A New Method for Fast Evaluation of the Cooray–Rubinstein Formula in Time Domain

The Cooray-Rubinstein formula is most widely used to evaluate the horizontal electric field generated by a lightning return stroke over a lossy ground. In this paper, a new method for fast evaluation of the Cooray-Rubinstein formula in time domain is proposed, by means of approximating the integral form of the modified Bessel function of the first kind using Gauss numerical integral. In the proposed method, the integral form of the modified Bessel function of the first kind is expressed by a summation of exponential functions, and a recursive convolution is achieved, which makes the calculation of the Cooray-Rubinstein formula in time domain much more efficient. Besides, the residues and poles due to the expression of the kernel function K( s) can be obtained directly for any ground conductivity and permittivity which makes the method proposed very simple and easy to program. The numerical examples demonstrate the validity and efficiency of the proposed method.