solar cycle effects on gnss-derived ionospheric total electron content ...

The Appleton-Hartree magneto-ionic theory applies to a medium that is electrically neutral with noresultant space charge, and an equal number of electrons and positive ions upon which a uniformmagnetic field is imposed. The ion content is not of direct consequence to electromagnetic wavepropagation, since the relative size of the ion means that it will not be excited by passing energy ofthis level to any significant extent (e.g. Steward, 1997). The electron density encountered by thesignal is of importance to this study.2.6.1 Phase refractive indexAt radio wave frequencies, the ionosphere may be regarded as a dispersive medium (Ratcliffe,1957). That is, the refractive index is a function of the radio wave frequency, the electron density,and to some lesser extent, the intensity of the Earth’s magnetic field. In order to derive the phaserefractive index, let us consider a plane polarized electromagnetic wave traveling in the x directionof the orthogonal coordinate system depicted in Figure 2.5. Let us also consider a uniform magneticfield that lies in the x-y plane and which makes an angle Θ with the direction of propagation. Thecomplex refraction index n is given by the Appleton-Hartree magnetoionic dispersion equation(Langley, 1996; Davies 1966; 1990; Hunsucker, 1991):n2= 1−2 4⎡ Y ⎤ ⎡TY⎤T2− − ⎢⎥ ± ⎢+ Y2 L ⎥⎣ 2( 1− X − jZ ) ⎦ ⎢⎣ 4( 1− X − jZ ) ⎥⎦( 1 jZ )where n is the complex refractive index ( µ jχ)The values of X, Y, and Z are dimensionless, defined as:X1/ 2(2.1)− with µ the real part and χ the imaginary part.XY2 2ωNN= = f ,(2.2)2 2ω fω f H H= = ,(2.3)ω fLTY = ω ωL, YT,ω= ω(2.4)31