#### Transcript unit 1

```An Introduction to the
Physics and Technology
of e+e- Linear Colliders
Lecture 1: Introduction and Overview
Nick Walker (DESY)
Nick Walker
DESY
DESY Summer
Student Lecture
th
USPAS Santa Barbara 16 June,st2003
31 July 2002
Course Content
Lecture:
1.
2.
3.
4.
5.
6.
7.
8.
9.
Introduction and overview
Linac part I
Linac part II
Damping Ring & Bunch Compressor I
Damping Ring & Bunch Compressor II
Final Focus Systems
Beam-Beam Effects
Stability Issues in Linear Colliders
the SLC experience and the Current LC Designs
This Lecture
• Why LC and not super-LEP?
• The Luminosity Problem
– general scaling laws for linear colliders
• A introduction to the linear collider sub-systems:
–
–
–
–
–
main accelerator (linac)
sources
damping rings
bunch compression
final focus
during the lecture, we will introduce (revise) some important basic
accelerator physics concepts that we will need in the remainder of
the course.
Energy Frontier e+e- Colliders
LEP at CERN, CH
Ecm = 180 GeV
PRF = 30 MW
Why a Linear Collider?
an electron in a magnetic field:
B
2
P 
e c
2
2
2
CE B
2
Energy loss per turn of a
machine with an average
 E / rev 
CE
4

Energy loss must be replaced by RF system
Cost Scaling \$\$
• Linear Costs: (tunnel, magnets etc)
\$lin  
• RF costs:
\$RF  E  E4/
• Optimum at
\$lin = \$RF
Thus optimised cost (\$lin+\$RF) scales as E2
The Bottom Line \$\$\$
L E P -II S u p e r-L E P
E cm G e V
180
L
km
27
E
G eV
1 .5
9
\$ to t 1 0 S F
2
500
H yp e rLEP
2000
The Bottom Line \$\$\$
L E P -II S u p e r-L E P
E cm G e V
180
500
L
km
27
200
E
G eV
1 .5
12
2
15
9
\$ to t 1 0 S F
H yp e rLEP
2000
The Bottom Line \$\$\$
L E P -II S u p e r-L E P
E cm G e V
180
500
H yp e rLEP
2000
L
km
27
200
3200
E
G eV
1 .5
12
240
2
15
240
9
\$ to t 1 0 S F
solution: Linear Collider
No Bends, but lots of RF!
e+
e5-10 km
• long linac constructed of many RF
accelerating structures
• typical gradients range from 25-100 MV/m
Note: for LC, \$tot  E
A Little History
A Possible Apparatus for Electron-Clashing Experiments (*).
M. Tigner
Laboratory of Nuclear Studies. Cornell University - Ithaca, N.Y.
M. Tigner,
Nuovo Cimento 37 (1965) 1228
“While the storage ring concept for providing clashingbeam experiments (1) is very elegant in concept it seems
worth-while at the present juncture to investigate other
methods which, while less elegant and superficially more
complex may prove more tractable.”
A Little History (1988-2003)
•
•
•
•
•
•
•
SLC (SLAC, 1988-98)
NLCTA (SLAC, 1997-)
TTF (DESY, 1994-)
ATF (KEK, 1997-)
FFTB (SLAC, 1992-1997)
SBTF (DESY, 1994-1998)
CLIC CTF1,2,3 (CERN, 1994-)
Over 14 Years of
Linear Collider
R&D
Past and Future
SLC
LC
E cm
1 00
5 00 - 100 0
G eV
P bea m
0 .0 4
5 - 20
MW
 *y
5 00 (5 0)
1-5
nm
E /E bs
0 .0 3
3 - 10
%
L
0 .0 003
~3
10
generally quoted as
‘proof of principle’
34
but we have a very
long way to go!
2
? -1
cm s
LC Status in 1994
1994 Ecm=500 GeV
f
[GHz]
L1033
[cm-2s-1]
Pbeam
[MW]
PAC
[MW]
ey
[10-8m]
y*
[nm]
TESLA
SBLC
JLC-S
JLC-C
JLC-X
NLC
VLEPP
CLIC
1.3
3.0
2.8
5.7
11.4
11.4
14.0
30.0
6
4
4
9
5
7
9
1-5
16.5
7.3
1.3
4.3
3.2
4.2
2.4
~1-4
164
139
118
209
114
103
57
100
100
50
4.8
4.8
4.8
5
7.5
15
64
28
3
3
3
3.2
4
7.4
LC Status 2003
2003 Ecm=500 GeV
TESLA
f
[GHz]
L1033
[cm-2s-1]
Pbeam
[MW]
PAC
[MW]
ey
[10-8m]
y*
[nm]
SBLC
JLC-S
JLC-C
JLC-X/NLC
VLEPP
CLIC
1.3
5.7
11.4
30.0
34
14
20
21
11.3
5.8
6.9
4.9
140
233
195
175
3
4
4
1
5
4
3
1.2
The Luminosity Issue
(cm-2 s-1)
Collider luminosity
approximately given by
is
2
L
n b N f rep
A
HD
where:
Nb
N
frep
A
HD
= bunches / train
= particles per bunch
= repetition frequency
= beam cross-section at IP
= beam-beam enhancement factor
2
For Gaussian beam distribution:
L 
n b N f rep
4  x
y
HD
The Luminosity Issue: RF Power
Introduce the centre of mass
energy, Ecm:
L
E
cm
n b N f rep  N
4  x y E cm
HD
n b N f rep E cm  Pbeam s
  R F  beam PR F
RF is RF to beam power
efficiency.
Luminosity is proportional
to the RF power for a given
Ecm
L 
 R F PR F N
4  x  y E cm
HD
The Luminosity Issue: RF Power
L 
Some numbers:
Ecm
N
nb
frep
= 500 GeV
= 1010
= 100
= 100 Hz
 R F PR F N
4  x  y E cm
HD
Pbeams = 8 MW
Need to include efficiencies:
RFbeam:
Wall plug RF:
range 20-60%
range 28-40%
linac technology choice
AC power > 100 MW just to accelerate beams and achieve
luminosity
The Luminosity Issues: storage ring vs LC
LEP frep = 44 kHz
L 
LC frep = few-100 Hz
(power limited)
 R F PR F N
4  x  y E cm
 factor ~400 in L already lost!
Must push very hard on beam cross-section at collision:
LEP: xy  1306 mm2
LC:
xy  (200-500)(3-5) nm2
factor of 106 gain!
Needed to obtain high luminosity of a few 1034 cm-2s-1
HD
The Luminosity Issue: intense beams at IP
L
1
4 E cm
 R F PR F
choice of linac technology:
• efficiency
• available power
 N

HD 
 



 x y

Beam-Beam effects:
• beamstrahlung
• disruption
Strong focusing
• optical aberrations
• stability issues and
tolerances
see lecture 2 on
beam-beam
The Luminosity Issue: Beam-Beam
3000
2000
Ey (MV/cm)
• strong mutual focusing of
beams (pinch) gives rise to
luminosity enhancement
HD
• As e± pass through intense
field of opposing beam,
[beamstrahlung] and loose
energy
• Interaction of
beamstrahlung photons
with intense field causes
copious e+e- pair
production [background]
x
y
1000
0
1000
2000
3000
6
4
2
0
y/y
2
4
6
see lecture 2 on
beam-beam
The Luminosity Issue: Beam-Beam
beam-beam characterised by Disruption
Parameter:
z
fbeam
Dx, y 
= bunch length,
= focal length of beam-lens
for storage rings, f beam
2 re N  z
  x , y  x  
z
y

and D x , y
z

f beam
1
In a LC, D y  1 0 - 2 0 hence f beam   z
Enhancement factor (typically HD ~ 2):
H Dx , y
3

D
x, y
1/ 4
 1  Dx,y 
1 D3
x, y


  ln



Dx,y
 0.8  x , y
 1  2 ln 
 z




‘hour glass’ effect
see lecture 2 on
beam-beam
3
3
2
2
1
1
Y
Y
The Luminosity Issue: Hour-Glass
0
0
1
1
2
2
3
3
2
1
0
Z
1
 = “depth of focus”
reasonable lower limit for
 is bunch length z
2
2
1
0
Z
1
2
The Luminosity Issue: Beamstrahlung
see lecture 2 on
beam-beam
2
 E cm 
N
 0.86

2 
2
2 m 0 c   z  ( x   y )
3
RMS relative energy loss
 BS
ere
we would like to make xy small to maximise luminosity
BUT keep (x+y) large to reduce SB.
Trick: use “flat beams” with  x
y
 BS
 E cm  N 2

 2

 z x
Now we set x to fix SB, and make y as small as possible to
achieve high luminosity.
For most LC designs, SB ~ 3-10%
The Luminosity Issue: Beamstrahlung
Returning to our L scaling law, and ignoring HD
L
 R F PR F  N  1
E cm
From flat-beam beamstrahlung
hence
L
 RF PRF
3/2
cm
E


  x
N
x

 BS  z
y
y
 z BS
E cm
The Luminosity Issue: story so far
L
 RF PRF
3/2
Ecm
 BS  z
y
For high Luminosity we need:
•
•
•
•
•
high RF-beam conversion efficiency RF
high RF power PRF
small vertical beam size y
large bunch length z (will come back to this one)
could also allow higher beamstrahlung BS if willing to live
with the consequences
Next question: how to make a small y
The Luminosity Issue: A final scaling law?
L
 RF PRF
3/2
cm
E
 BS  z

y
y

 ye n, y

where en,y is the normalised vertical emittance, and y is the vertical
-function at the IP. Substituting:
L
 RF PRF
3/2
cm
E
 BS 
z
e n, y
y

 RF PRF
 BS
z
Ecm
e n,y
y
hour glass constraint
y is the same ‘depth of focus’  for hour-glass effect. Hence  y   z
The Luminosity Issue: A final scaling law?
L
•
•
•
•
•
 RF PRF
 BS
Ecm
e n,y
HD
 y  z
high RF-beam conversion efficiency RF
high RF power PRF
small normalised vertical emittance en,y
strong focusing at IP (small y and hence small z)
could also allow higher beamstrahlung BS if willing to
live with the consequences
Above result is for the low beamstrahlung regime where BS ~ few %
Slightly different result for high beamstrahlung regime
Luminosity as a function of y
L ( cm - 2 s - 1 )
34
5 10

 z  100 m m
BS
 1
z
34
4 10
34
 z  300 m m
2 1034
500 m m
3 10
nb N 2 f
L
4 x y
700 m m
900 m m
1 1034
200
400
600
 y (m m )
800
1000
The ‘Generic’ Linear Collider
pre-accelerator
few GeV
source
KeV
damping
ring
few GeV
few GeV
bunch
compressor
250-500 GeV
main linac
extraction
& dump
final focus
IP
collimation
Each sub-system pushes the state-of-the-art in accelerator design
The Linear Accelerator (LINAC)
Ez
see lectures 3-4
on linac
c
z
travelling wave structure:
need phase velocity = c
bunch sees constant field:
Ez=E0 cos(f )
Ez
ct  
2
c
c
standing wave cavity:
z
bunch sees field:
Ez =E0 sin(wt+f )sin(kz)
=E0 sin(kz+f )sin(kz)
The Linear Accelerator (LINAC)
Travelling wave
structure
Circular waveguide
mode TM01 has vp>c
No good for
acceleration!
Need to slow wave
down using irises.
see lectures 3-4
on linac
see lectures 3-4
on linac
The Linear Accelerator (LINAC)
• Gradient given by shunt impedance:
– PRF
– RS
Ez 
RF power /unit length
shunt impedance /unit length
• The cavity Q defines the fill time:
– vg = group velocity, ls = structure length
• For TW, t is the structure
attenuation constant:
• RF power lost along structure (TW):
dPRF
dz
-
E
2
z
Rs
power lost to structure
t fill
PRF R s
2Q / w

 
 2 t Q /w  ls / v g
PR F , o u t  PR F , in e
SW
TW
- 2t
RF
- ib E z
would like RS to be
as high as possible
Rs 
w
The Linear Accelerator (LINAC)
see lectures 3-4
on linac
E z ,u - E z , l 


1
ib rs 
2



2t 0  e
1- e
- 2t
- 2t
0
0

1




The Linear Accelerator (LINAC)
see lectures 3-4
on linac
– current not constant but pulses! (tpulse = nb tb)
– for all LC designs, long bunch trains achieve steady
state quickly, and previous results very good
approximation.
– However, transient over first bunches needs to be
compensated.
V
t
The Linear Accelerator (LINAC)
NLC X-band structure:
Ez
bunch
 700 kV /m
The Linear Accelerator (LINAC)
wakefield
RF
Total
f = 15.5º
The Linear Accelerator (LINAC)
RMS E/E
Ez>
fmin = 15.5º
Transverse Wakes: The Emittance Killer!
tb
V (w , t )  I (w , t ) Z (w , 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
N LC RD DS1
bunch spacing
t 
2Q H O M
w
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
2
d yh
ds
tail
 k yy  0
2
tail eom:
2
d yt
ds
 k yt  k wf y h
2
Wakefields (alignment tolerances)
cavities
tail performs
oscillation
bunch
accelerator axis
tail
y
tail
tail
5 km
0 km
E
 YR M S  1
NW 
f -3 E

N

z
10 km
higher frequency = stronger wakefields
Z
-stronger focusing (smaller )
-smaller bunch charge
The LINAC is only one part
pre-accelerator
few GeV
source
KeV
damping
ring
few GeV
few GeV
bunch
compressor
250-500 GeV
main linac
extraction
& dump
final focus
IP
collimation
• Produce the electron charge?
Need to
understand how
to:
• Produce the positron charge?
• Make small emittance beams?
• Focus the beams down to ~nm at the
IP?
e+e- Sources
Requirements:
• produce long bunch trains of
high charge bunches
• with small emittances
• and spin polarisation
(needed for physics)
100-1000s @ 5-100 Hz
few nC
enx,y ~ 10-6,10-8 m
mandatory for e-,
nice for e+
Remember L scaling: L 
n N2
b
en
e- Source
• laser-driven photo injector
• circ. polarised photons on
GaAs cathode
 long. polarised e• laser pulse modulated to
give required time
structure
• very high vacuum
requirements for GaAs
(<10-11 mbar)
• beam quality is dominated
by space charge
(note v ~ 0.2c)
la
r
se
ph
o
s
to n
 = 8 4 0 nm
e lectro ns
20 m m
G aA s
cath od e
1 20 kV
e n  10 - 5 m
factor 10 in x plane
factor ~500 in y plane
e- Source: pre-acceleration
E = 76 M eV
E = 12 M eV
K
K
K
SHB
to D R in e cto r lin ac
so le n o id s
la se r
SHB = sub-harmonic buncher. Typical bunch length from
gun is ~ns (too long for electron linac with f ~ 1-3 GHz,
need tens of ps)
e Source
e
Photon conversion to e±
pairs in target material

e-
e
Standard method is ebeam on ‘thick’ target
(em-shower)
e-
eei-

e-
e Source :undulator-based
250GeV e- to IP
e+e- pairs
from
e- linac
N S N S N S N S N S
S N S N S N S N S N
~30MeV photons
undulator (~100m)
0.4X target
• SR radiation from undulator generates photons
• no need for ‘thick’ target to generate shower
• thin target reduces multiple-Coulomb scattering: hence
better emittance (but still much bigger than needed)
• less power deposited in target (no need for mult. systems)
• Achilles heel: needs initial electron energy > 150 GeV!
~ 30 MeV
0.4X0
10-2 m
5 kW
see lecture 5
Damping Rings
• (storage) ring in which the bunch train is stored for
Tstore ~20-200 ms
• emittances are reduced via the interplay of synchrotron
initial emittance
(~0.01m for e+)
e f  e eq  ( e i - e eq ) e
final emittance
-2T /t D
damping time
equilibrium
emittance
see lecture 5
Damping Rings: transverse damping
p replaced by RF such that pz = p.
y’ not changed by
photon (or is it?)

dipole
y’ = dy/ds = py/pz,
RF cavity
we have a reduction in amplitude:
y’ = -p y’
p
p
Must take average over all -phases:
tD 
2E
P
where
P

c C E 4
2 
2
and hence
tD 

2
E
3
LEP: E ~ 90 GeV, P ~ 15000 GeV/s, tD ~ 12 ms
see lecture 5
Damping Rings: Anti-Damping
u
1 
E -u
ecB
0 
E
ecB
u
a r 
ecB
new closed orbit 1  increase in emittance
dex
dt
dex
Equilibrium achieved when
Q
dt
0Q-
2
td
ex
Damping Rings: transverse damping
tD 

2
E
3
suggests high-energy and small ring. But
required RF power: PR F 
E
4

2
equilibrium emittance: e n , x 
an example:
•
•
•
•
see lecture 5
 nb N
E

2
Remember: 8tD
needed to reduce e+
vertical emittance.
Store time set by frep:
t s  ntrain / f rep
Take E  2 GeV
ntrain nb  tb c

Bbend = 0.13 T    50 m
2
<P> = 27 GeV/s [28 kV/turn]
hence tD  148 ms - Few ms required!!!
Increase <P> by 30 using wiggler magnets
see lecture 5
Damping Rings: limits on vertical emittance
• Horizontal emittance defined by lattice
• theoretical vertical emittance limited by
– space charge
– intra-beam scattering (IBS)
– photon opening angle
• In practice, ey limited by magnet alignment errors
[cross plane coupling]
• typical vertical alignment tolerance: y  30 mm
 requires beam-based alignment techniques!
see lecture 6
Bunch Compression
• bunch length from ring ~ few mm
• required at IP 100-300 mm
 E /E
long.
phase
space
 E /E
z
RF
 E /E
z
 E /E
z
dispersive section
 E /E
z
z
see lecture 6
The linear bunch compressor
u
z,0
initial bunch length
compression ration
beam energy
RF voltage
RF wavelength
longitudinal dispersion:
Fc=z,0/z
E
c
VRF
RF = 2 / kRF
R56
c  u
2
conservation of longitudinal
emittance
RF cavity  c 
k R F V R F  z ,0
E
Fc 
 V RF 
u
E c
k R F  z ,0
2
 c  u
E  u 



k R F   z ,0 
Fc - 1
2
Fc - 1
2
The linear bunch compressor
see lecture 6
chicane (dispersive section)
 z  R56
R 56  -
z

2
-
 c z ,0
F u
2
2
2
k R F V R F   z ,0  1



2
E

F
 u 
 z ,0  2 m m
 u  0.1%
  2%
 z  100 m m  Fc  20
f R F  3 G H z  k R F  62.8 m
E  2 G eV
V RF  3 1 8 M V
-1
R 5 6  0 .1 m
Final Focusing
final
doublet
(F D )
f1
f1
f2
IP
f2
f2 (=L*)
Use telescope optics to demagnify beam by factor m = f1/f2= f1/L*
Need typically m = 300
putting L* = 2m  f1 = 600m
see lecture 7
Final Focusing
L*  2 - 4 m

y

e n,y  y / 

y
 2 - 5 nm   y  100 - 300 μm
remember y ~ z
f  L*
at final lens y ~ 100 km
short f requires very strong fields (gradient): dB/dr ~ 250 T/m
pole tip field B(r = 1cm) ~ 2.5 T
normalised quadrupole strength: K 1  1 Br o
B 0
where B = magnetic rigidity = P/e ~ 3.3356 P [GeV/c]
see lecture 7
Final Focusing: chromaticity
1
for a thin-lens of length l:

 - K 1l y quad
f

1 
 K 1l
 - K 1l y quad 

 y IP  f  y quad
 y IP  y quad
2
f  L*
for rms ~ 0.3%
 y IP
2
2

2
  quad e y  rm s
2
 20 - 40 nm
 y IP   y  rm s
2
more general:
 is chromaticity
y 
2
K
1
( s )  ( s ) ds
chromaticity must be corrected using sextupole magnets
Final Focusing: chromatic correction
see lecture 7
magnetic multipole expansion:
 1
1
1
2
3
By ( x)  B    K1x  K 2 x 
K3x
2
3!




2nd-order
kick:
introduce horizontal
dispersion Dx
 - k1 y
y  
 - k 2 xy
kn 

l
0
K nds
sextupole
x  x  D x
 y   - k 2 xy - k 2 D x y 
geom etric
chromatic correction when
k2  -
chrom aticity
Dx
k1
need also to cancel
geometric (xy) term!
(second sextupole)
see lecture 7
Final Focusing: chromatic correction
dipole
IP
Dx
sextupoles
m

0
R 
0

0
0
0
1/ m
0
0
m
0
0
0 

0

0 

1 / m 
FD
L*
Final Focusing: Fundamental limits
see lecture 7
Already mentioned that  y   z
At high-energies, additional limits set by so-called Oide Effect:
to a beamsize growth at the IP
minimum beam size:   1.83  re
occurs when
  2.39  re
7
F
e

e
n
1
7
 en
2
F
e
5
7
3
7
F is a function of the focusing optics: typically F ~ 7
(minimum value ~0.1)
independent
of E!
Stability
• Tiny (emittance) beams
• Tight component tolerances
– Field quality
– Alignment
• Vibration and Ground Motion issues
• Active stabilisation
• Feedback systems
Linear Collider will be “Fly By Wire”
see lecture 8
see lecture 8
Stability: some numbers
•
•
•
•
Cavity alignment (RMS):
Linac magnets:
FFS magnets:
Final “lens”:
parallel-to-point focusing:
~ mm
100 nm
10-100 nm
~ nm !!!
see lecture 8
NQ
y 
*
k
NQ
Q ,i
i 1
gi 
i 1
0.5
 i  sin(  f i )
*
*
0.5
1
0
for uncorrelated offsets
y

*2

*
Y

2
*
1
NQ
  i k Q ,i  i sin (  f ij )
2
2
i 1
2

*2
y
N Q kQ  
500
1000
1500
2000
100nm RMS random offsets
0.5
0
*
*


e
/

Dividing by  *2
y
y ,n
and taking average values:
yj
0
i

 Yi g i  k Q   Yi g i
1
0.5
1
0
500
1000
1500
2000
2

2e y ,n
  Y  0.3
2
2
take NQ = 400, ey ~ 610-14 m,  ~ 100 m, k1 ~ 0.03 m-1  ~25 nm
see lecture 8
Beam-Beam orbit feedback
e
-
IP
 bb
y
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
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
Here Endeth the First Lecture
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