Degenerate eigenvalues in an impedance waveguide
Abstract
An analytical study is made of an equation for doubly degenerate eigenvalues of the transverse-operator spectrum of the wave equation with impedance boundary conditions. As an illustration, computer calculations of multiple eigenvalues in relation to one of the waveguide parameters are presented. Approximate formulas are provided for multiple roots of the characteristic equation and the corresponding impedance; their error is calculated. It is noted that the present approach can be used to calculate VLF fields in impedance waveguides.
- Publication:
-
VLF Propagation in the Earth-Ionosphere Waveguide Channel
- Pub Date:
- 1983
- Bibcode:
- 1983vpei.book...60B
- Keywords:
-
- Eigenvalues;
- Electrical Impedance;
- Ionospheric Conductivity;
- Ionospheric Propagation;
- Very Low Frequencies;
- Waveguide Antennas;
- Antenna Radiation Patterns;
- Boundary Conditions;
- Boundary Value Problems;
- Error Analysis;
- Null Zones;
- Spectrum Analysis;
- Transverse Waves;
- Communications and Radar