LIBS spark model
We start with a strongly idealized physical model to model a LIBS spark. We will gradually add to it to make it closer to physically real model, but even in its simplest form as presented here first it can be used as a basis for of much of our calculations.
Note: lots of things are missing with this idealized model model, such as 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.
The breaking of molecules, forming of new molecules, ionizations and excitations are assumed to happen in the same instant as energy deposition and we ignore it in model other than the resulting proportions. Each particle(atom, ion or molecule) on the disk gets their statistical portion of this energy and flies out in an explosion happening at every point in the disk.
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 doesnt accurately depict the true plasma plume, in reality there's lots and lots of collisions and the free range of an average single particle resulting from the explosion can be very short like in the micrometer range. But in any case even this model explains why the LIBS spark visibly happens not only on the surface but above the surface. Why the LIBS spark visibly happens so far above the surface was a mystery that bothered me for years of working with LIBS before I started thinking about it one holiday night. The model presented on this page is the result of the thinking that night.
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, energy deposition volume and element proportions.
From these we calculate temperature i.e. velocity distribution. We may want to use more than a single temperature to integrate over.
From which we calculate the ionization and excitation proportions and molecule and molecular excitation proportions for molecular-LIBS strong species if we have the specific elements required.
From ionizations and excitations we calculate the resulting spectrum for this laser spark event.
And in code and with an example case, as same in the notebook linked above, we have
Missing things from this model
Self absorption is not accounted for by the model. The bigger the plasma i.e. the stronger the laser pulse used the more important self absorption of elemental lines will be. With low power lasers we make very small sparks so we can assume transparency and ignore self absorption.
Many of the assumptions in the model are not physically correct as ultimately the time even the formulas we use are for rates of events and time dependancy is very true in real LIBS events. But for our calculations we dont need physically fully correct model, we just need something that approximates the resulting total emissions.
The quality and completeness of the modelled spectrum is reliant on the correctness and completeness of our reference data of atomic lines.