LIBS spark model
Note: lots of things are probably wrong with this idealized model model, especially the third assuption of ignoring collisions. For more understanding on laser induced plasma physical modelling read for example Moscicki et al. Moscicki, T., Hoffman, J. and Szymanski, Z. (2013) ‘The effect of laser wavelength on laser-induced carbon plasma’, Journal of Applied Physics, 114(8), p. 083306. Available at: https://doi.org/10.1063/1.4819892F .
To model physically the laser spark we use the following idealized model.
The laser energy is deposited on the sample surface in a circular disk as heat.
Each particle on the disk gets their statistical portion of this energy and flies out in an explosion happening at every point in the disk. The breaking of molecules, ionizations and excitations are assumed to happen in the same instant as energy deposition.
We ignore collisions after this first instant so the particles fly out with their own speed and ionizations and excitation level as if they were a lonely particle in vacuum.
The event is depicted in the drawings in figure 1. The shape of the resulting visible spark is calculated in pluto notebook on spark shape and result is shown in figure 2. This model explains why the LIBS spark visibly happens not only on the surface as one would naively expect but above the surface. Why the LIBS spark visibly happens so far above the surface was a mystery that bothered me for five years of working with LIBS until I started thinking about it one holiday night. Lesson learned is to really ponder about the mysteries I encounter. The thinking lead to the model presented on this page.
More importantly, with this model we calculate the atomic emission spectrum. An example calculation of a spectrum is done in pluto notebook on spark model.
Here without the code details.
We assume:
Laser energy
Deposition volume
From these we calculate:
start temperature
start velocity distribution
From which, assuming elemental content, we calculate:
ionizations and excitations
Ionizations and excitations give us the spectrum for this laser spark event
Missing things from this model
Self absorption is not accounted for by the model. What about molecular emissions? The quality and completeness of the modelled spectrum is reliant on the completeness of our reference data of atomic lines.