Laser-plasma interaction (LPI) is an important subject to a variety of disciplines in engineering and science, such as laser welding, pulsed laser deposition (PLD), laser-generated x-rays and laser-aided ignition of inertial confinement fusion (ICF). In particular, laser interaction with weakly ionized plasmas has invoked a great deal of interest to the laser manufacturing community because plasmas naturally appear and interact with a laser beam in such high energy manufacturing processes. Due to the complexity and richness of physics, numerical model studies have been pivotal in the understanding of LPI. A number of numerical models have been created to study LPI and help design LPI equipment, and there are basically two kinds of numerical models: the kinetic-based model and the hydrodynamic model. Although kinetic models (e.g., particle-in-cell model) have been very successful, they are computationally expensive in most cases and their application is rather limited. Hydrodynamic models are also a powerful tool for LPI simulations, but they fail in some circumstances because they are based on the continuum assumption.

In this study, a new numerical model based on the lattice Boltzmann method (LBM) is introduced to simulate laser interaction with weakly-ionized plasmas. The LBM Huayu Li is a kinetic theory based method, where the distribution functions of the individual species of particles in the plasma are solved and thus the macroscopic variables (such as number density and momentum) are obtained. In this study, the Boltzmann equation with ionization and recombination terms is solved. Since only number density and momentum can be correctly retrieved from the two-dimensional nine-bit (D2Q9) discretization scheme, a set of energy equations is derived from the Boltzmann equation and solved separately to calculate temperature fields. The electromagnetic field from both laser and plasma is updated by solving Maxwell's equations using the finite-difference time-domain (FDTD) method. In the implementation of the present model, a resealing scheme is introduced to select the appropriate simulation parameters for the LBM, so that the physical properties of the plasma can be used. This resealing scheme has been validated by hydrodynamic flow problems and the electron diffusion problem. In this study, a two-dimensional weakly-ionized helium plasma interaction with a continuous wave CO₂ laser beam is simulated.

This model is a mesoscale approach based on the kinetic theory and the LBM, so it has a number of inherent advantages over previous models. Because the LBM solver is employed, this approach is computationally efficient and easy to parallelize. In addition, this model is capable of predicting time-dependent number densities, velocities, and temperatures of all particle species for a fairly large scale problem without employing the continuum assumption. It is believed that this model has a lot of potential for the studies of weakly ionized plasmas in a wide spectrum of applications.