Formation-Zone Effect in Transition Radiation Due to Ultrarelativistic Particles

The formation-zone effect in transition radiation due to charged particles with large Lorentz factor $\gamma$, both in air and in aluminum, has been investigated. A stack of aluminum foils spaced uniformly apart was used as the transition radiator. Positrons of 1-to 4-GeV energy ($\gamma =2000\mathrm{} \mathrm{to} 8000$) corresponding to protons of energy 2000-8000 GeV) were employed. The formation-zone effect sets in at about 5 mils in air and at around 0.5 mil in aluminum.