The time dependent resistance and inductance of the electric discharges in pulsed gas lasers

A method of finding the time dependent resistances and inductances in the discharges in pulsed gas lasers is described in this work. According to this method the waveforms of the laser circuit voltages are digitized and their first and second derivatives are calculated. These are substituted into the differential equations governing the behavior of the system and relationships among the resistances and inductances are formed for every time. Using relationships from a sequence of four very closed adjacent time instants and considering that during this short time interval the resistances and inductances are varied linearly, their values can be found for this particular time interval. Repeating the same procedure for other time intervals and scanning the entire time region of the discharge, the time histories of the resistances and inductances of the discharges are revealed. These show strong variations in the “formation phase” of the discharge (first 50 nsec). Specifically the resistances drop rapidly (first 10 nsec) from very high values to low values, while the inductances increase to high values and subsequently decrease, forming an abrupt high peak. The steep drop of the resistances is due to the electron avalanche multiplication, while the peak of the inductances is due to the centripetal magnetic forces (Laplace forces), which cause a temporary constriction of the plasma. In the “main phase” of the discharge the resistances present a damping oscillation with the same frequency as the voltages, while the inductances present light fluctuations around constant values