Plasma channel evolution in the triggered lightning discharges

Abstract

Plasma channel evolution is of fundamental interest for the study of the lightning physics, the electrodynamics of the atmosphere and for electrical engineering practice. The subject of this dissertation is the development of detailed and efficient numerical algorithms for application in the study of the lightning channel evolution. First off all, the classical numerical methods for the calculating the three - dimensional integrals were used to calculate the axial electric field along the lightning channel axis. The results measurement of the negative triggered lightning discharge have been used as input parameters during calculation. Different engineering models were used in the calculation - the TL, the MTLE, the MTLP, the MTLE and the GTCS model. Obtained results for electric field as well as the point form of Ohm’s law have been used to calculate the profile of longitudinal electrical conductivity on the lightning channel. The comparison with the experimental results was performed. It has been shown that the mean values of the mentioned physical quantities are in accordance with the experimental results. On the basis of the experimental results and semi-empirical formulas, other essential parameters of the lightning channel (the concentration and the temperature of the carriers) can be estimated. After a detailed overview of all methods used in the literature to study the lightning channel dynamics, the decision was to use the GTCS model. For this purpose, it is necessary to precisely calculate the channel discharge function from Volterra integral equation of the first kind. This equation is solved analytically by Laplace transformation, as well as by the convolution quadrature method (CQ method). The Volterra equation is also solved by the modified composite trapezoidal formula method (MCTF method), which is one of the numerical methods used to provide a very high degree of accuracy with minimal approximations. Results showed excellent agreement with the analytical method. Obtained channel discharge function is used in the calculations of other physical parameters along radial and axial directions of the channel. Based on the afore stated results, the guidelines for further study of the lightning channel dynamics are given.

Еволуција канала је од базичног значаја за проучавање физик канала муње, електродинамика атмосфере као и за електроинжењерску праксу. Циљ ове дисертације је развој детаљних аналитичких и нумеричких алгоритама.