Reply to comment by Rajeev Thottappillil and Vladimir A. Rakov on ''Radio frequency radiation beam pattern of return strokes: A revisit to theoretical analysis''

We agree with TR that equation (10) of SJF is not general, since it was not meant to be. We should have made it more obvious. Nevertheless, we found it necessary for some readers to extend the SJF analysis. Current discontinuity at the wave front was a major concern of TR, and they have in the past treated it very carefully with thorough mathematic analyses [e.g., Thottappillil et al., 1998]. In this reply, by using the fundamental relation of equation (7) given by SJF, the discontinuity needs no special treatment. However, it might be reasonable to argue that the concept of current source/sink is analogous to the discontinuity. This reply further shows that the F factor is a fundamen tal radiation beam factor for moving current, which may, however, appear in different forms in different models. It is also shown that if one moves along with the current pulse, the analysis can be significantly simplified with only a few steps to arrive at the solution, in contrast to lengthy mathematical derivations in previous reports. After all, the derivation of equation (7) of SJF is nothing new, and similar treatment between moving and stationary frames can be found in almost all the classical electrodynamics textbooks. Our only contribution is introducing it to the lightning research community.