Український Науково-Технологічний Центр



Science and Technology Center in Ukraine

Project P-330

Application of the “self-scattering effect” to DPS-based diagnostics of HF-stimulated ionospheric irregularities

Technical report for Milestone 2 of Stage 2

Developing a physical model of the self-scattered signal excitation

| | |Volodymyr Galushko |

| | | |

| | | |

| | |Manager, Project № P-330 |

| | |PhD, Senior Scientist |

| | | |

| | |“ 23 ” December, 2008 |

Kharkiv-2008

|Project manager: Volodymyr G. Galushko, PhD |

|Phone: +38 057 7203 579, Fax: +38 057 7203 462, |

|E-mail: galushko@rian.kharkov.ua |

|Institutions: Institute of Radio Astronomy, National Academy of Sciences of Ukraine (IRA NASU) |

|Financing parties: USA |

|Operative commencement date: 01.09.2007 |

|Project duration: 3 years |

|Date of submission: “ 23 ” December, 2008 |

Abstract

Among the goals of Project P-330 one is “Developing a physical model of the self-scattered signal excitation” (Stage 2). This envisages construction and analysis of a theoretical model of the regular spatial structure produced by the powerful radio wave near the reflection level in the ionosphere. The reason is that the intensity of HF-induced irregularities depends on the heating signal power. Hence, it can be expected that the spatial distribution of artificial irregularities in the ionosphere should follow, to a certain extent, the field pattern produced by the incident and ionosphere-reflected signals from the powerful HF heater. This effect may influence the scattering characteristics of the HF-modified region in such a way to facilitate excitation of ionospheric interlayer duct channels by the self-scattered signals.

The Technical Report covering Stage 2 of the Project presents results of a theoretical analysis of the spatial field structure produced by the powerful radio wave in the ionosphere. The problem was treated within the ray optics approximation for a parabolic model of the electron density distribution in the ionosphere. A set of computer simulations has been performed and analyzed in dependence on the ionsopheric layer parameters, specifically the signal-to-critical frequency ratio, [pic]. It is shown that the field pattern in the ionosphere may assume a vertically stratified structure which can support excitation of ionospheric interlayer duct channels. The results obtained will be taken into account when analyzing scattering patterns and spectral characteristics of the self-scattered signals (Stage 3).

1. Introduction

Over the recent decades the ionosphere is increasingly used as a laboratory in which controlled active plasma experiments are performed. The first ionospheric modification facility was built in Colorado in 1971, followed by HF heaters in Puerto Rico, Russia, Norway and Alaska. Farley [1] and Gurevich [2] considered the possible modification effects of a powerful HF radio wave on the ionospheric F-region which consists primarily in a heating of the electron gas. However, the present interest is no longer focused on classical modification effects, but mainly on plasma turbulence excited in different frequency domains, corresponding to ion-acoustic, lower hybrid, Langmuir, upper hybrid and electron Bernstein wave modes. Studying the ionospheric effects which occur under the action of powerful HF radio emissions is of importance for understanding the mechanisms of plasma instability and generation of artificial irregularities which may affect the propagation of radio waves in a variety of frequency ranges. Such studies underlie new approaches to plasma diagnostics in the ionosphere, permitting one to better understand the physics of many processes in the geospace.

The diagnostic and investigation of the stimulated small-scale ionospheric irregularities is done within various radar-based methods. The techniques most widely used include the Doppler shift based registrations of HF sounding signals on either vertical or oblique propagation paths, HF and/or VHF backscatter radars and incoherent scatter radars. The characteristics of interest are rise and fall times, hysteresis effects, spatial spectra of the inhomogeneities, etc. (see, for instance, [3-6]).

The current Project suggests using the fundamental and a few higher-order harmonics of the emission from a heating facility for diagnostics of stimulated ionospheric inhomogeneities through observation of the self-scattering effect (SS) discovered by the team of Prof. Yuri Yampolski (the Institute of Radio Astronomy, National Academy of Sciences of Ukraine). Systematic observations of the fundamental and higher transmitted harmonics of the EISCAT, Norway аnd Sura, Russia heaters have shown that the powerful HF radio wave producing the “heating” effect is scattered itself from the stimulated inhomogeneities, demonstrating a fairly broad Doppler frequency spectrum. The Doppler shift occasionally may be as high as a few hertz [7]. A most interesting observational result of the Ukrainian group was that the scattered spectra of the kind could be detected simultaneously at several greatly separated reception points. The high level of correlation demonstrated by temporal variations of the self-scattered spectra at different observation sites suggested the source of the broadband signals to lie on a section common to all the propagation paths, hence somewhere in the heated volume (i.e. the disturbed area above the powerful transmitter).

So, the Project addresses three principal questions, namely identification of generation mechanisms for the ionospheric inhomogeneities; identification and study of propagation modes for the self-scattered signals, and application of the self-scatter effect for identifying and diagnosing the stimulated ionospheric inhomogeneities.

However, to answer the questions it seems expedient first to construct and analyze a theoretical model of the regular spatial structure produced by the powerful radio wave near the reflection level in the ionosphere. The reason is that the intensity of HF-induced irregularities depends on the heating signal power. Hence, it can be expected that the spatial distribution of artificial irregularities in the ionosphere should follow, to a certain extent, the field pattern produced by the incident and ionosphere-reflected signals from the powerful HF heater [8]. This effect may influence the scattering characteristics of the HF-modified region in such a way to facilitate excitation of ionospheric interlayer duct channels by the self-scattered signals.

The Technical Report covering Stage 2 of the Project presents results of a theoretical analysis of the spatial field structure produced by the powerful radio wave in the ionosphere. The problem was treated within the ray optics approximation for a parabolic model of the electron density distribution in the ionosphere. A set of computer simulations has been performed whose results show that the field pattern in the ionosphere may assume a vertically stratified structure which can support excitation of ionospheric interlayer duct channels. The results obtained will be taken into account when analyzing scattering patterns and spectral characteristics of the self-scattered signals (Stage 3)

1. Problem formulation and basic relations

As is known [9], the basic features of the F-layer modification are determined by the resonance processes of interaction between the pump wave and eigenmode oscillations of the ionospheric plasma. For a powerful HF wave at a given frequency [pic], there is an entire resonance layer of efficient plasma-wave interaction whose lower and upper boundaries correspond to the heights where the conditions of the upper hybrid, [pic], and Langmuir, [pic], resonances are met, respectively. This range is characterized by a rather complex field distribution produced by superposition of the incident and reflected pump waves. This may produce an additional nonlinearity due to the so-called differential heating, i.e., enhanced heating in the regions of enhanced wave intensity, giving rise to a pressure gradient force that pushes plasma from regions of higher wave intensity into regions of lower wave intensity. As a result, the spatial distribution of stimulated irregularities may show a vertically stratified structure which can be responsible for scattering of the proper emission from a heater. For this reason we have found it expedient to analyze the regular field pattern produced by a powerful HF wave near the reflection level in the ionosphere.

Consider a plane stratified ionosphere, the problem geometry is shown in Fig. 1. The problem will be treated within the ray optics approximation which provides a sufficient accuracy anywhere except caustic surfaces. The field amplitude [pic] at a point 1 is a sum of all the rays that arrive from a source located in the coordinate origin,

[pic], (1)

where [pic] and [pic] are amplitudes and phases of partial waves, the summation is over all the rays that can arrive at the observation point, including direct and those reflected from the ionosphere. The reflection condition follows from the Snell’s law and can be written as

[pic], (2)

where [pic] is the refractive index, with [pic] being the plasma frequency. Here we assume that [pic]. So, if the condition Eq. (2) is met along the way from the transmitter to the observation point, then the ray is treated as a reflected one. Otherwise it is a direct ray.

Fig. 1. Problem geometry

According to [10] filed amplitude [pic] at an arbitrary distance from the source can be represented as

[pic]. (3)

Here [pic] is a factor to characterize the radiation properties of the source (power and antenna pattern); [pic] is a horizontal distance to the observation point (at a height [pic]) equal to

[pic] (4)

for the direct rays while

[pic], (5)

for the reflected rays, with [pic] being the reflection height that can be determined from Eq. (2); and the exponential factor [pic], where [pic] (the signs “-” and “+” correspond to the incident and reflected waves, respectively), takes into account an additional phase shift that appears if the ray touches a caustic surface.

The ray phases are determined through integration of the refractive index along the trajectory [pic] to the observation point, viz.

[pic], (6)

where [pic] is the wavenumber, with [pic] being the wavelength.

In the ray coordinates Eq. (6) can be brought to the form

[pic] (7)

for the direct rays while

[pic] (8)

for the reflected rays.

Hence the calculation algorithm for the spatial field distribution near the reflection level in the ionosphere includes stages as follows:

1. Determination of all the rays arriving at a point [pic] through solving the respective trajectory equation (Eqs. (4) and (5)).

2. Calculation of the wave amplitudes and phases making use of Eqs. (3), (7) and (8).

3. Evaluation of the resultant field amplitude after Eq. (1).

It should be noted that HF heating of the ionosphere is normally performed at frequencies slightly below the critical one. For this reason further analysis will be performed for a parabolic distribution of the electron density which is a good approximation in the vicinity of the ionospheric maximum.

2. Spatial field distribution in a parabolic ionospheric layer

In this Section we will obtain specific expressions for calculating HF field distribution near the reflection level in a parabolic ionospheric layer with the following electron density distribution

[pic]

Here [pic] is the peak electron density in the layer, [pic] is the height of the layer maximum, and [pic] is the half-width of the layer.

Accordingly for the refractive index we have

[pic] (9)

where [pic] is critical, i.e. maximum plasma frequency of the layer.

Substitution of Eq. (9) into Eq. (2) yields the reflection height in the ionosphere, viz.

[pic]. (10)

Now we can obtain expressions for trajectories of the direct and reflected rays. By combining Eq. (9) with Eqs. (4) and (5), we arrive with account of Eq. (10) at

[pic] (11)

for the direct rays, while at

[pic], (12)

where [pic] and [pic].

Proceeding from Eqs. (11) and (12) we can obtain the derivatives [pic] figuring in Eq. (3), viz.

[pic]

[pic] (13)

[pic]

for the direct rays and

[pic]

[pic] (14)

[pic]

for the reflected rays.

Now we have all the expressions which are needed for calculating amplitudes of partial waves arriving at the observation point. However to find the resultant field distribution it is necessary to derive expressions for their phases. To that end let us substitute Eq. (9) into Eqs. (7) and (8) and integrate the result over trajectories of the direct and reflected rays to obtain, respectively,

[pic] (15)

and

[pic] (16)

for the direct and reflected waves.

So, now we are in a position to analyze spatial field distributions near the reflection level in dependence on the parameters of the ionospheric plasma. This was done with the use of a special software package developed within the Project. Some results are presented in the next section.

3. Results of computer simulations and discussion

Numerical analysis of the spatial field distribution near the reflection level in the ionosphere was performed with the use of a software package written in the MatLab computer language based on the expressions of Section 2. The program consists of two computer codes. The first one is intended for calculation and visual representation of ray trajectories launched at a zenith angle [pic] from the point of the source location with coordinates [pic], [pic] (see Fig. 2), while the second allows computing spatial field distributions over a 2D area. It is supposed that the ionospheric layer occupies the height range from [pic] to [pic]. Ray trajectories are calculated using a subroutine function CalcRay. The command call line is as follows:

[XU,ZU,Zt] = CalcRay(Zm,Ym,Fcr,F,Teta,X0,Z0,dX,dZ).

Fig. 2. Coordinate frame for calculating ray trajectories

The input parameters are the height of the layer maximum (Zm, km); layer half-thickness (Ym, km); critical frequency of the ionosphere (Fcr, Hz); radiated signal frequency (F, Hz); zenith angle of the ray departure (Teta, rad); coordinates of the ray departure point (X0 and Z0, km); array of two elements (dX and dZ, km) specifying the range XOZ where ray trajectories are constructed. At the output we have arrays of coordinates for ray trajectories (XU and ZU, km) and reflection height (Zt, km). If there is no reflection, then Zt= NaN (Not-a-Number).

The formulas of Section 2 have been generalized to the case of arbitrary coordinates of the ray departure point and zenith angles ([pic]). This has allowed placing the source at an arbitrary point in space, including inside the ionospheric layer. If the source is located within a “forbidden” area, then XU and ZU both assume NaN. The number of points to be calculated for each trajectory is given by the step dZr along the vertical inside the layer. By default the step is equal to the radiated signal wavelength.

Visual representation of the calculated trajectories is performed using the RayAreaPlotter program. The code is presented in the MatLab-script format. The routine generates initial parameters for the CalcRay procedure and calls it individually for each value of the zenith angle. The obtained arrays of ray trajectory coordinates are used for visual representation of the trajectories within the X0Z range. The number of rays and the amount of points along each ray trajectory is confined by the Random Access Memory (RAM) available for the MatLab system.

Fig. 3 presents several examples of calculating ray trajectories for a source located in the frame origin.

|[pic] |[pic] |

|a) |b) |

|[pic] |[pic] |

|c) |d) |

Fig. 3. Ray trajectories calculated for a parabolic layer with [pic]300 km, [pic]100 km and [pic]5 MHz. The source is located in the frame origin (Хо = Yo = 0 km). The radiated frequency [pic] assumes magnitudes 10 MHz (a); 7 MHz (b); 5.15 MHz (c) and 4.999 MHz (d)

As can be seen, with the heating frequency greatly in excess of the critical one (Fig. 3a) the ray trajectories are close to straight lines and show a practically uniform distribution over the XOZ region. The field above the heater is formed by the direct rays only, and hence the Joule heating mainly contributes to the plasma modification. As the radiated frequency approaches the critical one, the role of reflected waves becomes more essential and one can see regions with a higher density of the ray trajectories (Figs. 3b and 3c). In this case the condition of the upper hybrid resonance can be satisfied for the pump wave which mechanism is more efficient for plasma turbulization as compared with the Joule heating [9]. When the pump frequency is lower than the critical one (Fig. 3d) all rays are reflected from the ionosphere and the Langmuir resonance heating occurs in the ionosphere near the reflection level.

Analysis of the spatial distribution of ray trajectories suggests that greatest variations in the resultant field amplitude can be observed when the heating frequency is slightly higher than the critical frequency. Such cases were analyzed in more detail using the program for field amplitude calculations.

The program consists of the main module AmpCalc written as a MatLab-script file and several subprocedures. The main input parameters of the program are the critical frequency, Fp, in MHz; pump frequency, F, in MHz; height of the layer maximum, Zm, in km; layer half-width, Ym, in km; zenith angle of the radiation pattern orientation, TetaA, in degrees; azimuth of the radiation pattern pointing, FiA , in degrees; main lobe width, dA, in degrees; antenna pattern width, DA, in degrees; 1D array, D, of the observation points along the horizontal distance in meters; and 1D array, ZVar, of the observation points along the vertical in meters. In the current version of the program the XOZ range containing the set of the observation points should be specified inside the ionospheric layer ([pic]) within the first quadrant of the coordinate frame. For every of the observation points the total number of direct and reflected rays is calculated using the functions R_Dir and R_Ret, respectively. Then the functions R_Dir_3 and R_Ret_3 are involved to calculated zenith angles for each of the rays arriving at the observation point to within a specified accuracy (the default value of the error is 0.1 m). The determined zenith angles are used in calculations of the ray amplitudes which are computed with the functions A_Dir and A_Ret for the direct and reflected rays. The radiation patter is allowed for as

[pic]

with [pic] and [pic].

Here [pic] and [pic] are the zenith angle and azimuth of the antenna pattern maximum, respectively, [pic] is the departure angle of the ray within the vertical plane, [pic] is the main lobe halfwidth of the antenna pattern in radians, and [pic] is the total width of the antenna pattern.

The output of the program is a two-dimensional array of amplitudes in the nodes of the mesh of the observation points which also can be represented as equipotential curves of the field amplitude across the XOZ range. The graphics file in the MatLab (fig-file) is written in the hard disk along with the parameters of calculations (mat-file) which are

- coordinates of the observation points and the respective field amplitudes;

- number of the direct and reflected rays arriving at each observation point and the respective zenith angles;

- actual accuracy of the ray hit at the observation point;

- parameters of the ionospheric layer;

- source coordinates, radiated frequency and parameters of the radiation pattern.

The program was tested using a PC with the hardware and software configuration as follows: processor Intel Core 2 Duo 2.2 GHz, working storage 2 Gb, hard disk 250 Gb; and Windows XP Professional RUS SP3, MatLab 7.0.1 (R14) SP 1. The tests have shown that with the mesh cell of the observation points comparable with the radiated wavelength (50 to 100 m) and dimension of the XOZ range in a few kilometers along the height and distance the characteristic calculation time is several hours.

By way of example Fig. 4 presents spatial field distribution calculated for the ionospheric parameters and source characteristics identical to those used in the ray tracing whose results are shown in Fig. 3. As can be seen, the spatial field distribution demonstrates a quasiperiodic structure below the reflection level of the pump wave. The spatial period of the vertical stratification is about one half of the wavelength, i.e. 1 km in this case. Provided that the intensity of stimulated ionospheric irregularities is modulated by the pump field amplitude, one can expect creation of respective diffraction structures in the ionosphere which might be responsible for excitation and propagation of the self-scattered signals.

4. Conclusions

Following the Workplan for Stage 2 of the Project, equations have been derived and computation algorithms have been developed for the spatial filed distribution below the reflection level of an HF pump wave in the ionosphere. Based on the equations and algorithms a software program has been constructed for calculating HF field amplitudes. The program has been implemented in the MatLab environment and allows visual representation of the ray trajectories and resultant field distribution for a parabolic layer. Analysis of the HF field

[pic]

a)

[pic]

b)

Fig. 4. Spatial field distribution calculated for Хо = Yo = 0 kм, Zm = 300 kм, Ym = 100 kм, Fp = 5 MHz, F = 5.001 MHz, TetaA = FiA = 0о, and dA = DA = 10о

distribution in dependence on the ionospheric layer parameters has shown that for the ionospheric conditions typical of the cases where the self-scattering was observed the resultant field amplitude demonstrates quasiperiodic structures below the reflection level of the pump wave. The structures like these can be responsible for creation and excitation of ionospheric interlayer duct channel supporting long-range propagation of the self-scattered signals.

References

1. D. T. Farley. Artificial heating of the electrons in the F region of the ionosphere. J. Geophys. Res., vol. 68 (1963), p.p. 401-413.

2. A. V. Gurevich. Effect of radio waves on the ionosphere in the vicinity of the F layer. Geomagn. and Aeron., vol. 7 (1967), p.p. 230-236.

3. V. B. Avdeyev, V. S. Beley, A. F. Belenov et al. A review of the results of studying HF signal scattering from an artificially stimulated plasma turbulence obtained with the UTR-2 radio telescope. Izv.VUZ – Radiofizika, vol. 37 (1994), p.p. 479 -492.

4. G. G. Getmantsev, L. M. Erukhimov, N. A. Mityakov et al. Aspect-sensitive scattering of HF radio signals from stimulated ionospheric inhomogeneities. Izv.VUZ – Radiofizika, vol. 19 (1976), p.p. 1909-1912.

5. T. L. Franz, M. C. Kelley, A. V. Gurevich. Radar backscattering from artificial field-aligned irregularities. Radio Science, vol. 34 (1999), p.p. 467-475.

6. D. L. Hysell, M. C. Kelley, Y. M. Yampolski, et al. HF radar observations of decaying artificial field-aligned irregularities. J. Geophys. Res., vol. 101(1996), p.p. 26981-26993.

7. Zalizovski et al. Spectral features of the HF signal from the EISCAT heater as observed in Europe and the Antarctic. Radio Physics and Radio Astronomy, vol. 9 (2004), 261-273.

8. B. N. Gershman, L. M. Erukhimov and Yu. Ya. Yashin. Wave processes in the ionosphere and space plasma. “Nauka” Publishing House, Moscow, 1984.

9. A. V. Gurevich. Nonlinear effects in the ionosphere. Phys. Science – Uspekhi,, vol. 177, No. 11, p.p. 1145-1177.

10. Y. A. Kravtsov, Y. I. Orlov. Ray optics of inhomogeneous media. “Nauka” Publishing House, Moscow, 1980.

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