Lagrange multiplier techniques in structural analysis

Abstract

7.5-mm radius sphere at 10 mm Hg as seen by a 4.3-mm wavelength radar. The same kinds of comparisons have also been made for some previously published Canadian Armament Research and Development Establishment (GARDE) data, and similar results have been obtained. In all cases, it is evident that the theory is capable of predicting a very large decrease in cross section for these very thin plasma layers, something which was not possible with previous theories. The details of radar cross section variation with speed depend critically on the development of the ionization around the body. In particular, we find that the results are very sensitive to the rate constants used in the nonequilibrium flow field calculations. Thus, there is a need for very good flow field calculations before exact comparisons between the theoretical and experimental results can be made. Work is continuing along the lines of improving the diffraction theory used in the prediction of the radar cross sections of plasma-covered metal bodies and in the calculation of the flow fields around blunt bodies. In conclusion, it appears that a theoretical explanation has been found for the large decrease in the radar cross section of a blunt-metal body when it is covered by a very thin plasma sheath. The decrease depends on partial coverage of the body by the plasma layer. It is the angular gradients of the plasma properties around the body that cause severe diffraction of the radar wave. The details of the effect depend so critically upon the distribution of ionization in the plasma sheath that the effect may be useful as a flow field diagnostic.