  In Cartesian coordinate system, the fields generated by a point charge moving
parallel to the axis of a rectangular vacuum chamber can be formulated in terms
of eigenfunctions of the rectangular waveguide using the mode expansion method.
In combination with the conventional impedance theory, the Green-function forms
of the wake functions and impedance for space-charge effects can be obtained,
and are found to be functions of the positions of both the source and test
particles. Using the Green's functions calculated for a point charge, the wake
fields and impedance of a beam with various distributions can be calculated,
and should be useful to model the three-dimensional space-charge effects. This
paper summarizes our findings and also show comparisons to the existing
theories.
