Regular and chaotic behaviour of multimode gas lasers

The build-up of multimode gas laser spectra is studied on the basis of the full system of Lamb's equations of motion. Comparison is made with the results of the phase-averaged equations that constitute the so-called free-running approximation. It turns out that the range of validity of the latter is approximately given byr?0.5 wherer is the ratio of the homogeneous linewidth and the mode spacing (provided the former is mainly due to the decay of both the upper and the lower level). However, forr?2, the free-running approximation which generally predicts a steady-state spectrum to occur, breaks down. Actually, in this case multimode oscillation of a chaotic character takes place, and no steady-state regime is attained.