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

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

Wakefields J. J. Bisognano

A Picture J. J. Bisognano

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

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 J. J. Bisognano

Resonance Condition J. J. Bisognano

Some Typical Values J. J. Bisognano

What Does It Do? Good J. J. Bisognano

Maybe Useful J. J. Bisognano

What Does It Do? & Evil J. J. Bisognano

Bunch Compression z z z M56 Voltage ramp J. J. Bisognano

Bunch Compressors Pix Bentson, et al EPAC 2002 J. J. Bisognano

Dispersion and Emittance Growth Bentson, et al EPAC 2002 J. J. Bisognano

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 Shielding cut off Peak value J. J. Bisognano

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

Microwave Instability J. J. Bisognano

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

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