Modelling of Lightning First Short Stroke Current Waveform by Stepped or Nonlinear Capacitance Discharges

Due to the varying nature of lightning events, the wave shapes of the same type of lightning currents differ significantly. Typical descriptions of the wave shape in form of (multi) exponential approximations are aimed to provide handy equations to describe the energy turn over within the discharge channel. However, for considerations where the leader growth phase is of particular interest, these approximations may oversimplify the physical nature of the stepped downward and upward leader growth and its associated pre-discharge current. Further on, they assume an impressed discharge current instead of a cloud charge, which may not be appropriate for some cases. So, with the help of capacitive-resistive equivalent circuit diagrams, in which capacitances are switched or steadily increased, the temporal change of the electric field during the development of lightning leaders is simulated. Both discontinuous pre-growth in jerk steps or continuous steady pre-growth of leaders are considered here. As a result, the front part of lightning first short stroke impulse currents can be calculated in more detail either analytically or numerically.