![Total absorption coefficient, αIB\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha_{{{\text{IB}}}}$$\end{document}, versus time at the center (x = 0, see Fig. 1) of the target surface at laser irradiances of 0.45, 1.11, and 1.92 GW/cm² (wavelength 193 nm, duration 12 ns, cooling step 350 ns)](https://www.researchgate.net/publication/335480909/figure/fig4/AS:797462809825326@1567141358992/Total-absorption-coefficient-aIBdocumentclass12ptminimal-usepackageamsmath_Q320.jpg)
![Ablation depth of the aluminum target (wavelength 193 nm, duration 12 ns, cooling step 350 ns): comparison of predictions with and without considering the plasma-shielding effect and the experimental data [54]](https://www.researchgate.net/publication/335480909/figure/fig5/AS:797462814015491@1567141359067/Ablation-depth-of-the-aluminum-target-wavelength-193nm-duration-12ns-cooling-step_Q320.jpg)
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Applied Physics A (2019) 125:654
https://doi.org/10.1007/s00339-019-2951-8
A simple nite element model tostudy theeect ofplasma plume
expansion onthenanosecond pulsed laser ablation ofaluminum
YeqingWang1 · DavidW.Hahn2,3
Received: 24 April 2019 / Accepted: 19 August 2019 / Published online: 29 August 2019
© Springer-Verlag GmbH Germany, part of Springer Nature 2019
Abstract
In this paper, a simple model was proposed using finiteelement analysis (FEA) with a commercial FEA software ABAQUS
to simulate the two-dimensional (2-D) laser heat transfer in an aluminum material. Without relying on the conventional
hydrodynamic model, the proposed model not only predicts the evolutions of the temperature field and ablation profiles in
the target material, but also provides an estimation on the evolutions of electron density, plasma temperature, and plasma
absorption coefficient. The assumptions used in the model include the local thermal equilibrium and additional assumptions
regarding the average plasma temperature and vapor density. The assumptions allowed the laser heat transfer equation to
be solved together with the Saha–Eggert equation and conservation equations of matter and charge. When compared to the
existing hydrodynamic models, the proposed model solves a less number of nonlinear equations and hence is computationally
more efficient. The proposed FE model was employed to study the plasma-shielding effect on PLA produced by a 193nm
Excimer laser and a 266nm Nd:YAG laser. The predictions of ablation depths, electron density, and plasma temperature
agree well with the experimental data. Moreover, effects of the laser intensity and the average plasma temperature on the
efficiency of the plasma shielding during PLA were also investigated and discussed in this study.
1 Introduction
Technologies based on pulsed laser ablation (PLA) have
grown rapidly over the past few decades as evidenced by its
increasing applications in advanced machining [1], nano-
material manufacturing [2, 3], material surface processing
[4, 5], thin-film deposition [6], medical surgery [7], and
chemical analysis [8]. The significant advancement of these
technologies is a result of the numerous research efforts that
have been continuously devoted to understanding the fun-
damental laser ablation mechanisms. When a high-inten-
sity laser beam is directed onto a surface of a material, the
surface of the material absorbs energy from the laser beam
causing a rapid temperature rise of the surface. With the
increasing temperature, material quickly melts and leaves
the surface due to different ablation mechanisms, such as
evaporation and material phase explosion [9–13]. When
the laser intensity exceeds the optical breakdown threshold
of the material, a plasma plume is formed above the mate-
rial surface owing to the ionization of the material [8, 14].
The formation and expansion of the plasma plume result
in an attenuation of the actual laser energy that delivers to
the material surface as the incident laser beam transmits
through the plasma plume. Such a phenomenon is known as
the plasma-shielding effect. Meanwhile, the evaporation of
mass from the material surface produces a shockwave, which
also influences the overall ablation process [15]. Therefore,
laser ablation is a complex problem that involves laser–mate-
rial interaction, laser–plasma interaction, plasma–material
interaction, as well as shock wave–material interaction.
Despite continuous research efforts, the fundamental laser
ablation mechanisms are still widely unexplored [16]. This
paper, in particular, focuses on the plasma-shielding effect
during the PLA process.
Research efforts related to the plasma-shielding effect
of PLA based on experimental measurements have greatly
expanded the understanding of the laser ablation mecha-
nisms due to the development of novel experimental tech-
niques, such as the time-resolved shadowgraphy [11, 17,
* Yeqing Wang
yw253@msstate.edu
1 Aerospace Engineering Department, Mississippi State
University, MississippiState, MS39762, USA
2 Mechanical andAerospace Engineering Department,
University ofFlorida, Gainesville, FL32611, USA
3 Present Address: Aerospace andMechanical Engineering
Department, University ofArizona, Tucson, AZ85721, USA
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