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.

Talk Slides:
PDF

Related publications: Los Alamos archive
physics/0205001

(Coffee before the seminar starting 9:30 AM)

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