Nonlinear theory of relativistic Cherenkov generators based on irregular waveguides with allowance for finite wall conductance

On the theory of longitudinally inhomogeneous waveguides with impedance walls

“…This some what limits the generality of such treatment. One should also note the advantages of this approach over the approaches based on the use of curvilinear coordi nate systems [7,8]. Such coordinates help simplify the boundary conditions that become the same as in a reg ular waveguide and allow for the separation of vari ables.…”

“…An alternative approach based on the preliminary transformation of an irregular waveguide into a regular one with inhomogeneous anisotropic filling [7,8] via the introduction of curvilinear coordinates may also be used. However, it involves a great deal of analytic transformations and numerical calculations, is not always practical, and is applicable only to a limited number of cross sections.…”

Theory of irregular impedance waveguides: Generalized method of separation of variables

“…All partial zderivatives entering to (8) can be expressed in terms of 0 A , A and 0 B , B and their derivatives [14]:…”

“…978-1-4799-6864-0/14/$31.00 ©2014 IEEE developed in [8]. It utilizes a curvilinear coordinate system to transform the irregular waveguide to a regular one before performing any expansions.…”