1. Introduction

[2]  The electron collision frequency with heavy particles of the ionospheric plasma is one of the most important parameters of the upper atmosphere physics. The frequency determines various kinetic effects [Aggarwal et al., 1979; Itikawa, 1971] and the absorption of radio waves of different ranges depends on this frequency. There are two possibility of its determination: gas-kinetic modeling and empirical estimation. In both cases as a basis is taken the value called the electron effective collision frequency

(1)

where k is the Boltzman constant; m, T_e, and u are the mass, temperature, and velocity, respectively, of the electrons having the Maxwell distribution. The collision frequency depends on the velocity:

(2)

where n is the number of the colliding partners and q is the effective scattering cross section depending on the velocity. Taking (2) into account, equation (1) may be presented in the form

(3)

where

(4)

is the effective scattering cross section and

is the mean velocity.

[3]  Below we will use the denotation n _eff = n_e. The total effective collision frequency is the sum of partial values

the summation being performed over all heavy components X of the plasma. For the D region where the electron temperature is low enough, the dependence of the collision frequency with molecules N₂ and O₂ on the velocity is well approximated by [Budden, 1965]

which according to (1) gives n_e = (5/2) n_M. The n_M parameter is called a frequency of collisions of monoenergetic electrons.

[4]  At the gas-kinetic modeling of the effective electron collision frequency, to calculate values n_e, one needs to know the cross sections of the electron scattering at heavy particles of the plasma, their concentration, and electron temperature [Aggarwal et al., 1979; Banks, 1966; Gurevich and Shvartsburg, 1973; Itikawa, 1971; Mantas, 1974]. It is assumed at an experimental determination that the radio wave attenuation in the ionosphere is caused exceptionally by the absorption of their energy due to the electron collisions to ions and neutral particles of the upper atmosphere. Therefore it is accepted that using the data on absorption, one can obtain empirical estimates of n_e. The radio wave absorption is measured by different ways: by the A1 method (ground-based vertical pulse sounding), A2 method (registration of the intensity of space radio noises), at the oblique sounding and at the propagation of waves between a rocket and Earth surface, and in the cross-modulation experiments.

[5]  The first most complete comparison of the empirical and gas-kinetic results for the D and E regions showed [Thrane and Piggott, 1966] that the agreement between the two has place only in the D region. In the E region, beginning approximately from 100 km, the experimental values exceed the theoretical (gas-kinetic) ones. The discrepancy increases with height reaching a factor of 10 at a height of 120 km [Thrane and Piggott, 1966]. The empirical estimates of the collision frequency in the D region were obtained on the basis of rocket experiments and measurements by the cross-modulation method. In the E region the estimates were obtained mainly on the basis of the vertical sounding.

[6]  The comparison of the theory and experiment by Setty [1972] and Aggarwal et al. [1979] confirmed the conclusions of Thrane and Piggott [1966] and found the presence of similar discrepancies in the F region. The majority of the experimental results for the F region were obtained by the A1 method. The evaluations of n_e were mainly performed by the Appleton method or by its various modifications. [Setty, 1972; Thrane and Piggott, 1966]. Values of n_e in the F region were also determined from the absorption measurements by the A2 method [Benediktov and Tolmacheva, 1975; Gel'berg, 1986; Gel'berg et al., 1985; Kumari and Mahajan, 1971; Saha, 1971; Skrebkova, 1975; Zhulina, 1982]. It was found that at high [Gel'berg, 1986; Gel'berg et al., 1985; Zhulina, 1982] and low [Kumari and Mahajan, 1971; Saha, 1971] latitudes the empirical estimates of n_e also exceed the gas-kinetic ones and only at middle latitudes do they agree with each other [Benediktov and Tolmacheva, 1975; Skrebkova, 1975]. As far as the vast majority of the experimental results were obtained by the A1 method, the above indicated contradictions initiated the following questions. May the discrepancies be caused by incorrect taking into account of the methodical errors while interpreting the absorption measurements by the A1 method in the n_e terms [Thrane and Piggott, 1966]? Do there exist "hidden" or incorrect parameters leading to incorrect estimates of the gas-kinetic values of the collision frequency [Setty, 1972; Thrane and Piggott, 1966]?