On the Conditions for Recording Ionized Meteor Trails of Various Types

E. I. Fialko

(Presented by the scientific seminar of the Radio Engineering Faculty)

Introduction. Statement of the Problem

Knowledge of the dependence of the number of recorded meteors on the parameters of the radar and on the characteristics of the atmosphere and of the meteors is necessary both for interpreting observational results and for designing systems.

For the cases of overdense and underdense trails these dependences are different. Therefore, before using calculated relations, it is necessary to determine whether the system is capable of detecting underdense trails, or whether it can record only trails of the overdense type.

Of practical interest is the reception of echo signals from the region of the characteristic height \(h_m\). It is therefore expedient to obtain criteria that make it possible to estimate the capabilities of radars at slant ranges corresponding to the characteristic heights.

The present work is devoted to finding criteria that make it possible to judge the ability of a system to record trails of various types, both in the case of reliable and of random detection of meteors under conditions of normal reflection of radio waves from ionized trails.

Basic Relations

Low-sensitivity systems are capable of recording only trails of the overdense type (with linear electron density \(\alpha \gg 2.4 \cdot 10^{12}\ \text{el/cm}\)). The condition for detecting only overdense trails has the form [1]

\[ \frac{P_i G^2}{\varepsilon_n}\left(\frac{\lambda}{R}\right)^3 \lesssim 2 \cdot 10^3, \tag{1} \]

where \(P_i\) is the radiated power in the pulse;
\(G\) is the antenna directivity factor;
\(\varepsilon_n\) is the threshold-signal power; \(\lambda\) is the wavelength;
\(R\) is the slant range from the radar to the trail (along the normal).

Reliable detection of overdense trails takes place when conditions (1) and (2) [1] are simultaneously satisfied:

\[ \frac{P_i G^2}{\varepsilon_n}\left(\frac{\lambda}{R}\right)^3 \gtrsim \frac{520\lambda}{\sqrt{D T_{\min}}}, \tag{2} \]

where \(D\) is the diffusion coefficient; \(T_{\min}\) is the minimum necessary time during which the meteor radio echo exceeds the threshold level, corresponding to reliable detection; \(T_{\min}\) characterizes the response speed of the radar.

When conditions (1) and (2) are satisfied, a reflection that has reached the threshold level \((\varepsilon \simeq \varepsilon_n)\) has a duration \(T > T_{\min}\). If, however, the reflection that has reached the threshold level has a duration \(T < T_{\min}\), then both reliable and random detection of persistent meteor trails will occur; this condition has the form [1]

\[ 520\,\frac{\lambda}{\sqrt{D T_{\min}}} < \frac{P_i G^2}{\varepsilon_n}\left(\frac{\lambda}{R}\right)^3 \lesssim 2 \cdot 10^3 . \tag{3} \]

As the sensitivity of the system is increased, not only persistent trails will be recorded, but also trails of the intermediate \((\alpha \simeq 10^{12}\ \text{el/cm})\) and nonpersistent \((\alpha \ll 2.4 \cdot 10^{12}\ \text{el/cm})\) types.

In practice, trails with a linear electron density \(\alpha < 5 \cdot 10^{11}\ \text{el/cm}\) exhibit properties characteristic of nonpersistent trails.

A rough condition for recording nonpersistent trails has the form [2]

\[ \frac{P_i G^2}{\varepsilon_n}\left(\frac{\lambda}{R}\right)^3 \gtrsim 1.5 \cdot 10^4 . \tag{4} \]

A more exact condition takes into account the attenuation of the echo signal due to the fact that the initial radius of the column has a finite value, and diffusion has time to impart to the trail a parabolic form within the limits of the first Fresnel zone (during its formation) [2]:

\[ \frac{P_i G^2}{\varepsilon_n}\left(\frac{\lambda}{R}\right)^3 \xi^2 e^{-2\left(\frac{2\pi r_0}{\lambda}\right)^2} \gtrsim 1.5 \cdot 10^4 , \tag{5} \]

where

\[ \xi \simeq \frac{1 - e^{-1.5\Delta^{0.5}}}{1.5\Delta^{0.5}} \quad [3]; \tag{6} \]

\[ \Delta = \frac{16\pi^2 D R^{1/2}}{v\lambda^{3/2}} \quad [4]. \tag{7} \]

It should be noted that, in the case when the left-hand side of inequality (5) is approximately equal to \(1.5 \cdot 10^4\), trails with a linear density \(\alpha \simeq 5 \cdot 10^{11}\ \text{el/cm}\) barely reach the threshold level \(\varepsilon_n\), and therefore are detected randomly. Trails with larger \(\alpha\), however, can be detected reliably, but they will belong to trails of the intermediate and persistent types.

In order for trails with a linear electron density \(\alpha \simeq 5 \cdot 10^{11}\ \text{el/cm}\) to be detected reliably, the condition [2]

\[ \frac{P_i G^2}{\varepsilon_n}\left(\frac{\lambda}{R}\right)^3 \xi^2 e^{-2\left(\frac{2\pi r_0}{\lambda}\right)^2} e^{-2\frac{T_{\min}}{T_e}} \gtrsim 1.5 \cdot 10^4, \tag{8} \]

where \(T_e\) is the duration of the trail at the level \(\dfrac{u_{m_0}}{e}\), equal to [4]

\[ T_e=\frac{\lambda^2}{16\pi^2D}; \tag{9} \]

\(u_{m_0}\) is the initial amplitude of the reflection.

A system whose parameters satisfy condition (8) detects unstable trails both accidentally and reliably; trails of the intermediate and stable types, however, are detected only reliably.

Let us recall that these conclusions are valid for a given range \(R\), antenna directivity factor \(G\) (corresponding to the given direction), etc.

In addition, the conditions given have been obtained without taking into account accumulation effects, which may occur in the indication and recording of signals (for example, owing to the integrating properties of photographic film).

Method for Estimating the Maximum Capabilities of the System

Knowing the velocity of meteor bodies \(v\), we find the corresponding characteristic height \(h_m\) [4]; from the zenith distance of the radiant \(\chi\) and the angle \(\Theta\) in the echo plane, we find the slant range corresponding to the characteristic height (see Fig. 1):

Fig. 1. \(P\) is the direction toward the radiant of the stream; \(z\) is the zenith; \(\Pi\) is the echo plane (i.e., the plane perpendicular to the direction toward the radiant); \(\Gamma\) is the horizontal plane; \(M\) is the point of intersection of the meteor trail with the echo plane; \(O\) is the location of the radar; \(h\) is the height of point \(M\) above ground level; \(R\) is the slant range from the radar to point \(M\); \(\alpha\) and \(\beta\) are the azimuth and elevation angle of the direction toward the meteor; \(OA\) is the line of intersection of the echo plane with the plane passing through the zenith, the radiant, and the radar location; \(\Theta\) is the angle in the echo plane, measured from the line \(OA\) to the direction \(OM\).

\[ R=\frac{h_m}{\sin\chi\cdot\cos\Theta}. \tag{10} \]

The angle \(\Theta\) is measured from the line \(OA\) (the line of intersection of the echo plane with the plane passing through the zenith and the points of the radiant and the radar location) to the direction toward the normally reflecting—

…ing section of the ionized trail; the echo plane is perpendicular to the direction toward the radiant.

Knowing the radar parameters \(P_i, G, \varepsilon_n\), and \(\lambda\), and the slant range \(R\) (10), we check whether condition (1) is satisfied. If it is satisfied, then the system is of low sensitivity and is capable of recording only stable trails. Let us determine whether random detection is possible. Knowing \(v\), and consequently \(h_m\), we find \(D(h_m)\) [5 et al.]. If the system parameter \(T_{\min}\), characterizing its response speed, is known, we find the quantity

\[ \frac{520 \cdot \lambda}{\sqrt{D T_{\min}}} \]

and check the fulfillment of inequalities (2) and (3).

Fulfillment of conditions (1) and (2) indicates the absence of random detection, while fulfillment of condition (3) indicates the ability of the system to record both reliably and randomly detected trails of the stable type.

If, however, condition (1) is not fulfilled, then the system can record trails of the intermediate and, possibly, unstable types.

Fulfillment of condition (4) indicates that the radar can record unstable trails; but if neither inequality, (1) or (4), is fulfilled, then only trails of the stable and intermediate types can be detected.

To refine the possibility of detecting unstable trails, one must use condition (5); for this it is necessary to find the initial radius of the meteor trail \(r_0(h_m)\) [6] and compute the coefficient \(\xi\) (6) from \(\Delta\) (7).

Fulfillment of condition (8) indicates a high sensitivity of the system, capable of recording unstable trails. In order to determine whether reliable detection of unstable trails is possible, it is necessary, after finding the duration of the trail “at the level”

\[ \frac{u_{m_0}}{e}\,T_e \tag{9} \]

from \(D(h_m)\) [5], to check whether condition (8) is satisfied.

A system for which condition (8) is satisfied reliably detects trails of the intermediate, stable, and (partly) unstable types; the remaining part of the unstable trails is detected randomly; this occurs for \(h \approx h_m\).

It is quite obvious that, in an analogous way, one can estimate the capabilities of a radar not only with respect to meteors in the region of the characteristic height \(h_m\), but also for any \(h\) and \(R\); however, in doing so it is necessary to know \(r_0(h)\) and \(D(h)\).

Note on the classification of systems by sensitivity

It seems advisable to classify systems by sensitivity.

Systems satisfying condition (1) (capable of recording only stable trails) are assigned to low-sensitivity systems.

Systems satisfying condition (4) (capable of detecting unstable trails) are assigned to high-sensitivity systems.

Such a classification is, naturally, conditional, since one and the same system, for some \(R\) and \(G\), may prove to be highly sensitive, while for others it may be of low sensitivity, which corresponds to real operating conditions. For example, when observing a meteor stream using a fixed antenna, both \(R(h_m)\) and \(G(h_m)\) can vary over wide limits, and therefore during…

for some time the system may operate as a high-sensitivity one, and for the rest of the time as a low-sensitivity one.

For an objective classification of systems by sensitivity, it would be advisable to take \(G=G_{\max}\) and \(R\approx \mathrm{const}\) (for example, \(R=300\) km).

Conclusions

1. Before proceeding to interpret the results of observations or to calculate a system, it is necessary to establish what type of trails can be detected by the radar.

For this purpose one may use the sensitivity criteria (1), (2), (3), (4), (5), and (8).

1. It is advisable to classify radars by sensitivity, assigning them to low- and high-sensitivity locators in accordance with criteria (1) and (4).

References

1. E. I. Fialko. Confident and random radio detection of stable meteor trails. Izvestiya TPI, vol. 100, 84, 1962.

2. E. I. Fialko. Confident and random detection of unstable meteor trails. Radiotekhnika, vol. 16, No. 6, 24, 1962.

3. E. I. Fialko. Power of the signal reflected from a meteor trail under conditions of intense diffusion. Izvestiya TPI, vol. 100, 40, 1962.

4. T. R. Kaiser. Radio-echo studies of meteor ionization, J. Adv. Phys., 2, No. 8, 495, 1953.

5. J. S. Greenhow, E. L. Neufeld. The diffusion of ionized meteor trails in the upper atmosphere, Journ. Atm. Terr. Phys., 6, No. 2—3, 133, 1955.

6. L. A. Manning. The initial radius of meteoric ionization trails, Journ. Geoph. Res., 63, No. 1, 181, 1958.