UDC 551.510.535+550.388.2

GEOPHYSICS

G. S. IVANOV-KHOLODNYI

ESTIMATE OF THE CONCENTRATION OF NEGATIVE IONS IN THE $D$ REGION OF THE IONOSPHERE

(Presented by Academician E. K. Fedorov, February 18, 1967)

One of the most important questions in the modern study of the $D$ region of the ionosphere is the question of the concentration of negative ions $n_i^-$. Rocket measurements of the electron concentration $n_e$ at altitudes of 60–100 km make it possible to obtain, on the average, more or less reliable values of $n_e$ ($^1$), in agreement with ground-based measurements. At the same time, the rocket-measured values of $n_i^+$ and $n_i^-$ reported by different authors differ by as much as 2–2.5 orders of magnitude ($^{1-5}$). In this connection the relative values $n_i^+/n_e$ and $n_i^-/n_e$ turn out ($^5$) to be an order of magnitude higher than is given by the theory ($^6$), based on allowance for the mechanisms of formation and destruction of negative ions. The conclusions of the theory ($^6$) are disputed in a number of works ($^{7,8}$). Below an attempt is made to estimate the value $l^- = n_i^-/n_e$, starting from ionospheric data on the effective recombination coefficient $\alpha'$.

As is known, changes in the electron concentration in the $D$ region of the ionosphere are determined by the equation

\[ dn_e/dt = q/(1 + l^-) - \alpha' n_e^2. \tag{1} \]

The effective recombination coefficient $\alpha'$ is related to the dissociative recombination coefficient $\alpha^*$ and the coefficient of mutual neutralization of positive and negative ions $\alpha_i$ by the relation

\[ \alpha' = \alpha^* + \alpha_i l^-. \tag{2} \]

Thus, starting from $\alpha'$, one can determine the value $l^-$ if the constants $\alpha^*$ and $\alpha_i$ are known. For the value $\alpha^*$ we use $(2–3)\cdot 10^{-7}\ \text{cm}^3\cdot\text{sec}^{-1}$, which, according to the latest data ($^9$), corresponds to the atmospheric temperature at the altitudes under consideration. Let us consider in more detail the available data on $\alpha'$.

A review of the results of experimental measurements of $\alpha'$ in the $D$ region of the ionosphere was given by Mitra ($^{10}$). We note that individual measurements may differ from the mean values, shown by crosses in Fig. 1, by a factor of 2–3, which also characterizes the accuracy of the mean values of $\alpha'$. Fig. 1 also gives the values $q/n_e^2$ for daytime conditions ($^b$) during solar flares according to ($^{11}$), and for nighttime conditions ($a$) during polar blackouts according to ($^{12}$). According to (1), for stationary conditions the quantity $q/n_e^2$ should be greater than $\alpha'$ by a factor of $1 + l^-$. Taking into account that the differences between the indicated quantities at altitudes of 60–80 km lie within a factor of 1.5–2.5, one may conclude that even at 60 km $l^-$ is probably only slightly greater than unity. Apparently, more reliable estimates of $l^-$ can be obtained from comparison of $\alpha' n_e^2$ (see Table 1) for quiet conditions ($n_e$ taken from ground-based measurements ($^{13}$)) at altitudes of 50–60 km with the value of $q$, which here is determined only by cosmic rays. We used the latest calculations ($^{14,15}$), which give values of $q$ an order of magnitude higher than in ($^6$). The values of $l^-$ obtained for altitudes of 50 and 60 km are used to estimate the constant $\alpha_i$, and then we determine $l^-$ from $\alpha'$ for greater altitudes.

The excess of $\alpha'$ over $\alpha^*$ is equal to $\alpha_i l^-$. The dashed line in Fig. 1 gives the lower limit of $\alpha'$. Hence, from the data on $l^-$ for altitudes of 50–60 km we find $\alpha_i = (0.7–2)\cdot 10^{-6}\ \text{cm}^3\cdot\text{sec}^{-1}$, which is close to the value $\alpha_i = 1.6\cdot 10^{-6}\ \text{cm}^3\cdot\text{sec}^{-1}$ obtained from data on ionization at low altitudes of 5–30 km (it is given in the handbook ($^{16}$)). Using this value of $\alpha_i$,

one can obtain the values of \(l^-\) (and, taking into account \(n_e\), the values of \(n_i^-\)) given in Table 1. It is seen that at heights of 50–70 km the values \(n_i^+ = n_i^- + n_e\) are close to the new results of rocket measurements \((^2)\). The values of \(l^-\) are apparently determined to within a factor of 2–3. It is important to emphasize that the variation of \(l^-\) with height is determined only by the data on \(\alpha'\) and \(\alpha^*\).

Thus, the use of data on the profile \(\alpha'(h)\) makes it possible to estimate the relative concentration of negative ions at heights of 50–80 km.

Let us compare the obtained values of \(l^-\) with the theoretical values determined by the formula

\[ l^-=\frac{1.5\cdot 10^{-30}[O_2]^2}{\rho+kn}, \tag{3} \]

where \(n\) and \([O_2]\) are the concentrations of neutral particles and oxygen molecules, respectively; \(k\) may be regarded as an effective constant for reactions of electron detachment from negative ions as a result of collision processes. Using the data on the atmospheric model in \((^{16})\), one can find that the values of \(l^-\) in Table 1 satisfy formula (3) for \(\rho = 0.2\text{–}0.45\ \mathrm{sec}^{-1}\) and \(k=(3\text{–}10)\cdot 10^{-17}\ \mathrm{cm}^3\cdot\mathrm{sec}^{-1}\). We note that the value of \(\rho\) agrees with modern data \((^{15})\), while the value of \(k\) is close to Bailey’s estimates from independent data during PCA \((^{17})\). Indeed, as is known, the diurnal variations of radio-wave absorption during PCA are equal to \(\sim 4\), whence it follows that \(\rho+kn\approx 4k\). Taking into account that, according to rocket measurements, absorption occurs at heights of 65–75 km \((^1)\), we obtain \(k=(3\text{–}6)\cdot 10^{-17}\ \mathrm{cm}^3\cdot\mathrm{sec}^{-1}\). These conclusions are important for the photochemistry of the \(D\) region.

Fig. 1

Table 1

| | \multicolumn{4}{c}{\(h,\ \mathrm{km}\)} |
|---|---:|---:|---:|---:|
| | 50 | 60 | 70 | 80 |
| \(\alpha'\), \(\mathrm{cm}^3\cdot\mathrm{sec}^{-1}\) \((^{10})\) | \(2.5\cdot 10^{-5}\) | \(8\cdot 10^{-6}\) | \(2.1\cdot 10^{-6}\) | \(4.7\cdot 10^{-7}\) |
| \(n_e,\ \mathrm{cm}^{-3}\) \((^1,\ ^{13})\) | 20 | 50 | 160 | 800 |
| \(\alpha' n_e^2,\ \mathrm{cm}^{-3}\cdot\mathrm{sec}^{-1}\) | 0.01 | 0.02 | — | — |
| \(q,\ \mathrm{cm}^{-3}\cdot\mathrm{sec}^{-1}\) \((^{14})\) | 0.35 | 0.1 | — | — |
| \(l^-\) | 35 | 4 | 1.1 | 0.1 |
| \(n_i^-,\ \mathrm{cm}^{-3}\) | 700 | 200 | 180 | 240 |

Institute of Applied
Geophysics

Received
15 II 1967

CITED LITERATURE

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