Calculations of low-frequency radio emission by cosmic ray-induced particle showers

The radio technique for the detection of high energy cosmic rays consists in measuring the electric field created by the particle showers created inside a medium by the primary cosmic ray. The electric field is then used to infer the properties of the primary particle. Nowadays, the radio technique is a standard, well-established technique. While most current experiments measure the field at frequencies above $20$ MHz, several experiments have reported a large emission at low frequencies, below $10$ MHz. The EXTASIS experiment aims at measuring again and understand this low-frequency electric field. Since at low frequencies the standard far-field approximation for the calculation of the electric field does not necessarily hold, in order to comprehend the low-frequency emission we need to go beyond the far-field approximation. We present in this work a formula for the electric field created by a particle track inside a dielectric medium that is valid for all frequencies. We then implement this formula in the SELFAS Monte Carlo code and calculate the low-frequency electric field of EAS. We also introduce the sudden death pulse (SDP), an emission caused by the coherent deceleration of the shower front, and study its properties.