The US Particle Accelerator School

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The US Particle Accelerator School January 15-26,
2007 in Houston, Texas
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FINAL FOCUS LecturePart II
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BDS subsystems

• As we go through the lecture, the purpose of each
  subsystem should become clear
• The present BDS design also evolved from the
  picture shown here. The changes will be described
  in Part III

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Evolution of ILC BDS design in 2006
see lecture III
July 2006
Diagnostics BSY tune-up dump
2mr IR
b-collim.
E-collim.
20mr IR
Two collider halls separated longitudinally by
138m
FF
November 2006
14mr IR
14mr IR
One collider hall
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Evolution of ILC BDS design in 2006
see lecture III
November 2006
Sacrificial collimators
b-collim.
Diagnostics
14mr IR
BSY
14mr IR
One collider hall
E-collimator
FF
December 2006
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Parameters of ILC BDS
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Factor driving BDS design

• Strong focusing
• Chromaticity
• Beam-beam effects
• Synchrotron radiation
• lets consider some of this in more details

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Example of traditional Final Focus
Sequence of elements in 100m long Final Focus
Test Beam
beam
Focal point
Dipoles. They bend trajectory,but also disperse
the beam so that x depend on energy offset d
Sextupoles. Their kick will containenergy
dependent focusing x gt S (x d)2 gt 2S
x d .. y gt S 2(x d)y gt -2S y d ..
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
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Final Focus Test Beam
Achieved 70nm vertical beam size
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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

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Chromatic correction in FD
quad
sextup.
x h d

• Straightforward in Y plane
• a bit tricky in X plane

IP
KS
KF
Quad
If we require KSh 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.
Second order dispersion
chromaticity
Sextupole
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Definitions of chromaticity1st TRANSPORT
Storage Rings chromaticity defined as a change
of the betatron tunes versus energy.
In single path beamlines, it is more convenient
to use other definitions.
The second, third, and so on terms are included
in a similar manner
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).
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Definitions of chromaticity2nd W functions
Lets assume that betatron motion without energy
offset is described by twiss functions a1 and b1
and with energy offset d by functions a2 and b2
Show that if in a final defocusing lens a0, then
it gives DWL/(2b)
Show that if T346 is zeroed at the IP, the Wy is
also zero. Use approximation DR34T346d , use
R34(bb0)1/2 sin(DF), and the twiss equation for
da/dF.
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Synchrotron Radiation in FF magnets

• 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 left behind
v c
v lt c
Field lines
Energy spread caused by SR in bends and quads is
also a major driving factor of FF design
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Lets estimate SR power
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Lets estimate typical frequency of SR photons
For ggtgt1 the emitted photons goes into 1/g cone.
Photons emitted during travel along the 2R/g arc
will be observed.
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Lets estimate energy spread growth due to SR
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Lets estimate emittance growth rate due to SR
Dispersion function h shows how equilibrium orbit
shifts when energy changes
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Lets apply SR formulae to estimate Oide effect
(SR in FD)
Note that beam distribution at IP will be
non-Gaussian. Usually need to use tracking to
estimate impact on luminosity. Note also that
optimal b may be smaller than the sz (i.e cannot
be used).
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Beam-beam (Dy, dE , ?) 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 sz/fbeam)
• Energy loss during beam-beam collision due to
  synchrotron radiation
• Ratio of critical photon energy to beam energy
  (classic or quantum regime)

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Concept and problems of traditional FF
Final Doublet

• Chromaticity is compensated by sextupoles in
  dedicated sections
• Geometrical aberrations are canceled by using
  sextupoles in pairs with M -I

Y-Sextupoles
X-Sextupoles
Chromaticity arise at FD but pre-compensated
1000m upstream
Problems

• Chromaticity not locally compensated
• Compensation of aberrations is not ideal since M
  -I for off energy particles
• Large aberrations for beam tails

Traditional FF
/
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Traditional and new FF
Traditional FF, L 2m

• A new FF with the same
• performance can be
• 300m long, i.e. 6 times shorter

New FF, L 2m
new FF
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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)

1999 Design
2000 Design
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IP bandwidth
Bandwidth is much better for New FF
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Aberrations halo generation

• 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

Beam at FD
Halo beam at the FD entrance. Incoming beam is
100 times larger than nominal beam
Traditional FF
Incoming beam halo
New FF
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BDS design methods examples
Example of a 2nd IR BDS optics for ILC design
history location of design knobs
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In a practical situation
Laser wire at ATF

• 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
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Sextupole knobs for BDS tuning
IP

• Combining offsets of sextupoles (symmetrical or
  anti-symmetrical in X or Y), one can produce the
  following corrections at the IP
• waist shift
• coupling
• dispersion

Second order effect x x S (x2-y2) y y
S 2xy
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Sextupole knobs in SLC FF

• At first, used as a way to align sextupoles,
  using IP measurements of waists, dispersions and
  coupling
• In present design, sextupole placed on movers and
  their misalignment is used to create orthogonal
  knobs to correct the beam size

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Exercise on Sextupole knobs
IP

• Consider pair of sextupoles located as shown, and
  assume that horizontal dispersion is equal at the
  sextupoles. Assume that sextupoles are pi/2 from
  IP
• Derive the effect on the beam size due to
  symmetrical or anti-simmetrical misalignment of
  sextupoles in x or y

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Exercises (paper study and computer simulations)

• Project to design a Beam Delivery System
• choose IP parameters
• simulations study beam-beam effect
• design FD (choose L, length of FD quads)
• simulation create MAD model of FD
• estimate SR effects in FD
• simulations finds SR effects in your FD with
  DIMAD tracking
• determine required collimation depth
• analyze FD for aberrations
• estimate length of bend needed for FF
• simulation study chromatic corrections in MAD
  model
• estimate needed beam size of spoilers from
  survivability
• estimate wake field effect due to spoilers

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Choice of IP parameters

• Consider 1TeV CM ILC, but assume
• achieved bunch length is twice longer than
  nominal
• achieved bunch population twice higher than
  nominal, but bunch train is half as short
• Re-optimize IP beam parameters, taking into
  accountand using other factors that you have
  learned about

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Ex beam-beam study

• Use Guinea-pig code (Daniel Schulte)
• Input is simple and look like this

ACCELERATOR YOURLC1 energy 500
GeV particles 0.75 e10 sigma_x 250
nm sigma_y 2.0 nm sigma_z
100 micron beta_x 5.0 mm
beta_y 0.2 mm offset_x 0 nm
(total offset will be 2offset_x) offset_y
0 nm (-//-)
PARAMETERS LCPARS n_m20000 number of
macroparticles hist_ee_max1020 max E CM of
lumi spectrum
Analysing the results. Look into gp.out
lumi_fine (or lumi_ee) -- luminosity 1/m2
E_cm and E_cm_var -- CM energy and energy
spread due to beamstrahlung GeV bpm_vx,
bpm_vy -- average angular beam deflection after
collision microrad upsmax -- max value of
Upsilon parameter

• Calculate Luminosity, dE, deflection and L vs
  offset, L spectrum

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Ex on simple FD

• First, choose parametersof FD, such as L,
  length of lenses, etc
• Create a MAD opticsmodel of FD and simplified
  telescopeusing only two lenses

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Ex on simple FD

• Example of MAD input file for simplified
  telescope model

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Ex on SR in FD

• For FD that you will create
• Estimate beam size growth due to Oide effect
  for ILC parameters analytically

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Simulation of Oide effect in a FD
Simulate Oide effect for your beam parameters and
your telescope. Compare analytical estimations
with tracking by DIMAD. In particular, if the
IP sizes, vertical emittance and vertical
beta-function are already chosen, but horizontal
beta-function and emittance not yet defined, this
study could help to make a choice In the figure
show on the right, the Oide effect limits bx to
be larger than 15mm, i.e. the horizontal
emittance should be smaller than 4e-12 m (i.e.
smaller than 3.9e-6m for normalized emittance).
Picture shows the beam sizes obtained by tracking
with DIMAD. The sizes are luminosity
equivalent, which deemphasize the importance of
tails.
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Ex FD collimation depth

• For your FD, and your favorite vertex detector
  radius, find the required collimation depth in x
  and y

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Ex study chromaticity compensation

• Study MAD optics model of simplified telescope
  with inserted bend and sextupoles
• Study bandwidth when either
• T346 T126 or
• T346 T166
• are compensated

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Ex FD aberration

• For your FD, estimate effect on the beam size due
  to
• second order dispersion
• geometrical aberrations
• if they would not be compensated upstream

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Ex FD bends

• For your FD, find the min length of the bend that
  creates dispersion, to limit beam size growth
  caused by SR

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EX bend in telescope

• For simplified telescope, estimate length
  required to avoid SR beam size growth
• Study MAD optics model and use DIMAD tracking to
  verify energy spread due to SR after the bend

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Length required for the bends in FF
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. Lets estimate the required
length of the bend, taking this effect into
account.
Parameters length of bend LB, assume total
length of the telescope is 2LB, the el-star L ,
IP dispersion is h
Example 650GeV/beam, L3.5m, h0.005, Wx2E3,
and requesting Ds/slt1 gt LB gt 110m
Energy scaling. Usually h 1/g1/2 then the
required LB scales as g7/10
Estimate LB for telescope you created in Ex FD
simple
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Ex FD spoiler material

• For your FD, 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

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Ex FD-COLL wakes due to collimator

• For your FD, and for the collimation depth, beam
  size and beta at spoiler that you determined,
• find the effect of wake fields (COLL lecture) on
  jitter amplification
• if needed, choose an optimal tapering angle of
  the spoiler