Electric field of a relativistic electron avalanche

In the present study, electromagnetic fields of accelerating charges were utilized to evaluate the electromagnetic fields generated by a relativistic electron avalanche. In the analysis it is assumed that all the electrons in the avalanche are moving with the same speed. In other words, the growth or the decay of the number of electrons takes place only at the head of the avalanche. It is shown that the radiation is emanating only from the head of the avalanche where electrons are being accelerated. It is also shown that an analytical expression for the radiation field of the avalanche at any distance can be written directly in terms of the e-folding length of the avalanche. This makes it possible to extract directly the spatial variation of the e-folding length of the avalanche from the measured radiation fields.