deletions | additions       diff --git a/When_a_laser_beam_of__1.tex b/When_a_laser_beam_of__1.tex  index abc2f5f..2088fa5 100644  --- a/When_a_laser_beam_of__1.tex  +++ b/When_a_laser_beam_of__1.tex 
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I=(1-R)I_0 \exp(- \gamma r)  \label{eq:opticalIntensity}  \end{equation}  where $R$ is the reflexion coefficient of the medium (typically less than a few pourcents for a black mat medium such as the one used here, so can be neglected), neglected thereafter),  $I_0=\frac{1}{S}\frac{d E}{dt}$ the incident intensity distribution at the surface and $\gamma$ the absorption coefficient of the medium. %A measurement of We measured  the fraction of light which go through different thicknesses of the medium, cut by medium with  a microtome, indicates laser beam power measurement device (): it indicated  that $\gamma \approx$ 10$^4$ ???  m$^{-1}$ in our sample, meaning that most of the radiation is absorbed in the first hundred of micrometers. %Even if the sample is mainlyeFor low concentration medium, $\gamma$ is hard to calculate in our case, as the sample is composed of different materials, but the graphite, even in low concentration, absorbate much more than other components, so we can approximate $\gamma \approx \gamma_{graphite}$. For graphite particles of 1.85 $\mu$m at a concentration of 10 g.L$^{-1}$, the order of magnitude of $\gamma$ is 10$^4$ m$^{-1}$, meaning that most of the radiation is absorbed in the first hundred of micrometers of sample.  This is quite higher than metals where the radiation is absorbed within a few nanometres. 
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\end{equation}  where $\rho$ is the density, $C$ the heat capacity and $\kappa$ the thermal diffusivity.  The thermal diffusion path, equal to $\sqrt{4\kappa t}$, with $t$ the laser emission duration, duration (20 ns) and $\kappa$ = 1.43 10$^{-7}$ m$^2$.s$^{-1}$ for water \ref{Blumm_2003},  is equal to 0.1 $\mu$m. As $\gamma^{-1} \gg \sqrt{4\kappa t}$, propagation of heat is negligible during laser emission, and term $k \nabla ^2 T$ can be neglected in equation \ref{eq:eqChaleur}. Combination with equation \ref{eq:opticalIntensity} and integration over time lead then to a temperature $T$ at the end of the laser emission: \begin{equation}  T = T_0 + \frac{\gamma}{S \rho C} E \exp(-\gamma r)  \label{eq:eqTemperature} 
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