The no-reflection regime of radar detection of cosmic ray air showers

The ionization front of a cosmic ray air shower propagates in the atmosphere with almost the speed of light in vacuum, i.e., faster than a radio wave in the air. There can be no reflection of a radar signal from such a front. Instead, an additional transmitted wave, which travels behind the front in the backward direction, is generated. We study the frequencies, propagation directions, and amplitudes for the waves excited at the front and discuss their use for radar detection of air showers.