EM Fields Associated with a Vertical Antenna Geometry dz’dz’ z’z’ i(z’,t) R

Fields from infinitesimal dipole Equation derived by Uman et al. (1975) EM Fields Associated with a Vertical Antenna

Fields from infinitesimal dipole The so-called static term EM Fields Associated with a Vertical Antenna

Fields from infinitesimal dipole Induction EM Fields Associated with a Vertical Antenna

Fields from infinitesimal dipole and, radiation. EM Fields Associated with a Vertical Antenna

Fields from infinitesimal dipole Note: Thottappillil and Rakov (2001) have shown that the explicit distance dependence is not a sufficient indicator to divide the fields into their electrostatic, induction and radiation components. EM Fields Associated with a Vertical Antenna

Fields from infinitesimal dipole Only this term produces a non-zero energy flow. EM Fields Associated with a Vertical Antenna

The so-called radiation term contains the derivative of the current Question: Does a non-zero current derivative along the lightning channel implies the existence of radiated fields? This question was discussed by Rubinstein et al.* in *) M. Rubinstein, R. Thottappillil, and F. Rachidi, "Discussion on the influence of the time derivative of the current and the charge acceleration on the radiation fields from lightning channels," in Progress in Electromagnetics Research Symposium PIERS 2007, Beijing, China, EM Fields Associated with a Vertical Antenna

Rubinstein made the following reasoning considering the TL Model The current pulse propagates up undistorted with a constant velocity v EM Fields Associated with a Vertical Antenna

The Transmission Line Model t Current t Current derivative EM Fields Associated with a Vertical Antenna

di/dt Radiation field EM Fields Associated with a Vertical Antenna

The charge density at any given time is given by  z  = i(t - z/v)/v t Current z  EM Fields Associated with a Vertical Antenna

The charge can be represented graphically as follows EM Fields Associated with a Vertical Antenna

Observer on the ground. EM Fields Associated with a Vertical Antenna

Observer on the ground measures radiated field from TL channel. EM Fields Associated with a Vertical Antenna

Does an observer in empty space see radiation? Rubinstein’s thought experiment: EM Fields Associated with a Vertical Antenna

If the observer moves at the same constant speed, he or she sees a static charge. There can be no radiation ! EM Fields Associated with a Vertical Antenna

There can be no radiation either! Back to the case of a static observer EM Fields Associated with a Vertical Antenna

The difference is the ground where charge is being accelerated! EM Fields Associated with a Vertical Antenna

A non-zero time derivative of the current is not a sufficient condition to have radiation. Charge needs to be accelerated for radiation to exist. This property can find useful applications (Mönich, 1991, Rubinstein et al., 2007, Cooray and Cooray, 2010) For the TL model, no need to calculate the fields from each one of the segments. Fields from the ground attachment point suffice. For TL model with tortuosity, only a small discrete number of points radiate. Radiation from lightning strike to an overhead conductor / tower. For the TL model, no need to calculate the fields from each one of the segments. Fields from the ground attachment point suffice. For TL model with tortuosity, only a small discrete number of points radiate. Radiation from lightning strike to an overhead conductor / tower. EM Fields Associated with a Vertical Antenna