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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
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
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
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
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
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
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
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
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
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.