El. Saldin et al., ON THE COHERENT RADIATION OF AN ELECTRON BUNCH MOVING IN AN ARC OF A CIRCLE, Nuclear instruments & methods in physics research. Section A, Accelerators, spectrometers, detectors and associated equipment, 398(2-3), 1997, pp. 373-394
Existing theories of coherent synchrotron radiation (CSR) are develope
d for the motion of an electron bunch on a circular orbit and do not d
escribe the case of finite magnet length. In this paper we present the
CSR theory for a bunch of any length moving in an are of a finite ang
le. The radiative interaction of the electrons in the bunch is analyze
d for a line charge distribution using an ultrarelativistic approximat
ion. It is shown in particular that this interaction is important not
only inside the magnet but also on the straight part of the trajectory
after the magnet. Detailed analytical study of the CSR effects in the
electron bunch with a stepped distribution of the charge density has
been performed. The simple analytical technique of the radiative force
calculation has been developed. The analytical solutions in the form
of elementary functions are obtained for the radiative interaction for
ce, for the energy loss distribution along the bunch and for the total
energy loss of the bunch. The latter result is confirmed with calcula
tion of the energy of coherent radiation in the far zone. The criteriu
m for the applicable region of the existing theories to the case of a
finite magnet length is obtained.