GEOPHYSICS

G. S. IVANOV-KHOLODNY and L. A. ANTONOVA

IONIZATION IN THE NIGHTTIME IONOSPHERE

(CORPUSCULAR HYPOTHESIS)

(Presented by Academician E. K. Fedorov on 24 V 1961)

The source that creates the ionized layer in the upper atmosphere is generally considered to be solar short-wave radiation with (\lambda < 900) Å. During the day, at great altitudes, equilibrium is established between the rate of the processes of ionization of molecules and atoms by hard quanta, on the one hand, and the rate of the processes of recombination of electrons with ions, on the other. In the evening the ionosphere should be completely neutralized in a comparatively short time. Taking into account new data on recombination coefficients ((^1,^2)), it should be assumed that the electron concentration at the maximum of the ionospheric (F) layer should decrease by a factor of 10 in 3–30 min and by a factor of 100 in 1–10 hours. At lower altitudes the neutralization process proceeds still faster. In reality, after sunset the electron concentration in the ionosphere decreases strongly, but, contrary to expectation, remains at a comparatively high level, being only 3–10 times smaller than during the day ((^3)). An analogous picture is observed during solar eclipses. The ionosphere is also preserved during periods of deep polar nights at high latitudes. Therefore the existence of an additional source of ionization in the ionosphere at night is beyond doubt, although its nature remains unexplained.

Certain features of the behavior of the nighttime ionosphere and of the (F) layer—for example, significant irregular fluctuations of the electron concentration with time, the dependence of the height of the layer and of the electron concentration on geomagnetic latitude, the existence of local regions of enhanced ionization, etc.—lead one to suppose that the source of ionization of the nighttime ionosphere is charged particles, corpuscles. This idea has repeatedly been expressed by V. I. Krasovskii, beginning in 1957 ((^4)). The idea of ionization of the upper atmosphere by corpuscles received support after Van Allen et al. ((^5)) discovered, by means of rockets, fairly intense electron fluxes even at comparatively low altitudes, (\sim 100) km. The maximum intensity of the fluxes is observed in the auroral zone; however, these electron fluxes are very irregular and apparently exist at practically all latitudes. In the authors’ experiments ((^6)) a flux with an intensity of (\sim 10^{-2}) erg/cm(^2)·sec at an altitude of 80–100 km was observed both at middle and at high latitudes.

It is reasonable to assume that in the Earth’s magnetic field, not only in the radiation belts but also in all its other regions, there is, above the upper atmosphere, some number of trapped electrons. These electrons move along helical lines along the magnetic lines of force. Recently new evidence has been obtained for the existence of such fluxes or streams of electrons. Smith et al. established a columnar structure of the ionosphere above the maximum of the (F) layer ((^7)). O’Brien et al. ((^8)), with the aid of the satellite Explorer VII, directly above an auroral arc, recorded a significant enhancement of the electron flux.

Where the magnetic tube of force along which the electron flux moves enters sufficiently dense layers of the atmosphere, frequent collisions of electrons with atoms and molecules of the atmosphere occur, as do ionization of the atmosphere and an intense loss of electrons from the flux. Thus,

the distribution of the electron intensity along the tube of force will be determined, on the one hand, by the mechanism of electron production and by the distribution of the sources in the magnetic field, and, on the other, by the mechanism of loss of electrons from the magnetic tubes. Let us suppose that the principal mechanism by which the electrons of the flux lose their energy is inelastic collision with atmospheric particles. Assuming that under nighttime conditions ionization in the ionosphere is produced only by an electron flux of corpuscles, let us calculate their energy. Under equilibrium conditions the number of ions formed in (1\ \mathrm{cm}^3) in 1 sec, (q), is equal to the number of recombinations (\alpha' n_e^2), where (n_e) is the electron density at a given height (h), and (\alpha') is the effective recombination coefficient. If at height (h) the intensity of the flux of electrons falling on (1\ \mathrm{cm}^2) in 1 sec from 1 steradian in the direction determined by the angles (\vartheta) (the angle between the electron velocity vector and the vertical) and (\varphi) (azimuth) is equal to (n(E,h,\vartheta,\varphi)), then

[
q(h)=\int_{\vartheta=-0}^{\frac{\pi}{2}}\int_{\varphi=0}^{2\pi}\int_{E=0}^{\infty}
n(E,h,\vartheta,\varphi)\rho\frac{f(E)}{\cos\vartheta}\sin\vartheta\,d\vartheta\,d\varphi\,dE
=\alpha' n_e^2,
\tag{1}
]

where (\rho) is the atmospheric density; (f(E)) is the ion-formation coefficient, showing how many ion pairs are produced by one electron with energy (E) in traversing (1\ \mathrm{g}) of substance. In formula (1) it is taken into account that, in passing through a horizontal layer, an electron produces (1/\cos\vartheta) times more ions than a vertically incident electron. If (Q=\int_0^\infty q(h)\,dh) is the total number of recombinations in a column of the night ionosphere, then the energy flux of electrons is (I=Q\varepsilon), where (\varepsilon) is the energy lost by an electron in forming one ion pair. For electron energies (E>4\cdot10^3\ \mathrm{eV}), for atmospheric constituents (\varepsilon\simeq30\ \mathrm{eV}), and for smaller values of (E) it increases somewhat, reaching (\varepsilon\simeq60\ \mathrm{eV}) at (E\sim100\ \mathrm{eV}). Table 1 presents the initial data and the results of the calculations. The distribution of electron density (n_e) with height at night was obtained in a number of experiments by means of rockets ((^3,^9–^{11})). In order to reflect the quietest ionospheric conditions, Table 1 takes the smallest values of (n_e) according to these data.

The atmospheric density (\rho), obtained experimentally by rockets and satellites, is taken from the work of V. V. Miknevich et al. ((^{12})). The quantity (\rho_h\equiv\int_0^\infty \rho\,dh). In calculating the quantity (\alpha' n_e^2), the values of (\alpha') were taken from the work of A. D. Danilov ((^1)), in which it was assumed that for the reaction of dissociative recombination the rate coefficient is (\alpha^=10^{-6}\ \mathrm{cm}^3\cdot\mathrm{sec}^{-1}). Experimental determinations of this quantity give a scatter within one order of magnitude; therefore we shall take (\alpha^=10^{-6}–10^{-7}\ \mathrm{cm}^3\cdot\mathrm{sec}^{-1}). On the basis of the data of Table 1, from (1) we obtain (Q=\int_0^\infty \alpha' n_e^2 dh=2\cdot10^{10}\div2\cdot10^{11}\ \mathrm{cm}^{-2}\cdot\mathrm{sec}^{-1}), and the electron energy flux (I=1–10\ \mathrm{erg}/\mathrm{cm}^2\cdot\mathrm{sec}). We shall also make an estimate of the energy of the electrons in the flux. Assuming, for a preliminary estimate, that the electron flux has axial symmetry with respect to the vertical and that an isotropic flux of electrons falls on a horizontal plane in the ionosphere from the upper hemisphere, from (1) we obtain

[
2\pi\rho\int_0^\infty n(E,h)f(E)\,dE=\alpha' n_e^2.
\tag{2}
]

If the electron spectrum can be represented by a power law (n(E)\,dE\propto E^{-\gamma}dE), then for the upper part of the ionosphere the electron energy flux is

[
I\equiv\pi\int_0^\infty E n(E)\,dE=\pi E_{\mathrm{eff}}n(E_{\mathrm{eff}})\Delta_1 E,
\tag{3}
]

where (E_{\mathrm{eff}}) is the effective value of the energy, and (\Delta_1 E) is approximately equal to the half-width of the spectrum; for a power law (\Delta_1 E = E_{\mathrm{eff}}/(\gamma - 2)). Taking (3) into account, we obtain from (2) that at any height (h)

[
2\pi n(E_{\mathrm{eff}}) f(E_{\mathrm{eff}})\Delta_2 E = \alpha' n_e^2/\rho,
\tag{4}
]

where (\Delta_2 E), like (\Delta_1 E), depends on the form of the electron energy spectrum. The quantity (\alpha' n_e^2/\rho) in expression (4) in fact determines the ionizing power of electrons with effective energy (E_{\mathrm{eff}}). It is seen from Table 1 that this quantity increases sharply with height. Above the maximum of the ionospheric layer it remains almost constant, indicating the constancy of the electron flux in the upper part of the ionosphere. For the upper part of the ionosphere (\alpha' n_e^2/\rho \approx 5\cdot 10^{17}), which together with (3) gives

[
\frac{f(E_{\mathrm{eff}})}{E_{\mathrm{eff}}}\,\varepsilon
=
1.25\cdot 10^6 \frac{\Delta_1 E}{\Delta_2 E}\ \mathrm{cm^2\,g^{-1}}.
\tag{5}
]

Hence one can estimate the effective energy of the electrons. Note that expression (5) is practically independent of the adopted value of (\alpha'). This is obvious if another value (\alpha^) is taken, since (\alpha'\propto \alpha^). But even if

Table 1

* For (\alpha^* = 10^{-6}).

one takes completely different values of the effective recombination coefficient, for example Mitra’s data (13), then the numerical factor in (5) will be equal to (4\cdot 10^5), i.e., it will change little in essence. Assuming that (\Delta_1 E/\Delta_2 E \approx 1), from (5) we obtain (E_{\mathrm{eff}} = 200\ \mathrm{eV}). In this case the total number of electrons in the flux will be (5\cdot 10^9—5\cdot 10^{10}\ \mathrm{cm^{-2}\,sec^{-1}}). Thus, in order to explain the ionization of the ionosphere at night by corpuscles, it is necessary to assume the existence in the upper atmosphere of a powerful flux of comparatively soft electrons.

Let us calculate the electron spectrum more accurately. We shall assume that only electrons with energy (E'), characterized by the range (\rho_h), can reach the level (h) in the ionosphere. Then from (2) we obtain

[
2\pi \int_{E'}^{\infty} n(E) f(E)\, dE
=
\frac{\alpha' n_e^2}{\rho}.
\tag{6}
]

By differentiating both sides of (6) with respect to the parameter (\rho_h), we obtain

[
\pi n(E')
=
\frac{
\dfrac{\partial}{\partial \rho_h}\left(\dfrac{\alpha' n_e^2}{\rho}\right)
}{
2 f(E')\, \partial E'/\partial \rho_h
}.
\tag{7}
]

The results of calculations by this formula are given in Table 1. The values of the quantities (f(E')) and (dE'/d\rho_h) were taken according to reference data ((14), pp. 343 and 347). The electron spectrum obtained proves to be a power-law spectrum with (\gamma = 4.5).

Taking into account that the main outflow of electrons from the flux occurs in the ionosphere, and that above the ionospheric maximum their flux is almost constant, one should think that their source is located in the ionosphere itself. It is possible that some mechanism for accelerating electrons exists in the upper atmosphere.

One may wonder why the comparatively soft electrons indicated above have not yet been detected directly on satellites and rockets. The matter, however, is explained by the fact that the corpuscular-radiation and cosmic-ray detectors used up to now were sensitive only to electrons with (E > 10)—20 keV, i.e., they could measure only the “tail” of hard electrons in the spectrum. The spectrum of fast electrons was observed in aurorae by Meredith et al. ((^{15})), in the inner radiation belt by Holly and Johnson ((^{16})), and in the outer belt by Walt et al. ((^{17})). Approximation of the electron spectrum by a power law (n(E)dE \propto E^{-\gamma} dE) gives (\gamma) a value of 4—5. The same steep spectrum has been estimated for sporadic electron fluxes at an altitude of (\sim 100) km from their bremsstrahlung X-radiation recorded on balloons by Anderson ((^{18})).

Thus, the experimental data confirm that in various formations of the upper atmosphere the form of the electron spectrum is the same as that obtained above for the quiet ionosphere.

In the experiment of Meredith et al. ((^{15})) a detector was installed capable of recording a flux intensity (\geq 10^{9}\ \mathrm{cm}^{-2}\cdot\mathrm{s}^{-1}\cdot\mathrm{sterad}^{-1}) of soft electrons with energies in the interval 30—1000 eV. Of three rockets, one reached a maximum altitude of 178 km, but no soft electrons were recorded. According to the data of Table 1, electrons with energy (>500) eV can reach an altitude of 178 km, and their flux is (2\cdot 10^{7}\ \mathrm{cm}^{-2}\cdot\mathrm{s}^{-1}\cdot\mathrm{sterad}^{-1}), i.e., almost two orders of magnitude smaller than the detector in ((^{15})) could sense. This example shows that at high altitudes it is possible to measure experimentally the flux of soft electrons with the aid of this detector, or with Gringauz traps ((^{19})), which are still more sensitive.

It is evident that the Earth’s magnetic field must exert a substantial influence on the distribution of electron fluxes and their sources. In particular, the electron flux must depend on geomagnetic latitude. Electron fluxes should also leave a noticeable imprint on the picture of the daytime ionosphere. If, indeed, the electron sources are located in the ionosphere, then solar radiation must also influence the intensity of the fluxes. A more detailed analysis of ionospheric data in the region of the (F)-layer maximum, taking account of the lifetime of the flux electrons, may yield accurate data on the angular distribution of these electrons and on the nature of their source. All these questions should be considered separately.

Institute of Applied Geophysics
Academy of Sciences of the USSR

Received
14 III 1961

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