Longitudinal bunch dynamics study with coherent synchrotron radiation

An electron bunch circulating in a storage ring constitutes a dynamical system with both longitudinal and transverse degrees of freedom. Through a self-interaction with the wakefields created by the bunch, certain of these degrees may get excited, defining a set of eigenmodes analogous to a spectroscopic series. The present study focuses on the longitudinal modes of a single bunch. The excitation of a mode appears as an amplitude modulation at the mode frequency of the coherent synchrotron radiation (CSR) emitted by the bunch. The modulations are superimposed on a much larger continuum from CSR emission in the continuous mode. A given eigenmode is classified by the integer m which is the ratio of the mode frequency to the synchrotron frequency. The present measurements extend up to m = 8 and focus on the region near the instability thresholds. At threshold the modes are excited sequentially, resembling a staircase when the mode frequencies are plotted as a function of bunch length or synchrotron frequency. Adjacent modes are observed to coexist at the boundaries between the modes. An energy-independent correlation is observed between the threshold current for an instability and the corresponding zero-current bunch length. Measurements were made at five beam energies between 1.0 and 2.9 GeV at the Canadian Light Source. The CSR was measured in the time domain using an unbiased Schottky diode spanning 50-75 GHz.