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It is known that a high-peak-current beam in an electron storage ring emits a burst of coherent synchrotron radiation (CSR) in the THz region. This CSR is powerful and easily obtained with no special expense, but is not used by synchrotron radiation users. This is because the burst arises from a fine time structure in the bunch due to longitudinal beam instabilities, and is unstable. We quantitatively investigated its time structure to find out how unstable it is. The measurements of CSR from one bunch showed that with an average period of 10ms (comparable with the damping time, 12 ms) the fluctuation of averaged power was about 10%. This would be reduced to 1% with 100 bunches. The fluctuation ratio had small dependence on beam charge, rf acceleration voltage and momentum compaction factor. The successive bursts had a correlation because the beam had a memory of former bursts. This worked to reduce the fluctuation in long period. When the rf phase was modulated with 2fs (twice of the synchrotron oscillation frequency), the burst structure was modulated with 2fs and the long term fluctuation was reduced. This modulation can be used to eliminate background noise in user experiments.
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