1. Accelerator Physics Topic VIII Coherent Synchrotron Radiation
Joseph Bisognano
Engineering Physics &
Synchrotron Radiation Center
University of Wisconsin
J. J. Bisognano

2. 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)
J. J. Bisognano

3. Basic Principle
E(1), E(2)
Energy~ E(1)**2+
E(2)**2
J. J. Bisognano

4. Wakefields
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5. A Picture
J. J. Bisognano

6. 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 ~< (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
J. J. Bisognano

7. A “Simple” Analysis of CSR
R0=radius of pillbox; Rb =radius of particle orbit; 2b=height of pillbox
J. J. Bisognano

8. Potential Green’s Function
We solve for modes and look for condition that particle velocity matches the phase velocity of the mode
J. J. Bisognano

9. Boundary Condition
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10. Resonance Condition
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11. Some Typical Values
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12. What Does It Do? Good
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13. Maybe Useful
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14. What Does It Do? & Evil
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15. Bunch Compression z z z
M56
Voltage ramp
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16. Bunch Compressors
Pix
Bentson, et al EPAC 2002
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17. Dispersion and Emittance Growth
Bentson, et al EPAC 2002
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18. LCLS Bunch Compressor
Bentson, et al EPAC 2002
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19. 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

20. Properties of CSR Impedance
Shielding cut off
Peak value
J. J. Bisognano

21. Storage Ring Microwave Instablity
Similar instability in bunch compressors from finite R56-microbunching
J. J. Bisognano

22. Microwave Instability
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23. Observations of CSR - NSLS VUV Ring Carr et al. NIM-A 463 (2001) p. 387
Current Threshold for Detection
of Coherent Signal
Spectrum of CSR Signal
(wavelength ~ 7 mm)
J. J. Bisognano

24. Observations of CSR - NSLS VUV Ring Carr 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.
J. J. Bisognano