A Model Describing Stable Coherent Synchrotron Radiation in Storage Rings

We present a model describing high power stable broadband coherent synchrotron radiation (CSR) in the terahertz frequency region in an electron storage ring. The model includes distortion of bunch shape from the synchrotron radiation (SR), which enhances higher frequency coherent emission, and limits to stable emission due to an instability excited by the SR wakefield. It gives a quantitative explanation of several features of the recent observations of CSR at the BESSY II storage ring. We also use this model to optimize the performance of a source for stable CSR emission.

Figure 1

Calculated equilibrium longitudinal distribution for different currents per bunch using the shielded SR wake. BESSY II case with a natural bunch length of 2.5 ps.

Figure 2

CSR gain as a function of the wave number $1/\lambda$. The BESSY II data for two different currents per bunch are compared with the shielded SR calculation and with the curve for a Gaussian distribution of the same length.

Figure 3

CSR gain versus radiation wave number calculated using the shielded SR wake with (dotted line) and without (dashed line) the RW wake. The solid line shows the gain calculated with the FS SR wake. Case of BESSY II with $9.0\mu \mathrm{A}$ per bunch and 1.7 ps natural bunch length.

Figure 4

Example of source optimized for the CSR production using the criteria described in this Letter. The photon flux is compared with the cases of a conventional SR source (ALS) and of BESSY II CSR mode with 400 bunches, $19.2\mu \mathrm{A}/\mathrm{\text{bunch}}$, ${\sigma }_{z0}/c=1.8\mathrm{p}\mathrm{s}$, and 60 mrad horizontal acceptance.