Poster paper full text

Present paper suggests one possible physical mechanism of the reflected signal amplitude increasing at the final, third stage of anomalous attenuation developing what is observed in high-power (more than 20 MW) HF ionospheric heating experiments [1]. It is shown that quantitative and qualitative characteristics of this phenomenon can be explained by interaction of radio waves with large-scale (~10-50 km) irregularities in the heating region.

Main radio wave propagation peculiarity in presence of large-scale irregularities consists in complicated ray structure of the signal. At a relatively low level of electron density disturbance (when is of order of 1%) the multi-ray propagation takes place. The angular spectrum of radio wave arriving to the observation point becomes discrete in this conditions. Hence, the signal on the Earth's surface is a result of the interference of several different rays (see Fig. 1).

Fig. 1. Plot qualitatively explaining the mechanism of multy-ray reflections from a plasma layer with large-scale irregularities.

With the aid of numerical statistical modeling based on multiple ray tracing it is shown that in presence of large-scale irregularities the reflected signal amplitude mean value is increased significantly. Likeness of this effect with the phenomenon observed in experiment is illustrated by two plots, showing experimental data [1] on anomalous absorption temporal development (Fig. 2, time >1 c) and calculated dependence of the reflected signal mean amplitude on the irregularity level (Fig. 4). Quick growth of the large-scale irregularities may be due to the nonuniform heating caused by natural plasma irregularity in scale lengths 10-50 km.

Fig. 2. Typical view of the pump wave aplitude dependence on time for a single heating period, according to [Berezin I.V., Boiko G.N., Volkov B.M. et al. Izvestiya VUZov. Radiofizika, 1987 V.30, p.702 (in russian).].

The calculations were made for the common model of a plane plasma layer with superimposed wave-like large-scale irregularities:

Solving the 'extended geometric optics equation system' (Eq. 2) we can get the parameters of all 'echoes' for the given values of , and disturbance phase . We keep only those echoes which ranges differ not more than by 50 mks from the range of the strongest one. Then the interference task is solved. The full field amplitude is determined assuming the echo phases are random and uniformly distributed over the interval . The resulting value of is obtained by averaging over the echo phases and the disturbance phase . It is taken into account that number and parameters of the echoes are different for different values of .

Fig. 3. Dependence of the mean amplitude of the reflected from the ionosphere signal on the large-scale (10-50 km) electron density irregularity level. The amplitude of the signal reflected from a regular (without irregularities) layer has been taken for a unit. The irregularity level is in percent (0.01).

In the Figure 3 the dependences of on for five different values of (10, 20, 30, 40, 50 km) are presented. The is expressed in units of the undisturbed ( =0) reflection amplitude and is in percent (0.01). Here are the main features of the presented dependences:

1. the value of is always above 1;
2. for each the dependence of on passes three stages. The first: starting from =0, = 1, slow, more or less regular increase up to ~ 2-3. The second: sharp increase up to several tens, sometimes with several pikes and sharp return to the "stationary" value ~ 4-5. The third: absence of further growth, small oscillations near the "stationary" value ~ 4-5.
3. the second stage has the tendency to be shifted to the higher values of when increasing.

Interpretation of these results is quite simple.

When the reflection level is disturbed, the number of 'echoes' is increased and more energy is returned to the sounder location. The effect 'focusing prevailing over defocusing' also plays its (but less significant) role. All this explains the feature 1.

Stage 1: Number of echoes is increased, but the most probable local curvature radius of the reflection surface is much larger than the distance from the surface to sounder . (The relation for the 'near-zenith' reflections exists, where is the layer thickness).

Stage 2: According to the latter relation, the most probable value of is decreased and becomes of order of . The focusing in literal sense of the word takes place frequently and gives large contribution to .

Stage 3: The most probable value of becomes much smaller than . The number of reflection points achieves of saturation.

At last, the feature 3 is a consequence of the relation if = is being substituted into it.

Thus one can conclude that the considered phenomenon is not directly connected to the mechanisms of radio wave anomalous attenuation, such as multiple scattering on kilometer irregularities or transformation into plasma waves on small-scale irregularities (the latter one influences ordinary waves only). This circumstance must be taken into account for correct determining of the anomalous attenuation magnitude.

References

1. Berezin I.V., Boiko G.N., Volkov B.M. et al. Izvestiya VUZov. Radiofizika, 1987 V.30, p.702 (in russian).

Fig. 4. Typical statistical distribution of the total field amplitude of multi-ray signal.