25E02
Bow Shock Formation in Complex Plasmas
コンプレックスプラズマにおけるバウショック形成
Yoshifumi Saitou1, Yoshiharu Nakamura2, Tetsuo Kamimura3 and Osamu Ishihara2
齋藤和史1, 中村良治2，上村鉄雄3，石原 修2
1

2

Utsunomiya University, 7-1-2 Yoto, Utsunomiya 321-8585, Japan,
Yokohama National University, 79-5 Tokiwadai,Hodogaya-ku, Yokohama 240-8501, Japan,
3
Meijo University, 1-501 Tenpaku-ku, Shiogamaguchi, Nagoya 468-8502, Japan1
宇都宮大学 〒321-8585 宇都宮市陽東7-1-2
2
横浜国立大学 〒240-8501 横浜市保土ヶ谷区常盤台79-5
3
名城大学 〒468-8502 名古屋市天白区塩釜口1-501

A bow shock is observed in a wide area two-dimensional complex plasma. The bow shock is formed due toan interaction of a supersonic flow of charged micro-particles with an obstacle placed in the flow. The flow
velocity is controllable by the gravitational force through tilting the entire experimental device. The
structure of the bow shock is well explained by a polytropic hydrodynamic theory as well as molecular
dynamic simulation. It is observed that the wake-like structure is formed when the flow is subsonic andsome micro-particles are trapped in the tail of the void.

1. IntroductionCharged micro-particles of organic or inorganic
materials on the order of a micrometer or a fractionof a micrometer in diameter are often found inplasmas in the interstellar medium, in the cometaryenvironment, etc. [1]. It is possible for themicro-particles to be charged either positively ornegatively. Photoelectric emission makes the charge
positive and the presence of plasma particles makes
it negative.
Coulomb crystals were discovered in laboratory
experiments in 1994 and the discovery activatedstudies on the lattice formation, the phase transition,
the waves, and other phenomena in plasmas, which
was often called “complex plasmas”, including thecharged micro-particles.
In this paper, we report the experimental
observation of a two-dimensional bow shock
formation in a large area two-dimensional complex
plasma system with a stationary object. The
observed bow shock structure is compared with
polytropic theory and a molecular-dynamicsimulation. In addition, behavior of the
micro-particles in subsonic flow is investigated aswell.
It is known that the bow shock is observed invarious media. Existence of the bow shockindicates that the complex plasma system including
the charged micro-particles has physicaluniversality. The complex plasma system has agreat advantage in visualizing processes such as theself-organization or waves. It is expected that
progress of research works in the complex plasma

contributes to the various fields of physics.
2. Experimental Setup
The experiments were performed using themodified YCOPEX (Yokohama Complex Plasma
Experiment) device [2], which was a glass tube
with an inserted flat metal plate of 800 mm × 120mm and a conducting thin wire of 0.2 mm indiameter and 25 mm in length as a floating obstacle.
The entire device was possible to be tilted toward
the obstacle by a jack equipped at one end of thedevice. The charged micro-particles were prevented
from flowing by a raised up-and-down gate, which
was electrically grounded, even when the device
was tilted. By lowering the gate after tilting, themicro-particles began to flow. The flow was almost
to be two-dimensional.
To make the micro-particles visible in the naked
eye, two thin fan green laser lights and a camera
were placed outside the device. The micro-particles
were irradiated by the laser lights from the radial
directions. Scattered laser light from the particles
was observed and recorded by a camera.
The reached vacuum pressure was less than 0.4
Pa. Argon gas was used at a pressure of 3.6 Pa. To
avoid the drag forces due to the neutral gas particles
and the ions [2-5], the gas flow was stopped byturning off the vacuum pump and by cutting off thegas feeding. Plasma was generated with applying anrf signal of 5 W (13.56 MHz). The measured
plasma parameters were ne ~ 1014 - 1015 [m-3], Te ~ 4- 5 [eV], and the plasma potential was ~30 V.
The Au coated silica spheres with 5 μm indiameter and md = 1.68×10-13 [kg] in mass wereused as the micro-particles. The charge of theparticles were estimated to Q = Zd e ≈ – 4.4×104 e,
where e is the elementary electric charge [5]. The
levitation height of the particles was ~8 mm above
the grounded metal plate, where was known as thesheath-plasma boundary called the transient sheath.
3. Experimental Results
A wake-like structure is observed around the tailof the void as shown in Fig. 1, although there is nota clear structure around the leading edge of the voidwhen the flow is subsonic. In addition, it isobserved that a small amount of micro-particles are
frequently trapped in the tail part of the void.
An arcuate structure appears in front of theleading edge of the void when the flow issupersonic. In the present case, M = 1 when vf = 71[mm/s]. Furthermore, there are particles flown witha subsonic speed between the arcuate structure andthe stagnation point. It is known that existence ofsuch a local subsonic region in front of thestagnation point is one of the features of the bow
shock [6]. The structure is confirmed as a bow
shock.
A dependence of the density ratio ndp/nd0, wherend0 and ndp are the densities of the upstream area far
from the stagnation point and of the subsonic area
just in front of the stagnation point, on the Mach
number is studied to clarify one of thehydrodynamic properties of the bow shockobserved in the micro-particle flow. The resultshows that the micro-particle flow behaves as apolytropic fluid.
4. Molecular Dynamic Simulation
A molecular dynamic simulation is useful toconfirm the hydrodynamic properties of the bow
shock observed in the present experiment. It is
assumed that a micro-particle has the screened
Coulomb potential. A point-like charge is usedinstead of the thin conducting obstacle and the wallof the device in the experiment. The equation of
motion for each micro-particle including theelectrostatic interactions with other charges, thegravitational force, and the neutral drag force isnumerically solved. A periodic boundary condition
is applied to the flow direction.
It is found that the void is formed around thepoint-like charge and the bow shock is observed at
the leading edge of the void when the flow of thecharged particles is supersonic. These shapes agreewith those observed in the experiment. The
behavior as the polytropic fluid is also confirmed
by investigating the dependence of the density ratioon the Mach number. The polytropic index is foundto be 2.2.
5. Conclusion
The two-dimensional bow shock was observed at
the leading edge of the void in the complex plasma
experiment. The theoretical study and the molecular
dynamic simulation confirm that the bow shock
behaves as the polytropic fluid.
The wake-like structure was also observed in thetail of the void when the flow velocity was subsonic.
It was observed that a small amount of
micro-particles were trapped around the void tail.
Acknowledgments
This work is supported by Asian Office ofAerospace Research and Development under award
number AOARD 104158 and JSPS Grant-in-Aidfor Scientific Research (A) under Grant 23244110.
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DUSTY PLASMA PHYSICS (Institute of Physics
Publishing Ltd., London, 2002) Chap. 3, pp. 70-92.
[5] Y. Nakamura and O. Ishihara, Phys. Plasmas 16,043704 (2009).
[6]L. D. LandauandE. M. Lifshitz,
FLUID
MECHANICS (Butterworth-Heinemann, Oxford, 2002)
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Fig. 1 The wake-like structure and the trapped
particles when the flow is subsonic.