Parametric identification of the non-linear model of a Blumlein N₂-laser

In this work we propose a non-linear model of the Blumlein circuit for the excitation of a N₂-laser that produces a high order integro-differential equations system, when 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 discharge are considered current dependent and their time behavior is found by means of a parametric identification method based in the measured voltages in the charge capacitors. A Runge-Kutta method to solve the integral terms and a Gauss-Seidel algorithm for the parametric identification were used.