The propagation of high power microwaves through the atmosphere has been our big concern [1] since a relativistic magnetron, relativistic klystron, and newly developed microwave free-electron lasers [2] have entered for a high power microwave contest. For the purpose to study the essential aspect in the long-distant propagation associated with air breakdown, a reliable and efficient simulation code taking into account a variety of physical processes such as impact ionization, absorption by molecules in the atmosphere has been expected.
The presented simulation code is based on a set of fluid equation and the Maxwell equations which describe the interaction of a very strong electromagnetic pulse with a weakly ionized plasma. The Maxwell equations are reformulated by means of a slowly varying amplitude approximation and Fourier expansion in a local space and temporal time period. The local frequency and wave-number are defined and thier evolution equations are derived. The Maxwell equations reduce to a set of these evolution equations and slowly varying amplitude equations. All equations are solved with the finite-difference time-domain (FDTD) technique and the cubic interpolation technique (CIP) is introduced to avoid ,artificial numeric errors. Justification of the formulation is discussed in detail and a typical example of pulse propagation with air break-down will be given.