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## 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 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 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