Radiation Resulting from an Impulsive Current in a Vertical Antenna Placed on a Dielectric Ground

We consider the electromagnetic field generated by passing an impulsive current of the form of a delta function δ(t) through a vertical Dipole antenna placed on a dielectric ground. The problem is formulated in operational form, and the Hertzian potential Π is expressed as an integral over a Bessel function. This operational solution is then inverted, and the Hertzian potential Π(r,z,t) is expressed in terms of finite complex integrals over a fixed range. The integrals for Π were evaluated on the electronic computer of the Weizmann Institute, and the results for the case of a dielectric constant ε=9 are shown in Fig. 1. The field in the air starts with a finite value at the time of arrival of the wave front, and then increases in a monotone fashion towards the steady state value. In the ground, there is a cone of angle ${\sin }^{\text{−1}}\text{(1/}\sqrt{\epsilon })$ centered around the downward vertical, inside which the field starts again with a finite value and then decreases toward the steady state value. Outside this cone, the direct wave in the ground is preceded by a diffracted wave originating from secondary radiation emanating from the portion of the boundary where the air wave passed in advance of the ground wave. This diffracted wave starts with zero amplitude and increases thereafter, becoming logarithmically infinite at the time of arrival of the direct wave in the ground. After that the amplitude decreases continuously toward the steady‐state value.