2. Evaluation of the Impact of the SNE Regions

[7]  The problems of evaluation of the impact of SNE artificial ionization regions on the operation of radioelectronic systems due to its complicity should be solved in two stages. At the first stage, as a rule, the parameters of the medium disturbed by the explosion are studied. First of all, fairly exact methods of solution of the nonstationary equation of the transfer of SNE ionizing radiation in the inhomogeneous atmosphere are developed [see Lobolev, 1997a, 1997b; Kukhtevich and Mashkovich, 1979]. Then the problems of ionization and kinetics of the plasma parameters of the lower atmospheric layers by the X ray and penetrating radiation are considered.

[8]  The calculation of the LREI SNE parameters requires taking into account a large number of photochemical processes involving tens of chemical constituents. Variations in the electron concentration N(t) and ion composition in time are looked for as a result of integration of the system of differential equations of continuity for each parameter. The initial conditions are formed under action of gamma quanta, neutrons, and X rays with the formation rates of the constituents determined by the fission fragments and beta particles. In the general case to take into account correctly the influence on N(t) of minor neutral constituents one has to include into the equations (together with the chemical reactions) the transport terms. Integration of such a system of differential equations of a "rigid type" needs large resources of computer time, so for its solution sometimes one attracts special computing methods accelerating the computation process and introducing additional errors [see, e.g., Kozlov et al., 1982]. The approach realized by Kozlov [1967, 1971], Kozlov and Kudimov [1969], and Kozlov and Raizer [1966] provided development of methods and calculation algorithms which made it possible to simulate numerically parameters of the lower atmosphere disturbed by the explosion. The parameters agree satisfactorily with the experimental data. Actually, for the frequency range from 100 to 1000 MHz and more where the vast majority of the radiolocation, radio navigation, and radio communication equipment operates, the method provides the accuracy of N(t) calculations within LREI better than a few tens of percent. The problem of evaluation of the modeling accuracy of the disturbed by the explosion medium (where radio waves are propagating) is far from being trivial and we will come back to this problem at the end of the paper. Here we note that to provide a possibility to control the N(t) simulation accuracy in the LREI on the basis of radiophysical measurements available one has to develop methods of calculation of radiophysical effects with the error less than a few percent.

[9]  The studies of the second stage of the considered problem of evaluation of the SNE impact on operation of radioelectronics systems are reduced to solving of two problems. As a preliminary step one has to present the macroscopically continuous components of the dielectric permeability e_ik in terms of parameters characterizing the plasma, that is in terms of the concentration of electrons ( N ), ions ( N_i ), and neutral particles ( N_n ), as well as the distribution of their velocities. The second step involves solution of the Maxwell equations with the given e_ik (r,t) functions and the range of the w cyclic frequencies.

[10]  The plasma in LREI may be considered as a gas ((kT)/(e²N^1/3) 1 ), so to look for general expression for e_ik one should use the method of the kinetic equation which includes also the terms taking into account variations of the distribution function due to the processes of ionization and recombination. As for the initial data for the plasma parameters, the results of the LRIE calculations for the wide range of explosion altitudes and TNT equivalents of nuclear charges obtained by Kozlov [1967, 1971], Kozlov and Kudimov [1969], and Kozlov and Raizer [1966] are used. Table 1 based on the results of these publications shows (for the case q=5000 kT, H = 150 km and w = 10⁹ s ^-1 close to the worst case) the calculations of the LREI plasma parameters along the vertical from the explosion epicenter for the time moment t=1 s. Moreover, the vertical profiles of the effective collision frequencies of ions with neutral particles ( n _{eff, in} ), electrons with neutral particles ( n _{eff, en} ), and electrons with ions ( n _{eff, ei} ), are also shown. The corresponding absorption coefficients of radio waves (see equation (2)): m (w/c) a S/(1+S²) both for the Maxwell velocity distribution of particles ( m_in, m_en, and m_ei ), characterized by the temperature T and for distributions different from the equilibrium distributions due to the ionization processes (m^*_en ) are also presented in Table 1. One can easily see in Table 1 that within the height interval 30-90 km the values of e _ik are determined by the electron distribution f_e (r, v, t), and the distribution of their velocities may be considered as a Maxwell distribution with acceptable accuracy. Taking into account that for w 10⁹ s^-1 the input of LREI into the polarization distortions is negligibly small [Batyr et al., 1996], to describe macroscopically continuous properties of the plasma, one can use the complex permeability e = e' - ie'' = 1/3 Sp e_Ik (under w_H/ w = |e| H_E / mcw 0 )

(1)

Here K_e,n and K_{s, n} are the functions obtained in the scope of the kinetic theory

Figure 1

[see, e.g., Ginzburg, 1967, Figures 6.1 and 6.2];

(2)

where e and m are the charge and mass of an electron, c is the light velocity, H_E is the Earth magnetic field, and

The results of the performed estimations (see Table 1) show that for w 10⁹ s^-1 with the acceptable error not exceeding a few percent one can take K_e,n = K_s,n 1 and limit the study by the consideration of the permeability in the scope of the elementary theory [Ginzburg, 1967].

[11]  As the next step in the study of the problem of radio wave propagation in plasma one has to find solution of the Maxwell equations for the given spatial-time distributions of e(r, t) having certain scales of nonstationarity and spatial nonuniformity. One can show that for the LREI plasma the conditions of quasi-stationarity and quasi-uniformity are fulfilled already at t 1 s and w 10⁹ s ^-1. The characteristic scales of irregularities ( z ) of the artificial ionization regions for nuclear explosions are from a few kilometers to tens of kilometers, so in the l wavelength range we are interested in the value of the l/z ratio does not exceed portions of a percent. One can demonstrate [Semenov, 1974] that in our case the solution of the Maxwell equations in the zero approach of the geometric optics is reduced to integration of three equations: eiconal y

(3)

of the transport for the electric field amplitude F (k=w/c )

(4)

and the rotation angle of the polarization plane which (as it has been noted above) one may not consider for the propagation through LREI of radio waves with w 10⁹ s^-1. Integrating equations (3) and (4), one can calculate the electromagnetic field and the main radiophysical effects with the accuracy up to the terms 0 (l/z), that is, the methodical error of the calculations of radio wave distortions is negligibly small.