Angular dependence of the refractive index in the ionosphere

Abstract

Th e di s pe rs iQn prope rti es of a n a nisotropi c me dium, s uc h as the ionos phere in prese nce of the earth 's magne ti c fi e ld , are c onve nie ntly re prese nte d by the variations of the refractiv e index with th e direc tio n of propagati on. It is s hown tha t, fo r a numbe r of cases of prac ti cal inte rest, th e vari ati on of the ind ex n with th e angle 0 tak es a s pec ial form whi c h can b e e xpressed by a graphi cal co ns tru c ti o n; th e res ult n is re ad on a circ ula r scale, c aU ed the ind ex c ircle, a t the points where it is inte rsec ted by a s tra ight line whi c h de pe nd s in a simpl e mann e r o n the direc tio n of propagati o n o. The sa me co ns tru cti on a ppli es whe n the wave is e vanesce nt a nd th e n it giv es the imagin ar y valu e of th e refra c tive ind ex or extin ction ind ex.Th e range of appli cati on of t hi s co ns truc tio n includ es th e Apple ton-H a rtree equ ati on, its ge neralization for a ny numbe r of io ns , th e hydro magne tic wa ves in a me dium with finite co mpress ibiljty, a nd th e va ri ous a pp rox.im ati ons corres po ndin g to limiting or transiti onal cases -As trom wa ves, uni axial medi a, a nd Booker's h ydrom agn eti c approxim a tion . It could also be a ppli ed to magneti zed ferrites.For mos t a ppli ca ti ons th e inde x c ircle re prese ntati on ca n take th e pl ace of th e di s pe rsio n s urface. Th e milln features of thi s s urface-the numbe r of s hee ts, wh e th e r th e y are real o r im agin ar y, and th e directi on of th e asy mptotes -a re all di s pla yed on th e ind ex c ircl e. If th e need ari ses, it is easy to trace th e di s p e rs ion s urface a nd 1.0 foUow its de form a ti o ns as th e para mete rs of the me dium a re vari e d .

A Theory of Scattering From Irregularities in a Magneto‐Ionic Medium

“…We note that the anisotropic effect is important for frequencies and medium parameters for which the refractive index surface departs appreciably from that of a sphere. The nature of these refractive index surfaces has been thoroughly studied [Clemmow and Mullaly, 1955;Stix, 1962;Deschamps, 1965]. The theory has applications in studies of laboratory plasmas and the ionosphere.…”

A Comparative Study of Several Models of the Magnetoplasma

“…Analysis is usually made by assuming a certain model in which some facts are neglected and others idealized. Detailed investigations have been made on wave propagation in a cold magnetoplasma (for instance, Deschamps [1965]), and plots of dispersion surfaces have been given with X -•o•v2/,o 2 and Y -ore/o, as parameters, where ,o is the source frequency and ,o•v and om are the plasma resonance frequency and the gyroresonance frequency, respectively. Propagation in a warm magnetoplasma has also been studied.…”

Radiation of an Antenna in a Compressible Magnetoplasma

“…Alternatively w is a multivalued function of k: w;(k) with i taking 10 distinct values or, given w, the vector k must lie on a surface 6w section of @) at constant w. The surfaces @) or 6w will be called dispersion surfaces; 6w, except for a scale factor, is the index surface for the frequency w. These surfaces, or related ones, have been described in a number of publications, (Clemmow and Mullaly, 1954;Deschamps and Weeks, 1962;Allis, Buchsbaum, and Bers, 1963;Felsen, 1965;Deschamps, 1965). The use of the index surface in ray tracing has been thoroughly discussed by Felsen (1965).…”