On the Influence of the Intensity of Cosmic Interference on the Hourly Number of Meteorites Detected by Radio Means
Abstract Generated abstract
This paper examines how variations in cosmic radio noise affect the hourly number of meteors detected by radar, through their influence on the receiver threshold signal. Using the known dependence of detected meteor counts on threshold power and the relation between threshold power, antenna temperature, receiver noise, and bandwidth, the authors derive a general correction factor for reducing observed counts to the case of constant mean cosmic noise. They estimate the effect for observations at a wavelength of 10 m with a nondirectional antenna, using measured variations in antenna temperature and a typical sporadic meteor mass distribution parameter. The resulting correction is found to be relatively small, about within 15 percent, although the authors note that larger effects may occur for sharply directional antennas, longer wavelengths, or short-term cosmic and solar noise bursts.
Full Text
On the Influence of the Intensity of Cosmic Interference on the Hourly Number of Meteors Detected by Radio Means
E. I. Fialko, L. P. Serafinovich
(Presented by the scientific seminar of the Radio Engineering Faculty)
Formulation of the Problem
As is known, the hourly number of meteors \(N\) detected by a radar depends on the magnitude of the threshold signal.
In the range of wavelengths used for meteor radar, the magnitude of the threshold signal is determined mainly by the level of cosmic interference, which varies with time. As a result of this (in particular, as a result of the diurnal variation in the intensity of cosmic noise), the average hourly number of detected meteors will differ from that in the case of a constant threshold signal. Shine and Kerr [1], for example, believe that the midday maximum disappears if, in the experimental diurnal curve of hourly meteor numbers, a correction is introduced for the dependence of the sensitivity of the equipment on the intensity of cosmic noise. Lovell [2] disputes this conclusion, since at a frequency of \(70\) MHz, when using an antenna with a narrow beam, the influence of cosmic noise on the change in sensitivity is small and can easily be taken into account in the analysis. At the same time, Lovell does not deny that under the experimental conditions of Shine and Kerr, when observations were made at relatively low frequencies (\(f \simeq 18\) MHz) using an antenna with a broad beam, the effect of changes in the sensitivity of the equipment could play an essential role.
Elliott and Fraser, who used equipment with a frequency of \(69\) MHz, believe that changes in the effective temperature of the antenna introduce corresponding changes into the observed hourly meteor numbers [3].
Let us determine whether it is necessary to take into account a correction due to the influence of cosmic interference on the magnitude of the threshold signal when constructing the diurnal variation of the hourly number of meteors detected by a radar at a wavelength \(\lambda = 10\) m.
For this purpose, we shall first obtain an expression for the correction in general form.
Accounting for the Influence of the Intensity of Cosmic Interference on the Number of Detected Meteors
As already noted, the average hourly number of detected meteors \(N\) depends on the power of the threshold signal \(\varepsilon\) [4]:
\[ N \sim \varepsilon^{-\frac{s-1}{2}}, \tag{1} \]
where \(s\) is a constant characterizing the law of distribution of meteoric bodies by mass \(m\) [4]: \(p(m)\sim m^{-s}\).
The threshold-signal power may be represented in the form [5]
\[ \varepsilon=\kappa\cdot T_0\cdot \Delta f \left(\frac{T_a}{T_0}-1+F_c\right)\cdot \zeta, \tag{2} \]
where \(\kappa\) is Boltzmann’s constant; \(T_0\) is room temperature; \(T_a\) is the effective antenna temperature characterizing the intensity of cosmic noise; \(\Delta f\) is the effective receiver noise bandwidth; \(F_c\) is the receiver’s own noise factor, characterizing the intensity of the receiver’s internal (fluctuation) noise; \(\zeta\) is the observability coefficient, characterizing the excess of the minimum detectable signal over the interference level.
Owing to the variability of cosmic interference, the effective temperature \(T_a\), and consequently the magnitude of the threshold signal \(\varepsilon\), are functions of time.
The mean (in time) level of cosmic interference is characterized by the mean temperature \(\overline{T}_a\).
If the level of cosmic interference remained constant and corresponded to \(\overline{T}_a\), then the mean hourly number of detected meteors \(N_0\) would be, as follows from (1) and (2),
\[ N_0 \sim (\kappa\cdot T_0\cdot \Delta f\cdot \zeta)^{-\frac{s-1}{2}} \cdot \left(\frac{\overline{T}_a}{T_0}-1+F_c\right)^{-\frac{s-1}{2}}. \]
But, owing to the variability of the level of cosmic interference, the change in the mean hourly number of meteors proves to depend on \(T_a(t)\)
\[ N \sim (\kappa\cdot T_0\cdot \Delta f\cdot \zeta)^{-\frac{s-1}{2}} \cdot \left[ \frac{\overline{T}_a}{T_0}\cdot K_a-1+F_c \right]^{-\frac{s-1}{2}}, \tag{4} \]
where
\[ K_a=\frac{T_a(t)}{\overline{T}_a}. \]
Dividing (3) by (4) and carrying out simple transformations, we obtain
\[ N_0=N\cdot Q, \tag{5} \]
where
\[ Q= \left[ 1+ \frac{\dfrac{\overline{T}_a}{T_0}(K_a-1)} {\dfrac{\overline{T}_a}{T_0}-1+F_c} \right]^{\frac{s-1}{2}}. \tag{6} \]
In the case of a considerable excess of external interference over internal interference, i.e., when
\[ \frac{T_a}{T_0}\gg F_c+1, \]
expression (6) takes the form
\[ Q\simeq K_a^{\frac{s-1}{2}}. \tag{7} \]
In the case of small fluctuations in the intensity of cosmic noise, i.e. \((K_a - 1) \ll 1\), and a considerable excess of external noise over internal noise, formula (6) can be represented in the form
\[ Q \approx 1 + \frac{s - 1}{2}(K_a - 1)\left(1 - \frac{F_c - 1}{\dfrac{\overline{T_a}}{T_0}}\right). \tag{8} \]
Thus, having calculated \(Q\), one can take into account the influence of the instability of the receiver threshold signal on the diurnal variation of the hourly number of detected meteors.
Let us now proceed to estimating the correction at the wavelength \(\lambda = 10\) m.
Estimate of the correction at the wavelength \(\lambda = 10\) m
At \(\lambda = 10\) m,
\[ \frac{\overline{T_a}}{T_0} \gg F_c - 1 \]
and therefore the coefficient \(Q\) can be found from formula (7). We find
\[ Q_{\max} \approx K_{a\max}^{\frac{s-1}{2}}; \qquad Q_{\min} \approx K_{a\min}^{\frac{s-1}{2}}. \tag{9} \]
Using the results of measurements carried out with the aid of a half-wave vibrator [6], we find \(K_{a\max} \approx 1.3,\ K_{a\min} \approx 0.7\). For the case of sporadic meteors \((s \approx 2)\) [4] we have
\[ Q_{\max} \approx 1.15, \qquad Q_{\min} \approx 0.85. \tag{10} \]
Thus, the correction due to the influence of cosmic noise on the hourly number of detected meteors at \(\lambda = 10\) m, when reception is on a nondirectional antenna, as follows from (5), (6), (7), (9), and (10), is small—within \(\pm 15\%\).
Let us note that short-term “bursts” of noise, both of cosmic and of solar origin, are not taken into account here; these may prove significant when reception is on a directional antenna.
Let us note that, when a sharply directional antenna is used, the correction may prove significant (this case is subject to consideration). The correction may also prove significant when longer waves are used (for example, \(\lambda > 15\)).
Conclusions
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The correction to the number of meteors detected by radio means, due to the nonconstancy of the level of cosmic noise when reception is on a weakly directional antenna, is small (in the range of wavelengths presently used for meteor observations).
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If necessary, this correction can be taken into account (see formula 6).
LITERATURE
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Lovell A. C. B., A note on the interpretation of transient echoes from the ionosphere, J. Atm. Terr. Phys., 1956, v. 8, No. 4/8, 293.
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Ellyett C. D., Freser G. J., The influence of noise on radar meteor observations, Austr. Journ. of Phys., 1955, v. 8, No. 2, 273.
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Kaiser T. R., Radio-echo studies of meteor ionization, J. Adv. Phys., 1953, v. 2, No. 8, 495.
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Siforov V. I. Radio Receiving Devices, Oborongiz, 1954.
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Cottony H. V., Johler J. R. Cosmic radio noise intensities in the VHF band, Proc. I.R.E., 1952, v. 40, No. 9, 1053.