Non-linear model of the N2-laser excitation circuit

This paper presents a non-linear model of the Blumlein circuit for the excitation of an N2-laser that leads to a high order integer-differential equation system where each of the two discharges (the spark gap and the laser chamber) taking place in the circuit are simulated by an inductance and a resistance connected in series. The inductance and the resistance of each loop are considered current dependent and their time behaviour is found by means of a parametric identification method based on the voltages measured in the charge capacitors. A comparison between two representations of the induced emf in the different loops of the circuit is used. The first one is based on the dynamical (or derivative) inductivity and the second one on the statical (or integrative) inductivity. A Gauss-Seidel algorithm for the parametric identification was used.