Transcript An Introduction to the Physics and Technology of e+e- Linear Colliders

An Introduction to the
Physics and Technology
of e+e- Linear Colliders
Lecture 9: a) Beam Based Alignment
Nick Walker (DESY)
DESY Summer thStudent
Lecture
th
USPAS, Santa Barbara, 16 -27
2003
31st June,
July 2002
Emittance tuning in the LET
• LET = Low Emittance Transport
– Bunch compressor (DRMain Linac)
– Main Linac
– Beam Delivery System (BDS), inc. FFS
• DR produces tiny vertical emittances
(gey ~ 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 alignment
mma!
Basics (linear optics)
thin-lens quad approximation: Dy’=KY
gij 
gij
Yi
yi
yj
y j  0
 R34 (i, j )
Yj
yj
Ki
 j

y j     gij KiYi   Y j
 i 1

linear system: just superimpose oscillations caused by quad kicks.
Introduce matrix notation
Original Equation
 j

y j     gij KiYi   Y j
 i 1

Defining Response Matrix Q:
Q  G  diag(K)  I
Hence beam offset becomes
y  Q  Y
G is lower diagonal:
 0
g
 21
G   g31

 g 41


0
0
0
0
0
0
g32
0
0
g 42
g 43
0








Dispersive Emittance Growth
Consider effects of finite energy spread in beam dRMS
K

chromatic response matrix: Q(d )  G (d )  diag 
 1 d
G
G (d )  G (0) 
d d 0
lattice
chromaticity
R34 (d )  R34 (0)  T346d
dispersive orbit:
ηy 
Δy (d )
d

I

dispersive
kicks
  Q(d )  Q(0)   Y
What do we measure?
BPM readings contain additional errors:
boffset
static offsets of monitors wrt quad centres
bnoise
one-shot measurement noise (resolution sRES)
y BPM  Q  Y  b offset  b noise  R  y 0
random
fixed from
shot to shot (can be averaged
to zero)
 y0 
y0   
 y0 
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
quad mover
steerer
dipole corrector
Scenario 2: Quads aligned, BPMs offset
1-2-1 corrected orbit
BPM
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
 DE
  DE 
Δy   Q( )  Q(0)  
Y
E

 E 
 DE 
 M
Y
 E 
Problem:
Note: taking difference orbit Dy removes boffset
Solution (trivial):
Y  M1  Δy
Unfortunately, not that easy because of noise sources:
Δy  M  Y  b noise  R  y 0
DFS example
300mm random
quadrupole errors
mm
20% DE/E
No BPM noise
No beam jitter
mm
DFS example
Simple solve
Y  M1  Δy
In the absence of
errors, works
exactly
Resulting orbit is flat
Dispersion Free
original quad errors
fitter quad errors
(perfect BBA)
Now add 1mm random BPM noise to measured difference orbit
DFS example
Simple solve
Y  M1  Δy
Fit is ill-conditioned!
original quad errors
fitter quad errors
DFS example
mm
Solution is still Dispersion
Free
but several mm off axis!
mm
DFS: Problems
• Fit is ill-conditioned
– with BPM noise DF orbits have very large unrealistic
amplitudes.
– Need to constrain the absolute orbit
Δy  Δy
yy
 2
2
2
2s res
s res  s offset
T
minimise
T
• Sensitive to initial launch conditions
(steering, beam jitter)
– need to be fitted out or averaged away
R  y0
DFS example
Minimise
Δy  Δy T
y  yT
 2
2
2
2s res
s res  s offset
absolute
orbit now
constrained
remember
original quad errors
sres = 1mm
fitter quad errors
soffset = 300mm
DFS example
mm
Solutions much better
behaved!
! Wakefields !
mm
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 b-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)
yBPM,i  y0  si y0  boffset,i  bnoise,i
• Linearly adjust BPM readings to arbitrarily zero last BPM
• restore components, steer beam to adjusted ballistic line
62
Ballistic Alignment
angle = i
quads effectively
aligned to ballistic
reference
Dbi Dq
i
ref. line
Lb
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 the
Physics and Technology
of e+e- Linear Colliders
Lecture 9: b) Lessons learnt from SLC
Nick Walker (DESY)
DESY Summer thStudent
Lecture
th
USPAS, Santa Barbara, 16 -27
2003
31st June,
July 2002
Lessons from the SLC
• 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.
10
10
9
9
8
8
sX * sy
7
6
6
5
5
2
7
4
SLC Design
(sx * sy)
4
sX
3
3
sY
2
2
1
1
0
0
1985
1990 1991 1992 1993 1994 1996 1998
Year
D. Burke, SLAC
s x*s y (microns )
New Territory in Accelerator Design and Operation
Beam Size (microns)
IP Beam Size vs Time
The SLC
1980
1998
note: SLC was a single bunch machine (nb = 1)
taken from SLC – The End Game by R. Assmann et al, proc. EPAC 2000
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
2003 Ecm=500 GeV
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
gey
10-8m
3
4
4
1
sy*
nm
5
4
3
1.2
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
RF frequency
CLIC
(30GHz)
NLC
(11.4GHz)
SLC
(3GHz)
TESLA
(1.3GHz SC)
higher gradient = short linac 
higher rs = better efficiency 
High rep. rate = GM suppression 
smaller structure
dimensions = high wakefields 
Generation of high pulse peak
RF 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 (ey dilution) 
very large unconventional DR 
An Introduction to the
Physics and Technology
of e+e- Linear Colliders
Lecture 9: c) Summary
Nick Walker (DESY)
DESY Summer thStudent
Lecture
th
USPAS, Santa Barbara, 16 -27
2003
31st June,
July 2002
The Luminosity Issue
L
RF PRF
Ecm
d BS
HD
e n, y
b y s z
high RF-beam conversion efficiency RF
high RF power PRF
small normalised vertical emittance en,y
strong focusing at IP (small by and hence small sz)
could also allow higher beamstrahlung dBS if willing to
live with the consequences
• Valid for low beamstrahlung regime (<1)
•
•
•
•
•
High Beamstrahlung Regime
d BS
e y ,n
low beamstrahlung regime 1:
L  Pbeam
high beamstrahlung regime 1:
d BS
L  Pbeam
s z e y ,n
3
with
b y*  s z
2
Pinch Enhancement
L
RF PRF
Ecm
d BS
HD
e n, y
H D  H D ( Dy )
Dy 
sz
fbeam
2 Nb res z
2 Nb res z


gs y (s x  s y ) gs ys x
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
– rl
RF power /unit length
shunt impedance /unit length
Ez ( z )  PRF ( z )rl
• The cavity Q defines the fill time:
– vg = group velocity,
– ls = structure length
t fill
2Q / 


2t Q/  ls / vg
SW
TW
• For TW, t is the structure
PRF ,out  PRF ,in e2t
attenuation constant:
• RF power lost along structure (TW):
RF
dPRF
Ez2

 ib Ez
dz
rl
power lost to structure
beam loading
would like RS to be
as high as possible
Rs  
The Linear Accelerator (LINAC)
For constant gradient structures:
Vu  rl P0 L 1  e2t 
unloaded structure voltage

1
2t e 2t 
Vl  Vu  rl Libeam 1 
2t 
2
1

e


loaded structure voltage
(steady state)
P0 1  e 

rl L 1  (1  2t )e 2t
2t
iopt
3
2
optimum current (100% loading)
unloaded
av. loaded
The Linear Accelerator (LINAC)
Single bunch beam loading: the Longitudinal wakefield
NLC X-band structure:
DEz
bunch
 700 kV/m
The Linear Accelerator (LINAC)
Single bunch beam loading Compensation using RF phase
wakefield
RF
Total
f = 15.5º
RMS DE/E
Ez
fmin = 15.5º
Transverse Wakes: The Emittance Killer!
Dtb
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
2QHOM
Dt 
D
Slight random detuning between cells causes HOMs to decohere.
Will recohere later: needs to be damped (HOM dampers)
Single bunch wakefields
Effect of coherent betatron oscillation
- head resonantly drives the tail
d 2 yh
 k 2 yy  0
ds
d 2 yt
 k 2 yt   wwf yh
ds
tail
head
tail
head
Cancel using BNS damping:
d BNS
L2cell
1 Wqs z

16 E sin 2 ( b )
Wakefields (alignment tolerances)
cavities
tail performs
oscillation
bunch
accelerator axis
tail
Dy
head
tail
head
head
tail
5 km
0 km
d YRMS  1 E
NW b
3 E
f

N b
10 km
higher frequency = stronger wakefields
Z
z
-higher gradients
-stronger focusing (smaller b)
-smaller bunch charge
Damping Rings
initial emittance
(~0.01m for e+)
e f  e eq  (ei  e eq )e2T /t
equilibrium
emittance
final emittance
DEarc  Cg
E4
wiggler

Lwig
D
damping time
2 E ntrain
tD 

Pg 8 f rep
C  ntrain nb Dtb c

wiggler
DEwig  1.27 106 B 2 (T) E 2 (GeV)Lwig (m)
Bunch Compression
• bunch length from ring ~ few mm
• required at IP 100-300 mm
DE/E
long.
phase
space
DE/E
z
RF
DE/E
z
DE/E
z
dispersive section
DE/E
z
z
The linear bunch compressor
initial (uncorrelated) momentum spread:
initial bunch length
compression ration
beam energy
RF induced (correlated) momentum spread:
RF voltage
RF wavelength
longitudinal dispersion:
RF cavity d c 
E
du
sz,0
Fc=sz,0/sz
E
dc
VRF
lRF = 2/ kRF
R56
d c2  d u2
Fc 
 d c  d u Fc2  1
du
conservation of longitudinal
emittance
k RFVRF s z ,0
see lecture 6
 VRF
Ed c
E


k RF s z ,0 k RF
 du 
2
F

 c  1
 s z ,0 
The linear bunch compressor
chicane (dispersive section)
d cs z ,0 k RFVRF  s z ,0  1
dz
R56   2   2 2 


d
F du
E  du  F 2
 0 wiggler
R56 
  0 arc
2
Two stage compression used to reduce final energy spread
E0
COMP #1
F1
LINAC
DE
COMP #2
F2
 E0 
d f   F1d i   
  F2
 E0  DE 
 E0 
 FT d i 

E

D
E
 0

Final Focusing
dipole
IP
Dx
sextupoles
0
0
0 
m


0
1/
m
0
0

R 
0
0
m
0 


0
0
0
1/
m


chromatic correction S 
FD
L*
 
DyFD
1
L*
dy
L*
d ( x  d )
 
DxFD
L*
  S  x  d  y
DySX
   S ( x  d ) 2  y 2 
DxSX
Synchrotron Radiation effects
IP
x
dipole
LB
2
re λ e γ 5 L* 3 η' 3
 ΔE 

  19
L5B
 E 
Δσ*2
y
σ*2
y
FD
L*
 ΔE 
W 

E


2
2
y
FD chromaticity + dipole SR sets limits on minimum bend length
Final Focusing: Fundamental limits
Already mentioned that b y s z
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
minimum beam size:
occurs when
s  1.83  re
b  2.39  re
F  en
1
e
7
5
7
independent
of E!
7
F
ge

e
n
2
7
3
F is a function of the focusing optics: typically F ~ 7
(minimum value ~0.1)
LINAC quadrupole stability
NQ
NQ
y   kQ ,i DYi gi  kQ  DYi gi
*
i 1
i 1
gi
*
gi 
b
b
sin(Dfi )
i
*
g
1
0.5
0
0.5
1
0
for uncorrelated offsets
y*2 
b * DY 2
g*
NQ
2
2
g
k
b
sin
 i Q,i i (Dfij )
i 1
*
*

b
e
/
g
Dividing by s *2
y
y ,n
and taking average values:
y 2j
s *2
y

N Q kQ2 b g
2e y ,n
sing1e quad 100nm offset
1
500
1000
1500
2000
100nm RMS random offsets
0.5
0
0.5
1
0
500
1000
1500
2000
s D2Y  0.32
take NQ = 400, ey ~ 61014 m, b~ 100 m, k1 ~ 0.03 m1  ~25 nm
see lecture 8
Beam-Beam orbit feedback
e
IP
bb
Dy
FDBK
kicker
BPM
e
use strong beambeam kick to keep
beams colliding
Generally, orbit control
(feedback) will be used
extensively in LC
Beam based feedback: bandwidth
10
5
1
0.5
g = 0.01
g = 0.1
g = 0.5
g = 1.0
0.1
0.05
0.0001
0.001
0.01
0.1
f / frep
f/frep
Good rule of thumb: attenuate noise with ffrep/20
1
Ground motion spectra
Both frequency
spectrum and
spatial
correlation
important for
LC performance
2D power spectrum
measurable relative
power spectrum
P ( , k )
 ( , L) 
1


 P( , k ) 1  cos(kL) dk

see lecture 8
Long Term Stability
understanding of ground motion and vibration spectrum important
1 minute
1 hour 1 day 10 days
1
0.9
0.8
beam-beam
feedback +
upstream orbit
control
relative luminosity
0.7
No Feedback
0.6
0.5
0.4
0.3
beam-beam
feedback
0.2
0.1
example of slow
0
0.1
diffusive ground
motion (ATL law)
1
10
100
1000
tim e /s
10000
100000
1000000
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