25G12Interaction between dust particles charged in a plasmaand electrons on liquid helium surface
プラズマ中で帯電した微粒子と液体ヘリウム表面上の電子との相互作用
Masako Shindo, Megumi Chikasue, Takahiro Wakiya and Osamu Ishihara
眞銅雅子，近末恵美，脇屋誉大，石原修
Faculty of Engineering, Yokohama National University79-5 Tokiwadai, Hodogaya-ku,Yokohama 240-8501, Japan
横浜国立大学大学院工学研究院 〒240-8501 横浜市保土ヶ谷区常盤台79-5
Micron-sized particles with negative charge and larger mass density than liquid helium (LHe) are dropped
onto the LHe surface charged with electrons emitted from a hot filament. When a plasma is produced a few
cm above the surface, abrupt incease in LHe temperature makes floating particle observation difficult. In
the presence of electrons emitted from a hot filament on the surface, particles negatively charged areobserved floating and drifting on a horizontal plane a few mm below LHe surface. Interparticle distance isidentified to be on the order of the wavelength of surface waves. Our analytical study suggests that dust
particles float as a result of the interaction with the charged LHe surface .

1. Introduction
A two dimensional structure of micron-sizedcharged dust particles in a plasma is studied forthe purpose of observing dust waves andmodeling low-dimensional material properties.
Since LHe provides an ideal flat surface and hasstrong surface tension enough to sustain dust
particles, we have tried to charge up dust particles
in plasmas generated in LHe vapor and drop theparticles on LHe surface[1]. In this study, a newexperiment is proposed to levitate charged dust
particles on the charged LHe surface.
2. Particles and LHe surface with electrons
When electrons approach to LHe surface, they
are trapped on the surface via image force[1], so anelectron sheet appears on the surface. Under theexistence of the vertical electric field E0 at thesurface, the electric forces and the restoring forces
for a flat surface (surface tension and gravity)
produce surface waves with the dispersion
relation[2,3]:
 2   gk   k 3  2 0 E0 2 k 2  (1)where  expresses the mass density of the liquid, g
the gravitational acceleration,  the surface tension
and E0 the applied external electric field. Equation(1) indicates that instability appears at a criticalfield Ec=[4g/02]1/4 and the wave vector where theinstability develops is kc=[g/]1/2. The surface
waves with k=kc become unstable when E  Ec,
and a new equilibrium state in the charge
distribution develops, resulting in dimple formation.
Typically, a dimple contains 5×106 electrons andhas depth of a few tenths of a mm and a width of~kc-1, a few mm. The charged surface wave anddimples on the charged LHe surface are expected tointeract with charged particles near the surface.
2. Experimental apparatus
The experimental setup is shown in Fig. 1.
Liquid helium is transferred into a glass Dewar
bottle, and its temperature is lowered by evacuation
cooling to 1~2K. Inside the Dewar, a set of fourelectrodes are placed as described in Fig. 1(b),which is movable vertically such that LHe surface
is placed inside acrylic tube with the inner diameterof 40mm. Electrons are emitted from 1% thoriatedtungsten filament of 0.05mm in radius which isheated with the direct current of about 1A andbiased by Vf=-6V. Heating of the filament brings
slight increase in LHe temperature. The emittedelectrons are extracted through the hole withstainless mesh (100mesh/inch) with the diameter of
10mm at the bottom of the chamber by theaccelerating electrode biased by Va=10~20V toward
LHe surface. The electron density on LHe surface iscontrolled by filament current, Vf and Va. The
upward electric field is yielded between the bottom
and the ground electrode by applying dc voltage Vb.
Acrylic particles with 3 m in diameter and 1.16
g/cm3 in mass density are dropped from the top.
They obtain negative charge in the electron sourcechamber and fall onto LHe surface. A green laser(532nm) irradiates the horizontal plane along thesurface and particles are recorded by CCD camera.
An RF plasma (10kHz or 13.56MHz) is producedin the electron source chamber, but it causes abrupt
temperature increase which results in theperturbation on the surface. Thus, we could notobserve any floating particles during plasma
production in the present study. The suppression of
the perturbation on the surface is now underconsideration.

Fig.1. Schematic diagram of the measurement
system: (a) Cryogenic double glass Dewar system
to impound liquid helium with temperature lessthan 4K. Green laser and camera are set in front of
20mm-wide optical slits. (b) Electrodes with anelectron source chamber immersed in LHe.

3. Results and discussion
Electrons were constantly supplied from thefilament during the experiment, and thus the vapor
pressure increased slowly from 240Pa to 645Pa,
corresponding LHe temperature from 1.4 to 1.6K.
As
increasing
Vb>2.5kV(corresponding
E>1.1kV/cm), small ripples were observed on LHe
surface, and then strong perturbations appeared
followed by the surface collapse as observed
earlier[4]. Since no perturbations occurred without
filament emission for Vb>2.5kV, we can conclude
that LHe surface is successfully charged byelectrons and surface instability developed whenVb>2.5kV. In case Vb =0V with filament emission,
particles penetrated the surface toward the bottomelectrode. When dropping dust particles aftersetting filament current and electric field strength
properly so as not to generate the instability, someof them were found drifting on the horizontal plane
2mm below the surface. Figure 2 shows a snapshotof dust particles drifting in one direction on theplane at a speed of 6mm/sec. The direction of thedrift is indicated by the arrow in the figure. Theseparticles disappeared when they reach the acrylicwall. Reversing the polarity of the electric fieldsuddenly, all floating particles fell down to thebottom electrode. These experimental facts indicatethat charged dust particles interact with the surface
charge. The interparticle distance was about 1.8mm,
which is identified to be on the order of the wave
length of the surface wave given by  2 / kc ~3mm obtained with the liquid properties
corresponding to the present experiment; =0.15g/cm3 and  =3.3  10-4N/m at the vapor
pressure of 645Pa. The applied electric field wasabout 1kV/cm, much less than predicted
Ec ~4kV/cm, but further increase of the field
resulted in the strong perturbation of surface asmentioned before. Because of the weaker electricfield than Ec , dimple formation was not observed in
the present experiment.

Fig.2. A snapshot of drifting dust particles irradiatedby laser sheet below LHe surface. Periphery line ofLHe surface and slit lines on the Dewar are included
as references.

4. Summary
Floating charged dust particles 2mm below LHe
surface is observed clearly. Our analysis suggeststhat charged particles float as a result of interaction
with the charged LHe surface.
Acknowledgments
This work was supported by Grant-in-Aid forYoung Scientists (B) (20740318) and Grant-in-Aidfor Scientific Research (A) (23244110).
References[1] M. Shindo, N. Uotani and O. Ishihara: J. Plasma
Fusion Res. Series 8 (2009) 294.
[2] M. W. Cole and M. H. Cohen: Phys. Rev. Lett. 23(1969) 1238.
[3] K. Mima, H. Ikezi and A. Hasegawa: Phys. Rev. B14(1976) 3953.
[4] P. Leiderer: in Two-dimensional electron systems, ed.
by Eva Y. Andrei, Kluwer Academic Publishers,
2010, pp. 317-339.