DUSTY STRUCTURES IN STRATA OF GLOW DISCHARGE IN MAGNETIC FIELD

V. Yu. Karasev1,2, E. S. Dzlieva1, A. I. Eikhval’d1, A. Yu. Ivanov1
1 Institute of Physics, St. Petersburg State University, Ulianovskaya 1, Peterhof, St. Petersburg, 198504
Russia
e-mail: Viktor.Karasev@pobox.spbu.ru
2 REC 13 “Plasma” , Lenina 33, Petrozavodsk, Karelia, 185640, Russia
INTRODUCTION
One of the experimental methods of investigation of dusty plasma structures is the examination of
they behavior under the action of different external factors. The application of an external magnetic field
to dusty plasma proved to be a rather informative method. In [1–3], experiments with dusty structures in a
magnetic field were conducted in discharges of different types.
It was found in these experiments [4,5] that application of an external magnetic field causes rotation
of plasma–dust structures in strata. This rotation is complex and depends on the parameters of a
discharge, the concentration of dust particles, and the dimensions and geometrical orientation of a dust
structure, as well as the spatial arrangement of this structure in a particular section of a discharge tube.
The objective of this study is to interpret qualitatively the mechanism of the onset of rotational
motion of a dusty plasma structure in a magnetic field in strata of a glow discharge.
Fig.

EXPERIMENT 1. ROTATION VELOCITY MEASUREMENT
The method of observation consists in illumination, usually, with a laser knife, of a selected section
of the structure under study with subsequent videotaping. The experimental setup was similar to those
previously described in [4 – 6]. It is shown in Fig. 1. The particles of LiNbO3 whose density was 4.6
g/cm3 and whose size was estimated to be less than 3 mkm were used in the investigation. The
experiments were performed in Ne at discharge currents of 2.5 mA and pressures of 0.7 Torr.
In a dust structure a several layers were selected. The angular velocity of particles from each layer
was determined as the ratio of their linear velocity to the radius of rotation.
To characterize the rotation of each layer as a whole, angular velocities were averaged assuming
that the particles in the structure are identical. The resultant quantity, denoted as <ω>, is the angular
velocity averaged over the observation time and over all the particles of the layer.
Figure 2 shows the dependence <ω>(B) for two conventionally selected sections. The direction of
the magnetic field is taken to be the positive direction of the angular velocity.
Scanning over the height of the structure shows that the gradient of the average angular velocity is
directed upward at B < Bt and downward at B >Bt. (Bt corresponds <ω> = 0 )

Fig.2 . Dependence of the average angular velocity of a dust structure on the induction of a magnetic field: squares –
the upper section and rombs – the lower section. Gas discharge conditions: Ne under a pressure of 0.7 Torr;
discharge current, 2.5 mA; LiNbO3 particles.
Rotation of dust structure can be caused by ion drag force [3,7]. But possibility of radial plasma
flow inversion in magnetic field in stratum is not evident fact. We assumed that observation of rotation
generation can be a visual indicator of flows change.
EXPERIMENT 2. OBSERVATION OF THE ONSET OF ROTATION
A. The direction of rotation of a dusty plasma structure in a weak magnetic field (B < Bt) is
determined by ion flows directed radially toward the tube wall. The onset or cessation of rotation can be
observed if the dusty structure is somewhat displaced from the center of the discharge tube. As is known
[8], a radial temperature gradient causes a displacement of a dusty structure from the axis of the
discharge.
In the experiment, the upper cross section of the structure was illuminated by a horizontal plane and
videotaping was done from above. Then, the structure was displaced from the axis of the discharge tube at
such a distance (a few millimeters) that the rotation ceased, and the structure spontaneously returned to
the symmetry axis of the tube. We observed that, when the structure was displaced by some distance from
the axis of the discharge tube, vortices began to form in the structure (Fig. 3a). The vortices were formed
primarily in the central region of the structure. As the dusty structure approached the center of the
discharge, the vortices combined to form a solitary vortex. Then, this solitary vortex entrained all the
remaining particles. The geometry of the experiment is schematically shown in Fig. 4.
B. In order to displace the dusty structure from the axis of the discharge, the tube with the coils
was tilted at small angle to the vertical [6, 9]. The dusty structure is displaced to the tube wall under the
action of the force of gravity and, in this case, is retained in the stratum not only by a longitudinal but also
by a radial field. Our observations show that the onset of rotation of a dusty structure begins from its
peripheral layers (Fig. 3b), in which case ω↑↑B.

Fig. 3. Onset of rotational motion of a dusty structure displaced from the discharge axis (plane view). Lithium
niobate particles 2–4 μm in size. Gas discharge conditions: neon under the pressure P = 0.7 Torr and the discharge
current i = 2.5 mA. The structure is illuminated by a horizontal plane 2 mm thick. The magnetic field is directed
upward. The center of the discharge tube is indicated by the cross. The arrow shows the direction of rotation. (a) A
weak magnetic field, B = 110 G. The horizontal frame size is 8 mm; 15 successive frames are superimposed; in the
central area of the structure, a clockwise vortex is formed. (b) A strong magnetic field, B = 380 G. The horizontal
frame size is 9 mm; 20 successive frames are superimposed; at the periphery of the structure, particles execute a
counterclockwise motion.
Fig. 4. Schematic of the geometry of the experiment on the observation of the onset of rotation of a dusty plasma
structure in a magnetic field. The axis of the discharge tube is shown by the dot-and-dash line. The vertically
oriented ellipsoid 1 denotes a dusty structure displaced from the axis. The illuminated plane 2 is perpendicular to the
tube axis. The arrows indicate the directions of the magnetic field and of the angular velocity of rotation of the
visualized cross section (shaded in gray) of the structure. (a) A weak magnetic field ( ω↑↓B ). The highlighted cross
section is in the upper part of the structure. (b) A strong magnetic field ( ω↑↑B ). The highlighted cross section is in
the lower part of the structure. The tilt of the tube by a small angle is not shown.
CONCLUSION
It was found that the dependence of the angular velocity of rotation of a dusty plasma structure in
strata on the magnetic field is complex (nonmonotonic with the reversal of rotation).
If the rotation of a structure in weak magnetic fields is associated with radial ion flows toward the
tube wall, then it is likely that these flows arise in the dusty structure itself. For the quasi-neutrality of the
plasma within the dusty structure to be retained, the frequency of ionization should increase. The
possibility of this was discussed in [10]. In this case, due to the concentration gradient formed, the radial
ion flow is directed from internal regions of the structure to its periphery.
Our observations of the onset of rotation of a structure in strong magnetic fields allow us to state
the following. The rotation of a structure begins from its peripheral layers. This means that, evidently, a
component of the ion flow directed toward the structure exists in a strong magnetic field in the stratum.
Quantity estimations of ion drag force see in [11, 12].
V.Yu.K. acknowledges financial support from the Ministry of Education and Science of the Russian
Federation and a fellowship from the U.S. Civilian Research & Development Foundation (Award No.
RUX0-000013-PZ-06).
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