The Deep Physics Hidden within the Field Expressions of the Radiation Fields of Lightning Return Strokes

Vernon Cooray, Gerald Cooray
2016 Atmosphere  
Based on the electromagnetic fields generated by a current pulse propagating from one point in space to another, a scenario that is frequently used to simulate return strokes in lightning flashes, it is shown that there is a deep physical connection between the electromagnetic energy dissipated by the system, the time over which this energy is dissipated and the charge associated with the current. For a given current pulse, the product of the energy dissipated and the time over which this
more » ... er which this energy is dissipated, defined as action in this paper, depends on the length of the channel, or the path, through which the current pulse is propagating. As the length of the channel varies, the action plotted against the length of the channel exhibits a maximum value. The location of the maximum value depends on the ratio of the length of the channel to the characteristic length of the current pulse. The latter is defined as the product of the duration of the current pulse and the speed of propagation of the current pulse. The magnitude of this maximum depends on the charge associated with the current pulse. The results show that when the charge associated with the current pulse approaches the electronic charge, the value of this maximum reaches a value close to h/8π where h is the Plank constant. From this result, one can deduce that the time-energy uncertainty principle is the reason for the fact that the smallest charge that can be detected from the electromagnetic radiation is equal to the electronic charge. Since any system that generates electromagnetic radiation can be represented by a current pulse propagating from one point in space to another, the result is deemed valid for electromagnetic radiation fields in general. Even though the transmission line model or the physical scenario associated with it (i.e., propagation of a current pulse from one point in space to another with constant speed and without attenuation) is used mainly in lightning research, it can actually be used to represent other electromagnetic radiation systems as well. For example, if the duration of the current pulse is much longer than the time necessary for the current pulse to travel the length of the path, then the physical system and the resulting radiation fields become identical to those of a short dipole [6, 7] . Since the electromagnetic radiation is created by the acceleration of charges associated with the spatial and temporal variations of electric currents [8], this model should be able to represent any radiating system if we relax the assumptions of constant speed and absence of attenuation of the current waveform. For example, references given in the previous section (i.e., [3] [4] [5] ) show that by introducing attenuation and dispersion into this model, one can utilize it to model a more realistic return stroke. In this paper, the above-mentioned model is used to study the relationship between the electromagnetic radiation, the time over which this electromagnetic radiation is generated and the charge associated with the current. It will be shown that the product of the magnitude of the emitted radiation and the time over which it is emitted is deeply connected to the fact that the minimum charge that can be transported by the current pulse is equal to the electronic charge. However, the first step of our study is to evaluate the electromagnetic energy generated by the system under consideration. This evaluation is conducted by utilizing the electric fields of accelerating charges as presented by Cooray and Cooray [7, 9] . The relevant field equations are given in the following sections. Electromagnetic Fields Generated by A Current Pulse that Moves From One Point in Space to Another along A Straight Line with Uniform Velocity and without Attenuation The geometry under consideration is shown in Figure 1 . A current pulse originates at point S1 and travels with uniform speed u without attenuation or dispersion towards S2. At S2, the current is terminated. As shown by Cooray and Cooray [7, 9] the total electric field at point P, generated by this process, has five components. They are as follows: (i) the radiation field generated from S1 during the acceleration of charge when the current is initiated, (ii) the radiation field generated from S2 during the charge deceleration as the current is terminated, (iii) the electrostatic field generated by the negative charge accumulated at S1 when the positive charge travels towards S2, (iv) the electrostatic field generated by the accumulation of positive charge at S2, and (v) the velocity field generated as the current pulse moves along the channel. The magnetic field generated by the current flow consists of three terms, namely, two radiation fields generated at S1 and S2, and the velocity field generated as the current pulse propagates along the path. Let us now write down the expressions obtained by Cooray and Cooray [7, 9] for these field components.
doi:10.3390/atmos7020021 fatcat:usrochg7ejc4rchwxzyy76tvxm