Propagation over plane earth through an exponential atmosphere

Abstract

An exact so lu t io n is fo nnd for t h e field of a dipolc ovcr p la ne, finitely co ndu ctin g ear t h th r'o ug h a n atm osp here ill which t he refractivity va r ies exponentia lly w it h h eig ht. The m ethod of J l anke l t ransform s is used, so t hat t he fin a l l'esult t" kes t he fo rm of a n in tegral wi t h infin ite limi ts. Th is integra l is evalu ated numer ically for a typi cal pro fi le a nd for seve ra lwave le ngths, a nd t he results a re com p il rcd wit h t hose for a homogcnco us at mos ph ere . At s ho rt wavelcngths an d largc dista nces, t he stratifi ed at mosp here abovc a planc cart h can act as a ver.v efficient \\·avC'guid C' .

Diffraction of Radio Waves in a Stratified Troposphere

“…We assume two independent solutions of (9), rj{r) and rB(r), with the latter chosen so as to satisfy the radiation condition at infinity. Now the method of variation of parameters [Gerks and Anderson, 1964] may be employed to get the general solution of (8),…”