Accelerator physics topic viii coherent synchrotron radiation
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Accelerator Physics Topic VIII Coherent Synchrotron Radiation. Joseph Bisognano Engineering Physics & Synchrotron Radiation Center University of Wisconsin. Coherent Synchrotron Radiation.

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Accelerator physics topic viii coherent synchrotron radiation

Accelerator PhysicsTopic VIIICoherent Synchrotron Radiation

Joseph Bisognano

Engineering Physics &

Synchrotron Radiation Center

University of Wisconsin

J. J. Bisognano


Coherent synchrotron radiation
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


Basic principle
Basic Principle

E(1), E(2)

Energy~ E(1)**2+

E(2)**2

J. J. Bisognano


Wakefields
Wakefields

J. J. Bisognano


A picture
A Picture

J. J. Bisognano


Shielding of csr
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


A simple analysis of csr
A “Simple” Analysis of CSR

R0=radius of pillbox; Rb =radius of particle orbit; 2b=height of pillbox

J. J. Bisognano


Potential green s function
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


Boundary condition
Boundary Condition

J. J. Bisognano


Resonance condition
Resonance Condition

J. J. Bisognano


Some typical values
Some Typical Values

J. J. Bisognano


What does it do good
What Does It Do? Good

J. J. Bisognano


Maybe Useful

J. J. Bisognano


What does it do evil
What Does It Do? & Evil

J. J. Bisognano


Bunch compression
Bunch Compression

z

z

z

M56

Voltage ramp

J. J. Bisognano


Bunch compressors
Bunch Compressors

Pix

Bentson, et al EPAC 2002

J. J. Bisognano


Dispersion and emittance growth
Dispersion and Emittance Growth

Bentson, et al EPAC 2002

J. J. Bisognano


Lcls bunch compressor
LCLS Bunch Compressor

Bentson, et al EPAC 2002

J. J. Bisognano


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


Properties of csr impedance
Properties of CSR Impedance

  • Shielding cut off

  • Peak value

J. J. Bisognano


Storage ring microwave instablity
Storage Ring Microwave Instablity

Similar instability in bunch compressors from finite R56-microbunching

J. J. Bisognano


Microwave instability
Microwave Instability

J. J. Bisognano


Observations of csr nsls vuv ring carr et al nim a 463 2001 p 387
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

J. J. Bisognano


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.

J. J. Bisognano


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