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Pol Grasland-Mongrain edited The_absorption_of_the_laser__.tex
over 8 years ago
Commit id: 41b084b5a657faa5fdc69ae2d2ca2fad9ab615f9
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diff --git a/The_absorption_of_the_laser__.tex b/The_absorption_of_the_laser__.tex
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+++ b/The_absorption_of_the_laser__.tex
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Substituting low-energy experimental parameters ($\gamma^{-1} \approx$ 40 $\mu$m$^{-1}$, $S$ = 20 mm$^{2}$, $E$ = 10 mJ, $\rho$ = 1000 kg.m$^{-3}$, $C$ = 4180 J.kg$^{-1}$.K$^{-1}$) lead to a maximum increase of temperature of 3 K. This local increase of temperature gives rise to a local dilatation of the medium. The induced displacements can then lead to shear waves: this constitutes the \textit{thermoelastic regime}.
To describe this regime, we
suppose supposed the medium as homogeneous and isotropic; As the depth of absorption (about 50 $\mu$m) is hundred times smaller than the beam diameter (5 mm), we also
adopt adopted a 1D model. The stress $\sigma_{zz}$ is the sum between the axial strain component and the thermal expansion component \cite{scruby1990laser}:
\begin{equation}
\sigma_{zz} = (\lambda + 2 \mu) \frac{\partial u_z}{\partial z} - 3(\lambda + \frac{2}{3}\mu) \alpha \frac{ E}{\rho C S \zeta}
\label{eq:stressThermo}