  This paper studies the space charge impedances of a rectangular beam inside a
rectangular chamber, and the limiting case, e.g., a rectangular beam between
parallel plates, respectively. The charged beam has uniform density in vertical
direction and arbitrary distribution in horizontal direction. The method of
separation of variables is used to calculate the space charge potentials,
fields, and impedances which are valid in the whole perturbation wavelength
spectrum. Comparisons between the theoretical calculations and the numerical
simulations are also provided and they match quite well. It is shown that the
rectangular beam shape may help to reduce the longitudinal space charge
impedances.
