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