Recurrent Streamer Systems as a Means of Lightning Initiation

Ambient electric fields in storm clouds are insufficient to produce the dielectric breakdown required for lightning initiation and the development of stepped leaders. An explanation for how lightning is initiated despite the insufficient field strength is the presence of a region of locally intensified electric field. Griffiths and Phelps' seminal work on the topic demonstrated that systems of positive streamers intensify the E-field at the start of the system and subsequent systems passing through the charge debris of the previous system further intensifies it [Griffiths R.F. & C.T. Phelps, J. Geophys. Res., 81, 1976]. Insight into the streamer nature of lightning flashes warrants a reexamination of the Griffiths and Phelps (G&P) model to see under what conditions E-fields are intensified above the dielectric breakdown of air and the effects of physical parameters. We have reimplemented the model and validated our calculations against the results in G&P's original work.

The model treats a positive streamer system as a disk of positive charge of growing radius that propagates in the presence of an ambient E-field larger than the stability E-field value. This streamer system transports an increasingly positive charge while depositing increasingly negative charge in its wake in the form of disks of negative charge. The system stops due to leaving the field region above the stability value and the deposited charge intensifies the E-field back at the origin of the system. After this a subsequent streamer system is produced from a hydrometeor at the origin and travels through the negative charge left by the first passage, depositing more negative charge and transporting positive charge until the it's halted by the decreased E-field caused by the system front of the previous pass. This process can keep repeating until the cumulative E-field intensification is above that of the dielectric breakdown of air.

Our calculations confirm G&P's finding that a succession of only a few individual streamer systems can cause the electric field at the origin to intensify by an order of magnitude, in realistic levels of ambient electric fields in storms. The calculations also confirm that after a short region of exponential growth, the total charge in the streamer system front grows quadratically with distance. Coupled with the quadratic growth of cross sectional area of the streamer-system cone, this yields an approximately constant surface charge density and electric field ahead of the advancing front of the streamer system. It was also found that the E-field intensification in a given passage occurs rapidly, early in a system's progression.

Charge growth and resulting E-filed profiles of streamer systems were found to be independent to the step size chosen for the simulation, verifying the model's stability. The physical effects of the parameter choices were investigated, revealing that the initial charge of the system had little overall effect as charge rapidly converged within a few meters. Variations in the conical spreading angle of the streamers affect the degree of E-field intensification and the average potential energy of the streamers determines the pre-quadratic rate of charge growth as well as the location and extent of intensification. The ambient E-field profile affects charge growth and ultimately determines the propagation distance of the system. Improvement to the model were implemented to include self-consistent criteria to stop the streamer system propagation, and realistic thunderstorm electric field profiles. Modifying the parameters to agree with observed data allows for the model to give insight into the physical processes leading up to lightning initiation.