Differential equation associated with electromagnetic waves in an inhomogeneous medium where ∇ε(r)·E vanishes
✍ Scribed by S.N. Samaddar; C.J. Lombardo
- Publisher
- Elsevier Science
- Year
- 1970
- Tongue
- English
- Weight
- 691 KB
- Volume
- 289
- Category
- Article
- ISSN
- 0016-0032
No coin nor oath required. For personal study only.
✦ Synopsis
Series aolutione are obtained for a second-order ordinary differential equation associated with propagation of electromagnetic energy in an inhomogeneous plasma which varies in one direction only (say z) for the case where E, = 0. The electron den&y and collieion frequency distributions are represented by two different polynomiala. When the collieion frequency i8 a constant and the ekctron density, N(z) varies as a Jirst-or aeconddegree polynomial in z, the resulting differential equations can be represented by known junctions, such as Airy functions or confluent hypergeometric junctiona, respectively. It ia shown that the general series solution of the differential equation for which the electron den&y ia also an arbitrary polynomial can be reduced to the aforementioned transcendental functions in the respective special cusea.