Optics and Photonics Journal, 2012, 2, 278-285
http://dx.doi.org/10.4236/opj.2012.24034 Published Online December 2012 (http://www.SciRP.org/journal/opj)
Measurements of Plasma Electron Temperature Utilizing
Magnesium Lines Appeared in Laser Produced
Aluminum Plasma in Air
Ashraf M. El Sherbini1,2, Abdel Aziz Saad Al Amer1, Ahmed T. Hassan1,2, Tharwat M. El Sherbini2
1Department of Physics, Collage of Science, Al Imam Muhammad Ibn Saud Islamic University (AIMSIU),
Al Riyadh, KSA
2Laboratory of Lasers and New Materials (LLNM), Department of Physics, Faculty of Science, Cairo University, Giza, Egypt
Received August 14, 2012; revised September 16, 2012; accepted October 2, 2012
ABSTRACT
We have utilized the relative intensity of magnesium lines originated from the Mg I at 285.2 nm and Mg II at 280.27,
279.55 nm to measure the plasma electron temperature. The plasma was produced via interaction of Nd:YAG laser with
solid aluminum target contains traces of magnesium. The magnesium lines were found to suffer from optical thickness
which manifests itself on the form of scattered points around the Saha-Boltzmann line. We have utilized a simple
method used for rapid calculation to the amount of absorption to these lines via comparison of the electron densities as
deduced from magnesium lines to that evaluated from the optically thin hydrogen Hα line at 656.27 nm appeared in the
same spectra under the same condition. A correction to the magnesium spectral lines intensities was carried out; hence
the corrected temperatures were re-evaluated. The measurements were repeated at different delay times ranging from 1
to 5 μsec. This work emphasizes on the importance of correcting the emitted spectral line intensity against the effect of
self absorption before using them in the calculation of plasma electron temperature in laser induced breakdown spec-
troscopy (LIBS) experiments.
Keywords: LIBS; Self Absorption; Mg-Lines; Plasma Parameters
1. Introduction
The LIBS technique is one of the potentially growing
applied techniques used in the field of elemental analysis,
because of its simplicity and non-contact nature [1-10].
Its basic principle is based on exciting matter (solid, liq-
uid or gas) to plasma state through irradiation by high
power laser pulses.
The diagnostics of the plasma can be done through the
measurements of electron density (ne) and temperature
(Te). The optical emission spectroscopy (OES) is the tool
by which the plasma can be diagnosed [11]. The meas-
urement of the electron density through Stark broadening
effect requires a line which is free from self absorption
[12,13]. Self absorption occurs in general in any kind of
system capable of emitting radiation, such as plasma.
Moreover, the formation of the plasma in air shows, in
general, a strong gradient of temperature due to the cool-
ing effect of the surrounding air [14]. These cold periph-
eries of the plasma contain a high concentration of the
atoms at the low laying atomic states which can cause a
strong re-absorption to the emitted radiation lines [15-
17]. It was found that, especially the resonance and
strong lines are more likely to be subjected to self ab-
sorbed. The Mg II ionic lines are a good example of this
effect because they are either a resonance lines like; the h
and k lines at 279.55 and 280.27 nm respectively, or they
are relatively intense. However, these lines would be
good candidates for calculating the plasma electron tem-
perature. The wavelength separation is very small as well
as their separation in the upper excited states is relatively
large with respect to the expected plasma temperature (~
1 eV) [11,18,19]. Moreover, the h and k resonance lines
belong to the most exploited lines in astrophysical
plasma diagnostics [18] and therefore, they are also of
the interest in astrophysical plasma at large temperatures.
Moreover, the Stark broadening of these lines are well
known at electron density higher than 1015 cm–3 [18]. On
the other hand the appearance of the Mg I-resonance line
at 285.2 nm provides a assurance chance to construct the
Saha-Boltzmann plot with the help of the Mg II lines, but
unfortunately this line is a resonance line, hence one
should expect that it may be subjected to the effect of self
absorption.
It was suggested in Ref’s [12,20,21], that the use of the
C
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A. M. EL SHERBINI ET AL. 279
Hα line at a wavelength of 656.27 nm can garantee a re-
liable measurement of the electron density, since the line
is optically thin [20].
In this work, we shall adopt a straightforward proce-
dure to calculate the self absorption coefficients of the
plasma to the Mg I, II lines via comparison of the elec-
tron densities evaluated utilizing the Stark broadening of
the magnesium lines to the electron density as deduced
from the optically thin Hα-line [12]. We have calculated
the electron temperatures both before and after correction
to the lines intensities in order to show that the effect of
self absorption may lead to serious errors in temperature
measurements. The use of these lines can open the area
to use of the magnesium lines to measure the electron
temperature in the interstellar plasma.
2. The Effect of the Self Absorption on
Spectral Radiance
The process of re-absorption of the plasma to the light
photons in their path to outside the plasma active volume
is called the self absorption. It is well known that this
process affecting the spectral line shape i.e. the line in-
tensity decreases and its full width at half maximum
(FWHM) increases [22,23].
The self absorption (SA) coefficient at the line center
o

was defined as the ratio of the spectral radiance
(counts per sec) of a spectral line subjected to self ab-
sorption

o
I

to that of the same line in the limit of
negligible self absorption

oo
I

[19,23-25].




1e o
o
oo o
I
SA I















 (1)
Equation (1) indicates that the SA coefficient varies
from unity in case of perfectly optically thin line to the
limit of zero in case of completely self absorbed line [21],
and is the optical depth of the plasma
at the line center.
 
o   o
On the other hand, it was pointed out in Ref’s. [12,13]
that the process of the self absorption indeed affecting
the line intrinsic FWHM o

 through the process of
re-absorption, hence, the line FWHM become


which
is greater than o

. The SA coefficient was then ex-
pressed in terms of the ratio of the Lorentzian (FWHM)
components of the same line as [12].
1
o
SA








(2)
where 0.56

 , o

 is the intrinsic FWHM of the
Lorentzian component of the spectral line if the line is
optically thin and

 is the distorted Lorentzian com-
ponent of the same line which resulted from the effect of
the self absorption. An extensive analysis to Equation (2)
was carried out in Ref. [12], and showed that the direct
calculation of the electron density from the measured
Lorentzian component of the extra broadened line


must give an apparent (wrong) larger electron density


line
e
n values than the expected value calculated from
the same line if the line is optically thin. Therefore,
Equation (2) can be re-written in terms of ratio of the
electron densities as evaluated from the line suffered
from self absorption to that evaluated from the optically
thin Hα-line;




1 1
2 linelineline
2line
se e
se
nn

SA nH
n





 


 
 

 
(3)
In Equation (3) e
n

can be regarded as a sort of
equivalent density from the line in the limit of zero self
absorption [12], i.e. if the line is optically thin. We have
suggested [12] that e
n

can be replaced by the electron
density utilizing the optically thin Hα line at 656.27 nm
present in the same emitted spectra under the same ex-
perimental condition. It is worth noting that, the SA co-
efficient of a certain line can be calculated using Equa-
tion (3), then a correction to the spectral line intensity at
the line center can be calculated using Equation (1).
2.1. Stark Broadening of Mg I, II-Lines
The resonance (k and h) lines emitted by the Mg II ion at
wavelengths of 280.27 nm and 279.55 nm are of particu-
lar interest, because fully quantum mechanical calcula-
tions are available for these lines [25]. The measured
widths (FWHM) agree fairly well with semi-classical
calculations. They are usually normalized to a reference
electron density . Neglecting the ion
broadening contribution, the plasma apparent electron
density can be calculated from the Mg II ionic lines by
[19,21,23-25]:
17 3
10 cm
r
N 
2
e
s
n






r
N (4)
s

is the theoretical line full width Stark broadening
parameter, calculated at the same reference electron den-
sity 17 3
10 cm
r
N

. A number of experimental and
theoretical studies have been dedicated to measurement/
calculation of the Stark widths and shifts of the men-
tioned Mg II lines. In our work, the parameters
s

to-
gether with atomic parameters of the Mg II ionic lines
were taken from Ref. [18] and are given at Table 1.
Equation (4) also will be used to estimate the electron
density from the Mg I-line at the wavelength of 285.2 nm
at the reference density of 1016 cm–3.
2.2. Reference Plasma Parameters
Because our experiment was carried in open air, the

A. M. EL SHERBINI ET AL. 280
Table 1. The Stark broadening parameters and the atomic parameters of the Mg I, II lines.
Element Wavelength (nm) Aki
(s–1) Stark parameters (ωs) (pm)/Nr (cm–3) Kind of Transition Ek (eV) Ei (eV)gk
Mg I 285.21 4.91 × 108 0.42/1e16 Resonance 4.34 0 3
Mg II 279.55 2.60 × 108 5.1/1e17 Resonance 4.43 0 4
Mg II 280.27 2.57 × 108 5.1/1e17 Resonance 4.42 0 2
reference electron density can be derived from the opti-
cally thin Hα line appeared in the spectra [12,20,21]. The
presence of this line was attributed to the existence of a
very small concentration of water vapor (humidity) around
the target [12]. This line was critically studied in a pre-
vious publication [20] and was shown to have significant
practical properties; e.g. it exists long time after termina-
tion of the laser pulse, it has a large signal to background
ratio, relatively large Lorentzian (FWHM) component
which ensures a small error in calculating electron den-
sity and finally is optically thin [20].
Moreover, because the interaction was carried with the
surface of aluminum target in open air, the reference
electron temperature was derived from the optically thin
Al II ionic lines at 281.6, 358.6 and the 466.2 nm ap-
peared in the same spectra of the plasma under the same
experimental conditions. Constructing the Boltzmann
plot including the spectral intensity of such aluminum
lines leads to precise measurement to the reference
plasma electron temperature.
Figure 1. Experimental setup.
μm diameter quartz fiber cable positioned at distance of
12.5 mm normal to the laser axis and arranged to observe
a circle of cross section of only 2 mm in front of the tar-
get. The wavelength scale was calibrated using a low
pressure Hg-lamp (type Ocean optics). The instrumental
bandwidth was measured from the FWHM of the Hg
lines and was found to be 0.12 ± 0.02 nm. Identification
of the different lines in the LIBS spectrum was carried
out using Spectrum Analyzer Software version 1.6. The
relative response of the detection system was measured
using a standard Deuterium Tungsten-Halogen calibra-
tion light source (type DH-2000-CAL). Over the entire
experiment the gate time was kept at 1 μs and the delay
time was varied in equal steps from 1 - 5 μs.
3. Experimental Setup and Measurement
Procedures
The used experimental setup is shown in Figure 1. A
Q-switched Nd-YAG laser (Quantel, model Brilliant B)
was used at the emission wavelength of 1.06 μm. The
energy per pulse at the target surface was fixed at a level
of 670 mJ. An absolutely calibrated power-meter (Ophier,
model 1z02165) was used, measuring the 4% fraction of
the laser light reflected from a quartz beam splitter to
monitor the incident laser energy, which might changes
from one shot to another. The laser was focused on the
target by a quartz lens of focal length of 10 cm. The tar-
get was a certified aluminum based alloy with traces of
Mg (1.16%) polished and mounted on a xyz-stage to
present a fresh polished surface at each laser shot. The
acquired data was averaged over three shots under the
same conditions for estimating the reproducibility mar-
gins at each data point. The emitted light from the plasma
was analyzed using an echelle type spectrograph (type
Catalina, model SE 200) with a resolving power of 2400
and equipped with a time gated ICCD camera (1064 ×
1064 pix with 13 μm × 13 μm pixel size at a binning
mode of 1 × 1 (type Andor, model iStar DH734-18F). The
emitted light from the plasma was collected using a 25
4. Results and Discussions
The recorded spectra at different delay times ranging
from 1 - 5 μs at a gate time of 1 μs are shown in Figure 2.
We can notice the existence of Hα-line and the Mg I, II
emission lines as well as the Al II ionic lines in the short
wavelength region. The line spectra are superimposed on
a continuum component which decreases with the ad-
vance of acquisition delay time. This continuum is mainly
results from the free-free (Bremesstrahlung process) and
the free-bound transitions. This continuum should be
removed before proceeding in the spectral line shape
analysis.
A Voigt fitting and hence the extraction of the Lor-
entzian FWHM from the Mg II ionic lines at wavelengths
of 280.27, 279.55 nm and the Mg I line at 285.2 nm as
well as to that of the Hα-line was carefully done using
home made software running in MATLAB package. The

A. M. EL SHERBINI ET AL. 281
Figure 2. A sample of the emission spectra from plasma at different delay times showing the different lines appeared Hα, Mg I,
and Mg II as well as Al II ionic line at 281.6 nm (a); at arbitrary delay time of 5 μs (b); and the resolved lines at the short
wavelength region (c).
results of the best fittings to the different lines at an arbi-
trary delay times of 1, 3, 5 μs and at a fixed gate time of
1 μs are shown in Figure 3.
According to Equation (3), the deviation of the meas-
ured electron density calculated from the Mg I, II lines
with respect to that evaluated from the optically thin Hα
line indicates the existence of self absorption. A plot of
the apparent electron density calculated from the Lor-
entzian (FWHM) component from the three Mg I, II lines,
in comparison to that evaluated from the Hα are shown in
Figure 4. This figure confirmed that the Mg I, II lines are
influenced by the effect of the self absorption and hence
the higher the observed electron densities from the mag-
nesium lines.
The self absorption coefficients were calculated utiliz-
ing Equation (3) to the three Mg I, II lines at different
delay times with the results shown in Figure 5. A loga-
rithmic decrease in the SA values with delay time can be
observed, indicating an increase of the optical depth of
the lines with delay time. This means that as the plasma
become cooler with the delay time (as a result of expan-
sion) the population of the atoms in the lower state be-
comes higher and hence the more the absorption.
Moreover, the calculated SA values for the resonance
doublets (h and k) Mg II lines shows nearly an equal de-
creasing rates, which is in agreement with the known

A. M. EL SHERBINI ET AL. 282
Figure 3. The quality of the Voigt fitting to the different spectral Mg I , II-lines used in the investigation as well as the Hα-line
at delay times of 1, 3 and 5 μs.
absorption oscillator strengths of the lines (0.61 and 0.31
respectively).
A correction to the Mg I, II lines spectral radiances
was carried out according to Equation (1). Saha-Boltz-
mann plots were constructed [26,27] with the result as
shown in Figure 6, utilizing the Mg I, II lines intensities
both before and after correction against effect of self ab-
sorption. We can notice the scattering of the points cor-
responding to emission wavelengths of 280.27 and
279.55 nm before correction against this effect. After the
application of correction procedures and re-construction
of the plot, the points are tending to coincide with one
another forming a straight line. This figure primarily in-
dicates the effectiveness of the correction process.
In order to evaluate the reference electron temperature
we have utilizing the spectral radiances from the Al II
ionic lines at 281.6, 358.6 and the 466.2 nm to con-
structed the Boltzmann line with the result as shown in
Figure 7. One basic advantage of utilizing such alumi-
num lines is that they are optically thin [12]. One can

A. M. EL SHERBINI ET AL. 283
Figure 4. The temporal variation of the measured electron
densities utilizing the Hα line (lower solid squares), from the
Mg I line at 285.2 nm (solid inverted triangles), from the
Mg II ionic line at 279.2 nm (solid circles) and from the
ionic Mg II line at 280.2 nm (solid triangles).
Figure 5. A demonstration to the variation of the coeffi-
cients of self absorption for from the Mg I line at 285.2 nm
(solid inverted triangles), from the Mg II ionic line at 279.2
nm (solid circles) and from the ionic Mg II line at 280.2 nm
(solid triangles).
Figure 6. The Saha-Boltzmann plot utilizing spectral line
intensities from the Mg I, II lines before correction (lower
open figures) and after correction against self absorption
(upper solid figure). The slope of the upper line indicates a
temperature of 1.12 eV, while the lower dashed line 1.92 eV.
(Squares = Mg I line at 285.2 nm, inverted triangles at Mg
II 279.55 nm and the circle at Mg II 280.27 nm).
Figure 7. The Boltzmann plot utilizing the Al II ionic lines
(281.6 nm (square), 466.2 nm (inverted triangle) and 358.6
nm (solid circle) taken at an arbitrary delay and gate times
of 1 μs. The slope of the best fit straight line indicated tem-
perature of 1.14 eV.
notice the existence of the points on the straight line with
slope indicating the reference electron temperature.
Figure 8 shows the overall temperatures variation with
delay time as evaluated from the Mg I, II lines both be-
fore and after correction in comparison with the refer-
ence temperature as deduced from the Al II ionic lines.
We can notice that, the calculated electron temperatures
from the Mg II lines without correction against self ab-
sorption effects are larger than after correction. This
large deviation of the evaluated temperatures shows that
the Mg I, II lines, should be corrected against effect of
self absorption before used in plasma diagnostics.
5. Conclusion
We have measured the plasma electron temperature and
density utilizing three lines emerging from magnesium in
LIBS experiment. The effect of the self absorption on
three Mg II lines at 280.27, 279.55 and Mg I resonance
line at 285.2 nm were quantified utilizing simple formu-
las based on the measurement of the ratio of the apparent
electron density from the lines of interest to that derived
from the optically thin Hα line. The spectral line intensi-
ties were then corrected. The electron temperatures were
re-evaluated and compared to reference temperatures
utilizing the Al II ionic lines. This comparison shows an
excellent agreement between the reference temperatures
and the measured utilizing the magnesium emission lines.
The results shows that the Mg I, II lines appeared at the
short wavelength region of the LIBS spectrum are good
candidates for measuring the temperature of the plasma
in LIBS experiments, but after correction against self
absorption.
6. Acknowledgements
The experimental part of this work was conducted at the

A. M. EL SHERBINI ET AL. 284
Figure 8. Presentation to the variation of the measured
electron temperature with delay time utilizing Mg I, II lines
after correcting spectral intensities against effect of self
absorption (lower open circles), without correction (upper
solid circles) and from the Al II ionic spectral line intensi-
ties (red solid triangles).
Laboratory of Lasers and New Materials (LLNM), Phys-
ics Dep., Cairo Univ., Egypt. The authors express their
gratitude to the valuable discussions with Prof. S. H. Al-
lam and Dr. H. Hegazy.
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