  In this work a method based on self-mixing interferometry (SMI) is presented
for probing the concentration of plasma plumes induced by multi-pulse laser
ablation. An analytical model is developed to interpret the single-arm
interferometric signal in terms of plasma electron number density. Its time
dependence follows a power-law scaling which is determined by concurrent
effects of plume accumulation and propagation. The model has been applied for
the experimental study of plume formation at variable laser pulse frequencies
on different materials. The plume expansion dynamics has been observed with
high-speed imaging, and the SMI measurements allowed for a time-resolved
estimation of the electron number density. The intrinsic advantages of the SMI
technique in terms of robustness and low intrusiveness would allow for its
usage as a fast diagnostic tool for the dynamical scaling of laser-induced
plumes. Moreover it can be easily applied in laser-based manufacturing
technologies where plasma concentration monitoring and control is important.
