Henry G. Booker

A Theory of Radio Scattering in the Troposphere

The theory of scattering by a turbulent medium is applied to scattering of radio waves in the troposphere. In the region below the horizon of the transmitter, energy is received (1) by diffraction round the curved surface of the earth (modified as appropriate by atmospheric refraction), and (2) by scattering from turbulence in the region of high field strength above the horizon. At distances beyond the horizon that are not too great, we may think of (1) as giving the mean signal received, and (2) as giving the fading. However, contribution (2) usually decreases with distance more slowly than contribution (1). Beyond a certain distance, therefore, contribution (2) becomes predominant and the mean signal is no longer given by (1). (See Fig. 3.) Values of the scale of turbulence and of the departure of refractive index from mean expected on meteorological grounds are fully adequate to explain the scattered field strengths observed experimentally.

A theory of scattering by nonisotropic irregularities with application to radar reflections from the aurora

Abstract A model of the distribution of ionization in an aurora is developed that can explain the aspect sensitivity of radar echoes obtained at VHF during auroral activity. Even when the radar is in the midst of a zone of auroral activity, echoes are obtained only from low angles of elevation in roughly the northern quadrant. However, both the horizontal and vertical angles over which echoes are obtained increase significantly as frequency is decreased from 100 to 25 Mc/s. These observations can be explained in terms of columns of ionization parallel to the earths magnetic field. The size of the columns must, however, be much smaller than suggested by Chapman (1952) or by Booker , Gartlein , and Nichols (1955). The column size required is of the order of 40 in in length and 1 m in diameter, smoothed so as to avoid discontinuities at the surfaces. It is quite doubtful whether the formation of such short columns of ionization can be associated directly with the formation of visual rays, even though the same axis of symmetry is involved in both cases. The size of irregularities required to explain the observations is in fact of the order of magnitude likely to be involved in atmospheric turbulence, and it is quite likely that the earths magnetic field could create substantial nonisotropy in the associated irregularities of electron density. Thus the strength of auroral echoes and their aspect sensitivity could be entirely explained as back-scatter arising from nonisotropic atmospheric turbulence in an E region having a maximum electron density about a hundred times the normal value. Simple turbulence cannot, however, explain the remarkable fading phenomena associated with auroral reflections ( Bowles , 1954).

Fitting of multi-region ionospheric profiles of electron density by a single analytic function of height

Abstract A single analytic function of height is devised that has the flexibility required to represent simultaneously the principal features of the D-, E-, F1- and F2-regions of the ionosphere. Such a function, free of mathematical singularities, is essential for obtaining satisfactory wave-solutions to ionospheric problems using methods more exact than the phase-integral (WKB) approximation. The method is applicable to profiles of atmospheric parameters besides electron density.

Theory of refractive scattering in scintillation phenomena

Abstract For a plane wave incident upon a thin plane one-dimensional phase-changing screen that has an outer scale Lo, an inner scale Li and an intervening inverse power-law spectrum (spectral index p), calculations are made of the spatial power spectrum of intensity fluctuations in a reception plane parallel to the screen. The outer scale is taken to be large compared with the Fresnel scale F, and results are obtained for a range of values of the spectral index and of the mean square fluctuation of phase (ΔΦ) 2 . For large values of (ΔΦ) 2 , lens action occurs in the screen, producing focal action in the reception plane. A lens scale F [2 (ΔΦ) 2 ] 1 4 is defined, as well as a focal scale l that varies from L o [(ΔΦ) 2 ] −1 2 at p = 5 to L o [2 (ΔΦ) 2 ] −1 at p = 2. When refractive scattering dominates, l−1 is the upper roll-off angular spatial frequency for intensity fluctuations in the reception plane whether this is the focal plane or not. The lower roll-off angular spatial frequency occurs at a scale such that its geometric mean with the focal scale is equal to the Fresnel scale. Refractive scattering dominates even for weak scattering if p ~ 5 or p > 5. For lower values of p, diffractive scattering dominates unless the lens scale exceeds the focal scale. Refractive scattering dominates when the focal scale is small compared with the lens scale. Saturation of the intensity spectrum occurs when the focal scale is small compared with the Fresnel scale. The scintillation index tends to unity as (ΔΦ) 2 → ∞ for all p. The turbulence parameter approximation is satisfactory for a range of spectral indices near 2, but not for p ~ 3 and p > 3.

The role of acoustic gravity waves in the generation of spread-F and ionospheric scintillation

Abstract In the aggregate, acoustic gravity waves in the F -region constitute a spectrum of geophysical noise extending from the frequencies involved in diurnal variations up to the Brunt-Vaisala buoyancy frequency. They drive a roughly uniform power spectrum of travelling ionospheric disturbances (TIDs) with vertical scales of the order of the atmospheric scale height H and with horizontal scales extending from the radius of the Earth down to H . It has been known since the 1950s that this permits multiple normals onto the F -region from an ionosonde, thereby creating the multiple-trace type of spread F on ionograms. At shorter scales the spectrum of TIDs decreases in strength and, below the mean free path of the neutral atmosphere, creates a spectrum of plasma turbulence aligned along the Earths magnetic field. Progressively shorter scales are responsible for phase scintillation, for amplitude scintillation and for blur-type spread F on ionograms. A weak extension of the spectrum to scales less than the ion gyroradius is responsible for spread F and transequatorial propagation in the VHF band. Under evening conditions in equatorial regions a band of TIDs with wavelengths of the order of 600 km can, at times, have a phase velocity that matches the drift velocity of the plasma ( Rottger 1978). This band of TIDs is then amplified until it breaks ( Klostermeyer 1978). The associated explosive increase in plasma turbulence creates the plume phenomenon discovered by Woodmn and La Hoz (1976).

A theoretical model for equatorial ionospheric spread-F echoes in the HF and VHF bands

A theory of spread-F echoes is presented particularly suitable for equatorial regions, especially under presunrise conditions. In the HF band the theory is based on a spectrum of irregularities of ionization density extending from an outer scale [wavelength(2π)] linked to the scale-height of the atmosphere down to an inner scale of the order of the ionic gyroradius. The irregularities are assumed to be aligned along the Earths magnetic field and to have lengths of the order of the outer scale. Inverse power-law spectral indices from 0 to 6 are considered mathematically, and from 1 to 4 numerically. Spectral indices between 1 and 3 fit observations of presunrise equatorial spread-F satisfactorily. An essential feature of the fit arises from the assumed cut-off in the turbulence spectrum at the ionic gyroradius. It is also assumed, however, that a weak extension of the spectrum, probably in the form of an angular spectrum of compressional plasma waves, exists from the ionic gyroradius down to the electronic gyroradius, and on this basis a theory is presented of spread-F echoes in the VHP band. The spectrum of turbulence in the F-region plasma is pictured as maintained by travelling ionospheric disturbances caused by atmospheric gravity waves.

Comparison between the extended-medium and the phase-screen scintillation theories

Abstract By numerically solving the fourth moment equation, comparisons are made between (i) situations in which fluctuations of refractive index extend uniformly from the transmitter to the receiver and (ii) situations in which the fluctuations are confined to a phase screen. The comparisons are made for inverse power-law phase spectra having a total mean square fluctuation of phase (ΔΦ) 2 , an outer scale L0 and an inner scale 0.01 L0. Four values of the spectral index are investigated, including the Kolmogoroff value. The comparisons are made for a wavelength such that the Fresnel scale is intermediate between the outer scale and the inner scale, so that both refractive and diffractive scattering are involved. The study extends from situations dominated by weak diffractive scattering up to ones dominated by multiple refractive scattering. It is found that, provided that the equivalent screen (i) is centrally located, (ii) has the same type of fluctuation spectrum and (iii) generates the same value of (ΔΦ) 2 as the extended medium, then the scintillation index and the intensity autocorrelation function in the reception plane are approximately the same in the two cases. Results are very dependent on how many refractive scatterings occur between the transmitter and the receiver, but they are not very dependent on how these refractive scatterings are distributed along the path.

A comparative study of ionospheric measurement techniques

Abstract Comparisons are presented between different methods of measuring ionospheric profiles of electron-density, electron-temperature and ion-temperature. The methods compared are listed for the upper ionosphere in Table 1 (above 100 km) and for the lower ionosphere in Table 2. Only comparisons involving closely simultaneous observations at closely the same location are included. From 100 km down to perhaps 70 km, the radio rocket method appears to have the greatest accuracy. Nevertheless, the ground-based partial reflection and wave-interaction methods need to be developed for continuous observation of electron-density profiles. Moreover, other methods are valuable for monitoring purposes. Above 100 km, satellite methods, particularly the topside ionosonde, are important for obtaining global coverage. But for accuracy of measurement of electron-density, electron-temperature, ion-temperature (and several other aeronomically vital parameters), ground-based methods, particularly the incoherent scatter radar, are superior in the altitude range from one hundred to several hundred kilometers. In many respects, however, satellite and ground-based methods are complementary.

Use of scintillation theory to explain frequency-spread on F-region ionograms

Abstract Frequency-spread on F -region ionograms is to be explained primarily with the aid of large-scale irregularities of ionization density in the F -region of the ionosphere. Large-scale irregularities are ones whose sizes extend from the Fresnel scale up to the outer scale. This means scales ranging from about two kilometres up to some tens of kilometres, or wavelengths ranging from about ten kilometres up to several hundred kilometres. Irregularities of scale in excess of the Fresnel scale cause refractive scattering of a vertically incident wave on its upward journey through the F -region and on its return journey. Irregularities also cause the critical surface separating underdense ionization from overdense ionization to be rough. Irregularity scales from the Fresnel scale up to the outer scale cause reflection from this surface to take the form of glints. However, this mechanism by itself does not produce enough frequency-spread to explain satisfactorily the more extensive forms of spread- F . In these circumstances refractive scattering of a wave on its upward journey into the F -region ceases to be small-angle scattering before the reflecting stratum is reached. Return of energy to the ionosonde becomes possible by multiple refractive scattering alone. This is diffuse scattering by irregularities ofionization density with scales ranging from the Fresnel scale up to the outer scale. The mathematical theory of scintillation needs to be extended so as to cover development of large-angle multiple refractive scattering.

Quantitative explanation of strong multi-frequency intensity scintillation spectra using refractive scattering

Abstract Under evening equatorial conditions, strong intensity spectra observed simultaneously on transmissions through the ionospheric F-region at 40, 140 and 360 MHz from a stationary satellite are explained quantitatively in terms of refractive scattering using the approach of Booker and Majidiahi (1981). Use is made of an outer scale (wavelength/2gp) of 50 km, an inner scale of 5 m and an integrated mean square fluctuation of ionization density [ ∝ (ΔN) 2 dz ] of 1028 m−5. The spectral index required to fit the observations is 3, and no major departure from this value is permissible either way. This produces the correct spectral behavior at high fluctuation frequencies and the correct ratios of the upper roll-off frequencies at the three wave frequencies. The RMS fluctuation of phase is about 130 rad at 360 MHz, 340 rad at 140 MHz and 1200 rad at 40 MHz. At 40MHz the scale of the intensity fluctuation at ground level is about 10m, and this is caused by refractive scattering in the ionosphere at scales of the order of the outer scale; removal of practically all fluctuations in the ionosphere at scales below the Fresnel scale leaves the fine structure of the intensity spectrum at ground level virtually unaffected.