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An Introduction to thePhysics and Technologyof e+e- Linear Colliders
Lecture 9: a) Beam Based Alignment
Nick Walker (DESY)
DESY Summer Student Lecture31st July 2002USPAS, Santa Barbara, 16th-27th June, 2003
Emittance tuning in the LET
• LET = Low Emittance Transport– Bunch compressor (DRMain Linac)– Main Linac– Beam Delivery System (BDS), inc. FFS
• DR produces tiny vertical emittances (y ~ 20nm)
• LET must preserve this emittance!– strong wakefields (structure misalignment)– dispersion effects (quadrupole misalignment)
• Tolerances too tight to be achieved by surveyor during installation
Need beam-based alignmentmma!
YjYi
Ki
yj
gij
1
j
j ij i i ji
y g K Y Y
Basics (linear optics)
0
34 ( , )j
iij
j y
yg
y
R i j
linear system: just superimpose oscillations caused by quad kicks.
thin-lens quad approximation: y’=KY
1
j
j ij i i ji
y g K Y Y
YQy
Idiag(K)GQ
Original Equation
Defining Response Matrix Q:
Hence beam offset becomes
Introduce matrix notation
21
31 32
41 42 43
0 0 0 0
0 0 0
0 0
0
g
g g
g g g
G
G is lower diagonal:
Dispersive Emittance Growth
Consider effects of finite energy spread in beam RMS
( ) ( )1
K
Q G diag Ichromatic response matrix:
latticechromaticity
dispersivekicks0
34 34 346
( ) (0)
( ) (0)R R T
GG G
dispersive orbit: ( )( ) (0)y
Δy
η Q Q Y
What do we measure?
BPM readings contain additional errors:
boffset static offsets of monitors wrt quad centres
bnoise one-shot measurement noise (resolution RES)
0BPM offset noise 0 0
0
y
y
y Q Y b b R y y
fixed fromshot to shot
random(can be averaged
to zero)launch condition
In principle: all BBA algorithms deal with boffset
Scenario 1: Quad offsets, but BPMs aligned
BPM
Assuming:
- a BPM adjacent to each quad
- a ‘steerer’ at each quad
simply apply one to one steering to orbit
steererquad mover
dipole corrector
Scenario 2: Quads aligned, BPMs offset
BPM
1-2-1 corrected orbit
one-to-one correction BAD!
Resulting orbit not Dispersion Free emittance growth
Need to find a steering algorithm which effectively puts BPMs on (some) reference line
real world scenario: some mix of scenarios 1 and 2
BBA
• Dispersion Free Steering (DFS)– Find a set of steerer settings which minimise the
dispersive orbit– in practise, find solution that minimises difference
orbit when ‘energy’ is changed– Energy change:
• true energy change (adjust linac phase)• scale quadrupole strengths
• Ballistic Alignment– Turn off accelerator components in a given section,
and use ‘ballistic beam’ to define reference line– measured BPM orbit immediately gives boffset wrt to
this line
DFS
( ) (0)E E
E E
E
E
Δy Q Q Y
M Y
1 Y M Δy
Problem:
Solution (trivial):
Note: taking difference orbit y removes boffset
Unfortunately, not that easy because of noise sources:
noise 0 Δy M Y b R y
DFS example
300m randomquadrupole errors
20% E/E
No BPM noise
No beam jitter
m
m
DFS example
Simple solve
1 Y M Δy
original quad errors
fitter quad errors
In the absence of errors, works exactly
Resulting orbit is flat
Dispersion Free
(perfect BBA)
Now add 1m random BPM noise to measured difference orbit
DFS example
Simple solve
1 Y M Δy
original quad errors
fitter quad errorsFit is ill-conditioned!
DFS example
m
m
Solution is still Dispersion Free
but several mm off axis!
DFS: Problems
• Fit is ill-conditioned– with BPM noise DF orbits have very large unrealistic
amplitudes.
– Need to constrain the absolute orbit
T T
2 2 2res res offset2
Δy Δy y y
minimise
• Sensitive to initial launch conditions (steering, beam jitter)– need to be fitted out or averaged away
0R y
DFS example
Minimise
original quad errors
fitter quad errors
T T
2 2 2res res offset2
Δy Δy y y
absolute orbit now
constrained
remember
res = 1m
offset = 300m
DFS example
m
m
Solutions much better behaved!
! Wakefields !
Orbit not quite Dispersion Free, but very close
DFS practicalities
• Need to align linac in sections (bins), generally overlapping.
• Changing energy by 20%– quad scaling: only measures dispersive kicks from quads.
Other sources ignored (not measured)– Changing energy upstream of section using RF better, but
beware of RF steering (see initial launch)– dealing with energy mismatched beam may cause problems
in practise (apertures)
• Initial launch conditions still a problem– coherent -oscillation looks like dispersion to algorithm.– can be random jitter, or RF steering when energy is changed.– need good resolution BPMs to fit out the initial conditions.
• Sensitive to model errors (M)
Ballistic Alignment
• Turn of all components in section to be aligned [magnets,
and RF]
• use ‘ballistic beam’ to define straight reference line (BPM
offsets)
• Linearly adjust BPM readings to arbitrarily zero last BPM
• restore components, steer beam to adjusted ballistic line
62
BPM, 0 0 offset, noise,i i i iy y s y b b
Ballistic Alignment
bi qi
Lb
quads effectively aligned to ballistic reference
angle = i
ref. line
with BPM noise
62
Ballistic Alignment: Problems
• Controlling the downstream beam during the ballistic measurement– large beta-beat– large coherent oscillation
• Need to maintain energy match – scale downstream lattice while RF in ballistic
section is off
• use feedback to keep downstream orbit under control
An Introduction to thePhysics and Technologyof e+e- Linear Colliders
Lecture 9: b) Lessons learnt from SLC
Nick Walker (DESY)
DESY Summer Student Lecture31st July 2002USPAS, Santa Barbara, 16th-27th June, 2003
Lessons from the SLC
IP Beam Size vs Time
0
1
2
3
4
5
6
7
8
9
10
1985 1990 1991 1992 1993 1994 1996 1998
Year
Beam
Size
(micr
ons)
0
1
2
3
4
5
6
7
8
9
10
x*
y
(micr
ons
2 )
SLC Design(x * y)
X
Y
X * y
New Territory in Accelerator Design and Operation
• Sophisticated on-line modeling of non-linear physics.
• Correction techniques expanded from first-order (trajectory) to include second-order (emittance), and from hands-on by operators to fully automated control.
• Slow and fast feedback theory and practice.
D. Burke, SLAC
The SLC
1980 1998
taken from SLC – The End Game by R. Assmann et al, proc. EPAC 2000
note: SLC was a single bunch machine (nb = 1)
SLC: lessons learnt
• Control of wakefields in linac– orbit correction, closed (tuning) bumps
– the need for continuous emittance measurement(automatic wire scanner profile monitors)
• Orbit and energy feedback systems– many MANY feedback systems implemented over the life time of
the machine
– operator ‘tweaking’ replaced by feedback loop
• Final focus optics and tuning– efficient algorithms for tuning (focusing) the beam size at the IP
– removal (tuning) of optical aberrations using orthogonal knobs.
– improvements in optics design
• many many more!
The SLC was an 10 year accelerator R&D project that also did some physics
The Alternatives
TESLA JLC-C JLC-X/NLC CLIC
f GHz 1.3 5.7 11.4 30.0
L 1033 cm-2s-1 34 14 20 21
Pbeam MW 11.3 5.8 6.9 4.9
PAC MW 140 233 195 175
y 10-8m 3 4 4 1
y* nm 5 4 3 1.2
2003 Ecm=500 GeV
Examples of LINAC technology
9 cell superconducting Niobium cavity for TESLA (1.3GHz)
11.4GHz structure for NLCTA
(note older 1.8m structure)
Competing Technologies: swings and roundabouts
SLC(3GHz)
RF frequencyCLIC(30GHz)
TESLA
(1.3GHz SC)
NLC(11.4GHz)
higher gradient = short linac
higher rs = better efficiency High rep. rate = GM suppression smaller structuredimensions = high wakefields Generation of high pulse peakRF power
long pulse low peak power large structure dimensions = low WF very long pulse train = feedback within train SC gives high efficiency Gradient limited <40 MV/m = longer linac
low rep. rate bad for GM suppression (y dilution) very large unconventional DR
An Introduction to thePhysics and Technologyof e+e- Linear Colliders
Lecture 9: c) Summary
Nick Walker (DESY)
DESY Summer Student Lecture31st July 2002USPAS, Santa Barbara, 16th-27th June, 2003
The Luminosity Issue
,
BSRF RFD
cm n y
PL H
E
zy
• high RF-beam conversion efficiency RF
• high RF power PRF
• small normalised vertical emittance n,y
• strong focusing at IP (small y and hence small z)
• could also allow higher beamstrahlung BS if willing to live with the consequences
• Valid for low beamstrahlung regime (<1)
High Beamstrahlung Regime
BSbeam
,y n
L P
low beamstrahlung regime 1:
32
BSbeam
,z y n
L P
high beamstrahlung regime 1:
*y z with
Pinch Enhancement
,
BSRF RFD
cm n y
PL H
E
( )
2 2
( )
D D y
b e z b e zzy
beam y x y y x
H H D
N r N rD
f
Trying to push hard on Dy to achieve larger HD leads to single-bunch kink instability detrimental to luminosity
The Linear Accelerator (LINAC)
• Gradient given by shunt impedance:– PRF RF power /unit length– rl shunt impedance /unit length
• The cavity Q defines the fill time:– vg = group velocity, – ls = structure length
• For TW, is the structureattenuation constant:
• RF power lost along structure (TW):
( ) ( )z RF lE z P z r
2 / SW
2 Q/ / TWfills g
Qt
l v
2, ,RF out RF inP P e
2RF z
b zl
dP Ei E
dz r
power lost to structure beam loading
RF
would like RS to be as high as possible
sR
The Linear Accelerator (LINAC)
For constant gradient structures:
unloaded
av. loaded
20 1u lV r P L e unloaded structure voltage
2
beam 2
1 21
2 1l u l
eV V r Li
e
loaded structure voltage(steady state)
3
22
0opt 2
1
1 (1 2 )l
ePi
r L e
optimum current (100% loading)
The Linear Accelerator (LINAC)
Single bunch beam loading: the Longitudinal wakefield
700 kV/mz bunchE NLC X-band structure:
The Linear Accelerator (LINAC)
Single bunch beam loading Compensation using RF phase
wakefield
RF
Total
= 15.5º
RMS E/E
Ez
min = 15.5º
Transverse Wakes: The Emittance Killer!
tb
( , ) ( , ) ( , )V t I t Z t
Bunch current also generates transverse deflecting modes when bunches are not on cavity axis
Fields build up resonantly: latter bunches are kicked transversely
multi- and single-bunch beam breakup (MBBU, SBBU)
Damped & Detuned Structures
NLC RDDS1 bunch spacing
Slight random detuning between cells causes HOMs to decohere.
Will recohere later: needs to be damped (HOM dampers)
HOM2Qt
Single bunch wakefieldsEffect of coherent betatron oscillation
- head resonantly drives the tail
head
tail
22
22
0 head
tail
hy
tt wf h
d yk y
ds
d yk y w y
ds
2cell
BNS 2
1
16 sin ( )z LW q
E
Cancel using BNS damping:
Wakefields (alignment tolerances)
bunch
0 km 5 km 10 km
head
head
headtailtail
tail
accelerator axis
cavities
y
tail performsoscillation
RMS
3
1 Z
z
EYNW
f EN
higher frequency = stronger wakefields
-higher gradients
-stronger focusing (smaller )
-smaller bunch charge
Damping Rings
2 /( ) DTf eq i eq e
final emittance equilibriumemittance
initial emittance(~0.01m for e+)
damping time
wiggler
wiggler
Lwig
4
arc
EE C
6 2 2wig wig1.27 10 (T) (GeV) (m)E B E L
train
rep
2
8D
nE
P f
train b bC n n t c
Bunch Compression
• bunch length from ring ~ few mm• required at IP 100-300 m
RF
z
E /E
z
E /E
z
E /E
z
E /E
z
E /E
long.phasespace
dispersive section
The linear bunch compressor
,0 2
,0 ,0
1RF RF z c uc RF c
RF z RF z
k V E EV F
E k k
2 22 1c u
c c u cu
F F
conservation of longitudinal emittance
RF cavity
initial (uncorrelated) momentum spread: u
initial bunch length z,0
compression ration Fc=z,0/z
beam energy ERF induced (correlated) momentum spread: c
RF voltage VRF
RF wavelength RF = 2/ kRF longitudinal dispersion: R56
see lecture 6
The linear bunch compressor
2
,0 ,056 2 2 2 2
1c z zRF RF
u u
z k VR
F E F
chicane (dispersive section)
Two stage compression used to reduce final energy spread
COMP #1 LINAC COMP #2F1
F2EE0
01 2
0
0
0
f i
T i
EF F
E E
EF
E E
56
0 wiggler
0 arcR
Final Focusing 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*
FD *
FD *
SX
2 2SX
( )
( )
yy
Lx
xL
y S x y
x S x y
*
1S
Lchromatic correction
Synchrotron Radiation effects
IP
FD
x dipole
L*
LB
5B
33 *5ee
2
L
η'Lγλr19
E
ΔE
2*2y 2
y*2y
Δσ ΔEW
σ E
FD chromaticity + dipole SR sets limits on minimum bend length
Final Focusing: Fundamental limits
Already mentioned that
At high-energies, additional limits set by so-called Oide Effect:synchrotron radiation in the final focusing quadrupoles leads to a beamsize growth at the IP
zy
1 57 71.83 e e nr F minimum beam size:
occurs when 2 37 72.39 e e nr F
independent of E!
F is a function of the focusing optics: typically F ~ 7(minimum value ~0.1)
0 500 1000 1500 2000
1
0.5
0
0.5
1
0 500 1000 1500 2000
1
0.5
0
0.5
1100nm RMS random offsets
sing1e quad 100nm offset
LINAC quadrupole stability
*,
1 1
**
sin( )
Q QN N
Q i i i Q i ii i
ii i i
y k Y g k Y g
g
* 2
*2 2 2,*
1
sin ( )QN
i Q i i iji
Yy k
for uncorrelated offsets
2 22 2
*2,
0.32
j Q QY
y y n
y N k
take NQ = 400, y ~ 61014 m, ~ 100 m, k1 ~ 0.03 m1 ~25 nm
Dividing by and taking average values:
*2 * *, /y y n
Beam-Beam orbit feedback
use strong beam-beam kick to keep beams colliding
see lecture 8
IP
BPM
bb
FDBK kicker
y
e
e
Generally, orbit control (feedback) will be used extensively in LC
Beam based feedback: bandwidth
0.0001 0.001 0.01 0.1 1
0.05
0.1
0.5
1
5
10
f / frep
g = 1.0g = 0.5g = 0.1g = 0.01
f/frep
Good rule of thumb: attenuate noise with ffrep/20
Ground motion spectra
( , )
1( , ) ( , ) 1 cos( )
P k
L P k kL dk
2D power spectrum
measurable relativepower spectrum
Both frequency spectrum and spatial correlation important for LC performance
Long Term Stability
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0.1 1 10 100 1000 10000 100000 1000000
time /s
rela
tive
lum
ino
sity
1 hour 1 day1 minute 10 days
No Feedback
beam-beam feedback
beam-beam feedback +
upstream orbit control
understanding of ground motion and vibration spectrum important
example of slow diffusive ground motion (ATL law)
see lecture 8
A Final Word
• Technology decision due 2004• Start of construction 2007+• First physics 2012++• There is still much to do!
WE NEED YOUR HELP
for
the Next Big Thing
hope you enjoyed the course
Nick, Andy, Andrei and PT