Self-interactions within an electron bunch moving under the action of external forces may spoil the high brightness required for a SASE-FEL operating in the x-ray regime. Here part of a study, which deals with transverse self-fields, will be reported. We address the problem of a 1D line bunch moving first in a circle and, second, in an arc of a circle, both analytically and from a fully electrodynamical viewpoint.

First, a two-particle system moving on a circle is studied: exact and approximated expressions for the transverse force are found. Such force is centrifugal, in agreement with simple arguments from relativistic dynamics. Both tail-head and head-tail interactions turn out to be important. By integrating results for the two-particle model, we consider the transverse interaction between a line bunch and a test particle in front of it. Expressions for the transverse force result, which are studied in different limiting cases. A constant centripetal term is present in the long bunch limit. This term is due to the transient, in the behavior of the force in a two-particle system, between the small- and the large-distance regime.

Second, the problem of a 1D line bunch moving in an arc of a circle is studied. We start considering a two-particle system to find exact and approximated results for the transverse force in all possible transient configurations. We report a very good agreement with TRAFIC4. Then, the transverse interaction between a line bunch and a test particle is analyzed. In particular, the case of injection from a straight section into a hard-edge bending magnet is treated. The expressions for the transverse force are, again, in very good agreement with TRAFIC4. Finally, by simple composition of rectangular bunches, a formula for the calculation of the transverse interaction is found for the case of a bunch with arbitrary density distribution. Such expression is r egularized to a formula independent of the distance between test particle and bunch by subtraction of the steady-state transverse self-interaction.


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Related publications:    Los Alamos archive physics/0205001



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