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 Multiple scattering from artificial irregularities, HF-induced in the ionospheric F region, may cause significant attenuation of both ordinary and extraordinary radio waves in addition to the anomalous absorption of ordinary waves by their conversion into plasma waves. We have confirmed the existence and detailed features of this effect at the Sura heating facility by measurements of the attenuation of the powerful pump wave and weak probing waves of extraordinary polarization. Extraordinary waves are attenuated during heating, 1.5–12 dB below a background (nonheating) attenuation value caused by scattering from natural irregularities. Irregularities involved into the multiple scattering process have geomagnetic field-transverse scales of l⟂ ∼ 0.1–1 km. To determine characteristics of these irregularities, a simple inverse problem solution procedure is implemented.
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 Anomalous attenuation of radio waves reflected in an HF-heated region of the ionosphere has been observed in ionospheric modification experiments since the early seventies [Allen et al., 1974; Belikovich et al., 1975; Berezin et al., 1987; Frolov et al., 1997]. Main attention was given to the anomalous attenuation of ordinary waves not caused by electron collisions. Also known as “anomalous absorption” (AA), this phenomenon is caused by nonlinear conversion of ordinary waves into upper hybrid plasma waves when scattered by small-scale (l⟂ ∼ 1–50 m) field-aligned irregularities. The theory of this conversion is well developed [see, e.g., Vas'kov and Gurevich, 1975; Grach et al., 1978; Das and Fejer, 1979; Robinson, 1989; Gurevich et al., 1996; Bronin et al., 1999a]. A similar effect for extraordinary waves was neglected by experimenters because nonlinear interaction of extraordinary waves with plasma waves is not possible in the ionosphere [Gurevich, 1978]. Nevertheless, there are some experimental data demonstrating rather high anomalous attenuation for extraordinary waves [Belikovich et al., 1975; Erukhimov et al., 1980; Frolov et al., 2000]. Erukhimov et al.  suggested that anomalous attenuation for both X- and O-mode probing waves is determined by aspect-sensitive scattering from HF-induced irregularities with spatial scales l⟂ ∼ 100–200 m across the geomagnetic field lines. To explain this phenomenon in detail, considerable attention has been focused recently on the theory of multiple scattering from intermediate-scale (l⟂ ∼ 0.1–1 km) plasma density irregularities [Bronin and Zabotin, 1992; Zabotin, 1993; Zabotin et al., 1998; Bronin et al., 1999c; Zabotin et al., 2001]. It has been established by theoretical calculations [see, e.g., Zabotin et al., 1998] that multiple scattering causes a spatial redistribution of the radiation, leading to a significant decrease of intensity (10–15 dB and more) in the vicinity of a sounding station, compared to measurements carried out in the smooth ionosphere. Thus, when intermediate-scale and small-scale irregularities are developed together, multiple scattering may cause attenuation of extraordinary waves and contribute to the total attenuation of ordinary waves.
 Our present purpose is three-fold: to study features of anomalous attenuation for both pump and probing extraordinary waves experimentally, to suggest a mechanism explaining this phenomenon, and to demonstrate the possibility to use X-mode sounding for diagnostics of artificial plasma turbulence. The experimental results have been obtained in a dedicated experimental campaign at the Sura heating facility near Vasil'sursk, Russia (56.13°N latitude, 46,10°E longitude) performed in September 1999. HF waves of both ordinary and extraordinary polarization (frequencies 5.752 or 7.815 MHz, with effective radiated power 150 and 250 MW, respectively) were used for ionosphere modification. We used cycles of 3 or 5 minutes “on” to create saturated turbulence, at least for irregularities with l⟂ ≤ 1 km, and 7 or 10 minutes “off” to approach practically “cold-start” conditions.
2. Theoretical Grounds for the Anomalous Attenuation Effect
 The AA for ordinary waves is closely connected with generation of artificial small-scale (l⟂ ≤ 50 m) field-aligned irregularities [Frolov et al., 1997]. These striations are produced in a plasma by development of the thermal (resonance) parametric instability of the O-mode HF pump wave (PW) in overdense ionosphere heating at vertical incidence [Vas'kov and Gurevich, 1975; Grach et al., 1977; Das and Fejer, 1979; Gurevich et al., 1995; Istomin and Leyser, 1997]. Conversion of PW energy into upper-hybrid plasma waves is accompanied by growth of the irregularities, and a decrease in amplitudes of both the PW and O-mode probing waves sounding the disturbed volume at frequencies close to the PW frequency. The AA magnitude may be greater than 20 dB, depending strongly on PW power and other parameters [Belikovich et al., 1975; Robinson, 1989]. For a known irregularity spatial spectrum it may be most conveniently estimated using the conversion cross-section value [Bronin et al., 1999a]. A typical AA development time ranges from a few hundred milliseconds to a few seconds after PW “on”.
 The AA affects only ordinary waves because extraordinary waves are reflected below the upper-hybrid resonance region. In contrast, even in absence of mode conversion, scattering from intermediate-scale irregularities can affect both O- and X-mode waves. Such irregularities occur often in the natural ionosphere [see, e.g., Szuszczewicz, 1987]. They are also generated in heating experiments by, for example, the self-focusing instability of the PW [Vas'kov and Gurevich, 1976]. It should be mentioned that measurements of radio wave attenuation in the unperturbed ionosphere [Setty et al., 1971; Vodolazkin et al., 1983; Bronin et al., 1999b] have demonstrated anomalously high values that cannot be explained by reasonable collisional losses. Since the intensity of small-scale natural irregularities in the unperturbed midlatitude ionosphere is typically very small [Szuszczewicz, 1987], the mode conversion mechanism cannot explain this attenuation, whereas multiple scattering is a good alternative candidate.
 A theoretical description of multiple scattering from the ionospheric irregularities is a fairly complex problem, even for the geometry of vertical sounding. Generally, it is necessary to take into account the regular refraction as well as the gyrotropy of the medium. If only the intensity of the reflected signal is of interest, the problem may be solved by means of radiative transfer theory [Bronin and Zabotin, 1992; Zabotin, 1993; Zabotin et al., 1998; Bronin et al., 1999c]. For a randomly irregular plane ionospheric layer this approach offers an approximate solution in analytical form. According to Zabotin et al. , the energy flux at a point with coordinate on the Earth's surface may be written as
 Here P0 is the flux of radiation energy at the point in absence of scattering; θ1 and φ1 are effective angles of arrival of the energy flux, determined by the following transcendental equation:
where is the point of arrival at the Earth's surface of the ray that (in absence of scattering) has the angles of arrival θ, φ; the quantity depends jointly on the geometry of the ray paths in a plane layer, and the spatial spectrum of the irregularities.
 From expressions (1) and (2) it follows that an observer situated at the point will detect two effects caused by multiple scattering: (i) a change of the arrival angles, and (ii) alteration of the received signal intensity. A sharp decrease of intensity is indicated very near a sounding station, and a slight increase at larger distances. According to Zabotin et al. , at midlatitudes the anomalous attenuation, defined as L = 10 · lg(P0/P), can be 10–15 dB or even more.
 Expression (1), together with the ionospheric layer profile and parameters of the spatial spectrum of plasma density fluctuations, provide the basis for a quantitative model of anomalous attenuation. For diagnostics of ionospheric irregularities the model can be applied to the inverse problem: plasma-fluctuation spectral parameters are determined by fitting the experimental data by least squares. With measurements of extraordinary wave attenuation, we might hope to use the following analysis scheme: (i) estimation of intermediate-scale irregularity spectrum parameters; (ii) separation of the multiple-scattering and mode-conversion contributions to the total anomalous attenuation of the ordinary wave; and finally, (iii), estimation of the spectral properties of small-scale striations. Full implementation of this procedure, however, requires extended data sets that currently cannot be provided by the equipment available. For example, simultaneous measurements of ordinary and extraordinary wave attenuation, using a fine frequency grid, are desirable, but have not yet been performed. Absolute attenuation measurements would be useful also. In particular, the “background” fraction attributable to natural irregularities should be determined, before heating of the ionospheric plasma. However, at present we obtain only relative estimates of anomalous attenuation. Nevertheless, we will show below that some valuable results may be obtained from the available data.
3. Experimental Results
 Experiments at the Sura heating facility on September 6, 7, and 9, 1999 were conducted in evening and night hours when the linear (collisional) absorption of radio waves in the ionosphere D and E regions was negligible. The ionosphere was heated by coherent HF radiation from three transmitters, each with 250 kW of output power. With antenna gain, the effective radiated power (ERP) was 150 MW ERP at 5.75 MHz and 250 MW ERP at 7.8 MHz. In the September 9 session the heater power was varied from cycle to cycle, but we have used data relating to 150 MW ERP only. The heating cycle on September 6 and 7 was 5 minutes on and 10 minutes off; on September 9 the scheme was 3 min on, 7 min off. The useful measurement interval was about 4 hours (15 heating cycles), 3 hours (12 heating cycles), and 5 hours (12 heating cycles) on 6, 7, and 9 September, respectively. In the experiment of September 6 heating used O-mode PW at 5.752 MHz; X-mode probe waves were recorded at 7 frequencies: 4.069, 4.669, 5.669, 6.069, 6.269, 6.424 and 6.849 MHz. The experiment of September 7 used 7.815 MHz X-mode PW; amplitudes of X-mode probing waves were recorded at 6 frequencies: 5.424, 6.624, 7.224, 7.624, 7.789 and 8.024 MHz. On September 9 X-mode PW at 5.752 MHz was employed; the amplitudes of X-mode probing waves were recorded at 7 frequencies: 4.469, 4.969, 5.369, 5.569, 5.769, 5.969, 6.169 MHz. A “Katran” receiver (pass band 4 kHz) was used for registration and digitization of the PW amplitude, and “Brusnika” receivers (pass band 1 kHz) were used for registration and digitization of the probing wave amplitudes. Probe waves with a pulse duration of 100 μs were linearly polarized. Ionospheric echoes were received by an antenna array of extraordinary polarization with 15 dB suppression of the ordinary component.
 During the heating experiments, both vertical and oblique ionosphere sounding monitored the electron density profile. According to ionosonde data, foF2 exceeded the PW and probing frequencies, except at the end of the September 7 session, so seven cycles at the highest probe frequency have been excluded from data processing for that case.
 The amplitude time series of a probe wave and the PW for the September 6 session are shown in Figure 1; the time interval between data points is 0.2 sec. The effect constituting the subject of the paper is plainly evident in this format: It can be clearly seen that periods of heater turn-on are accompanied by a significant decrease in the amplitude of the probing waves.
 To determine the essential features of this phenomenon it is useful to smooth the amplitude time-variations by superposed epoch averaging. This is shown for the data of September 6, 7 and 9 in Figures 2–4 respectively. Four distinct stages of probe signal evolution may be distinguished. The first stage, immediately preceding ‘PW-on’, is characterized by random natural variations around a median value Aoff. Just after PW-on there is a transitional stage in which the general signal amplitude decreases gradually to a smaller value Aon. This is the development stage of the anomalous attenuation effect. During the next stage, lasting until PW-off, there are random amplitude variations around Aon, more rapid than in the first stage. After PW-off a relaxation stage occurs, as the ionosphere restores to its natural state and the signal amplitude increases gradually to the initial median value Aoff. With some inessential variations, this behavior is typical for all probe-wave frequencies and during all observation days. Features of the reflected PW amplitude are also of interest. There is nothing exceptional in the attenuation of the ordinary PW for the data obtained on September 6 (Figure 2): This effect is attributed mainly to the mode conversion mechanism and has been studied thoroughly [Belikovich et al., 1975; Robinson, 1989]. In our measurements the AA magnitude was about 11 dB, and the development time was nearly one second, in accord with commonly accepted features of the thermal parametric instability. Anomalous attenuation of the X-mode probe waves develops on a much longer timescale; therefore, this attenuation is not associated with the small-scale striations that cause AA. Small-scale irregularities develop very efficiently by the O-mode PW which power is extremely high in this case, with rapid development of O-mode anomalous absorption. Furthermore, for such heating power large-scale (>10 km) irregularities are strongly generated in the disturbed volume influencing the signal intensity [Zabotin and Zhbankov, 2000]. It is difficult to distinguish the effect of scattering of the O-mode PW in the background of these powerful effects, but it is certainly present. More important is the significant magnitude of anomalous attenuation, which occurs for the extraordinary PW used on September 7, and 9 (see Figures 3 and 4). Attenuation of ∼12 dB developed in about 40 s on September 7, and 4–5 dB in ∼20 s on September 9. When combined with earlier obtained results [Erukhimov et al., 1980; Frolov et al., 2000], we conclude firmly that anomalous attenuation of extraordinary waves (both probe and pump) is a phenomenon quite typical of heating experiments.
 There are some other common features of the data presented in Figures 2–4 that are not connected directly with heating. For example in Figure 2, near 30, 350 and 380s, sudden changes of the probing wave amplitudes are observed simultaneously at all frequencies. This is a result of the ionosonde activity: An ionosonde used in our experiments is located near the receiving installation site and radiated with a period of 15 min, resulting in additional interference. We have excluded such time intervals from data analysis.
 We characterize anomalous attenuation by the decibel weakening of the wave intensity, LR = 20 · lg(Aoff/Aon). Two other parameters of interest are the development and relaxation times, τdev and τrel. They are determined by fits to the averaged data within corresponding temporal intervals: A(t) = Aon + (Aoff − Aon) exp (−t/τdev) for t ≥ ton and A(t) = Aon + (Aoff − Aon)[1−exp(−t/τrel)] for t ≥ toff. The results appear in Figures 5–7. The maximum and minimum LR are about 9.6 dB and 1.5 dB respectively, in Figure 5. We estimate the instrumental error to be less than 1 dB. All three data sets show a common tendency, with LR gradually decreasing as probe frequency increases. This result differs significantly from that of Erukhimov et al. , where the attenuation was found to increase with increasing frequency. The distinction can be explained by a huge difference of PW power: 20 MW ERP in the experiments reported by Erukhimov et al. , and 150–250 MW ERP in our present measurements. Control measurements performed in August 2000 have fully confirmed this conclusion, suggesting that more powerful HF waves lead to creation of stronger irregularities in a wider height interval, so that more anomalous attenuation is manifest at lower frequencies. However, further experimental and theoretical investigations are needed to gain an improved understanding of this phenomenon.
 The characteristic times τdev and τrel do not demonstrate any regular dependence with probe frequency. However, for each of the three sequences the maximum development times are observed for probe waves reflected in the central part of the heating region, close to the PW reflection level. Most τdev values are in the range 5–40 s, nicely corresponding to the development time for artificial intermediate-scale irregularities [Frolov et al., 1997, 2000]. Notice that on September 9, with X-mode PW at 5.752 MHz, τdev remained near the smallest values, 2–5 s. The typical times for the three highest probe frequencies on September 7 differ noticeably from the common pattern: this may result from the proximity of these frequencies to the F2 critical frequency (f0F2 ≈ 7.9 MHz), and may also affect their relaxation times τrel. Excluding these considerations, τrel lies in the interval 13–70 s for all three sessions, and has only very small variations at a given frequency. One can see also that, as a rule, τdev ≤ τrel. These features of the characteristic times have a natural explanation if irregularity formation and decay are influenced by ambipolar diffusion. In the development stage, HF heating augments diffusion because the temperature and electron-density gradients coexist, whereas during relaxation this driving force is absent. There are no marked differences attributable to PW polarization.
4. Some Remarks on the Inverse Problem
 Following standard concepts [e.g., Erukhimov et al., 1987] we suppose that artificial irregularities ΔN/N in the scale length range of interest are strongly extended along the geomagnetic field lines; we characterize them by the following simple power spatial spectrum:
where ϰ⟂ is the component of irregularity harmonic orthogonal to the geomagnetic field lines, ϰ0⟂ = 2π/Lm, Lm is the irregularity outer scale length, and δ(x) is the Dirac delta function. It is convenient to normalize the spectrum by the structure function value , defined for the scale length R = l⟂ = 1 km. Details of this procedure can be found in [Zabotin et al., 1998]. Thus the spectrum is characterized by three parameters, δR, p, and Lm.
 Our data are not sufficient to determine these spectrum parameters independently (mainly because of the small number of probe frequencies). To make progress, we assign to two of them rather typical predetermined values, Lm = 10 km and p = 2.5, and propose to look for a dependence of δR on altitude.
 Notice that our data cannot contain, in principle, any information about the background level of the attenuation caused by natural ionospheric irregularities, which must therefore also be modeled. For example, suppose that natural irregularities are described by the same spectrum (3), with the same parameters Lm = 10 km and p = 2.5, and that their amplitude (denoted as δN to distinguish it from the heating-induced δR) does not depend upon the altitude. In other words, we suppose that heating of the ionosphere causes only a modification in the altitude distribution of the amplitude of the plasma density irregularities, while their spectral index remains unchanged. In this case the quantity δN is a free parameter in our calculations. This model of the turbulence spectrum is not entirely adequate for either natural or artificial irregularities: real spectra demonstrate somewhat different behavior for different scale length ranges [Szuszczewicz, 1987; Erukhimov et al., 1987]. In case of artificial turbulence, the spectrum often shows a maximum in the scale range l⟂ ∼ 0.1–0.5 km [Erukhimov et al., 1980, 1987; Frolov et al., 2000]. This paper does not provide an ultimate diagnostic procedure taking into account the diversity of real spectra and electron density profiles; results in this section demonstrate only some scope for such diagnostics.
 The general scheme for calculation of the irregularity amplitude is as follows (see also Figure 8). First, we determine for each probe frequency the background attenuation LN corresponding to the given value of δN. The total attenuation after complete development of the effect is L = LN + LR, where LR is the experimentally determined quantity (see the previous section). The resulting value of δR can be determined by solving the equation
where is given by the expression (1), which is a nonlinear function of δR. The resulting nonlinear equation (4) can be solved numerically by a simple method (e.g., dichotomy).
 We use two simplifications in our calculations: Linear segments replace the real electron density profile, with the appropriate reflection-level gradient for each frequency. This is acceptable because of the dominance of reflection-level irregularities in the multiple scattering process. Also, we ignore the influence of the geomagnetic field on the ray path, and assume an isotropic plasma for the calculation of P.
 The dimensionless quantity ΔN/N depends not only on electron density perturbation ΔN, but also on the mean value, N, which changes significantly in the range of altitudes considered. On the other hand, one would expect that for irregularities generated in the vicinity of the PW reflection level, field-aligned (ambipolar) diffusion tends to equalize ΔN. Thus ΔN may give more valuable physical information for artificial irregularities. Thus we present results obtained by solving the inverse problem in the form of ΔNvs. altitude dependencies for different values of δN (Figure 9).
 Consideration of the results in Figure 9 shows, first of all, that artificial irregularities with l⟂ ∼ 0.1–1 km are detected in a wide altitude range, >40 km, evidently limited by the probe frequencies used. This extent significantly exceeds that of the resonance region (about 1–5 km) where artificial plasma turbulence is directly exited by HF ionosphere heating. Increasing the probe frequency range would test the presence of artificial irregularities at other altitudes. Choosing larger δN results in larger ΔN, developing more rapidly for higher altitudes. The condition δN = 0 results in a pronounced general tendency for ΔN to decrease with altitude, which is difficult to explain. However, even for a relatively low and quite realistic value of δN ≈ 0.001, we obtain a rather reasonable dependence of ΔN on altitude.
 An important result of the September 1999 heating campaign at the Sura facility is the clear demonstration of consistent and significant (1.5–12 dB) anomalous attenuation of both pump and probing extraordinary waves. This cannot be explained by the mode conversion mechanism involving small-scale (l⟂ < 50 m) field-aligned irregularities, which is active solely for ordinary waves. We suggest another attenuation mechanism which is independent of their polarization, based on multiple scattering from plasma density irregularities with scale lengths l⟂ ∼ 0.1–1 km. Correspondence of theory and experiment in this work accords with other evidences of the significant role of multiple scattering in radio sounding of the natural and HF-pumped ionosphere.
 Another interesting conclusion follows from the similarity of anomalous attenuation that results from O-mode and X-mode heating. The weak dependence of intermediate-scale irregularities on pump wave polarization suggests something like the self-focusing instability as a candidate mechanism.
 The very high PW power (150–250 MW ERP) used in these experiments might create some complications, for example, by generation of strong large-scale irregularities (>10 km). Multiray reflections from large-scale irregularities are accompanied by an increase of the averaged signal amplitude [Zabotin and Zhbankov, 2000], an effect clearly seen in the PW amplitude of Figure 2: After reaching a minimum value, the PW amplitude is slightly increased. According to Berezin et al. , this occurs when pump power exceeds 20 MW ERP. The increase can coexist with (and thus diminish the apparent effect of) anomalous attenuation. Therefore, performing experiments with rather low pump power would be of particular interest, when anomalous attenuation could be observed in pure form.
 A simple algorithm for solving the inverse problem has been implemented in this work to find the distribution of the HF-induced intermediate-scale electron density disturbances ΔN in a wide range of altitudes. The calculations give reasonable values of ΔN, which are in good agreement with modern concepts of artificial irregularity formation. This is a direct opportunity to measure the ΔN distribution along geomagnetic field lines. Only the probe-wave frequency range limits the altitude interval for this diagnostic. We look to improvements of the method: in particular, simultaneous measurements of anomalous attenuation for extraordinary and ordinary waves will provide diagnostics of very different scale lengths: small (∼1–50 m) and intermediate-scale (∼100–1000 m) irregularities. Advanced techniques should also provide the possibility to measure the background anomalous attenuation caused by natural irregularities.
 The work was carried out under the support of the Russian Foundation for Basic Research (grants 99-02-17525, 99-02-16479, and 02-02-17475).