Transparent solids may show strong absorption when irradiated by a high-intensity laser pulse. Such laser induced breakdown is due to the formation of a free-electron gas. We investigate theoretically the role of ionization processes in a defect-free crystal, including in our model two competing processes: strong-electricfield ionization and electron impact ionization. Free-electron heating is described in terms of electron-phononphoton collisions. Relaxation of the free electron gas occurs through electron-electron collisions and electronphonon collisions. The latter are also responsible for energy transfer from the free-electron gas to the phonon gas. We solve numerically a system of time dependent Boltzmann equations, where each considered process is included by its corresponding collision integral. Our results show formation, excitation, and relaxation of the electron gas in the conduction band. We find that strong-electric-field ionization is mainly responsible for free-electron generation. No avalanche occurs at femtosecond laser irradiation. The electron density and the internal energies of the subsystems are calculated. Critical fluences obtained using various criteria for damage threshold are in good agreement with recent experiments.

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Free oscillations of the keyhole in penetration laser beam welding are studied theoretically with regard to characteristic frequencies, damping rates and stability at large amplitudes. The normal modes form a discrete set which may be characterized by axial and azimuthal numbers. Due to viscous damping, only the lowest modes survive many oscillation periods, which yields a limited range of frequencies for the dynamic response of the keyhole to fluctuations of external welding parameters.

The dynamic behaviour of a keyhole in laser welding is studied theoretically. Starting from the stationary state, where the recoil pressure from ablating particles is in equilibrium with the surface tension at the keyhole wall, the collapse time due to a sudden laser shut-down is calculated. The characteristic time constant (r0 3 rho / gamma )1/2 of the system (r0 is the initial keyhole radius, rho is the density of the melt, gamma is the gamma coefficient of surface tension) which is approximately 0.1 ms for Al, Fe and Cu turns out to be a lower limit of the keyhole closing time. Linear stability analysis of the stationary state reveals that under conditions relevant in practice, the keyhole is expected to perform oscillations with frequencies of several hundred Hertz. The results of this investigation are particularly important for pulsed laser applications.

The dynamic behaviour of the keyhole in penetration laser beam welding is essential for the entire welding process, and is closely connected to welding seam defects and splash generation. To improve understanding of the process and to help interpret measured process signals, forced oscillations of the keyhole due to fluctuations of the CW laser power are theoretically studied. It is shown that even very small laser power fluctuations can lead to strong keyhole oscillations dominated by eigenfrequency response. Because the governing differential equation is nonlinear, bifurcation effects can occur which tend to broaden eigenfrequency peaks in the keyhole vibration spectrum. Calculated Fourier spectra are in good agreement with corresponding measurements of the ultraviolet and near infrared light emission during welding with an industrial CW laser.