Review of Three Equivalent Approaches for Computing Electromagnetic Fields from an Extending Lightning Discharge

Three different general approaches for calculating the electromagnetic fields at any point in space from a lightning return stroke, which is modelled as an extending linear antenna, are reviewed and compared. In the first approach, known as the dipole approach, the electric field is completely expressed in terms of the retarded current on the lightning channel and in the second approach the electric field is expressed in terms of the current and local charge density in retarded time. In the third approach the electric field is completely expressed in terms of the apparent charge density, that is, the charge density that would be seen in the channel by a remote observer at retarded time. In general, apparent charge density is different from the local charge density in retarded time. Analytically these three electric field expressions are equivalent, which is verified numerically also. Besides, it is shown that the magnetic field can be completely expressed in terms of the apparent charge density, as opposed to the traditional expression for magnetic field involving only the retarded current. It is also shown that the division of electric field into static, induction, and radiation field components are not unique in the first two approaches, even though the total field is the same. Numerical calculations of electric fields and magnetic fields predicted by the transmission line (TL) model of the return stroke are presented at different distances from origin and at different angles to the vertical for different return stroke speeds. This also provides a numerical verification of the general electric and magnetic field expressions from the third approach against the first approach. Index Terms Lightning, Return Stroke, Dipole, Monopole, Apparent Charge, Continuity Equation, Lorentz Condition, Electric and Magnetic Fields.