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Notes: Abstract We present a comparison of the observed behavior of the F region ionosphere over Millstone Hill during the geomagnetically quiet and storm period on 16/23 March, 1990, with numerical model calculations from the time-dependent mathematical model of the Earth’s ionosphere and plasmasphere. The effects of vibrationally excited N2(v) and O2(v) on the electron density and temperature are studied using the N2(v) and O2(v) Boltzmann and non-Boltzmann distribution assumptions. The deviations from the Boltzmann distribution for the first five vibrational levels of N2(v) and O2(v) were calculated. The present study suggests that these deviations are not significant at vibrational levels v = 1 and 2, and the calculated distributions of N2(v) and O2(v) are highly non-Boltzmann at vibrational levels v 〉 2. The N2(v) and O2(v) non-Boltzmann distribution assumption leads to the decrease of the calculated daytime NmF2 up to a factor of 1.44 (maximum value) in comparison with the N2(v) and O2(v) Boltzmann distribution assumption. The resulting effects of N2(v 〉 0) and O2(v) 〉 0) on the NmF2 is the decrease of the calculated daytime NmF2 up to a factor of 2.8 (maximum value) for Boltzmann populations of N2(v) and O2(v) and up to a factor of 3.5 (maximum value) for non-Boltzmann populations of N2(v) and O2(v). This decrease in electron density results in the increase of the calculated daytime electron temperature up to about 1040/1410 K (maximum value) at the F2 peak altitude giving closer agreement between the measured and modeled electron temperatures. Both the daytime and nighttime densities are not reproduced by the model without N2(v 〉 0) and O2(v 〉 0), and inclusion of vibrationally excited N2 and O2 brings the model and data into better agreement. The effects of vibrationally excited O2 and N2 on the electron density and temperature are most pronounced during daytime.

Notes: Abstract We present a comparison of the electron density and temperature behaviour in the ionosphere and plasmasphere measured by the Millstone Hill incoherent-scatter radar and the instruments on board of the EXOS-D satellite with numerical model calculations from a time-dependent mathematical model of the Earth’s ionosphere and plasmasphere during the geomagnetically quiet and storm period on 20/30 January, 1993. We have evaluated the value of the additional heating rate that should be added to the normal photoelectron heating in the electron energy equation in the daytime plasmasphere region above 5000 km along the magnetic field line to explain the high electron temperature measured by the instruments on board of the EXOS-D satellite within the Millstone Hill magnetic field flux tube in the Northern Hemisphere. The additional heating brings the measured and modelled electron temperatures into agreement in the plasmasphere and into very large disagreement in the ionosphere if the classical electron heat flux along magnetic field line is used in the model. A new approach, based on a new effective electron thermal conductivity coefficient along the magnetic field line, is presented to model the electron temperature in the ionosphere and plasmasphere. This new approach leads to a heat flux which is less than that given by the classical Spitzer-Harm theory. The evaluated additional heating of electrons in the plasmasphere and the decrease of the thermal conductivity in the topside ionosphere and the greater part of the plasmasphere found for the first time here allow the model to accurately reproduce the electron temperatures observed by the instruments on board the EXOS-D satellite in the plasmasphere and the Millstone Hill incoherent-scatter radar in the ionosphere. The effects of the daytime additional plasmaspheric heating of electrons on the electron temperature and density are small at the F-region altitudes if the modified electron heat flux is used. The deviations from the Boltzmann distribution for the first five vibrational levels of N2(v) and O2(v) were calculated. The present study suggests that these deviations are not significant at the first vibrational levels of N2 and O2 and the second level of O2, and the calculated distributions of N2(v) and O2(v) are highly non-Boltzmann at vibrational levels v 〉 2. The resulting effect of N2(v 〉 0) and O2(v 〉 0) on NmF2 is the decrease of the calculated daytime NmF2 up to a factor of 1.5. The modelled electron temperature is very sensitive to the electron density, and this decrease in electron density results in the increase of the calculated daytime electron temperature up to about 580 K at the F2 peak altitude giving closer agreement between the measured and modelled electron temperatures. Both the daytime and night-time densities are not reproduced by the model without N2(v 〉 0) and O2(v 〉 0), and inclusion of vibrationally excited N2 and O2 brings the model and data into better agreement.

Notes: Abstract The choice of a function approximating the exposure dependence of the amplitude transmission of negative recording media is considered from the standpoint of the theory of measure within the framework of the algebraic model of the system in the geometrical optics approximation. Two processes are taken into account: photodetection in the quasi-linear and the overexposure ranges and light modulation by transparencies made by the method of negative photodetection. Formal construction of the algebra is shown to lead to the approximation by Sugeno negation. Comparison with the approximation by a power polynomial is made.