Transcript ILC AcceleratorLec2o.. - ILC-Asia

ILC Accelerator
2/2
Remaining of “Acceleration”
Damping ring
Some other parts of LC (if we have time)
Test facilities
2008.09.22
Kiyoshi Kubo (KEK)
Injector linac
ILC
Particle source
Damping ring
Bunch compressor
Ring to Main Linac Transport
Dump
Main Linac
Collimation and
Final focus
• Collision
– High luminosity requires small vertical emittance
– beam-beam force
• Final focus and Collimation
• Acceleration
– Beam parameter for high power efficiency
– High gradient
• Damping Ring
• Bunch compressor (if possible)
• Test facilities
Noting about upstream of damping ring.
Collision
Saturday
Today
Why higher gradient?
Based on present status, conservative
accelerating field of superconducting cavity, for
large scale stable operation
~ 25 MV/m (?)
ILC design 31.5 MV/m
Studying for even higher gradient
Higher Gradient reduce site length
60
For ECM 1 TeV
Site length (km)
55
L(km)=1000/G(MV/m)/0.7+3.8
50
45
40
35
30
25
(Old parameters)
30
35
40
45
50
55
Gradient (MV/m)
This is very clear.
But importance depends on where the machine is built.
1/3
Higher Gradient reduce Cost ?
Rough dependence of cost on gradient G
Construction cost
Tunnel
a/G
reduce length
Acc. cavities
b/G
reduce number of
cavities
RF source
c + dG
Cryogenics
eG + f /G
*
**
Operation cost (power)
RF
Cryogenics
g(c + dG)
h(eG + f /G)
*
**
2
* Power to beam/cavity  G , Power for filling/ca vity  G
2
* * Wall loss/cavity  G , Heat leakage/cavity  constant
There must be cost minimum gradient.
2/5
Cost minimum is 35~45MV/m (?)
(example of calculations)
Present ILC design is 31.5 MV/m, still lower than cost minimum?
1/7
SUMMARY of Acceleration
• Performance of cavity: Max. field gradient and Q0
– Surface quality (practical limit)
– Cavity shape (fundamental limit)
• Beam parameter
– RF power efficiency
– Cavity wall loss  cryogenics power
– Limit from damping ring
– Compromise
• Lorentz detuning
• Cost vs. accelerating gradient
– ILC design gradient is still lower than cost minimum. (?)
1/8
Damping Ring
Creation of low emittance beam
Limit of number of bunches
Etc.
Important conclusions of
Saturday’s story
• We need small vertical emittance beam for
high luminosity.
• Main Linac’s pawer efficiency requires
large number of bunches per pulse.
1/9
What is emittance, again
Emittance (<> denotes average over particles in the beam)
 x   x 2  x'2    xx'  2
x (horizontal position) can be replaced by y (vertical)
(For longitudin al, x  z, x'  ΔE/E0 )
~ (beam size) x (angular divergence)
if ignore the correlation
Expressing beam quality. Because:
Determines beam size limit at collision point.
Invariant during beam transport (in ideal case).
(Beam size is varying along a beam line.)
2/11
Emittance is based on mean squares of particle distribution
• Good measure of beam quality, for Gaussian or Gaussian like
distribution, without long tail. without particles far from the core of
the beam
• But, not always:
Beam A:
2E10 particles
sy=20 mm, sy’=1 mrad
Which is better?
Beam B:
2E10 – 2E4 particles
sy=10 mm
sy’=1 mrad
2E4 particles
17 mm
A and B have the same emittance.
B is better looking at luminosity
but the small part, far away from the core, may cause problems (e.g. background)
Be careful. Emittance is not always representing beam quality well.
2/13
But,
Emittance is a very good, useful,
simple and well defined parameter
representing beam quality in most
cases.
(See also the 20th slide from here.)
1/14
Normalized emittance
(Lorentz factor) x emittance
E
 x  2  x 2  x'2    xx'  2
mc
1

 x 2  p x2    xp x  2
mc
Transverse momentum does not change in acceleration.
Normalized Emittance does not change.
Angle is changed in acceleration.
 Emittance is reduced in acceleration.
1/15
Why damping rings are necessary?
• Emittance of beam from particle sources is much larger
than required. Much larger than achievable in damping
rings.
Normalized emittance (m) of ILC design
1/16
electron
positron
Before Damping ring
x
y
7E-5
7E-5
~1E-3
~1E-3
After Damping ring
x
y
8E-6
2E-8
8E-6
2E-8
Why emittance is “damped” in damping rings
• Beam energy is constant
– Energy is lost due to synchrotron radiation.
– Compensated in RF cavities.
RF cavities
By radiation, angle pf particle is (almost) not changed:
Emittance is not changed. Normalized emittance is reduced.
By acceleration, transverse momentum is not changed:
Normalized emittance is not changed. Emittance is reduced
2/18
Basic dynamics in circular accelerators (1)
coordinate system
Design orbit
  
y  x, z

d
z

x //
ds

z
usually vertical
direction of design orbit, longitudinal
usually horizontal
1/19
Basic dynamics in circular accelerators (2)
Assume particle energy is constant
• Closed orbit
– One-turn closed line, which can be a orbit of a
certain particle.
• The particle is on this line in any turns.
– Depend on particle energy.
xCO (C  s )  xCO ( s )
s : distance along the beam line
C : circumfere nce of the ring
1/20
Basic dynamics in circular accelerators (3)
• Orbit of each particle is not necessarily closed
– Transverse oscillation around the closed orbit
(x and y directions) [betatron oscillation]
x( s)  xCO ( s)  x ( s)
x ( s)  2 J ( s) cos( ( s)   )
beta-function
 ( s )  d / ds -1
 (C  s )   ( s ) : common for all particles,
J and  : constant, different for different particles
  J 
1/21
Emittance is average of J
< > : average over all particles
Basic dynamics in circular accelerators (4)
• Dispersion
– Energy dependence of closed orbit
xCO ( s,  )  xCO ( s,0)   x  O( 2 )
  E / E0 : relative enrgy deviation
 x is called "dispersion "
(same for vertical)
1/22
Basic dynamics in circular accelerators (5)
• Synchrotron oscillation
– Oscillation in energy - longitudinal position
RF cavities:
advanced particle is accelerated,
delayed particle is decelerated.
Vacc
t
High energy particle goes around long pass
Low energy particle goes short pass in one turn.
In one turn, z  z   ,     V ' z (for small z)
dz / dt   , d / dt   z
 Harmonic oscillation
1/23
Basic dynamics in circular accelerators
(Summary)
•
•
•
•
•
1/24
Coordinate system
Closed orbit
Dispersion
Betatron (transverse) oscillation
Synchrotron (longitudinal) oscillation
Why emittance is “damped” in damping rings
• Beam energy is constant
– Energy is lost due to synchrotron radiation.
– Compensated in RF cavities.
RF cavities
By radiation, angle pf particle is (almost) not changed:
Emittance is not changed. Normalized emittance is reduced.
By acceleration, transverse momentum is not changed:
Normalized emittance is not changed. Emittance is reduced
Radiation damping
(transverse motion)
Radiation loss
A
B
C
acceleration
pt
beam direction
Roughly,
 P 
1 dpt
~  P / E0   x, y (t ) ~  x, y (0) exp  t 
pt dt
 E0 
Radiation loss/time
Design energy
2/26
Radiation damping
(longitudinal motion)
Radiation power in magnetic field  E 2
Higher energy particles loose more energy in unit time.
 Damping
Roughly,
E (t ) ~ E (0)  P ( E0  E )t  P ( E0 )t
P ( E0 ) 


~ E (0) 
E (0)t ~ E (0)1  2
dE
E0 

dP
 2 P
  z (t ) ~  z (0) exp 
 E0
2/28

t 

Radiation excitation
e-/e+
1, Number of photons and photon energy are uncertain.

2, Photon angle is uncertain.
radiation in
magnetic field
energy and angle of electron (positron)
becomes uncertain
Effect of angle fluctuation is usually very small, compare with the
effect of energy fluctuation.
Photon energy : u , angle :  , Average : " "
u2 ~ u 2
 2 ~ 1/  2 ,
(  Ebeam /mc 2 )
 Energy fluctuatio n of beam particles ~ u
 Angle fluctuatio n of beam particles ~ (1 /  ) (u / Ebeam )
2/30
Radiation excitation
The energy fluctuation is source of
Energy spread, directory
Bunch length, through synchrotron oscillation
Transverse emittance through dispersions
(through coupling between energy
and transverse motion)
 see next two slides
2/30
In classical theory
Beam line with 4 bending magnets
Look orbits of two particles with different energy.
non-zero dispersions
zero dispersion
zero dispersion
Radiation is exactly predictable.
beam line can be designed to make:
The final orbits are the same if the initial orbits are the same
Orbit does not depend on energy
1/31
In quantum theory
Beam line with 4 bending magnets
non-zero dispersions
Average orbits of two different initial
energy particles
Possible orbit of
one particle
zero dispersion
zero dispersion
Average over many particles is predictable.
Beam line is designed for average (center of mass of the beam).
But,
The final orbit of each particle is uncertain.
2/33
Equilibrium emittance
• Radiation excitation and radiation damping are
balanced at some point.
 d x, y 


  x, y
 dt damp
 d x, y 


: no dependence on  x, y
 dt excite
 d x, y 
 d x, y 



 
 0 : equilibrium
 dt damp  dt excite
1/34
Equilibrium Transverse emittance
Horizontal: Design almost determines equilibrium emittance.
Because designed horizontal dispersion is large.
• Usually, ring is constructed in a horizontal plane.
– Dispersions cannot be avoided in bending region.
– Radiation in bending magnets contribute excitation.
Vertical: Errors determine equilibrium emittance.
• In perfect machine, there is no coupling between vertical motion and
other degrees of freedom.
• Errors (alignment of magnets, etc.) create vertical dispersions (E-y
coupling) and x-y coupling
– These couplings are dominant source of
vertical emittance.
2/36
For low vertical emittance
• Accurate alignment of magnets
• Mechanical stability and electric stability of magnets
• Accurate beam position monitors
Low emittance beam creation has been studied using ATF
at KEK (see later), and is being studied using CesrTA at
Cornell.
• Normalized vertical emittance (y)
Design of ILC Damping Ring
2.0 x 10-8 m
Achieved in ATF Damping Ring < 2.1x10-8 m
– ATF Damping ring is much smaller than ILC’s and beam energy
is low. (140 m vs. 6 km, 1.3 GeV vs. 5.0 GeV)
2/38
By the way,
Particle distribution in e-/e+ circular
accelerators
The equilibrium distribution is determined from
large number of random processes.
From “central limit theorem”, the distribution is
(close to) Gaussian (normal distribution).
This is one of the main reasons why emittance
represents beam quality very well.
1/39
On Damping Time
SKIP
(inverse of damping rate)
• Emittance should be damped between beam pulses.
– ILC: 200 ms/pulse
• Damping rate determines equilibrium emittance too.
–
(equilibrium between damping and excitation)
• Radiation in bending is relatively weak in large rings.
 Damping wigglers in straight sections.
SKIP
Appendix: Damping time
 x(t)   x( 0 ) exp (  2t/τ x ),  y(t)   y( 0 ) exp (  2t/τ y ),
 z(t)   z( 0 ) exp (  2t/τ z ),
1 / τ x  (1   )  P ,0  / 2 E0
1 / τ y  P ,0  / 2 E0
1 / τ z  (2   )  P ,0  / 2 E0
 P ,0 : Average radiation power for design energy particle
 : Determined by optics
1 / τ x  1 / τ y  1 / τ z  2  P ,0  / E0
Intra-beam scattering - another excitation
Particles in a bunch have various momentum.
Some times, two particles collide each other.  exchange momentum.
Scattering of particles in a bunch:
 Momentum exchange between three directions
2/41
Intra-beam scattering :
Momentum exchange between three directions
Typical momentum spread of three directions in ILC damping ring design.
spx
spy
spz
Laboratory frame
Beam CM frame
45 keV/c
45 keV/c
2 keV/c
2 keV/c
7 MeV/c
0.7 keV/c
y
From statistical consideration,
scattering is regarded as heat
transfer between three directions.
x
z
Dominantly, Heat transfer from horizontal
direction to longitudinal direction
2/43
Intra-beam scatterings increase energy spread
and transverse emittance
Dominant result of intra-beam scatterings is
Heat transfer from horizontal direction to longitudinal direction.
(Causing Energy fluctuation of particles.)
Very similar to radiation excitation.
Radiation excitation: only in magnetic field. (mainly in bending magnets)
Intra-beam scattering: Everywhere
Copied from “radiation excitation”
The energy fluctuation is source of
Energy spread, directory
Bunch length, through synchrotron osccillatin
Transverse emittance through dispersions
(through coupling between energy and transverse motion)
2/45
Effect of intra-beam scattering is significant in ILC
damping rings, because of
high density (large bunch charge and small beam size),
and relatively low energy.
Now, equilibrium condition is
 d x, y 
 d x, y 
 d x, y 




 
 
0
 dt damp  dt rad. excite  dt intra -beam
Tail formation due to hard scatterings
Hard scattering: large angle change. Rarely occurred.
core
Jump
damping
Central limit theorem:
Large number of random processes  Normal distribution
Hard scattering is no longer “large number”.
 Making long tails.
2/48
Beam loss due to hard scatterings
Typical momentum spread of three directions in ILC damping ring design.
spx
spy
spz
Laboratory frame
Beam CM frame
45 keV/c
45 keV/c
2 keV/c
2 keV/c
7 MeV/c
0.7 keV/c
Energy acceptance of the ring
E
Laboratory frame
Beam CM frame
~ 50 MeV
5 keV
Smaller than horizontal momentum spread
large angle scattering can cause beam loss.
 Reduction of beam life time.
2/50
This effect is important for circular colliders and light source rings (beam is in the
rings for hours),
but not for damping rings, where beam is in the ring only for 200 ms.
Limit of number of bunches and
beam current in Damping Rings
• Injection/extraction kicker speed
• Instabilities
– Electron cloud in e+ ring
– Ions in e- ring
1/51
Injection/ extraction Kicker speed
Limit of number of bunches
Bunch spacing in linac: ~300 ns
Compressed in damping ring as short as possible
 Circumference/bunch spacing = max. bunch number / pulse
Extract (inject) bunch by bunch using very fast kicker magnet.
Kicker speed determine the bunch spacing
 circumference/number of bunches
Kicker field
300 ns
Damping Ring
extraction
Main Linac
2/53
Electron cloud instability in positron ring
Formation of electron cloud
beam pipe
(Multi bunch effect)
Synchrotron radiation photons hit
beam pipe wall.  photo electrons
Some electrons hit the wall again and create
secondary electrons.
Electrons are attracted to positron beam and accumulated.
secondary
electrons
e+
e- cloud
3/56
photo
electrons
e-
e+
Important for
positron ring.
Electron beam does
not attract electrons
 electron cloud
formation is (much?)
less significant.
Electron cloud instability
Instability due to electron cloud (Single bunch effect)
• Electrons move to head part of positron bunch.
• Following part of bunch is kicked by the gathered electrons.
(With small position deviation between head and tail)
• Electrons move toward that part of the bunch.
• same for following parts
Interaction between the positrons in a bunch and electrons in the cloud
causes oscillations of the positrons and electrons.
 This is instability.
Beam current (bunch spacing) is limited.
2/58
Cures: Preventing/reducing electron
accumulation
•
•
•
•
Beam pipe surface treatment for low secondary electron emission
Beam pipe geometry reducing electron emission
Beam pipe geometry reducing electrons travel toward beam
Electron absorber (positive electrodes in beam pipe)
•
Appling magnetic field reducing electrons travel toward beam
B
e+
In the magnetic field,
Electrons cannot reach around the beam.
Some of these have been already demonstrated (e.g. B-factories).
More studies using CesrTA (Cornell U.) starting this year.
2/60
Ion Instability in electron ring
Electron bunch collides and Ionizing residual gas
electrons are repelled and
ions are attracted and remained
electron bunch
ions +
+
+ +
+
+ +
residual gas
Following bunches are kicked by ions created by leading bunches.
Ions are attracted by the following bunches.
Following bunches also create ions.
interactions between bunches and ions can cause big oscillation
after many bunch passing through the ions.
2/62
Introducing gaps in bunch train mitigates Ion Instability
mini-bunch train
mini-bunch train
Ions are disappeared in the train gap
 no interaction between different mini-trains
 still instability may be significant in each min-train
(Fast Ion Instability)
Number of bunches in mini-trains is limited.
If there is ions remained between gaps (or there is no gap)
And ions remained multi-turn.  “conventional” ion instability.
1/63
SUMMARY of Damping Ring
•
•
•
•
1/64
Radiation damping
Radiation excitation (quantum effect)
Intra-beam scattering
Limit of bunch numbers, beam current
– Injection/Extraction kicker speed
– Instabilities
Bunch Compression
• Bunch length in damping ring (6~9 mm) is
much longer than suitable at IP (0.3 mm).
• Long bunch in damping ring
– Power of RF cavities
– Instabilities (peak current)
• Short at IP
– luminosity (e.g. hourglass effect)
•  Bunch is compressed after damping
ring.
Principle of Bunch compressor
RF cavities
Make z  E correlation
accelerate
head
decelerate
Put a bunch near zero-cross of
RF field.
Wiggler or chicane
Make E  z correlation
Lower energy particles take
longer pass
 Delayed
Higher energy particles take
shorter pass
 Advanced
Principle of Bunch compressor
in phase space
RF cavities
Wiggler or chicane
E
Z
Area in the phase space (longitudinal emittance) is preserved.
Decrease bunch length, increase energy spread.
SKIP
2-stage bunch compressor system.
Why two stage?
Reduce relative energy spread
• 1-stage compression will make energy spread too large.  Large
chromatic, dispersive effect
• In 2-stage system, beam is accelerated after 1st stage, then relative
energy spread is reduced.
Reduce effect of longitudinal bunch position jitter from damping ring
• 1-stage: rotate about 90 degree in phase space.
– position  energy, energy  position
• 2-stage: rotate about 180 degree,
– position  position, energy  energy
• Beam energy in damping ring is very stable, but longitudinal position
is not.
• Longitudinal position jitter in the main linac and at IP is important.
• Energy jitter at main linac entrance is not important, negligible
compared with final beam energy.
SKIP
2-stage bunch compressor system.
• 1-stage compression will make momentum spread too
large.  Large chromatic, dispersive effect
1 RF unit, 3 cryomudules
8 cavities and 1 quad/module
14+1 spare RF units,
each is identical to ML RF unit
3 cryomudules/unit,
26 cavities and 1 quad/unit
“wiggler”
stage-1, 9 mm  1 mm
5  4.88 GeV
“wiggler”
stage-2, 1 mm  0.3 mm
4.88 GeV  15 GeV
ILC Bunch Compressor
Longitudinal Phase Space distribution
SKIP
RF
RF
Wiggler
Before BC1
Middle of BC1
Middle of BC1
Wiggler
After BC1
After BC2
By Peter Tenenbaum
http://www.slac.stanford.edu/~quarkpt/bc/2007/
Spin Rotator
electron and positron sources produce longitudinally polarized beam.
In the damping ring: polarization is in vertical direction.
At collision, polarization is longitudinal direction.
 spin should be rotated
particle source
damping ring
or
or
turn around
or
spin rotators
or
or
Main linac - BDS
IP
or
Spin Rotator
Spin rotates around magnetic field direction..
Rotation around z-axis
solenoid
solenoid
solenoid
Arc 7.9deg
+I in horizontal
-I in vertical
(Pair of solenoid
for removing x-y coupling)
solenoid
+I in horizontal
-I in vertical
Rotation around y-axis
Polarization direction can be set from the vertical to any arbitrary angle.
Test facilities
Advertisement
Major test facilities for ILC
Accelerating system (cavities and cryomodules)
• TTFFLASH (DESY)
• STF (KEK)  see later slides
• ILCTA(?) (FNAL)
• ...........
Damping rings
• ATF (KEK)  see later slides
• CesrTA (Cornell)
Final focus
• ATF2 (KEK)  see later slides
(This is old version)
???
???
STF phase-1
Construction of accelerating system.
(in small scale)
“S1 Global” project at STF (KEK)
Before STF phase 2
Demonstration of 1 Cryo-module (8 cavities) operation
Average acc. field >= 31.5 MV/m
Four cavities by KEK
Two cavities from DESY
Two cavities from FNAL
cryostat by INFN
cryostat by KEK
Phase 2 of STF (KEK)
Demonstration of 1 RF unit of ILC,
3 cryomodules, 26 cavities,
Average acc. field >31.5 MV/m
figure from ILC RDR
ATF (Accelerator Test Facility) at KEK
ATF - prototype of damping ring of (warm) linear colliders
• In operation for more than 10 years.
• Producing very small emittance beam and extract it.
– Techniques of production of very small emittance.
– Development of various instrumentations.
ATF2 - prototype of final focus system of ILC
• Test and demonstrate the ILC final focus scheme and
stabilization of beam.
• Operation of newly constructed beam line will start in
November, 2008.
ATF including ATF2 at KEK
Final focus system
Newly constructed
Extraction line
140 m ring
1.3 GeV Linac
~ 100 m
ATF injector Linac
ATF Damping Ring
Parameters of ATF2 final focus
Energy is much lower (x1/200)
Normalized emittance
is comparable
 emittance is larger (x200)
 Beam size at IP is larger
(x10)
Difficulty, sensitivity to various
errors are comparable.
horizontal beam size ~2 um
vertical beam size
~40 nm
~700 nm
~ 6 nm
First Goal of ATF2 project
Demonstration of the focusing method of ILC
• ~40 nm RMS vertical beam size
• Will be confirmed using Shintake-monitor
Beam size monitor for ATF2-IP
(Tokyo Univ., KEK)
by Terunuma
laser bend
detector

e-
FFTB result
Result in FFTB at SLAC
Installation at ATF2-IP (2008/5)
Second Goal of ATF2 project
Demonstration of beam stabilization
•
~2 nm vertical jitter
• Feedback using nano-BPM (beam position monitor with
nano-meter resolution)
ATF2 - international collaboration
• ATF started as a project of KEK.
– But big contributions in operation, beam studies and
improvement of the machine from over seas.
– Operation/study plans are controlled by international
committees.
• ATF2 started as an international project
– Design, construction and operation are all international
collaboration.
– Construction cost is shared by three regions. (except for infrastructures)
– Model of ILC, though the scale is much smaller.
• Major members from France and Asia
– LAL, LAPP, IHEP, KNU, PAL, KEK, U.Tokyo, (CERN)
Beam position monitors for ATF2, made by PAL (Korea)
photo by Toge
Construction of ATF2 beam line, Quad magnets are made by IHEP(China)
photo by Toge
Installation of final quad magnet system
photo by Toge
Daily ATF Operation meeting
photo by Araki
END
Preservation of Low Emittance
(in main linac)
Preservation of Low Emittance
• Need very low emittance beam at IP, especially
in vertical.
• Emittance becomes very low in the damping
ring.
• Transport and accelerate the beam from the
damping ring preserving the low emittance is a
big issue. (Vertical projected emittance is the
most important, and difficult to preserve.)
If area in phase space is preserved,
it is not necessarily emittance preservation.
y’
y’
y
y
Even if 6-dimensional volume is preserved,
Projected emittance can be increased.
y
y
z
z
y’
y’
y
y
Coupling between vertical motion to other degree of freedom
should be avoided or should be well controlled.
Two major sources of emittance dilution
• Wakefield
(Coupling between y and z)
– Transverse wakefield of accelerating cavities
• Short range: in a bunch
• Long range: inter-bunch
• Dispersive effect
(Coupling between y and E)
– Particles with different energy have different
orbit
• Different angle change in magnetic field
• Different angle change in tilted accelerating field
Transverse Wakefield
Leading particle
induce EM field
Following particle feel the filed
In rotationally symmetric structure,
Transverse field strength is proportional to offset of leading particle.
(If the offset is small.)
: called “dipole mode field”
Transverse momentum change of particle of longitudinal position z:
p x  W ( z  zi )qi xi
i
wakefunction
Charge and transverse
position of i-th leading
particle
Short range wakefield
current and charge are induced
at discontinuities
Induced fields catch up following particles
Transverse Wakefield of Accelerating cavities
• Short range - Single bunch effect
– Wakefunction is monotonic function of distance
– Not seriously important for ILC
60
Transverse-short-wake
(from TESLA-TDR formula)
40
2
W (V/pC/m )
50
T
30
20
10
0
0
0.0005
0.001
s (m)
0.0015
0.002
Transverse Long range Wakefield of Accelerating cavities
- Multi-bunch effect
• Wakefunction is sum of some resonance modes
– Each mode has its own frequency and damping constant
• Damping is important
• It is important to make some “spread” of frequencies, cavity by cavity.
(All cavities should not be precisely identical.)  Avoid resonant
growth of oscillation.
200
150
If so, kicks in all cavities have the same phase.
TESLA-TDR
2
W (V/pC/m )
100
T
1
2
50
0
-50
-100
-150
3
n
-200
0
50
100
150
200
time (ns)
2nd bunch is kicked by field induced by 1st bunch
3rd bunch is kicked by field induced by 1st and 2nd bunches
nth bunch is kicked by field induced by n-1 precedent bunches
Damping of Wakefield
Two HOM (Higher Order Mode) Couplers at both sides of a cavity
TESLA-TDR
Special shapes:
Accelerating mode should be stopped.
HOM should go through.
- trapped mode may cause problem.
TESLA-TDR
Wakefunction envelope from HOMs (from TESLA-TDR) with/without
random frequency spread (50 cavities) and damping
(V/pC/m )
No spread
2
100
W
envelope
10
s =0, no damp
f
s =0, damp
1
f
0
3
3
1 10
3
2 10
3
3 10
3
4 10
3
5 10
6 10
fs =0.1%, no damp
f
s =0.1%, damp
100
f
10
W
envelope
2
Random spread
sf/f=0.1%
(V/pC/m )
time (ns)
1
0
3
1 10
3
2 10
3
3 10
time (ns)
3
4 10
3
5 10
3
6 10
SKIP
Due to low RF frequency of ILC, using superconducting cavity,
wakefield is much less serious, compare with warm LC (X-band or
higher frequency).
length scale by factor 1/a
frequency change by factor a
Wakefunction of every dipole (transverse) mode
W sin  t   a3W sin a  t 
Amplitude of long range wake (multi - bunch effect)
W  a3W
Short range wake : Slope at the beginning (single bunch effect, t  0)
W  a 4W
Emittance dilutions due to Dispersive effect
• Any transverse kick in EM field will cause dispersion (energy
correlated orbit difference):
• Momentum change of a particle in an ultra relativistic beam in any
EM fields does not depend on its energy.
• Then, angle change is inversely proportional to its energy.
• Beam going through off center of quadrupole filed
– Misalignment of quadrupole magnet
– Injection error
– etc.
• Tilting of accelerating field
– Tilting misalignment of accelerating cavities
• This is a very important for ILC.
Appendix: Dispersion
Expressing energy dependence of transverse position of the beam:
x  x0   x,n n
( x can be replaced by y )
n1
  ( E  E0 ) / E0
 x,1
is called dispersion, or linear dispersion.
Higher terms are sometimes called higher order dispersions.
This is good in storage rings but is not well defined in transport lines and
linear accelerators. Instead of this, we can define as follows.
 x      x      x,n n
n1
    denotes average over particles in energy range     
Result of simulation with quad magnet misaligment
Each ellipse show monochromatic beam. Ten different energyies.
-0.00013
0.0002
-0.000135
0.00015
0.0001
-0.000145
x'
x'
-0.00014
5 10
-0.00015
0
-0.000155
-0.00016
-0.00035
-5
-5 10
-0.0003
-0.00025
x
-0.0002
-5
-0.0001
-0.0015
-0.00145
-0.0014
-0.00135
-0.0013
x
Going through 1 quad off center  First order dispersion
Going through 2 quads off center  2nd order dispersion
.....
Going through n quads off center  n-th order dispersion
First order dispersion can be measured and corrected.
But higher order dispersion is difficult to measure and correct.
 It is desirable to correct (first order) dispersion everywhere locally.
Cure of emittance dilutions due to Dispersive effect
• One promising method is “Dispersion Free Steering”
• Steering beam to minimize dispersion
– Need to measure dispersion:
• Need to change beam energy.
• Need beam position monitors (every quad has)
– Need many steering magnets (every quad has)
This orbit is no good.
This is much better.
Example of simulations
emittance along the linac
-8
2.6 10
Standard survey-alignemnt error, DFS
-8
2.5 10
300 μm
Quad strength
0.25%
Quad roll
-8
2.4 10
y (m)
Quad Offset
300 μrad
RF Cavity Offset
300 μm
RF Cavity Pitch
200 μrad
-8
2.3 10
-8
2.2 10
BPM Offset
(initial)
300 μm
Cryomodule
Offset
200 μm
Cryomodule Pitch
20 μrad
-8
2.1 10
-8
2 10
0
2 10
3
3
4 10
3
6 10
8 10
distance (m)
3
4
1 10
4
1.2 10
SUMMARY of Preservation of Emittance
• Two major sources of emittance dilution
• Wakefield
– Short range: Monotonic with distance
– Long range: Resonant modes; Detuning
• Dispersive effect
– Misalignment quad magnets (offset) and
cavities (tilt)
– Cured by Dispersion Free Steering in ILC
main linac