Poster paper full text

Abstract

Computer simulations of energy transfer of radio–wave radiation from situated on the ground point source in randomly irregular ionosphere for the case of total internal reflection have been conducted using specially designed algorithm with utilizing of Monte–Carlo method. Distribution of reflected radiation on the ground is computed. The data obtained show the presence of the effect of anomalous attenuation of the signal power received near the sounder caused by radio–wave multiple scattering. This result is in agreement with another study of the anomalous attenuation effect having been conducted on the basis of the approximate analytical solution of the radiative transfer equation.

I. INTRODUCTION

All known space and laboratory types of plasma have small–scale irregular structure, which effects on the radiation distribution. The electromagnetic wave scattering on random irregularities of electron density leads to spatial–angular redistribution of radiation energy flux. Such influence can be remarkable if the scattering is multiple, i.e. the optical thickness for the scattering process is considerably greater than a unit.

This situation takes place, in particular, in HF radiosounding of the ionosphere. Recently it was found that even in relatively quiet ionospheric conditions the optical thickness for the scattering of radiowave with frequency 3-8 MHz on kilometer-scale density irregularities is considerably greater than a unit [1,2], i.e. the multiple scattering regime is realized.

In papers [2,3] the problem of total internal reflection of radio-wave radiation of situated on the ground point source from irrregular ionospheric plasma slab has been considered. As a theoretical instrument, the radiative transfer equation for plane-stratified magnetoactive plasma containing random irregularities has been used. The approximate analytical solution of the transfer equation for this problem has been derived. One of the results of this study is the discovering of the effect of the decreasing of radiation power receiving in the vicinity of the sounder. This efferct arises from the wave multiple scattering on random irregularities.

The anomalous attenuation effect under vertical radiosounding of the ionosphere with HF waves from the Earth’s surface is well known one and it has been observed in a number of experiments. So, following the papers [2,3], the multiple scattering of radio waves on random irregularities of plasma electron density can be considered as one of the physical mechanisms of the phenomenon. But the approach based on the approximate analytical solution of the radiative tranfer equation used in these papers is a new one. Therefore, the investigation of the radio-wave multiple scattering as possible mechanism of the anomalous attenuation effect using another methods is an actual problem.

This paper employs quite independent approach to this phenomenon investigation. The disscused above problem concerning the reflection of radiation of point source from irregular ionospheric slab is solved numerically using simple scatterng model with application of Monte-Carlo method. In the algorithm designed, the radiation transfer is determined by two factors: wave multiple scattering and strong refraction. As it is shown further, the account of this two factors in simple form gives the possibility to account for the anomalous attenuation effect.

II. PHYSICAL MODEL

The slab of randomly irregular ionospheric plasma is modeled by a series of horizontal planes. Location of each plane is determined by integer value of optical thickness of plasma situated between this plane and lower ionospheric slab boundary. The optical thickness is computed for vertical ray trajectory. So, movement from the plane to the next one corresponds to the change of the optical thickness to a unit.

Fig.1

Radiation energy transfer in the slab is modeled by distribution of some particles carring small portions of radiation energy. Fig. 1 shows the example of trajectory of such particle (for simplification two-dimential case is presented). Propagation of the particle is determined by the following rules:

1. Movement of the particle between planes is assumed to be rectilineal. Of course, in real slab the radiation energy is transfered along the ray trajectories which are bended in the inhomogeneous plasma. For simplification, in this model the segments of ray curves between planes are appoximated by the segments of straight lines.
   
2. When the particle is arrived to each plane the scattering act is played. Using random number generator the new direction of movement is chosen. All possible new directions have equial probabilities. The cases in which the acsenting particle is scattered in descenting one are eliminated. If we denote with an angle between direction of movement and the vertical direction (see fig.1), the former rule will mean that for acsenting particle, when scattering, this angle can take values from zero to , and for decsenting one – from to .
   
3. For the acsenting particles after each scattering act the reflection condition is checked. The isotropic plasma approximation is used. In the inhomogeneous plasma slab the level of reflection is determined by the condition

   , (1)

   where - refractive index, , - plasma electron frequency, - wave frequency, - the angle of ray entrance in slab (see Fig. 1). The level of reflection is determined using (1). If the value of is situated between the current and the next planes then the particle is reflected. Otherwise, the particle is moving up further.

Following the scheme described, the great amount of particles is tested. As a result, the distribution of concentration of particles on the ground, which is proportional to the distribution of energy of reflected radiation, is obtained. In the accepted model this distribution dependes only on one variable - the distance from the source.

III. NUMERICAL RESULTS

The computations were conducted for linear electron density profile with the distance to the slab =150 km and the slab thickness =100 km. The wave frequency is 3 MHz.

For optical thickness calculation the spectrum model with infinitely stretched irregularities suggested in [1,2] was used. Emploing formulars from these papers, it is easy to determine the levels at which the optical thickness takes integer values.

The radiation energy distribution was determined by division of the axis to the small 10 km regions and counting the number of particles having arrived in each region.The overall number of the particle tested is 1000000.

The results is shown in fig.2. Two slabs with optical thickness and were chosen. In each of two graphs togeter with the distribution of scattered radiation energy (bold line) the distribution of radiation energy reflected without scattering account, i.e. in absence of irregularities (thin line), is sited.

Fig. 2

The obtained distributions of the scatterad radiation energy have the following pecularities. In the vicinity of the sounder (near the point r=0) strong decreasing of the signal power is marked. The region of the attenuation has linear scale about several tens of kilometers. With the increasing of r the power is increasing from the point r=0 . After that, some hole followed by the smoothly decreasing dependence is observed.

The conclusion of this work is that the multiple scattering of radio-waves causes considerable decreasing of the level the reflected radiation near the sounder. So the multiple scattering is the mechanism capable to account for the anomalous attenuation effect.

REFERENCES

1. Bronin A.G., Denisenko P.F., Zabotin N.A., Geomagn. Aeron. - 1993, v.33, p.169-172 (in russian).

2. Zabotin N.A., Bronin A.G., Zhbankov G.A., LANL e-Print archive, http://xxx.lanl.gov/abs/physics/9803032

3. Zabotin N.A., Izvestiya VUZov. Radiofizika, 1993, V.36, N 12, pp.1075-1088 (in russian).