  Electron accelerators and synchrotrons can be operated to provide short
emission pulses due to longitudinally compressed or sub-structured electron
bunches. Above a threshold current, the high charge density leads to the
micro-bunching instability and the formation of sub-structures on the bunch
shape. These time-varying sub-structures on bunches of picoseconds-long
duration lead to bursts of coherent synchrotron radiation in the terahertz
frequency range. Therefore, the spectral information in this range contains
valuable information about the bunch length, shape and sub-structures. Based on
the KAPTURE readout system, a 4-channel single-shot THz spectrometer capable of
recording 500 million spectra per second and streaming readout is presented.
First measurements of time-resolved spectra are compared to simulation results
of the Inovesa Vlasov-Fokker-Planck solver. The presented results lead to a
better understanding of the bursting dynamics especially above the
micro-bunching instability threshold.
