Large Doppler shift in RADAR detection of ultra-high energy cosmic rays

Radar detection of cosmic ray air showers has been discussed for 60 years, but never clearly observed. The topic was reexamined by Gorham in 2001 and some serious simulations were done by Takai, who also initiated the Mariachi project utilizing commercial television transmissions as a signal source. The air showers from ultra-high energy cosmic rays are expected to generate a plasma with plasma frequency in the high VHF region. One factor limiting the received signal strength is the short ion recombination time in air at low altitude. However, a major factor which has not been the center of attention so far is the possible large Doppler shifts for non-specular reflection, and the soft transition between specular and diffuse for small objects and short time scales. We discuss recent work on receivers, and simulations of the Doppler shift. These simulations assume a very short ion recombination time in the lower atmosphere, and use an extremely simple mathematical model. A central feature of our simulations is large Doppler shift from non-moving material.