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The distribution function which given by Grad cannot be used to describe the ionospheric ion velocity distribution due to the larger anisotropic temperature appears in the high-latitude ionosphere. In this article, based on the Boltzmann equation, the relaxation collision model (RCM) was used to substitute the Boltzmann collision integration, and a non-Maxwell ion velocity distribution function with the 16-moments approximation for the bi-Maxwell distribution was given, and the ion transport equation with the 16-moments approximation was also derived and solved. Moreover, the ion velocity distribution, the solution of transport equation and the incoherent scattering spectra with the 13-moments and 16-moments approximation for the relaxation collision model were simulated, analyzed and compared. The research shows that compared with the 13-moments approximation, the 16-moments approximation with the bi-Maxwell distribution is more suitable to describe the characteristics of the anisotropic temperature ion distribution in the high-latitude ionosphere.

Multi-path time delay spread is a very important factor in the bit error rate of high-frequency ionospheric communication channels and in the target detection performance of over-the-horizon radars. In this study, the probability density distribution of multi-path time delay and Doppler shift of ionospheric radio signal are derived using Rayleigh fading. Moreover, the probability density distribution of time delay, average power of the received signal, and received signal variance are discussed in detail. Using a designed experimental circuit, the measured value of the multi-path time delay spread is obtained from three given radio paths by the sweep-frequency pulse sounding technique. The average value of the multi-path time delay spread that changes with the ratio K, which is the operating frequency of the basic maximum usable frequency, is also analyzed and fltted using the least-squares fltting method. Theoretical and statistical research shows that for a given radio path and speciflc frequency, the multi-path time delay spread approximately follows a normal distribution. The average time delay spread decreases with the increase in the ratio K; however, it eventually approaches a steady value. The results of this research provide an empirical reference for further prediction and estimation of the time delay spread of a radar wave propagating through the ionosphere.

The expression of anisotropic temperature ion distribution function under the 13-moment approximation is obtained by solving a set of moment equations based on the Boltzmann equation for a relaxation collision model and with consideration of the anisotropic temperature ion distribution. And the incoherent scatter spectrum with an anisotropic temperature ion distribution is simulated in different directions based on the electromagnetic radiation theory of Sheffield. The effects of different electrical field strengths, ratios of electron temperature to ion temperature, and ion-neutral collision frequencies on the incoherent scatter spectrum are all discussed. Finally, the value of theoretical simulation is compared with the measured value of incoherent scattering spectrum. The result show that the incoherent scatter spectrum of ions seriously deviates from the form of the Maxwellian distribution in the equilibrium state. This phenomenon can be attributed to the effects of anisotropic temperature ion distribution, the larger convection electric field, and other factors in high latitude ionosphere.

The signal distortion will be taken place and a set of attenuation time series will also be produced due to the interaction between the radio wave and the ionospheric irregularities when radio wave propagates through the ionosphere. In this article, based on the traditional chaotic time series prediction and the characteristic of the attenuation time series of the ionosphere, the traditional chaotic prediction method is modified, and a more suitable method is given. Final, by using the modified method, a set of attenuate amplitude time series of the radio signals which propagates through the ionosphere were predicted, and analyzed its prediction accuracy. The results showed that the modified prediction method is very good and accuracy at the short-term.

Based on the theory of ionospheric conductivity and the international reference ionosphere model (IRI-2007), the Pedersen and Hall conductivity change in different phases of the solar cycle during quiet geomagnetic activity was discussed. Meanwhile, because the International Reference Ionosphere model does not reflect the polar ionospheric conductivity very well during the geomagnetic storm. So applied the average energy and the energy flux of the precipitating electrons, the relation between the conductivity and the average energy and the energy flux of the precipitating particles under different energy spectrum function and the geomagnetic activity was analyzed. The results show that the variation of the ionosphric conductivity is good consistent with the change of the field-aligned currents in the polar region, and at the same time, it influenced by the solar activity and the geomagnetic substorm.

The modified Rytov theory was applied to study the Laser beam propagating through the atmospheric turbulence under the double slant path. According to the Born approximation and the kolmogorov atmosphere turbulence power spectrum, the general expression of the optical scintillation both on target's plane and on receiver's were given, and further based on the atmospheric structure constant of ITU-R, the characteristic of the optical scintillation index was analyzed with different parameters altitude. The study showed that the characteristic of optical scintillation index on the target's plane and the receiver's have a nearly connection with the characteristic of scattering field except the altitude effect and so on.

Usually, in laser radar, remote sensing and other optical technology application system, some dual effect will be imposed on the receive beam when it propagates through the atmosphere turbulence and reflected by the retroreflector. Under strong fluctuation, based on the extend Huygens-Fresnel principle, Rytov approximation and its modified theory, a detailed discussion about the beam reflect scintillation characteristic by the point target and the Lambertian surface through the atmospheric turbulence in level path were given. Finally, the main factors which affect the reflect beam scintillation index were analyzed by compared the results of the experimental and theoretical value.

The pulse wave will be affected by the dispersion of the background medium and the scattering of the electron density irregularities while it propagates through the ionosphere turbulent medium. In this article, based on the time moment and the analytical solution of the two-frequency mutual coherence function which obtained by the method of the integral equation iteration. The time characteristic of the pulse signal propagates through the ionospheric media of the polar region was detailedly discussed. By using the ionospheric datum of the south pole, the average arrival time changing with the spectrum index of the irregularities, the inner scale, the outer scale and so on was also analyzed. The numerical simulation show the average arrival time is mainly dominated by the propagation items of the group velocity, and was less affected by the higher-order dispersion of the background medium and the random scattering of the irregularities.

We calculate the effective electrical conductivity in a two-dimensional two-phase composite with checkerboard geometry, solving numerically the truncated set of linear equations for (n+1) coefficients determining the electric potential [Bao Ke-da, Axell, and Grimvall, Phys. Rev. B 41, 4330 (1990)]. Accurate values for this geometry are given at high concentrations 0.1${\mathit{c}}_{1}$0.5 and high conductance ratios ${10}^{2}$${\mathit{S}}^{2}$\ensuremath{\le}${10}^{6}$. Even near the percolation threshold, our analytic expression for the potential can give convergent solutions. In order to study the role of the geometric form of fiber cross sections we compare our results with the transverse conductivity of fibers with other cross sections, thus illustrating that in some cases the geometry of the cross section becomes important.

The susceptibility, range function and RKKY interaction of 1-dimensional dilute magnetic alloys are given. The special features are: there is only ferromagnetic phase transition for small values of 1-dimensional range function and RKKY interaction are a longer distance interaction than the 3-dimensional case. Comparisons between our theory and others' are made.