Effects of correlation in transition radiation of super-short electron bunches

The effect of correlations between electrons in transition radiation is investigated. The correlation function is obtained with help of the approach similar to the Debye–Hückel theory. The corrections due to correlations are estimated to be near 2–3% for the parameters of future projects SINBAD and FLUTE for bunches with extremely small lengths (∼1–10 fs). For the bunches with number of electrons about $\sim 2.5\ast {10}^{10}$ and more, and short enough that the radiation would be coherent, the corrections due to correlations are predicted to reach 20%.