Observation of Wakefields and Resonances in Coherent Synchrotron Radiation

We report on high resolution measurements of resonances in the spectrum of coherent synchrotron radiation (CSR) at the Canadian Light Source (CLS). The resonances permeate the spectrum at wave number intervals of $0.074{\mathrm{cm}}^{-1}$, and are highly stable under changes in the machine setup (energy, bucket filling pattern, CSR in bursting or continuous mode). Analogous resonances were predicted long ago in an idealized theory as eigenmodes of a smooth toroidal vacuum chamber driven by a bunched beam moving on a circular orbit. A corollary of peaks in the spectrum is the presence of pulses in the wakefield of the bunch at well-defined spatial intervals. Through experiments and further calculations we elucidate the resonance and wakefield mechanisms in the CLS vacuum chamber, which has a fluted form much different from a smooth torus. The wakefield is observed directly in the 30–110 GHz range by rf diodes, and indirectly by an interferometer in the THz range. The wake pulse sequence found by diodes is less regular than in the toroidal model, and depends on the point of observation, but is accounted for in a simulation of fields in the fluted chamber. Attention is paid to polarization of the observed fields, and possible coherence of fields produced in adjacent bending magnets. Low frequency wakefield production appears to be mainly local in a single bend, but multibend effects cannot be excluded entirely, and could play a role in high frequency resonances. New simulation techniques have been developed, which should be invaluable in further work.

Figure 1

Interferogram as a function of path length difference.

Figure 2

Fourier transform of the interferogram.

Figure 3

Fluted vacuum chamber at the FIR dipole with bending radius $R=7.143\mathrm{m}$ and deflection angle $\theta =15°$. The maximum excursion of the outer wall from the beam is 33 cm. The diode detector is at the end of the horizontal pipe at the left of the figure.

Figure 4

rf diode measurements in the time domain (oscilloscope traces) with a 50–75 GHz detector. Diode mounting and polarization: 1—backward horizontal; 2—backward vertical; 3—forward horizontal (with adjustment of time base). For clarity the curves have been separated vertically.

Figure 5

Simulated $E_x^2$ at backward port vs $ct$, after a low pass filter to account for detector response. The origin of time $t$ is when the bunch is 5 cm before the entrance to the bend. Only the lowest mode in $y$ is included.