Pergamon Journal of Atmospheric and Terresrrial Physics, Vol. 51, No. 7, pp. 74>747, 1995

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Mjodelling of transequatorial propagation of HF radio waves

V. P. Uryadov, N. V. Ryabova, I. Yu. Ignat’eva and V. A. Ugrinovsky

Radiophysical Research Institute, Nizhny Novgorod 603600, Russia

(Received injinalform 6 April 1994; accepted 22 April 1994)

Abstract-In the geometrical optics approximation, a synthesis oblique ionogram of ionospheric and magnetospheric HF radio wave signals propagating between magnetic conjugate points has been carried out. The magnetospheric HF propagation is considered for a model of the waveguide formed by field- aligned irregularities with depleted electron density. The characteristic peculiarities of the magnetospheric mode have been determined : (i) strong dispersion of the group delay with a frequency at 14-18 MHz, from - 1.4 to 0.6 ms/MHz for magnetically conjugate points at geomagnetic latitudes Q, = 30”, 40” and 50”, respectively, (ii) spreading - 1-2 ms, and (iii) a possibility of propagation between magnetic conjugate points at moderately low geomagnetic latitudes Q0 - 30-40” at frequencies exceeding 1.5 times the maximum usable frequency (MUF) of multi-hop ionospheric propagation.

II. INTRODUCTION

The transequatorial propagation of HF and VHF waves is of interest due to a number of circumstances associated with peculiarities of the equatorial iono- sphere. According to existing concepts, trans- equatorial propagation (TEP) of HF and VHF waves is divided into three types. The first type is the diurnal type of TEP connected with the equatorial anomaly of the F-layer in the vicinity of f 15” of the magnetic equator. The presence of pronounced maxima of the electron density in these regions gives rise to a whis- pering gallery mode mechanism of TEP at frequencies up to 60 MHz (Gibson-Wild, 1969). The second type of TEP correlates with large scale disturbances (I N l&100 km) and spread-F and is connected with radio wave forwa.rd scattering by the ionospheric irregularities (Ferguson and Booker, 1983 ; Rottger, 1973). The third t:ype of TEP is observed in evening hours and is registered at frequencies exceeding 100 MHz (McNamara, 1973, Nielson and Crochet, 1974). These frequencies exceed the frequencies of signals which can propagate due to the whispering gallery mechanism, and the power received is larger than expected due to radio wave scattering. According to the experimental data (Heron, 1981) the zone of high-frequency TE:P signal reception is limited in lati- tude and longitude directions, and spatially linked to the magnetic conjugate region. Possible mechanisms of the evening type of VHF TEP have been discussed by a number of authors. In the paper by Bowen et al. (1968), on the basis of measurements of arrival angles and group delay of signals at 77 MHz over the Oki- nawa (Japan)-Darwin (Australia) path, it was con-

eluded that the cause was wave ducting along the geomagnetic field lines. The assumption made by Kuriki et al. (1972) of VHF TEP by double scattering is confirmed by the frequency dependence of the received power (P cc f -‘O-f -I’), but, in view of the large observed signals strengths, this assumption requires unrealistically large integration volumes. Besides, it is also difficult to explain the more coherent trackable spikes revealed in Doppler analysis (Nielson and Crochet, 1974; Heron and McNamara, 1979). We can consider that a set of data on the evening VHF TEP supports the waveguide magnetospheric mechanism connected with duct propagation along field-aligned irregularities with depleted electron den- sity (Platt and Dyson, 1989a), or with propagation inside large-scale equatorial bubbles with large local density gradients (Platt and Dyson, 1989b).

It should be noted that there are fewer inves- tigations of HF TEP than of VHF TEP (Grossi and Padula-Pintos, 1971; Bukin, 1978). For the HF range, as well as the aforementioned mechanisms of TEP, the standard mechanisms of multi-hop ionospheric propagation are possible, complicating the interpret- ation of the experimental data. In this connection, modelling which includes both ionospheric and mag- netospheric mechanisms of radio wave propagation is of importance in developing experiments and in interpretating data on sounding HF TEP.

2. THE WAVEGUIDE MODEL

For this paper, modelling of the ionospheric part of HF TEP was carried out within the framework

743

V. P. Uryadov et al.

permittivity, and rJ is the radius of curvature of the field line.

For the dipole magnetic field we have (Mladonsky and Helliwell, 1962) :

R, coscD(1+3 sin2@)3/2 r., =

3 cos’@~ (1-t sin%) ’ (2)

Ionospher where R, is the Earth’s radius, @h is the geomagnetic latitude of the duct field line at the Earth’s surface (see, Fig. l), @ is the geomagnetic latitude of a point z along the duct, where z, the distance from point 1, is given by Al’ pert (1972) :

Fig. 1. Geometry of ray trajectories between magnetic con- jugate points.

+ $lnlsinB+/~~]}, (3)

of the geometrical optics approximation given in the monograph by Filipp et al. (1991) for a model of the ionosphere in the form of a sum of Chapman layers describing the E-, Fl- and n-regions (Ching and Chiu, 1973) without taking into account the effects of the geomagnetic field.

From the methodological viewpoint, for modelling of the magnetospheric part of HF TEP, it is expedient to use the analogy of wave propagation in optical waveguides (Unger, 1980). The role of waveguides in our case is played by ducts which are formed by irregularities of depleted density with transverse dimensions, II N 0.5/2 km (Gurevich, 1979), and elongated along the geomagnetic field lines.

The ray geometry for HF TEP is shown sche- matically in Fig. 1. In the geometrical optics approxi- mation, the equation describing the ray trajectories in the magnetospheric waveguide in the plane yz can be written in the form (Gurevich, 1979) :

d*y I au _=-- dz= 2 ay’

u(y,z) = - A&Oi,z) I 2~

Eo (4 r,(z) ’ (1)

where y is the coordinate perpendicular to the mag- netic field line around which the waveguide is formed, z is the coordinate along the duct axis, e. is the dielec- tric permittivity, AE is the perturbation of the dielectric

where (I+ is the geomagnetic latitude of point 1, W0 is expressed by @, and the initial height of the duct h as :

112

*cos@,. (4)

The dielectric permittivity of the undisturbed medium for frequencies f >> fh(fn is the gyrofrequency) :

.?N(z) Eo(Z) = 1-p

nmf’ (5)

It varies along the duct in accordance with variations of the plasma density N(z).

The change of the dielectric permittivity is equal to :

AE(v,z) = - e2AN(y, z)

nmf’ ’

where AN(y, z) is the perturbation of the plasma den- sity in the field-aligned irregularities forming the mag- netospheric waveguide. Trapping the wave by the duct is determined by the dependence of AN on y. Assuming a parabolic variation of the plasma density disturbance with the coordinate y we have :

AN(y,z) = -AN,(z)(l -~*/a*). (7)

The transverse dimensions of the duct a(z) are written in the form (Gurevich, 1979) :

Modelling transequatorial HF propagation 745

a, cos3 Q, a=

(1 +sin* @)“* ’ (8)

where a0 is the duct width in the plane of the magnetic equator.

Substituting (6)--(7) into equation (l), we obtain :

e2AN, (z) a,nmfza2Y-r” = 0. (9)

In the calculations, it has been assumed that the back- ground electron density N[z (Q)] and the density dis- turbance in the irregularities AN[z(@)] along the duct have the form (Al’pert, 1972) :

N[z(@)] = (r2-J exp (cc) (10)

AN,[z(@)] =: ~~~~exp~~). (11)

The value 5 is chosen from the condition of continuity of the background ‘electron density when passing from the internal to external ionosphere. rl is the parameter characterizing the size of the electron density irregu- larities.

The system of equations (2)-(11) was used for the numerical modelling of the magnetospheric part of HF TEP. Here, the initial conditions were taken from the trajectory calculations of a wave propagating from the transmitter on the Earth’s surface up to the point of the ray escaping from the ionosphere.

3. RESULTS OF MODELLING

The algorithms developed have been used for the synthesis of ionograms, taking account of the iono- spheric end of the waveguide magnetospheric modes. The calculation of the ionograms of magnetospheric signals (MS) has been performed assuming an iso- tropic antenna.

Calculations of the ionograms were made according to a long-term prediction for a period of high solar activity (R = 179, February, T = 8 h LT) for mag- netically conjugate points with different values of a0 located in the Far East longitude zone. The Far East zone has been chosen in calculations from the view- point that the wide-band (Af= 3-30 MHz) chirp sounder (Ivanov ef al., 1991) is located in the Khab- arovsk region (at Vyazemsky, (I+, 2: 38”), which can be used for experiments on HF TEP between magnetic conjugate points in Russia (Khabarovsk region) and Australia.

In the calculations, the relative value of the electron

(a) 42 I

40

38

32 I

36

c4 i

l&e,;3 ( , , ,

14 18 22 26 30 34 38 42 46 50 f, MHZ

00 641 (4

f, MHZ f, MHz

Fig. 2. Calculation of oblique ionograms of ionospheric (IS) and magnetospheric (MS) signals, for the Far East longi-

tudinal sector, R = 179, February, 08.00 LT. a-@,, = 30” (NE, 2-SE, 3-2F2, &3F2, 54F2, &5F2),

b--m, = 40” (1_4F2,2-5F2, 3-6F2,4-7F2, 5%8F2), c-0, = 50” (lAF2,2-5F2, 3_6F2,4-7F2, 5-8F2,6-9F2).

density perturbation in the irregularity forming the magnetospheric duct is taken to be equal to 6N = [( (AN/N)‘)]“* = 5 x lo-*, and the duct width in the magnetic equator plane is taken to be a, = 1, = 2 km. Results calculated for different values of the geomagnetic latitude Q0 are presented in Fig. 2a,b,c. The lower part of each figure contains the traces of the ionospheric signal (IS), whereas the upper part gives the ionogram trace due to MS (shaded by vertical lines) propagation. The MS trace includes the magnetospheric part of the path and the ionospheric parts from the transmitter up to the point of the ray entering the duct, and from the point of the ray escap- ing from the duct down to the point of reception on the Earth. From the figures we can see a marked difference in MS and IS ionogram traces. For IS, the propagation group delay typically increases with frequency because of the deeper penetration into the ionospheric layer at high frequencies. For MS propa- gation, the inverse is observed-the propagation time

V. P. Uryadov et al.

Fig. 3. The dependence of angles 0 of rays trapped in the magnetospheric duct at HF TEP on the radiating angle p from the Earth’s surface for different frequenciesf.

a--Q, = 30” (l-15 MHz, 2-25 MHz, 3-35 MHz, 4-50 MHz) b-Q, = 40” (1-15 MHz, 2-20 MHz, 3-25 MHz, 4-30 MHz)

c-Q, = 50” (I-14 MHz, 2-16 MHz).

of the signal decreases as the frequency increases. Of interest is the considerable spreading of MS sig-

nals, achieving a value N 1-2 ms at frequencies of l& 18 MHz. In real gee/ionospheric conditions, con- sidering the distribution of ducts over L and taking into account the magnetoinic splitting, it should be expected that the traces on MS ionograms will be split and the MS ionogram will have a discrete structure. The discrete structure of magnetospheric HF signals with relative time delays l-2 ms has been observed in the experiment of Ben’kova et al. (1978) at fixed frequencies.

To analyse the frequency dependence of the MS group delay, a calculation has been made for radiation angles j at which complete trapping of the wave in the magnetospheric duct occurs. These data are of interest from the viewpoint of selecting the antenna with optimal directivity patterns to investigate the magnetospheric HF signal propagation. The depen- dence of angles f? at which rays remain trapped in the duct angle p, for different geomagnetic latitudes CD, of corresponding points and different sounding frequencies, is shown in Fig. 3a,b,c; 0 is the angle between the wave vector at the output of the ray from the ionosphere and the duct axis at point 1 (see Fig. 1). It can be seen from the figure that there is a frequency dependence of the angles j?. For all geomagnetic lati- tudes, the radiation angle interval A/3 narrows the frequency increase and the beam centre of radio waves radiated from the Earth shifts to smaller values of /?. Since, ducts with smaller L values correspond to

Table 1. Maximal usable frequencies for IS and MS propa- gation

% 30” 40 50”

IS MUF MHz 35 25.6 24.4 MS MUF MHz 55 35 18

smaller values of 8, the decrease of z and Ar with fre- quency for MS is evidently associated with the fact that at high frequencies, wave trapping is possible only in ducts located at lower L values to which smaller values of group delay correspond.

We should note an interesting peculiarity of behav- iour of maximum usable frequencies (MUF) for IS and MS propagation with different values of geo- magnetic latitudes Q,, of the corresponding points. These data are given in Table 1.

We can see that, for moderately low geomagnetic latitudes @,, - 30”-40”, MS MUF is markedly greater than IS MUF, and for higher geomagnetic latitudes (@,o- SO”) MS MUF is smaller than IS MUF. Such a dependence is due to the stricter trapping conditions for high latitude ducts.

4. CONCLUSIONS

In the framework of the geometrical optics approxi- mation, a modelling of oblique ionogram has been made for HF ionospheric and magnetospheric signals

Modelling transequatorial HF propagation 747

a fast decrease of the MS group delay time takes place as the frequency increases. In the lower part of the MS frequency range, 14-18 MHz, zg = ar/af - - 1.4 ; - 0.7 ; - 0.6 ms/MHz for conjugate points at geomagnetic latitudes Q,, - 30” ; 40” ; and 50”, respec- tively.

propagating between magnetically conjugate points. It is shown that the waveguide model with field- aligned irregularities with depleted electron density can be sufficiently effective for propagation in the mag- netospheric mode. A comparison is made between ionograms of ionospheric and magnetospheric modes. It is shown ,that, for values of irregularity par- ameters with deplleted electron density II = 2 km, 6N - 5 - lo-‘, which form magnetospheric ducts at HF TEP at moderately low geomagnetic latitudes CD0 - 30”40”, the relation MS MUF/IS MUF is 1.4-1.6, while at higher latitudes (a,, - SO’) MS MUF/ IS MUF is 0.74. According to our calculations, the spreading of MS signals amounts to -1-2 ms and

In conclusion we note that modelling of IS and MS ionograms permits us to obtain a sufficiently complete picture of HF TEP. The modelling results can be used in carrying out experiments and in interpretation of data on HF TEP.

Acknowledgements-This paper was supported by the Russian Fund of the Fundamental Researches under grant 93-02-15893.

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