Accelerator Physics Topic VIII Coherent Synchrotron Radiation

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Accelerator PhysicsTopic VIIICoherent
Synchrotron Radiation

• Joseph Bisognano
• Engineering Physics
• Synchrotron Radiation Center
• University of Wisconsin

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Coherent Synchrotron Radiation

• Since the spectrum of synchrotron radiation in
  free space extends down to arbitrarily long
  wavelengths, a bunched beam would couple to
  angular frequencies of order 1/bunch time length
• This was a major concern in the early days of
  talk about storage rings, since the coherent
  power scales as (Ne)2 rather than Ne 2

Shielding to the Rescue!
Current frequency distribution
shielding
shielding
S is normalized power spectrum (SYLee)
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Basic Principle
E(1), E(2) Energy E(1)2 E(2)2
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Wakefields
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A Picture
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Shielding of CSR

• In terms of a resistive coupling, the free space
  impedance is
  /Z/n/ 300 n-2/3 ohms
• Shielding sets in at n lt ?(R/h) -3/2 h is
  distance from conducting wall, and
  /Z/n/ peaks out at 150 h/R, 130 ohms resistive,
  85 ohms reactive
• This shielding prevents long bunches from
  radiating as a unit only incoherent radiation
• As machines have evolved to picosecond and
  subpicosecond bunches, with linac recirculation
  arcs and bunch compressors, coherent radiation is
  now important
• This shielding is not the same as the cutoff
  frequency in a waveguide it involves the bending
  radius in addition to chamber dimensions

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A Simple Analysis of CSR
R0radius of pillbox Rb radius of particle
orbit 2bheight of pillbox
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Potential Greens Function
We solve for modes and look for condition that
particle velocity matches the phase velocity of
the mode
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Boundary Condition
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Resonance Condition
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Some Typical Values
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What Does It Do? Good
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Maybe Useful
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What Does It Do? Evil
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Bunch Compression
z
z
z
M56
Voltage ramp
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Bunch Compressors
Pix
Bentson, et al EPAC 2002
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Dispersion and Emittance Growth
Bentson, et al EPAC 2002
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LCLS Bunch Compressor
Bentson, et al EPAC 2002
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Dynamical Effects of CSR
Presence of modulation
(microbunches) in bunch density

CSR may become significant
Collective forces associated with CSR induce
instability
Instability feeds back, enhances
microbunching
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Properties of CSR Impedance

• Shielding cut off
• Peak value

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Storage Ring Microwave Instablity
Similar instability in bunch compressors from
finite R56-microbunching
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Microwave Instability
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Observations of CSR - NSLS VUV RingCarr et al.
NIM-A 463 (2001) p. 387
Spectrum of CSR Signal (wavelength 7 mm)
Current Threshold for Detection of
Coherent Signal
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Observations of CSR - NSLS VUV RingCarr et al.
NIM-A 463 (2001) p. 387
Detector Signal vs. Time

• CSR is emitted in bursts.
• Duration of bursts is
• Separation of bursts is of the order of few ms
  but varies with current.