Electromagnetic fields of a relativistic electron avalanche with special attention to the origin of lightning signatures known as narrow bipolar pulses

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 model of the avalanche was utilized to test the idea whether the source of the lightning signatures known as narrow bipolar pulses could be relativistic avalanches. The idea was tested by using the simultaneously measured electric fields of narrow bipolar pulses at two distances, one measured far away from the source and the other in the near vicinity. The avalanche parameters were extracted from the distant field and they are used to evaluate the close field. The results show that the source of the NBP can be modeled either as a single or a multiple burst of relativistic avalanches with speed of avalanches in the range of 2-3 × 108 m/s. The multiple avalanche model agrees better with the experimental data in that it can also generate the correct signature of the time derivatives and the HF and VHF radiation bursts of NBP.