Numerical analysis of the electrical and optical behaviour of a�pulsed nitrogen laser through time-dependent resistances and inductances

Abstract

In the present work, a comprehensive theoretical investigation of the performance of a pulsed nitrogen laser is realized through the time-dependent resistances and in- ductances of its electric discharge. This is the first computa- tional laser model that takes this effect into account. These time-dependent resistances and inductances were determined directly through a method, that exploits the experimentally recorded voltage and current signals. When time-dependent quantities are used in the differential equations of the electric circuit and the laser rate equations, the solutions are in excel- lent agreement with experimental measurements. Particularly, the two discharges in the spark-gap and laser chamber create a high peak in the inductance values. This occurs in the first 40 ns of the corresponding discharge. These peaks strongly influence the electrical and optical behaviour of the system. Concretely, these peaks reduce the optical pulse energy in our nitrogen laser by about 40%, in comparison to the case that assumes constant inductances. ents of the driving circuit. Unfortunately, there has been no way of finding the time dependence of these elements to date. Very recently, we developed a method of finding the time- dependent resistances and inductances of the discharges in a pulsed gas laser by exploiting the voltage (3) or current (4) waveforms. Although this method is described in detail in (3) and (4), briefly speaking, we can say that the experimen- tal waveforms of the voltages or currents are digitised and their derivatives are calculated. Substituting these into the in- tegrodifferential equations that govern the behaviour of the system, relationships between the unknown resistances and inductances are formed for every time instant. Solving the system of four relationships from a sequence of four very close adjacent time instants and considering that during this short time interval the resistances and inductances vary lin- early in time, their values at these particular four very close adjacent time instants can be found. Repeating this proced- ure for the next sequence of four very close adjacent time instants and continuing to scan the entire time region of the discharge in this way, the time histories of the resistances and inductances of the discharges are revealed. More details on this method can be found in (3) and (4). The aim of this work is a comprehensive theoretical in- vestigation of a pulsed gas laser through the known time- dependent parameters of the discharges of the laser system. To the best of our knowledge, this is the first analysis of a laser system with real time-dependent resistances and in- ductances of the discharges. Furthermore, the results of our analysis are compared with those derived from models that assume constant inductances. This comparison will give an estimation of the importance of the variations of the induc- tances in time and their role in the performance of a pulsed gas laser.