Calculations of electric fields for radio detection of Ultra-High Energy particles

The detection of electromagnetic pulses from high energy showers is used as a means to search for Ultra-High Energy cosmic ray and neutrino interactions. An approximate formula has been obtained to numerically evaluate the radio pulse emitted by a charged particle that instantaneously accelerates, moves at constant speed along a straight track and halts again instantaneously. The approximate solution is applied to the particle track after dividing it in smaller subintervals. The resulting algorithm (often referred to as the ZHS algorithm) is also the basis for most of the simulations of the electric field produced in high energy showers in dense media. In this work, the electromagnetic pulses as predicted with the ZHS algorithm are compared to those obtained with an exact solution of the electric field produced by a charged particle track. The precise conditions that must apply for the algorithm to be valid are discussed and its accuracy is addressed. This comparison is also made for electromagnetic showers in dense media. The ZHS algorithm is shown to describe Cherenkov radiation and to be valid for most situations of interest concerning detectors searching for Ultra-High Energy neutrinos. The results of this work are also relevant for the simulation of pulses emitted from air showers.