Abstract
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.
Highlights
For a long time it has been realized that uniformly filled ellipsoidal electron bunches, known as ‘‘waterbag’’bunches, are the ideal particle distributions for controlled, high-brightness charged particle acceleration
We extend the analytical theory of Coherent transition radiation (CTR) to ellipsoidal electron bunches with soft edges, which include all bunch shapes from perfectly smooth Gaussians to hard-edged ellipsoids
We only evaluate the coherent part of the spectrum and ignore the incoherent part, which is valid because of the large number of electrons ( 108 ) present in a typical bunch
Summary
For a long time it has been realized that uniformly filled ellipsoidal electron bunches, known as ‘‘waterbag’’. The bunch shape is always assumed to be Gaussian, in which case the CTR temporal electric field and power spectrum are known analytically [14,15]. The electric field spectrum of CTR radiated by a electron bunch with the shape of a sphere [16], and the form factor of a ellipsoidal electron bunch [17], are known analytically but were never considered as a realistic option for diagnosing electron bunches. We extend the analytical theory of CTR to ellipsoidal electron bunches with soft edges, which include all bunch shapes from perfectly smooth Gaussians to hard-edged ellipsoids This makes the detection possible of realistic waterbag bunches.
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