On the Question of a Radar Method for Studying Meteors
Abstract Generated abstract
This paper addresses the use of radar observations to determine the mass distribution of meteoric bodies, especially in the small mass range where visual observations are limited and subject to substantial correction. Building on Kaiser’s relation between meteor echo rates and radar parameters, it argues that the exponent of a power law mass distribution can be estimated with a single radar by comparing counts obtained at different receiver threshold sensitivities rather than by using multiple stations or widely varying transmitter power. The paper derives the corresponding formula for the exponent and discusses practical receiver arrangements, including multichannel systems and a preferred single-channel method with periodic noise-generator switching. Its contribution is a simpler operational procedure for estimating meteor mass distribution parameters from radar echo counts.
Full Text
On the Radar Method of Meteor Research
E. I. Fialko
(Presented by the scientific seminar of the Radio Engineering Faculty)
Preliminary Remarks. Formulation of the Problem
Knowledge of the law of distribution of meteoric bodies by mass is necessary for solving very important problems: determining the spatial density of meteoric matter; clarifying the influence of meteoric ionization on the state of the ionosphere (and, in particular, confirming the meteoric hypothesis of the origin of the sporadic \(E\) layer in middle latitudes), on radio-communication conditions, etc.
The distribution of meteors by mass is usually approximated by a power law \([1, 3]\)
\[ p(m)=\frac{b}{m^S}, \tag{1} \]
where \(m\) is the mass of the meteor,
\(b\) and \(S\) are constants.
The value of \(S\) can be determined from visual observations; however, in doing so it is necessary to introduce substantial corrections connected with the subjectivity of visual observations \([5]\).
Moreover, visual observations can reveal the distribution law in the region of comparatively bright meteors, whereas the more essential task is to clarify the distribution in the region of small masses. This is all the more significant because, according to observations of zodiacal light, the number of small particles in interplanetary space is considerably greater than follows from (1) for values of \(S\) obtained from visual observations \([1, 5]\).
Radar observations may make it possible to remove this contradiction and allow not only the magnitude of the exponent \(S\) to be refined, but also the form of the distribution law of meteoric masses to be specified; this law, apparently, is approximated by a more complicated function than (1).
Kaiser \([3, 4, 5]\) developed a method for determining the coefficient \(S\), based on comparison of the hourly numbers of meteors.
Using the experimental data of McKinley [6], Kaiser found that for sporadic meteors \(S \simeq 2\), and for the Quadrantid stream \(S \simeq 1.7\) (earlier Lovell [2] found that for the Quadrantids \(S \simeq 1\)).
In these experiments [6], the transmitter power was varied periodically, and two radar stations with different powers and somewhat different wavelengths were also used.
The determination of \(S\) from hourly rates obtained with two locators having substantially different wavelengths would need refinement, since the dependence of the hourly meteor rate on wavelength requires clarification.
Determining \(S\) by comparing hourly rates obtained by locators with different transmitter powers entails the need to have 2 (or more) radar stations.
Determining \(S\) with the aid of a single station with adjustable transmitter power is associated with technical difficulties if the power has to be varied over wide limits (for studying the distribution over a wide range of meteor masses).
In this connection, it is desirable to develop a simple, operational method for determining \(S\) when only one radar is available.
Basic relations
Kaiser showed [3, 4] that the ratio of the hourly rates of meteors detected by two radars having identical directivity characteristics of their antenna systems can be found from the approximate formula:
\[ \frac{N_1}{N_2} = \left[ \frac{P_1 \lambda_1^3}{\varepsilon_1} \cdot \frac{\varepsilon_2}{P_2 \lambda_2^3} \right]^{\frac{S-1}{2}}, \tag{2} \]
where \(N\) is the mean number of meteors detected by the radar per unit time (for example, in 1 hour);
\(P\) is the peak power radiated by the transmitter;
\(\lambda\) is the wavelength;
\(\varepsilon\) is the power of the receiver threshold signal;
\(S\) is a constant characterizing the distribution of meteors by mass;
the subscripts 1 and 2 refer, respectively, to the first and second radar stations.
Thus, having 2 (or more) radars with different parameters, one can, by comparing hourly rates, find the values of \(S\).
But the same result can be obtained with one radar if two receivers are available (with different real sensitivity), or one receiver with adjustment of the threshold signal,
\[ \frac{N_1}{N_2} = \left[ \frac{\varepsilon_2}{\varepsilon_1} \right]^{\frac{S-1}{2}}, \tag{3} \]
whence\(^1\)
\[ S = 1 + 2 \cdot \frac{\lg \dfrac{N_1}{N_2}} {\lg \dfrac{\varepsilon_2}{\varepsilon_1}} . \tag{4} \]
\(^1\) Formulas (2)—(4) are valid for radio echoes of the nonsteady type [5]. In the case of receiving radio echoes of the steady type [5], as is not difficult to show,
\[ S = 1 + \frac{1}{2} \cdot \frac{\lg \dfrac{N_1}{N_2}} {\lg \dfrac{\varepsilon_2}{\varepsilon_1}} . \]
To determine \(S\) in the region of small \(m\), it is necessary to work at comparatively large \(\lambda\), to use a highly directional antenna, and, in addition, it is desirable to have a transmitter with high radiated power.
Some methods for varying \(\varepsilon\)
Reception of signals reflected from meteors under conditions of different real sensitivity can be carried out in several ways, for example:
- The method of multichannel reception—several receivers are used (or one multichannel receiver) with different threshold signals (Figs. 1 and 2).
Fig. 1. Two-channel receiving device with adjustment of the threshold signal by using a noise generator.
A—antenna.
1,2—amplifier channels.
3—preliminary amplifier.
4—noise generator.
5—interference-level indicator.
6,7—cathode-ray indicators.
Fig. 2. Two-channel receiving device with adjustment of the threshold signal by using an attenuator.
A—antenna.
1,2—amplifier channels.
3—preliminary amplifier.
4—attenuator.
5—interference-level indicator.
6,7—cathode-ray indicators.
- The method of single-channel reception—one receiver is used with periodic variation of the threshold signal (Figs. 3 and 4).
The threshold signal may be varied either by means of a noise generator (Figs. 1 and 3), or by means of a voltage divider (attenuator) (Figs. 2 and 4).
Adjustment and comparison of the threshold signals may be carried out with the aid of a simple indicator consisting of a detector (or thermocouple) and a pointer instrument.
The preferable variant is that of a single-channel receiver with periodic switching of the noise generator (for example, the generator is switched on for 1 minute, after which for 1 minute it remains switched off); one cathode-ray indicator with linear (diametral) sweep and brightness-
by a mark; photographic recording is carried out on film moving continuously in front of the indicator screen—in a direction perpendicular to the sweep line—at a low speed (for example, 1 cm/min).
When the noise generator is connected, a mark is supplied (for example, by perforating the photographic film).
Fig. 3. Single-channel receiving device with a periodically switched-on noise generator.
A—antenna.
1—preliminary amplifier.
2—main amplification channel.
3—noise generator.
4—interference-level indicator.
5—cathode-ray indicator.
Fig. 4. Single-channel receiving device with a periodically switched-on attenuator.
A—antenna.
1—preliminary amplifier.
2—attenuator.
3—main amplification channel.
4—interference-level indicator.
5—cathode-ray indicator.
To determine \(N_1\) and \(N_2\) separately, the meteor reflections recorded on the film are counted for the times when the noise generator was respectively switched on or switched off.
Having counted \(N_1\) and \(N_2\), and having recorded the ratio of the threshold signals \(\dfrac{\varepsilon_1}{\varepsilon_2}\), we find \(S\) from formula (4). Changing \(\varepsilon\) is also possible by changing the discrimination level, as well as the counting level (using an amplitude marker).
REFERENCES
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Levin B. Yu. Physical Theory of Meteors and Meteoritic Matter in the Solar System. Publishing House of the Academy of Sciences of the USSR, 1956.
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Lovell A. Meteor ionization and ionospheric anomalies, UFN, vol. XXI, issue 1, 1950.
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Kaiser T. R. Theory of the Meteor Height Distribution Obtained from Radio-Echo Observations. I. Shower Meteors. Mon. Not. of the Royal Astr. Soc., 1954, v. 114, No. 1, p. 39.
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Kaiser T. R. Theory of the Meteor Height Distribution Obtained from Radio-Echo Observations. II. Sporadic Meteors. Mon. Not. of the Royal Astr. Soc., 1954, v. 114, No. 1, p. 52.
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Kaiser T. R. Radio Echo Studies of Meteor Ionization, J. Adv. Phys., 1953, v. 2, No. 8.
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McKinley D. W. R. Variation of Meteor Echo Rates with Radar System Parameters, Can. Journ. Phys., 1951, v. 29, No. 5, pp. 403—426.