Abstract: That the disconsistency between the plane one-dimension assumption and the law that the microwave energy flux per unit area is inversely proportional to the square of the propagation distance is pointed out. The fundamental equations of the HPM propagation in the atmosphere under the beam flux one-dimension assumption are given. The characteristics and scaling laws of the ionization atmosphere are studied in detail. When n/nc is not too small, the great difference on the tail-erosion between the plane one-dimension and the beam one-dimension assumptions is presented.