
5
Vertical size is smallest
L
 f rep
4
 n b

N x

2 y
H
D

5
BDS

6
• As we go through the lecture, the purpose of each subsystem should become clear

7
• 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
• 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
(The emittance e is constant, so, to make the IP beam size ( e b ) 1/2 small, you need large beam divergence at the IP ( e / b ) 1/2 i.e. short-focusing lens.)
• It is very similar for electron or positron beams
• But one have to use magnets

• Beta function b characterize optics
• Emittance e is phase space volume of the beam
• Beam size: ( e b ) 1/2
• Divergence: ( e / b ) 1/2
• Focusing makes the beam ellipse rotate with “betatron frequency”
• Phase of ellipse is called “betatron phase”
9

10
Just bend the trajectory
Focus in one plane, defocus in another: x’ = x’ + G x y’ = y’– G y
Second order effect: x’ = x’ + S (x 2 -y 2 ) y’ = y’ – S 2xy
Here x is transverse coordinate, x’ is angle
Etc…

11
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:
R
X, Y




1/M
0
X, Y

0
M
X, Y


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).
final doublet
(FD)
IP f
2 f
1 f
2 f
1 f
2
(= L * )
Use telescope optics to demagnify beam by factor m = f 1/ f 2= f 1/ L*
Matrix formalism for beam transport: x out  i
R i j x in j x i
 x x' y y'
Δl
δ





















• 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
12

How to focus to a smallest size and how big is chromaticity in FF?
Size: ( e b ) 1/2
Angles: ( e / b ) 1/2
IP
Size at IP:
L * ( e / b ) 1/2
+ ( e b ) 1/2 
E
L *
• 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 D /  ~ 
Typical:

E
E
L*/ b *
L* -- distance from FD to IP ~ 3 - 5 m b * -- beta function in IP ~ 0.4 - 0.1 mm
Beta at IP:
L * ( e / b ) 1/2 = ( e b * ) 1/2
=> b * = L *2 / b
Chromatic dilution:
( e b ) 1/2 
E
/ ( e b * ) 1/2
= 
E
L * / b *
• For typical parameters, D /  ~ 15-500 too big !
13
• => Chromaticity of FF need to be compensated

Sequence of elements in ~100m long Final Focus Test Beam beam
Focal point
Dipoles. They bend trajectory, but also disperse the beam so that x depend on energy offset d
14
Necessity to compensate chromaticity is a major driving factor of FF design
Sextupoles. Their kick will contain energy dependent focusing x’ => S (x+ y’ => – S 2(x+ d ) 2 => 2 S x d + ..
d )y => -2 S y d + ..
that can be used to arrange chromatic correction
Terms x 2 are geometric aberrations and need to be compensated also

15
Achieved ~70nm vertical beam size

16
Field left behind
• 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
Field lines
Energy spread caused by SR in bends and quads is also a major driving factor of FF design
• SR in FD quads is also harmful (Oide effect) and may limit the achievable beam size

17
Lumi ~
N 2
σ x
σ y
D y
~

N σ z
σ x
σ y
Beam-beam (D y
, d
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
(D y
~  z
/f beam
)
δ
E
~
N
2

σ 2 x
σ z
• Energy loss during beam-beam collision due to synchrotron radiation

~
N

σ x
σ z
• Ratio of critical photon energy to beam energy (classic or quantum regime)

18
H
D and instability
D y

2
 r e

N
 x
 z y
D y
~12
Nx2
D y
~24

19
• Chromaticity
• Beam-beam effects
• Synchrotron radiation
– let’s consider it in more details

20
Field lines
Field left behind
R R + r r

R c v
1



R
2γ
2
Energy in the field left behind (radiated !):
W
 
E
2 dV
Ε  e
The field the volume r
2
V
 r
2 dS
Energy loss per unit length:
2 dW

E
2 r
2  dS r e
2 r
2 r

R
Substitute and get an estimate:
2γ
2 dW dS
 e
2 γ 4
R
2
Compare with exact formula: dW dS

2
3 e
2 γ 4
R
2

For

>>1 the emitted photons goes into 1/
 cone.
1/γ
During what time
D t the observer will see the photons?
v

= c
A B
Observer
R
Photons emitted during travel along the 2R/
 arc will be observed.

2
Photons travel with speed c, while particles with v.
At point B, separation between photons and particles is dS

2R
γ 
1
Therefore, observer will see photons during
Δt  dS
 c
2R c γ

1
 β

 c
R
γ 3
Estimation of characteristic frequency
21
ω c

1
Δt
 c
γ 3
R v c
Compare with exact formula:
ω c

3
2 c
γ 3
R

We estimated the rate of energy loss : dW
 dS e
2 γ 4
R
2
And the characteristic frequency
ω c
 c
γ 3
R
The photon energy ε c
  ω c

γ 3  c
R

γ 3
λ e mc
2
R
Number of photons emitted per unit length dN dS

1 e c dW dS


R
γ where e
2 r
 e mc
2
(per angle q : e
2
α 
 c
λ e
 r
α e
N
 α γ θ
)
22
The energy spread
D
E/E will grow due to statistical fluctuations ( ) of the number of emitted photons : d


ΔE/E

2 dS

 ε 2 c dN dS
1

γmc 2

2
Which gives: d


ΔE/E

2
 dS
 r e
λ
R e
3
γ 5
Compare with exact formula: d


ΔE/E

2

 dS
55
24 3 r e
λ e
R
3
γ 5

Dispersion function h shows how equilibrium orbit shifts when energy changes
When a photon is emitted, the particle starts to oscillate around new equilibrium orbit
Emit photon
Amplitude of oscillation is Δx  η ΔE/E
23
Compare this with betatron beam size:
And write emittance growth:
Δε x

Δx 2
β
σ x

Resulting estimation for emittance growth: dε x dS

η 2
β x d


ΔE/E

2

 dS
η 2
β x r e

ε x
β x

1/2
λ e
R
3
γ 5
Compare with exact formula (which also takes into account the derivatives): dε x dS


η 2 


β x
η '
H
β x
 β ' x
η
/2
2
 
55
24 3 r e
λ e
R
3
γ 5

24
Final quad
R
IP divergence:
θ *
 ε/β *
IP size:
σ *
 ε β *
Energy spread obtained in the quad:
ΔE
E
2
 r e
λ e
R
3
γ 5
L
L
Which gives
Radius of curvature of the trajectory:
σ 2  σ 2
0

 
2
R

L /
θ *
L *
σ 2
 ε β *

C
1
Growth of the IP beam size:


L
*
L


2 r e
λ e
γ 5


ε
β *


5/2
ΔE
E
2
( where C
1 is ~ 7 (depend on FD params.))
σ min
This achieve minimum possible value:

1 .
35 C
1/7
1


L
*
L


2/7
 r e
λ e
  
5/7 β optimal

When beta* is:
1 .
29 C
1
2/7


L
*
L


4/7
 r e
λ e

2/7 γ
 
3/7
Note that beam distribution at IP will be non-Gaussian. Usually need to use tracking to estimate impact on luminosity. Note also that optimal b may be smaller than the
 z
(i.e cannot be used).

• Chromaticity is compensated by sextupoles in dedicated sections
• Geometrical aberrations are canceled by using sextupoles in pairs with M= -I
Chromaticity arise at FD but pre-compensated 1000m upstream
500
400
300
X-Sextupoles Y-Sextupoles h x h y b y
1/2
Final
Doublet
0.15
0.10
0.05
0.00
200 b x
1/2
-0.05
100
-0.10
Problems:
• Chromaticity not locally compensated
25
– Compensation of aberrations is not ideal since M = -I for off energy particles
– Large aberrations for beam tails
– …
0 -0.15
0 200 400 600 800 1000 1200 1400 1600 1800 s (m)
Traditional FF

• Chromaticity is cancelled
by two sextupoles interleaved with FD , a bend upstream generates dispersion across FD
26
• Geometric aberrations of the FD sextupoles are cancelled by two more sextupoles placed in phase with them and upstream of the bend

dipole
D x
IP sextupoles
27
R






 m
0
0
0
1/
0
0
0 m
0
0 m
0 1/
0
0
0 m 




FD
L*
• 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

28 x + h d sextup.
quad
• Straightforward in Y plane
• a bit tricky in X plane:
IP
Quad:
K
S
Sextupole:
K
F
D x'

D x'

(1
K

F
δ)
(x
 ηδ) 
K
F
(
 δx  ηδ 2
)
K
2
S
(x
 chromaticity
ηδ) 2 
K
S
η
(
δ x

ηδ 2
)
2
Second order dispersion
If we require K
S h
= K
F to cancel FD chromaticity, then half of the second order dispersion remains.
D x'

(1
K

F
δ)
(x
 ηδ) 
K b
match
(1
 δ) x

2 K
F
(
 δx 
ηδ 2
)
2
K b
match

K
F
K
S

2 K
F
η
Solution:
The b
-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.

29 new FF
Traditional FF, L* =2m A new FF with the same performance can be
~300m long, i.e. 6 times shorter
New FF, L* =2m

• 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)
1999 Design
2000 Design
500 0.15
0.10
400
300
200 h x h y b x
1/2 b y
1/2
0.05
0.00
-0.05
30
100
-0.10
0 -0.15
0 200 400 600 800 1000 1200 1400 1600 1800 s (m)
500
400
300
200
100
0
0 100 b x
1/2
200 b y
1/2
300 h x h y
0.14
0.12
0.10
0.08
0.06
0.04
0.02
0.00
-0.02
-0.04
-0.06
400 s (m)

31
Bandwidth is much better for New FF

32
• Traditional FF beam tails
Incoming beam halo generate 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
Beam at FD
Traditional FF
100
80
60
40
20
0
-20
-40
-60
Traditional FF
-80 New FF
X (mm)
-100
-100 -80 -60 -40 -20 0 20 40 60 80 100
Halo beam at the FD entrance.
Incoming beam is ~ 100 times larger than nominal beam
New FF

• Even if final focus does not generate beam halo itself, the halo may come from upstream and need to be collimated
A
FD
33
Halo
Beam
Final
Doublet (FD) q halo
= A
FD
/ L*
L*
Vertex
Detector q beam
= e /  *
IP
SR 
• 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
=> q halo
/ q 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.

• 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 collimator
34
• 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

35
• 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/cm 2 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, 3-20x10 9 e-, 1mm bunch length, s~45-200um 2 . Test sample is Cu, 1.4mm thick. Damage was observed for densities >
7x10 14 e-/cm 2 . Picture is for 6x10 15 e-/cm 2

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.
36
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.

Temperature rise for thin spoilers (ignoring shower buildup and increase of specific heat with temperature):
37
The stress limit based on tensile strength, modulus of elasticity and coefficient of thermal expansion. Sudden T rise create local stresses. When D T exceed stress limit, micro-fractures can develop. If D T exceeds 4T stress
, the shock wave may cause material to delaminate. Thus, allowed D T is either the melting point or four time stress limit at which the material will fail catastrophically.

38
• 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
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.

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

41
• Betatron spoilers survive up to two bunches
• E-spoiler survive several bunches
• One spoiler per FD or IP phase betatron spoilers
E- spoiler

42
skew correction
Energy diag. chicane &
MPS energy collimator
MPS betatron collimators
4-wire 2D e diagnostics kicker, septum sigma (m) in tune-up extraction line polarimeter chicane betatron collimation tune-up dump

• 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 )
Single octupole focus in planes and defocus on diagonals.
An octupole doublet can focus in all directions !
43
• Octupole Doublets (OD) can be used for nonlinear tail folding in ILC FF

D q 
• Two octupoles of different sign separated by drift provide focusing in all directions for parallel beam:
 r
3 e
 i 3 j 

 r
3 e i 3 j

1
  r
2
L e
 i 4 j 3


* x
 iy
 re i j
D q  
3

2 r
5 e i j 
3

3 r
7
L
2 e i 5 j
Focusing in all directions
Next nonlinear term focusing – defocusing depends on j
Effect of octupole doublet (Oc,Drift,-Oc) on parallel beam,
DQ
(x,y).
• For this to work, the beam should have small angles , i.e. it should be parallel or diverging
44

• 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
Oct.
QD6 QD0
QF1
45
Tail folding by means of two octupole doublets in the ILC final focus
Input beam has (x,x’,y,y’) = (14 m m,1.2mrad,0.63
m m,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

46
QD6
Oct.
QD6
QF5B
QD2
QF1
IP
QD0
QF1
QD0
QF5B
IP
QD2

Halo collimation
47
Assumed halo sizes. Halo population is 0.001 of the main beam.
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.

48
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
2.2m
Long magnetized steel walls are needed to spray the muons out of the tunnel

50
Example of a 2 nd IR
BDS optics for ILC; design history; location of design knobs

Laser wire at ATF
• 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
Laser wire will be a tool for tuning and diagnostic of FF
• 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
51

52
IP
• 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?

• Periodic signals can be characterized by amplitude (e.g. m m) and frequency
• Random signals described by PSD
• The way to make sense of PSD amplitude is to *by frequency range and take
7sec hum
Cultural noise
& geology
Power Spectral Density of absolute position data from different labs 1989 - 2001
53

54
Cartoon from Ralph Assmann (CERN)

55 e

IP
D y q bb
FDBK kicker
BPM use strong beam-beam kick to keep beams colliding e


56
Sub nm offsets at IP cause large well detectable offsets
(micron scale) of the beam a few meters downstream

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.
Luminosity for ~100 seeds / run
0.2
Position scan
Angle scan
0.5
1.0
Luminosity through bunch train showing effects of position/angle scans (small).
Noisy for first ~100 bunches (HOM’s).
57
[Glen White]
Injection Error (RMS/  y
): 0.2, 0.5, 1.0

x x
58
RF kick
   x
2    c z
2


  c z
20mr 100μm
 2μm factor 10 reduction in L !
use transverse (crab) RF cavity to ‘tilt’ the bunch at IP

Crab Cavity
~0.12m/cell
59 Slide from G. Burt & P. Goudket
~15m
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
IP

Phase jitter need to be sufficiently small electron bunch
Static (during the train) phase error can be corrected by intra-train feedback positron bunch
60
Slide from G. Burt & P. Goudket
Crossing angle
2mrad
10mrad
20mrad
Δx
Interaction point
Phase error (degrees)
1.3GHz
0.222
0.044
0.022
3.9GHz
0.665
0.133
0.066

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
61 et al., SLAC K.Ko et al.

62 without compensation
 y
/
 y
(0)=32
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 with compensation by antisolenoid
 y
/
 y
(0)<1.01

63
70mm cryostat
1.7m long
Preliminary Design of Anti-solenoid for SiD
0.1
0
-0.1
-0.2
-0.3
0
Four 24cm individual powered 6mm coils,
1.22m total length, r min
=19cm
0.3
15T Force
0.2
2 4 6 8 10
316mm
456mm

64
• 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-eluminosity), 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
DID field shape and scheme
Orbit in 5T SiD
SiD IP angle zeroed w.DID
DID case anti-DID case

66

Shared Large Aperture
Magnets
SF1
QD0
SD0 QF1
Disrupted beam & Sync radiations
Q,S,QEXF1
60 m
Beamstrahlung
Incoming beam pocket coil quad
Rutherford cable SC quad and sextupole
67

• 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
68
80
60
40
2 mrad
20 mrad
14 mrad
14 mrad + DID
14 mrad + Anti-DID
20
0
0.0
0.5
1.0
1.5
2.0
Beampipe Radius (cm)
2.5
3.0
Shown the forward region considered by
LDC for 20mrad (K.Busser) and an earlier version of 2mrad IR

69
• Collider hall sizes and detector assembly procedure for GLD (earlier version)

70

71
• 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)

10m
72
• 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/hr

73
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 on Cu target 9r.l at s=-8m
Pacman 1.2m iron and 2.5m concrete
18MW lost at s=-8m.
Packman has Fe: 1.2m, Concrete: 2.5m
dose at pacman external wall dose at r=7m
0.65rem/hr (r=4.7m) 0.23rem/hr

• 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
74
20mr extraction optics

75
• 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

I (A)= B (Gs)* h (cm)*10/(4  )
P (W)=2* I (A)* j (A/m 2 )* r ( W
* m)* l (m)
Bend
I (A)=1/2* B (Gs)* h (cm)*10/(4  ) Quad
P (W)=4* I (A)* j (A/m 2 )* r ( W
* m)* l (m)
I (A)=1/3* B (Gs)* h (cm)*10/(4  )
P (W)=6* I (A)* j (A/m 2 )* r ( W
* m)* l (m)
76
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 r ~2*10 -8 W *m.
For water cooled magnets the conductor area chosen so that current density j is in the range 4 to 10 A/mm 2

77

Optics Design of ATF2
(A) Small beam size
Obtain  y
~ 35nm
Maintain 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
Beam
New diagnostics existing extraction
New Beamline
78
Earlier version of layout and optics are shown

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
Laser-wire beam-size
Monitor (UK group)
Laser wire at ATF
IP Beam-size monitor (BSM)
(Tokyo U./KEK, SLAC, UK)
79
Cavity BPMs with
2nm resolution, for use at the IP
(KEK)
Cavity BPMs, for use with Q magnets with 100nm resolution (PAL, SLAC, KEK)

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!

81
• There are 7 tasks
• Some of them sequential, some independent
• Very rough estimations would be ok

82
• For given FD:
• Estimate beam size growth due to Oide effect for nominal ILC parameters and other 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
• 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
• 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
• 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
• 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
• 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 big bend to IR polarimeter chicane to IR to dump

88
• 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
• 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

1 st : 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 x i
 x x' y y'
Δl
δ



















 is driven by the first order transfer matrix R such that x i out 
R i j x in j
The second, third, and so on terms are included in a similar manner: x i out 
R i j x in j

T i j k x in j x in k

U i j k n x in j x in k x in n

...
90
In FF design, we usually call ‘chromaticity’ the second order elements T
126 and T
346
. All other high order terms are just ‘aberrations’, purely chromatic (as T
166
, which is second order dispersion), or chromo-geometric (as U
32446
).

2 nd : W functions
91
Lets assume that betatron motion without energy offset is described by twiss functions

1 with energy offset d by functions

2 and b
2
Let’s define chromatic function
W W

 i A

B

/ 2 and b
1 i
 
1
B

δ

β
β 
 β
β
1

Δβ
And where: and
1/2 δ β
2
 dβ ds
  dα ds

A
K


β
δ
α
2

β
1
β
2


α
1
β
β
1

2
1/2


1
 α 2

β

Δα
δ

K

α
β e
Δβ pc
δ dB y dx and
Can you show this?
ΔK 
K(δ( K(0)
δ
 
K W evolution: dW

2i ds
β
W
 i
2
β ΔK knowing that the betatron phase is d
 ds

1
β can see that if
D
K =0, then W rotates with double betatron frequency and stays constant in amplitude. In quadrupoles or sextupoles, only imaginary part changes.
Show that if in a final defocusing lens

=0, then it gives
D
W=L*/(2 b
*)
Show that if T
346 is zeroed at the IP, the W notes, page 12, to obtain R
34
=( bb
0 y is also zero. Use approximation
D
R
34
=T
346
* d
, use DR
) 1/2 sin(
D
), and the twiss equation for d

/d

.

TRANSPORT  Twiss
1) If you know the Twiss functions at point 1 and 2, the transfer matrix between them is given by
92
α
β
2) If you know the transfer matrix between two points, the Twiss functions transform in this way:


R
R
21
11

R
11
β

R
12
α
0
0


R
12
α
0
R
11
β
0




R
R
12
22



 R
11
α
R
11
α
0
0

And similar for the other plane

R
12
R
12


1
1


β
β
0
0
α
0
2
α 2
0






Φ 
η
η
Φ
'
0



R
R
11
η
0
21
η arctg


0


R
R
R
11
β
12
0
η '
0
22
η
R

12
'
0
R


12
R
R
α
0
16
26



Length required for the bends in FF bend
We know now that there should be nonzero horizontal chromaticity W x 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 L
B the telescope is 2*L
B
, assume total length of
, the el-star L * , IP dispersion’ is h ’
Dispersion at the FD, created by bend, is approximately
η max

3 L
2
B
Can you show this ?
2 R
Recall that we typically have h max
~ 4 L * h ’ , therefore, the bending radius is
R

3
8 L
L
2
B
* η'
The SR generated energy spread is then
ΔE
E
2

19 r e
λ e
γ 5
L
* 3 η' 3
L
5
B
And the beam size growth
Δσ 2
σ 2

W x
2
ΔE
E
2
Example: 650GeV/beam, L * =3.5m, h ’=0.005, W x
=2E3, and requesting
D/
<1% => L
B
> 110m
Energy scaling. Usually h ’ ~ 1/ 
1/2 then the required L
B
93 scales as

7/10
Estimate L
B for telescope you created in Exercise 2-4.