Spectroscopic investigation of the 3D plasma clusters’ environment

T. Antonova¤, B. M. Annaratone¤, T.Sato¤,†, H.M.Thomas ¤ and G.E. Morfill¤
¤Max-Planck Institut fur Extraterrestrische Physik, D-85740, Garching, Germany
†Institute of Fluid Science, Tohoku University, Japan
Abstract. 3D plasma clusters have been formed inside a quasineutral plasma of very small size (64mm3) obtained by applying
rf to a small electrode at the edge of a main plasma. In order to know the density of such plasma spectroscopic analysis at 3
wavelength has been performed. By using a photomultiplier the emission structure of the small plasma as well as the whole
discharge has been obtained. The optical thickness of plasma allowed us to apply the steady-state corona model for plasma
density calculation. The last has been estimated to be ‘ 2£1016m¡3 in small plasma, one order higher than in main plasma
volume.
Keywords: 3D plasma cluster, the plasma, spectroscopic analysis, intensity
PACS: 52.27.Lw, 52.70.Kz
EXPERIMENTAL EVIDENCE
The topic of 3D plasma clusters is of great relevance in complex (dusty) plasma science. In ground experiments it is
very difficult to obtain isotropic 3D structures because of gravity. The dynamical behavior of clusters is a challenge
for investigation, since it requires a 3D diagnostic to detect fast processes. In order to characterize the processes in
the clusters it is necessary to know the parameters of the plasma at the position, where the clusters are situated. In
this paper we present a study of the environment, in which 3D plasma clusters are formed [1]. Because of very small
size and the rf nature of this plasma Langmuir probes can not be used. Therefore the spectroscopic analysis has been
chosen as the most suitable method of plasma diagnostics.
The experiments have been performed in PKE-Nefedov chamber with glass walls. The upper electrode is radiofrequently
driven at 13.56 MHz, the lower electrode is the segmented “adaptive” electrode, which consists of 57 squared
segments, each of 16 mm2 area. Applying additional rf voltage on one segment it is possible to get a glow ( small
’plasma ball’ or ’secondary plasma’) inside the sheath of main plasma. This ’secondary plasma’ is situated just above
the lower electrode, as it is shown in Fig.1, and its brightness depends on the amplitude of the applying rf voltage.
Melamine formaldehyde particles of 3.4mm diameter were injected into a discharge and levitated in the plasma sheath
near the lower electrode. When the ’small plasma ball’ appears particles are gathered in this glow from 2D layers in the
plasma sheath. More details about adaptive electrode are given in ref. [2]. In our experiments the voltage on the driven
electrode was 300Vpp; on the small segment – about 150Vpp in opposite phase. Since all clusters have been obtained in
Argon discharge at the pressures about 60 Pa, spectroscopic measurements have also been made at this pressure and
at 30 Pa for comparison.
SPECTROSCOPIC ANALYSIS
The spectroscopic analysis of ’plasma ball’ intensity has been done using a photomultiplier with three filters ( wave
length l =350nm, which corresponds to a bunch of ionic lines with the upper level of excitation about 23 eV; l =550nm
with 3 relevant atomic lines of 549.5nm (15,33 eV), 555,8nm (15.13 eV), 560.6nm (15.11 eV); and l =810nm with
two atomic lines of 811.5nm (13.07 eV), 810.3nm (13.1 eV)). We have used a small tube of 0.4mm diameter, length
215mm to get a space resolution of 0.5mm in the center of the chamber (see Fig.2). By scanning vertically the chamber
we have obtained the structure of our discharge with main plasma glow, two sheath regions and ’plasma ball’ glow.
The resolution gives us 8 points in the ’secondary plasma’ scanning. In Fig.3 the light emission structures at 30 and 60
Pa are shown. In these two figures the large peak from the left presents very bright glow just above the lower electrode,
where the ’secondary plasma’ is. Almost all our clusters are situated in this region. After that one can see small peak,

FIGURE 2. Sketch of the spectroscopic measurements in plasma chamber. PMP-photomultiplier, T and r are the length and the
radius of the additional tube, L – the distance between walls in chamber, l – the dimensions of plasma emission. (Not in scale).
which is bigger at 60 Pa and vanishes at 30 Pa. This is the spherical shape part of our small ’plasma ball’ (see Fig.1).
the second large peak, which is present for 60 Pa as well as for 30 Pa, is the main plasma glow. The intensity of
’secondary plasma’ is higher than intensity of main plasma in all spectrums at 60 Pa and it is lower at 30 Pa. At lower
pressures the small ’plasma ball’ disappears because of the expansion of the main plasma sheath.
Corona model In order to estimate the density of the ’secondary plasma’ from the spectroscopic data the steady-state
corona model has been used. The model assumes that the electron density is low enough that collisional de-excitation
can be neglected. Than all upward transitions can be considered collisional from ground state and all downward
transitions are radiative. This model is applicable in several cases for analysis of low density laboratory plasma, when
plasma is optically thin, i.e. absorption of radiation can be ignored [3]. We have made the experimental determination
of the plasma optical depth by ’mirror method’. For this purpose a mirror was placed behind the plasma source to
compare a single pass intensity Is and a total reflected intensity IT . In these terms the optical depth t can be written as:
t = ln
Is
IT ¡Is
: (1)
If t < 1 the plasma is optically thin and absorption is low. The intensity measurements have been made using a powermeter
with a mirror in the pressure range from 30 up to 90 Pa. The optical depth t was equal to 0.6, this confirms that
our plasma is optically thin and the steady-state corona model is a reasonable approximation.
In this model the intensity of a line can be expressed over the electron distribution function and the cross section of
the emission:

where G is the geometric constant factor, si j =Ai js (e ) is the cross section for the emission of a photon of frequency
(hn )i j emerging from the electron impact at an energy e on a ground-state atom, where Ai j is the atomic transition
probability between quantum levels i and j. n1 is the population density on the ground level. The energy range of
the spectral lines allows us to use the linearized cross section, when the collisional excitation occurs due to the highenergy
electrons in the tail of the Maxwellian distribution [4]. Here n(e ) µ exp(¡e =kTe) falls off steeply, so that a linear function can be used for the cross section: si j =C(e ¡ET ), where ET is the ionization potential, C is a constant
depending on the specific line. By assuming Maxwellian distribution for the electron energy distribution function and
for the case of Argon ions the intensity of a line can be written as I = GCn1ce(ET +2Te)e
¡ET
Te , where ce is the electron
thermal velocity ce = (8kTe=pme)1=2.
In order to calculate ion density in our plasma, we can compare intensities of two lines – ionic Ii and atomic Ia,
which have been taken with two filters, 350nm and 850nm, respectively:
Ii
Ia
=
Gi
Ga
Ci
Ca
ni
na
ETi+2Te
ETa+2Te
e
¡(ETi¡ETa)
Te : (3)
Here ETi and ETa are the upper levels for the most probable lines of Argon in UV (l =350nm) and Infrared
(l =850nm). The constants Ci and Ca can be found by using the ratio of intensities Ii=Ia but only in the volume of
main plasma, where the ion density is known from the electric probe measurements ni » 1015m¡3, the density of
neutrals na at our pressure of 60 Pa is equal to 1:2£1022m¡3, electron temperature Te is about 3eV. For the ratio in
eq.3 the maxima of intensity in main plasma for each spectrum have been used. The ratio of geometrical factors we
consider the same for two spectrums in main plasma. With these parameters the ratio of constants Ci=Ca is found to
be 2:8£106. Now from the same ratio of intensities (eq. 3) in the ’secondary plasma’ the ion density can be found. It
has been calculated equal to 1:6£1016m¡3.
Calculation of geometrical factors The second method to calculate the ion density in ’secondary plasma’ is to
compare the intensities of ionic lines (UV spectrum) in main plasma volume and in small ’plasma ball’. In the
hypothesis that the electron distribution is not modified the constants Ci can be cancelled out, but we have to take
into account a large difference in geometry between main plasma and small ’secondary plasma’. Hence, it is necessary
to calculate the geometrical volumes of plasma and ’plasma ball’, from where the light is taken. The volume of the
light from the main plasma has been calculated as the emission of a cone section, integrated over the dimensions of
the plasma l(see Fig.2), including the length of additional tube, which has been used to get better resolution:

where l1 and l1 are the beginning and the end of the emission, T=215mm and r=0.2mm are the length and radius of
additional tube, R is the radius of the cone base, R = tana(l +T=2), tana = r=T=2. The factor pr2=4p(l +T)2 is a
weighting factor, which assumes that the light should depend on the distance from the photomultiplier. The factor 1=3
before the integral takes into account the reduction of the light taken from the center and periphery of the cone base.
For ’secondary plasma’ this integral reduces to:

where h is a height of the small glow, rc is the corresponding radius, which decreases from 2mm in the center to 0 at
the edge of this glow. The ratio G=g ranges from 8 up to 15 depending on corresponding radius. Thus, the ion intensity FIGURE 4. The density profile in ’secondary plasma’ with respect to the distance from the lower electrode (70mm) up. Two
vertical lines show the upper and lower borders between which the plasma clusters are situated.
calculated from eq.3 with the ratio of constants Ci=Ca for the main plasma volume should be multiplied by this factor
to give the ion density in the small ’plasma ball’. The maximum calculated density of ’secondary plasma’ is of the
order of 2£1016m¡3.
Density profile in the ’secondary plasma’ Using the taken intensity data we can build the density profile in the
’secondary plasma’ and compare with the position of our clusters in order to know more precisely the parameters
of the plasma surrounding the clusters. Since the scanning of ’plasma ball’ gives us 8 points with the scanning step
of 0.5mm, the density has been derived from the ratio of intensity in each point to the corresponding radius of the
small glow (see eq.5) I=rc. The height of small glow is 4.5mm that is larger than the the radius in the center (2mm),
therefore it is likely a half of an ellipse with the major radius 4.5mm and minor – 2mm. Than the corresponding radius
rc in each point of scanning has been estimated from the equation of ellipse. The density profile is shown in Fig.4
with respect to the distance from the lower electrode. The vertical lines indicate the mean position of the clusters.
It is clear that clusters are situated around the maximum of the density. Hence, we can conclude that the density of
’plasma ball’, which surrounds our clusters, is equal to the maximum density estimated from the spectroscopic analysis
‘ 2£1016m¡3.
Conclusion This work demonstrates the results of spectroscopic analysis of 3D plasma clusters’ environment, which
is a plasma of very small sizes. The spectroscopic analysis has been chosen as the only possible non-invasive method.
Using the steady-state corona model and calculation of the geometrical volumes of main and ’secondary’ plasmas the
density of small ’plasma ball’ has been obtained. This fact is fundamental for the future plasma cluster investigations,
since it gives us the possibility to estimate the characteristic length in the plasma and, hence, the scaling of the distance
between particles in the clusters, which defines the cluster structures. Electron losses on particles of 3:4mm diameter
are always too small to modify the density distribution.
REFERENCES
1. T. Antonova, B. M. Annaratone, D. D.Goldbeck, V. Yaroshenko, H. M. Thomas and G. E.Morfill, Phys. Rev. Lett., 96, 2006, p.
115001.
2. B. M.Annaratone, M. Glier, T. Stuffler, H. Thomas, M. Raif and G. E. Morfill, New. J. Phys., 5, 2003, p. 92.
3. I. H. Hutchinson, “Electromagnetic radiation of bound electrones,” in Principles of plasma diagnostics, Press Syndicate of the
University of Cambridge, Cambridge, 1987, p.199 212–213.
4. Yuri. P.Raizer, “Production and decay of charged particles,” in Gas discharge physics, edited by J. E. Allen, Springer-Verlag,
Berlin, 1987, p. 53.

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