Oral presentation - full text

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As it follows from the title of our paper, I shall speak about two mechanisms of anomalous attenuation, one of the basic effects been observed under ionospheric heating by powerful HF waves. These two plots are to remind us how this effect manifested itself in the first experiments at Plattoville (left panel) and Gorkii (right panel).

In several seconds after beginning of the heating cycle the diagnostic ordinary wave amplitude is decreased by 10 – 20 dB in comparence with its preceeding value. After the heating is switched off, the diagnostic wave amplitude is rapidly restorated. In the first classical works main attention was given to anomalous attenuation of ordinary wave. The effect for extraordinary wave was considered weak.

In comparence with classical data the following example of anomalous attenuation may be called unusual. This plot has been taken from the work by Erukhimov, Komrakov and Frolov. We can see that attenuation coefficient behaves equally for both ordinary and extraordinary probe waves in wide frequency band. Their joint attenuation achieves of 10 dB at the right end of the frequency band. The pump wave frequency was 5.75 MHz in this experiment. It is shown here. As we know today, frequency band occupied by the heating region is narrow (about 300 KHz). The diagnostic frequencies used correspond to waves reflected outside of the heating region. And that causes the unusual character of the anomalous attenuation data. The outer regions are influenced by the heating region, but physical processes there are the same as in the natural ionosphere.

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Similar anomalous attenuation effect is observed under natural conditions. In the early works on this topic it was expressed in terms of the enhanced effective electron collision frequency (usual values of collision frequency are shown by empty circles). The standard technique of -profile restoration from the vertical sounding amplitude measurements data was used. Very soon it had became clear that no collisional mechanism exists being able to explain the excess of the amplitude attenuation over usual collisional values.

The next plot shows an example of results of anomalous attenuation measurements using digital ionosonde "PARUS" here at Troitsk. It is seen that probe waves of both polarization types experience the same attenuation.

The last example of natural anomalous attenuation has been taken from the paper by Wright, Argo and Pittway. These are dinasonde ionograms obtained at Huancaio (equatorial region), supplied with echo amplitude data (bottom of each panel). Top panel — four superimposed absolutely un-spread ionograms. Bottom panel — the same day, midnight, fully-developed equatorial spread-F. Note: echo amplitudes for frequencies above 6 MHz have been shifted by 15 – 20 dB below this reference line. Irregular structure caused additional attenuation!

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What are mechanisms of anomalous attenuation?

The first one is well known mode conversion mechanism. Due to dispersion properties of ordinary and slow extraordinary waves the narrow altitude range in the ionospheric layer exists where their coupling via scattering is possible.

The theory of this mechanism has been well developed. But I have possibility to refer to our own recent revision of this theory presented as poster paper at this Symposium. We did not break the basics but tried to free the theory from all unnecessary simplifications and to make it extremely clear. The obtained expression for anomalous attenuation is intended, of course, only for numerical investigation.

Here are main features of mode conversion mechanism:

1. It works only for ordinary probe wave, because extraordinary one is reflected below the coupling region.
2. Small-scale irregularities (less then 50 m) play main role in mode conversion. Sufficiently large level of such irregularities is required.
3. Mode conversion mechanism does not work at equatorial latitudes.

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The second mechanism of anomalous attenuation is multiple scattering. Importance of usual scattering was supposed long ago, because the mode conversion mechanism is not able to explain all experimental facts concerning the anomalous attenuation. But how usual scattering does this — it was not clear long time. Now we have the theory of this mechanism and the main statement of this theory — scattering must be multiple.

The following criterion of multiple scattering region realization exists: the optical depth of the plasma layer must be greater than unit. Our calculations show that this criterion is fulfilled frequently both in natural and in modified ionospheric layer.

Multiple scattering requires of special theoretical instruments for its description. Those who are interested in details are invited on my personal Web page, where many references to our papers and their full texts can be found. Here I only list the theory key points.

We proceeded from the basic relations of the multiple scattering theory.

Our first result was radiative transfer equation for magnetized plasma which applicability field is sufficiently broad.

The invariant coordinates concept has allowed us to present the transfer equation for a plane plasma layer in the most simple form of radiation energy balance equation.

The small-angle scattering approximation in the invariant ray coordinates has been suggested and approximated solution describing the radiation reflected from plasma layer has been obtained.

Some results of numerical analysis of this solution are presented on this plot. The map of anomalous attenuation values in the sounding station vicinity is shown. The nearly-elliptic region with strong attenuation exists which sizes are approximately 400 km in the NS direction and 100 km in the EW direction. The attenuation achieves of 15 dB at the place of sounding station location under chosen parameters. Another important result of the theory — main contribution to this effect give irregularities with scale length from several hundred meters to several kilometers.

This plot was for Nizhni Novgorod latitude. And this one is for Arecibo latitude. Other parameters are the same. One can see that latitude dependence is not very strong for multiple scattering mechanism. Perhaps, anomalous attenuation been observed at Arecibo will be easier explained by multiple scattering mechanism.

Main conclusions of analytical theory have been confirmed by the quite independent method of Monte-Carlo simulations. The results are also presented at this symposium as poster paper.

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So, we have two mechanisms of anomalous attenuation. And question arises: where each of them is of importance? We answer by the following table.

Mode conversion mechanism does not affect the probe x-wave. That is why the first line is evident.

In case of natural ionosphere and in case of reflection from outside of heating region the mechanism of amplification of small-scale irregularities (such as thermal parametric instability) is absent. That is why it is improbable that mode conversion mechanism could significantly contribute there. The only possible exclusion is auroral latitudes of natural ionosphere.

The most interesting case is reflection of ordinary probe wave from inside the heating region. Here the thermal parametric instability supplies high level of small-scale irregularities. And it is known that kilometer-scale irregularities are developed side by side with artificial turbulence of other scales. Thus, both mechanisms can act here jointly.

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How one can divide contributions of two mechanisms and use them for irregularity diagnostics when they act jointly? We suggest the following procedure.

The first step is using of extraordinary probe wave for kilometer-scale irregularity diagnostics. Here one deals with only multiple scattering mechanism.

We planned to carry out such experiment at Sura facility by this symposium. However life has introduced its corrections. The experiment has been delayed due to difficulties with maintenance of the Sura facility. But I have possibility to illustrate this step by successful realization of this approach under natural conditions.

The work included: vertical sounding using digital ionosonde "PARUS" at Troitsk, data processing in order to determine the anomalous attenuation values, implementation of our algorithm of the inverse problem solving which output is irregularity parameters.

The second step is calculation of multiple scattering contribution into the ordinary probe wave anomalous attenuation. Information about the irregularity spectrum obtained at the first step is used. Solution of the direct problem in the framework of our theory is to be used.

The third step is using of the mode conversion theory relations to determine the small-scale irregularity level from the remainder of the ordinary wave anomalous attenuation.

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While new experimental data are absent, we apply the inverse problem solving technique to existing anomalous attenuation data obtained for reflections outside the heating region. I mentioned these results at the beginning of my report.

The work essence is the following. The same irregularities are responsible for anomalous attenuation of both ordinary and extraordinary probe waves in this case. That is why the inverse problem must give the same altitude dependence of the irregularity level for both ordinary and extraordinary wave data.

If we assume purely linear dependence of the irregularity level on altitude, we obtain similar but different parameters for this dependence from ordinary and extraordinary wave data. However, if we assume that some "hump" exists in the heating region (caused by more rapid irregularity growth there), we obtain very good agreement. Quite natural result!

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Our conclusions:

• • Multiple scattering effects are of importance for interpretation of results of heating experiments. I spoke only about probe wave. But multiple scattering may influence spatial distribution of energy of pump wave. This circumstance can appear important for such projects as HAARP.
  • Effect of anomalous attenuation of extraordinary probe wave deserves of detail study (it gives direct information on artificial kilometer-scale irregularities).
  • And the last remark. The theory is ready for describing and utilization of the forthcoming experimental data.

Oral presentation - slides

1. Anomalous attenuation under ionospheric heating:

Classical examples

Unusual example of anomalous attenuation (probe waves are reflected from outside of the heating region, both modes are weaken equally)

(According to L.M.Erukhimov, G.P.Komrakov, V.L.Frolov, 1980)

2. Anomalous attenuation under natural conditions:

Dynasonde data

Comparison of un–spread ionograms (part a, top) with fully–developed equatorial spread F (part b, bottom). Each part displays echo stationary–phase group range, R¢ (f) and echo intensity, dB(f). Four Huancayo dynasonde ionograms, 2040–2140 75°W, 83–03–14 (O–mode echoes only), are superimposed in each part: In (a), at 1630, 1635 LT (pre–sunset, with foE and Es–q near 100 km); and 1900, 1905 LT (post–sunset, after photochemical decay of D and E regions). A reference level of = 80 dB is marked in each panel. (From J. W. Wright, P. E. Argo and M.L.V. Pitteway, 1996)

3. The mode conversion mechanism of anomalous attenuation:

• • Interaction region ;

  • Mode coupling condition ;

  • Irregularity scale length ; — less than 50 m

  • O-wave only

Expression for the anomalous attenuation:

where , is plasma frequency, is dielectric tensor of regular plasma, , , is dispersion tensor for regular plasma, – the cofactor matrix, - refractive index of ordinary wave and is the unit polarization vector for ordinary wave, is the root of equation , corresponding to plasma waves. (A.G. Bronin, S.M. Grach, N.A. Zabotin, 1998 — Poster paper at this Symposium)

4. Multiple scattering as independent mechanism of anomalous attenuation

4.1. Criterion of multiple scattering regime:

Optical depth > 1

• mean field behaves so:

4.2. Theory of multiple scattering in a plane plasma layer:

Details of the theory can be found at http://www.rsu.ru/rsu/zabotin

¯

¯

¯

4.3. Numerical calculation results:

a) numerical estimates of analytical solution

Irregularity level = 0.003 in 1 km

Spectrum index = 2.5

Frequency = 6 MHz

Latidude of Nizhni Novgorod

Anomalous attenuation up to 15 dB

Main contribution - from kilometer-scale irregularities

Multiple scattering mechanism — low-latitude conditions:

Irregularity level = 0.003 in 1 km

Spectrum index = 2.5

Frequency = 6 MHz

Latidude of Arecibo

Anomalous attenuation up to 12 dB

b) Results of independent Monte-Carlo calculations

(N.A.Zabotin, E.S.Kovalenko, 1998 — Poster paper at this Symposium)

5. Where each of two mechanisms is of importance?

* MC - Mode Conversion mechanism; MS - Multiple Scattering mechanism

• • MC does not affect X-wave
  • The mechanism of amplification of small-scale irregularities (thermal parametric instability in case of heating) does not exist at natural conditions (except, probably, high latitudes)
  • Both O- and X-waves are equally weaken under natural conditions and outside of heating region
  • MC does not work at equatorial region
  • MC and MS affect O-wave jointly inside the heating region

6. How one can divide contributions of two mechanisms and use them for irregularity diagnostics when they act jointly (inside the heating region)?

6.1. First step - using of extraordinary probe wave for kilometer-scale irregularity diagnostics. Here one deals only with multiple scattering mechanism.

The first successful realization of this approach under natural conditions included the following:

• Vertical sounding using digital ionosonde "PARUS"
• Anomalous attenuation data
• Algorithm of the inverse problem solving
• Irregularity parameters

(A G Bronin, N A Zabotin, G A Zhbankov, I B Egorov, A L Karpenko, V V Koltsov, E V Kuznetsov; To be published at Geomagn. & Aeron., 1998)

6.2. Second step - calculation of multiple scattering contribution into the ordinary probe wave anomalous attenuation. Information about the irregularity spectrum obtained at the fist step is used.

• Solution of the direct problem is to be used

6.3. Third step - using of the mode conversion theory relations to determine the small-scale irregularity level from the remainder of the ordinary wave anomalous attenuation.

7. Solving the inverse problem for anomalous attenuation data obtained for reflections outside the heating region

(Data from: L.M.Erukhimov, G.P.Komrakov, V.L.Frolov, 1980)

• Results are in better agreement when growth of kilometer-scale irregularities in the heating region is taken into account.

8. Conclusions

• • Multiple scattering effects are of importance for interpretation of results of heating experiments
  • Effect of anomalous attenuation of extraordinary probe wave deserves of study in more details (it gives direct information on artificial kilometer-scale irregularities)
  • The theory is ready to explain forthcoming experimental data