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<H3><A NAME="SECTION00033300000000000000">
Rectangular case again</A>
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<P>
Known approach for rectangular case � perturbation theory
(Gluckstern; Palumbo).
<P>
Following Chao's analysis but in Cartesian coordinates we can get
similar expression for all the fields. Ignoring space charge in
ultrarelativistic limit we will get constant longitudinal electric
field in the pipe. Integrating this over frequency we will get the
same expression for 0 order longitudinal wake as in circular case.
<P>
1st order solutions based on Poisson equation and Leontovich
boundary condition.
<P>
Form factors received for rectangular case are quite similar to
elliptical
<P>
In fact we can utilize standard eigenfunctions approach developed
for dielectric layered waveguide for rectangular case. Different set
of eigenfunction - so we need to use different orthogonality
relations to get normalization constant. This is under investigation
now.
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<ADDRESS>
german_kourevlev
2006-01-19
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