Density and magnetic field strength dependence of radio pulses induced by energetic air showers

We have studied the effect of changing the density and magnetic field strength in the coherent pulses that are emitted as energetic showers develop in the atmosphere. For this purpose we have developed an extension of ZHS, a program to calculate coherent radio pulses from electromagnetic showers in homogeneous media, to account for the Lorentz force due to a magnetic field. This makes it possible to perform quite realistic simulations of radio pulses from air showers in a medium similar to the atmosphere but without variations of density with altitude. The effects of independently changing the density, the refractive index and the magnetic field strength are studied in the frequency domain for observers in the Cherenkov direction at far distances from the shower. This approach is particularly enlightening providing an explanation of the spectral behavior of the induced electric field in terms of shower development parameters. More importantly, it clearly displays the complex scaling properties of the pulses as density and magnetic field strength are varied. The usually assumed linear behavior of electric field amplitude with magnetic field strength is shown to hold up to a given magnetic field strength at which the extra time delays due to the deflection in the magnetic field break it. Scaling properties of the pulses are obtained as the density of air decreases relative to sea level. A remarkably accurate scaling law is obtained that relates the spectra of pulses obtained when reducing the density and increasing the magnetic field.