We discuss electric fields generated by cosmic ray air showers at large impact parameters b.

Figure: electric field E (a) polarization map for a shower going through the map at point B. Acceleration of positrons is to the right but the polarization is not always opposite to it. (Polarization of E (v) would be to the left everywhere.) Figure: electric field E (a) polarization map for a shower going through the map at point B. Acceleration of positrons is to the right but the polarization is not always opposite to it. (Polarization of E (v) would be to the left everywhere.)
An approximation relevant to this situation is given. The formulation makes explicit the relationship between the shower profile and the radio pulse shapes at large b, putting forward one important observational consequence, namely the decrease of the high-frequency cutoff fc ≈ 1/b2 when the impact parameter increases. The approximation is also used to give a detailed comparison between two emission models, the geosynchrotron model and the transverse current model.

Published by T. Gousset, J. Lamblin, S. Valcares, in Astroparticle Physics 31, February 2009, P. 52-62 https://doi.org/10.1016/j.astropartphys.2008.11.005