  The beam lifetime in an electron storage ring is also limited by the loss
rate of the stored electrons due to the elastic coulomb scattering of electrons
with the nuclei of residual gas atoms. The contribution to the beam lifetime
due to this elastic scattering depends upon the shape factor which is governed
by the shape of the vacuum chamber. In this paper, analytical expressions for
the shape factor for a rectangular and an elliptical vacuum chamber as a
function of longitudinal position along the circumference in a storage ring are
derived using an approach in which the position of electrons at the focusing
quadrupole is transformed to the location of defocusing quadrupole and vice
versa to define the parts of the vacuum chamber, where the loss of electrons
takes place at the location of quadrupoles. The expressions available in the
literature are for the average shape factors. The expression of shape factor
for a rectangular chamber derived in this paper are similar to the expression
for average shape factor quoted in the literature, whereas a new expression for
elliptical shape of vacuum chamber having no resemblance with the available
expression for average shape factor is obtained. A comparative study of shape
factors at each scattering location in the ring obtained from derived
expressions and with the existing expressions are reported using Indus-2
lattice parameters for rectangular and elliptical shapes of the chamber. A
comparison of average shape factors for these two shapes using derived as well
as existing expressions is also reported. These studies indicate that the
effect of the rectangular and elliptical shape of vacuum chamber on beam
lifetime due to elastic coulomb scattering between electrons and nuclei of
residual gas molecules is nearly same.

Accelerator Physics