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High-power microwave (HPM) weapon, which is destructive to electronic systems, has developed rapidly due to the great progress of HPM devices and technologies. Plasma with distinctive electromagnetic characteristics is under advisement as one of potentially effective protection materials. Therefore, research on avalanche ionization effect in plasma caused by the interaction between HPM and plasma is of significance for its HPM protection performance. Based on the method of fluid approximation, the wave equation, the electron drift diffusion equation and the heavy species transport equation, explaining the propagation of microwave and the change of the charged particles inside plasma, are established to study the avalanche ionization effect under the HPM radiation. A two-dimensional physical model is built with the help of software COMSOL according to the plasma protection array designed to disturb the propagation of the HPM pulses. It can be shown that the emergence of avalanche effect is greatly affected by the incident power of microwave, and the generation time would be influenced by the initial electron density. Moreover, it can be observed that the avalanche effect appears only when the plasma array is irradiated for a period of time, which means that the performance of HPM is presented as gathering effect, and a large amount of energy is needed to change the internal particle balance in plasma. In addition, the electron density inside the plasma changes rapidly and complicatedly while the avalanche effect comes into being. Besides, the cutoff frequency of the plasma exceeds the frequency of the incident wave with the increase of electron density, which leads to that the electromagnetic wave cannot propagate in the plasma, so that the plasma can be used to protect the HPM irradiation.

The effective-medium theory is extended to calculate the equivalent dielectric constants of hollow spheres. The Maxwell-Garnett, inverted Maxwell-Garnett, and Monecke rules are adopted to investigate the hollow ice spheres. Compared with P. Yang's paper, very different Maxwell-Garnett and inverted Maxwell-Garnett formulas but identical mean permittivity values are presented. In order to verify the validity of effective-medium theory in Mie scattering calculation of hollow dielectric spheres, n-layered Mie solution is adopted to calculate the scattering of hollow ice spheres. The mean permittivity values are used in common Mie scattering calculation of uniform sphere. By comparison, it is evident that the effective-medium theory is suitable for small size parameters. For size parameter is about ten, the effective theory is suitable for a very thin hollow ice sphere. At last, it is pointed out that the effective-medium theory make Mie scattering calculation of hollow spheres easier, and can be extended further to non-uniform and eccentric hollow spheres.