Theory of coherent transition radiation generated by ellipsoidal electron bunches

We present the theory of coherent transition radiation (CTR) generated by ellipsoidal electron bunches. We calculate analytical expressions for the electric field spectrum, the power spectrum, and the temporal electric field of CTR, generated by cylindrically symmetric ellipsoidal electron bunches with hard and soft edges. This theory is relevant for diagnostics of ellipsoidal electron bunches. Realization of such bunches would solve the problem of space-charge induced emittance degradation