An Approximate Wave Equation for an Axially Symmetric Periodic Waveguide

The field problem of wave propagation in a waveguide of periodically varying section is investigated. An orthogonal curvi-linear coordinate system is developed leading to a separable wave equation. As a result, the problem is reduced to solving Hills Equation. The discussion is limited to the case of a waveguide with slowly varying radius but there is some expectation that useful results would be obtained, particularly for axial fields, without this restriction.