Bunch Compression in the International Linear Collider

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Bunch Compression in the International Linear
Collider

• Kellen Petersen
• August 9, 2005
• University of Utah
• Mentor Professor Gerald Dugan (Cornell)
• with Dr. Andy Wolski, Jiajun Xu, Jeff Smith,
• and Prof. Lawrence Gibbons

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What is a Linear Collider?

• Advantages
• Electromagnetic Radiation is Negligible (even at
  high energies)
• More Cost Effective at Higher Energies
• ILC can verify LHC discoveries and contribute its
  own discoveries
• Disadvantages
• Collision Frequency is Low
• Difficult to make high number of particles stable

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What is the International Linear
Collider?
A planned future particle accelerator that
extends about 30 km long and collides electrons
and positrons at collision energies of about
500-1000 GeV
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Bunch Compressors

• Why are BCs needed?
• Damping Rings produce bunches few mm while Main
  Linac requires 100-300 um
• Advantages
• Shortens bunch lengths
• Produces highly stable output

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How does a Bunch Compressor work?

• A Bunch Compressor reduces the rms bunch length
  while increasing the rms energy spread. This is
  accomplished through rotations of the
  longitudinal phase space of the bunch.
• Components
• RF Power
• Phase Slip (wiggler, arc, chicane)

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What is Phase Slip?
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What is Phase Slip?

• Wiggler, Arc, Chicane

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What is Phase Slip?

• This is the rotation of the long. phase space
  which shortens the bunch length

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Schematic Layout of Bunch
Compressor (NLC)

• Components
• RF Power
• Phase Slip (wiggler, arc, chicane)

Two-Stage BC Design
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Design and Operational Issues

• 6 mm rms bunch length compressed to 100-300 um
• Transverse emittances must be preserved
• Phase variations should not produce IP energy
  variations
• Synchrotron Radiation Emittance Growth
• Sensitivities to transverse and longitudinal
  errors

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Bunch Compressor Designs

• Single Stage Bunch Compression
• Two-Stage Bunch Compression (A B)
• Three Stage Bunch Compression
• A Two 90 Rotations in Long. Phase Space
• (total 180)
• B Undercompression in First Stage (total 90)

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Single Stage vs. Two-Stage Bunch Compressor

• Advantages of Single Stage Design
• Less expensive
• Shortens bunch length to 300 um
• Advantages of Two-Stage Design
• Allows for acceleration between the two stages,
  leading to energy spread of lt1 (and not 3)
• Possibility of tuning Bunch Compressor to bunch
  lengths of 150 um and 300 um
• Provides for different transformations in Phase
  Space

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Studies Done on BCs

• G1 Single Stage (300 um)
• Twiss Parameters (in BC and BC w/ Main Linac)
• Long. Phase Space Distribution
• Emittance Preservation (Perfect and 1 sy offset)
  
• Orbit (absolute and normalized) with 1 sy offset
• Long. Sensitivity Studies

• G3 2-Stage (150A 150B)
• Twiss Parameters (in BC and BC w/ Main Linac)
• Long. Phase Space Distribution
• Emittance Preservation (Perfect and 1 sy offset)
• Orbit (absolute and normalized) with 1 sy offset
• Long. Sensitivity Studies
• Transverse Sensitivity Studies
• Synchrotron Radiation Emittance Growth

compared to Lucretia results from SLAC compared
to corresponding G1 results still in progress
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Simulations using TAO

• The Tool for Accelerator Optics
• Developed at Cornell University
• Accelerator Design and Analysis Enviroment
• Uses the Bmad Library

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Bunch Compressor Parameters
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Bunch Length vs. Energy Spread
G3 Two-Stage Bunch Compressors
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G1 Single Stage BC Studies

• Accomplishments
• Studied various aspects of this design
• Verified results obtained by simulations done at
  SLAC
• Able to run MAD decks in TAO and show that
  simulations are running correctly

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G3 Two-Stage BC Studies

• I studied various aspects of both the G3 150A and
  G3 150B designs
• Here I show some of the results of the for the
  150B design

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Long. Phase Space Distribution
G3 150B BC Design
"Bunch compression is an inherently nonlinear
process."--Paul Emma
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Emittance Preservation
Perfect
1 sy Vertical Offset
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Synchrotron Radiation Emittance Growth

• Synchrotron Radiation is emitted in wigglers of
  the Bunch Compressor (where the Phase Slip
  occurs)
• Effects
• Transverse Emittance Growth
• Increased Energy Spread

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Synchrotron Radiation Emittance Growth
Two Methods of Calculating SR Emittance Growth
Analytic Calculation via Helms Method using
Mathematica

• Tracking 100,000 particles with several seeds
  through TAO with radiation turned on and
  measuring the change in emittance

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Synchrotron Radiation Emittance Growth
Comparison of Analytical and Tracking
Calculations of Radiation Growth for Generation 3
(G3) Bunch Compressor Designs
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Longitudinal Sensitivity Studies
Studies done on G3 150A and G3 150B BCs

• Variations in
• Energy
• Energy Spread
• Arrival Time
• Bunch Length

• Errors in
• MDR Extraction Phase
• BC1 RF Phase
• BC1 RF Amplitude
• BC2 RF Phase
• BC2 RF Amplitude

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• MDR Phase
• Extraction Error
• for Two-Stage BC
• G1 vs. G3
• 150B

G1
G3
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Transverse Sensitivity Studies

• G3 design is a more optimal lattice designed to
  reduce dispersive emittance growth
• EXAMPLE
• Consider the case where there is a perfect
  lattice except for an rms BPM offset of 10 um wrt
  to the survey line
• SLAC results show a much smaller emittance
  growth for G3 BCs

We are looking forward to TAO results of the G3
transverse sensitivities!
from SLAC BC Design Web page normal-mode
normalized emittance growth results obtained at
SLAC
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Conclusions

• Ran MAD decks in TAO and completed studies on
  various potential ILC BC designs
• Verified the bunch length, energy spread, and
  transverse emittances
• Investigated effects of Damping Ring phase errors
  and RF phase and amplitude variations
• Determine emittance growth of 1 sigma vertical
  offset
• Calculate the emittance growth from synchrotron
  radiation

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Thanks

• My mentor Prof. Gerry Dugan
• Andy Wolski, for his knowledge and encouragement
• Jiajun Xu, to whom I asked many questions and
  with whom I spent a lot of time working
• Prof. David Sagan and Jeff Smith, for helping me
  with TAO--among other things
• Prof. Lawrence Gibbons for all of his help
• Prof. Rich Galik, for all he has done in
  organizing this REU Program

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Beam Properties at Injection

• Charge 2e10 (3.2 nC)
• Energy 5 GeV
• Energy Spread 0.15
• Bunch Length 6 mm

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Twiss Functions of G3 150B BC
G3 150B BC Design