Linear and non-linear laser spectroscopy in studies of lowtemperature and high-density plasmas

K.Dzierzega(1), W.Zawadzki(1), S.Pellerin(2), B.Pokrzywka(3) and K.Musiol(1)
(1) Institute of Physics, Jagellonian Univ., ul. Reymonta 4, 30-459 Krakow – Poland
(2) LASEP – Centre Universitaire de Bourges, BP 4043, 18028 Bourges cedex 2 – France
(3) Mt. Suhora Observatory, Cracow Pedagogical University, ul. Podchorazych 2, 30-083 Krakow – Poland
Abstract. We will discuss the linear (Thomson scattering) and nonlinear (phase-conjugate degenerate four-wave mixing)
laser spectroscopy methods in terms of their application to study low-temperature (kBTe ~1 eV) and high density
(ne>1022 m-3) arc plasmas. We will discuss their advantages and limitations as for instance their influence on the plasma
Particularly, we will present the experimental results of our investigations of the electron heating in Thomson scattering
(TS) experiments carried out in atmospheric-pressure argon thermal plasma. The spatially and temporally (in time of the
laser pulse duration) resolved TS spectra enabled us to follow the evolution of Te. These experimental results will be
compared to the modeling results obtained by Murphy.
The results of plasma diagnostics obtained using TS were combined with the results of degenerate four-wave mixing
spectroscopy to determine Stark width and shift of the 696.543 nm ArI line.
Keywords: Laser Thomson Scattering, Degenerate Four Wave Mixing, Argon, Arc plasma
PACS: 52.70.Kz, 52.25.Os, 52.80.Mg
The laser scattering experiments on plasma provide a substantial amount of information on plasma parameters
such as the electron density ne, the electron temperature Te and the heavy-particle densities and temperatures. Laser
spectroscopy can also be a powerful method to study the interaction between plasma.

The main advantages of laser methods consist in high spatial, temporal as well as spectral resolutions. Moreover,
the ability of some laser methods to select only atoms with given velocities results in great reduction or even
complete elimination of the Doppler broadening. On the other hand, due to the small cross sections for some of these
laser scattering processes the experiments require high power pulsed lasers which can result in strong plasma
In this communication, the Thomson scattering (TS) and the phase-conjugate degenerate four-wave mixing
(DFWM) laser methods will be discussed in terms of their application to study low-temperature (kBTe ~1 eV) and
high density (ne>1022 m-3) plasmas, respectively for the plasma diagnostic and for the precise determination of the
Stark broadening of the spectral lines.
Electron heating by the laser pulse
Thomson or incoherent scattering is the process of scattering of low energy photons (ћω « mec2) on free electrons
present in a plasma. The theory of Thomson scattering has been presented in detail in many publications [1, 2, 3, 4].
The interpretation of the experimental Thomson-scattered spectra is, in most cases, straightforward and gives
simultaneous direct access to ne and Te. This method is attractive because it does not require assumption about local
thermodynamic equilibrium (LTE).
On the other hand, due to very low cross section for the Thomson scattering process, measurements require high
power pulsed lasers in order to obtain a detectable signal level. The high laser powers may result in significant
disturbance of the plasma state predominantly due to electron heating by the laser pulse in the inverse
bremsstrahlung process.
The corrections of Te for the laser power are commonly based on estimations made by Kunze [1]. According to
these calculations the relative change in electron temperature is directly proportional to the laser power. Such
dependence suggests measurements of Thomson-scattered spectra at different laser powers and then simple
extrapolation of the determined electron temperature to the zero laser power. Such a linear extrapolation, in the case
of thermal plasmas, yielded Te well in excess of the expected values. These discrepancies were observed in many
experiments with the laser Thomson scattering as a diagnostic tool. [5, 6].
The problem of the electron heating by the incident laser beam has been recently studied by Murphy [7]. He
solved a one-dimensional equation for the electron heating by absorption of laser radiation and cooling due to such
processes as: electron thermal conduction, energy transfer to heavy particles by elastic and inelastic collisions and by
radiative emission. These calculations show highly nonlinear dependence of the derived electron temperature on the
laser power and that the usual linear extrapolation leads to an overestimate of the electron temperature.
We have studied the electron heating in Thomson scattering experiments obtained for atmospheric-pressure
argon thermal plasma. The spatially and temporally (in time of the laser pulse duration) resolved LTS spectra
enabled us to follow the evolution of Te. These experimental results will be compared to the theoretical ones
obtained with the model of Murphy.
Experimental set-up
The details concerning plasma generator one can find in [8]. In our experiment, the arc was generally operated at
atmospheric pressure in pure argon and at the discharge current about 100A. For the LTS experiments, we used a
second harmonic of a Nd:YAG laser (λ=532 nm) which delivered laser pulses of energy Ep up to 200 mJ and of
about 6 ns duration time. The beam was passing through the beam attenuator and then it was focused to the spot of
150 μm radius on the plasma axis and a few millimeters z above the cathode tip. The scattered light was collected at
a angle of 79.5° with respect to the laser beam.
The investigated plasma volume was imaged onto the entrance slit of a spectrograph (1.6 nm/mm reciprocal
dispersion) with an enlargement factor equal 1. In order to improve S/N ratio the polarizer with the polarization axis
parallel to the laser beam polarization vector was placed on the path of the scattered light beam. Finally, the
scattered spectrum was registered using a gated two-dimensional intensified charged-coupled (ICCD) array with the
gate width as short as 2.. The gate was delayed with respect to the triggering laser pulse.
Results and discussion
In the first experiment, energy of the laser pulse was set to 150 mJ while the gate width of the ICCD camera was
2.5 ns with 0 ns delay time with respect to the center of the laser pulse. The TS spectra obtained from the plasma
across the laser beam, have shown that both the distance between two peaks and their width increase while
approaching the center of the laser beam. It follows that plasma parameters (ne and Te) vary with the laser beam
which implies the disturbance of the plasma state by the laser pulse.
Under similar discharge conditions, we have investigated the temporal evolution of the Thomson scattered
spectra setting the ICCD gate width to 2 ns and measuring the scattered light at different moments of the laser pulse.
We have clearly observed changes of the spectrum of the scattered light during the laser pulse: the spectral distance
between two peaks and their width first increase with rising the pulse and then start to decrease at the delay time of
+6.0~ns after the maximum of the laser pulse. This is the direct result of plasma temperature and electron density
variations due to the interaction of plasma with the laser pulse.
The temporal evolution of plasma parameters (ne and Te) during the laser pulse was determined from the
registered TS spectra [Cf. Figure 2]. The gate width was set to 2.5 ns and the axial volume, 6 mm above the cathode
tip was investigated at different energies of the laser pulse. For the range of investigated energies of the laser pulse,
Te rapidly growths after switching on the laser pulse. The higher laser energy the higher final temperature can be
reached at given initial plasma conditions. Since the decay of Te is slower than the decay of the laser pulse it follows
that plasma processes are not fast enough to make it thermal at each moment of the laser pulse. At the same time the
rapid increase of the electron density is observed only in the case of the highest laser energy, while no significant
variation of ne is observed during the laser pulse for lower pulse energies. It implies that for these lower energies
photoionization processes are of minor importance unlike the electron heating by the laser pulse.
Finally, measurement of the temporal behavior of the electron heating and extrapolation to the beginning of the
laser pulse seems to be more adequate method to determine the plasma conditions than extrapolation to the zero
laser power. Particularly, although the initial Te estimated this way are of large uncertainty due to very limited
temporal resolution of the experiment they were found to be very.

This work was supported in part by Polish Committee for Scientific Research (grant 1 P03B 090 26), Region
Centre (France) and by project d’Actions Intégrées-Polonium 01412ZH.
1 K.Dzierzega, W.Zawadzki, B.Pokrzywka and S.Pellerin, “Experimental investigations of plasma perturbation in Thomson
scattering applied to thermal plasma diagnostics”, [submitted to Phys. Rev. E]
2 H.J.Kunze, “The laser as a tool for plasma diagnostics” in Plasma Diagnostics, W.Lochte-Holtgreven ed., pp.550-616,
North-Holland Publishing Company, Amsterdam, 1968.
3 D.E.Evans and J.Katzenstein, “Laser light scattering in laboratory plasmas” Rep.Prog.Phys. 32 (1969) pp.207-271
4 J.Sheffield, Plasma Scattering of Electromagnetic Radiation, Academic Press, New York, London, 1975.
5 S.C.Snyder, G.D.Lassahn and L.D.Reynolds, “Direct evidence of departure from local thermodynamic equilibrium in a freeburning
arc-discharge plasma” Phys.Rev.E 48 (1993) pp.4124–4127
6 R.E.Bentley, “A departure from local thermodynamic equilibrium within a freely burning arc and assymetrical Thomson
electron features”, J.Phys.D 30 (1997) pp.2880-2886
7 A.B.Murphy, “Electron heating in the measurement of electron temperature by Thomson scattering: Are Thermal Plasmas
Thermal?” Phys.Rev.Lett. 89 (2002) pp.025002
8 B.Pokrzywka, K.Musiol, S.Pellerin, E.Pawelec and J.Chapelle, J.Phys.D 29 (1996) pp.2644-2652
9 R.L.Abrams and R.C.Lind, Opt.Lett. 3 (1978) 205
10 K.Dzierzega, L.Bratasz, S.Pellerin, B.Pokrzywka and K.Musiol, Physica Scripta 67 (2003) 52

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