Microgravity Experiments Using Parabolic Flights for Dusty Plasmas

*Kazuo Takahashi*

## **Abstract**

The chapter is dedicated to descriptions of the microgravity experiments, which were done by using parabolic flights and for analyzing behaviors of dust particles in plasmas, i.e., dusty plasmas under microgravity. There are projects of the microgravity experiments of the dusty plasmas using the International Space Stations, where time for microgravity is long and has a scale of hours. Conversely, it is significant to find out phenomena of the dusty plasmas in the short time scale of a few 10 s including the transition from gravity to microgravity, which is performed by parabolic flights of aircrafts on the earth. Methodology and results of the experiments are shown here for further investigations of the dusty plasmas in future.

**Keywords:** dusty plasma, coulomb crystal, microgravity experiment, parabolic flight

## **1. Introduction**

Dust particles in plasmas have been investigated under microgravity for this quarter century, since they attract interest of physicists working on the dusty plasmas which are plasmas containing them and the Coulomb crystals formed by them resulting from charging and strongly coupled interactions [1–4]. Experiments of the dusty plasmas under microgravity were initiated by a Russian team accessing to a space station of the Mir in the late 1990s. The team was a pioneer for the experiments and started to collaborate with a German team [5]. After collaboration between the teams, the experiments under microgravity came to be done by other facilities, drop towers in Germany and Japan [6], sounding rockets used by a German team and the International Space Station (ISS) intensively promoted by the Russian-German joint project of the PKE-Nefedov and PK-3 plus [7, 8]. The project on the ISS of PK-4 has been in progress since 2014 by an international team organized by the European Space Agency [9–11]. In this history, microgravity experiments by using aircrafts with parabolic flights have played an important role in feasibility studies for missions on the ISS. Opportunities of the parabolic flights for the dusty plasmas have been mainly provided in campaigns from the ESA and the Japan Aerospace Exploration Agency (JAXA). A Japanese team was engaging in the experiments with apparatuses similar to PK-3 plus and PK-4 to contribute preliminary results of these projects. Here the results obtained by the team are introduced as knowledge for experiments in the future. It costs a lot and takes so

long time to prepare and perform the microgravity experiments by the aircrafts. Pieces of information in the chapter help successors to reduce money and time and get much more scientific merit in future microgravity experiments.

## **2. Microgravity experiments by parabolic flights**

## **2.1 Background**

The Japanese team experienced the missions of PK-3 plus, where the team aimed at demonstrating a critical phenomenon in dusty plasmas [12–14]. The PK-3 plus had a configuration of parallel-plate electrodes for rf (13.56 MHz) discharges. The team did microgravity experiments by aircrafts using the chamber the same as the PK-3 plus in Japan. This opportunity allowed the team to proceed to the next parabolic flight campaign for the next project of PK-4. The team built the apparatus of PK-4J whose glass tube for discharges was scaled down from the original one to load a rack system on the aircrafts for parabolic flights in Japan. The PK-4J had two phases of the microgravity experiments in Japan. The Phase 1 was dedicated to sophisticate the apparatus and acquire wide experience for the experiments using the parabolic flights. In the other, Phase 2, the behaviors of the dust particles were observed in cylindrical discharges [15], which had been preliminarily studied in numerical simulations [16, 17]. In parallel with the microgravity experiments, measuring parameters such as ion density and electron temperature in plasmas had been developed to reach comprehensive analyses of phenomena observed under microgravity [18–21].

## **2.2 Parabolic flights**

In Japan, the parabolic flights are carried out by a company, Diamond Air Service, Inc. It has two aircrafts (**Figure 1**). One is smaller than the other and equipped with two racks. The larger one has four racks. Everything for the experiments is integrated into the rack before loading on the aircraft. The whole rack is inspected that all components inside are tightly fixed and checked before flights not to electromagnetically interfere with the aircrafts during operation. The aircraft makes a condition free from gravity with a flight pattern of parabola in an airspace above the Sea of Japan or the Pacific Ocean. It takes 1 h to obtain a set of parabolas not more than 15 times a day. **Figure 2(a)** shows a graph of an altitude as a function of time corresponding to the flight pattern of the aircraft. Angles of elevation and

accelerations to be feel onboard are also indicated on the graph. The 1 G is corresponding to the acceleration of gravity on the earth, i.e., 9.8 m/s<sup>2</sup>

*Microgravity Experiments Using Parabolic Flights for Dusty Plasmas*

*DOI: http://dx.doi.org/10.5772/intechopen.90530*

less than 2 G.

**49**

**Figure 2.**

*i.e., 9.8 m/s<sup>2</sup>*

parabola, the aircraft rapidly accelerates and gains speed while getting the nose down between 60 and 20 s. After that, it elevates steeply while getting the nose up between 20 and 0 s and reaches the release point of an elevation of 45°, where a pilot closes the throttle. The aircraft continues flying by its inertia and makes the parabola between 0 and 20 s, where gravity is well balanced with the inertia. This is why everything onboard does not feel gravity. One can typically have a time of 20 s under microgravity during the aircraft moving up and dropping down in around 1000 m. After the parabola, the aircraft recovers speed and its altitude. Before and after the parabola, a load force normally acts on the aircraft by the acceleration

*accelerations onboard the aircraft measured in a parabolic flight. The x, y, and z are corresponding to the directions parallel to the traveling direction of the aircraft, to its wing, and to the gravity, respectively.*

*(a) A flight pattern of the aircraft to obtain a condition under microgravity shown by an altitude of the aircraft as a function of time. The figure shows an angle of elevation and the acceleration parallel to gravity in a unit of G which can be felt by everything onboard. Here the 1 G is equivalent to the acceleration of gravity on the earth,*

*. One can feel free from gravity during around 20 s in a parabola. (b) The time variations of*

**Figure 2(b)** is a graph of accelerations onboard the aircraft measured in a parabolic flight. The accelerations were detected by the directions of *x*, *y*, and *z* parallel to the traveling direction of the aircraft, to its wing, and to the gravity, respectively. The acceleration in the *z*-direction, i.e., parallel to gravity, dropped down to 0 G (μG) after an entry to parabola with 1.8 G and kept a constant stable

detected to be less than 4 <sup>10</sup><sup>2</sup> G and had no effect on the experiments. However,

for around 20 s. In the *y*-direction along to the wing, the acceleration was

. To make a

#### **Figure 1.**

*Aircrafts for parabolic flights operated by DAS. There are two types of the aircrafts. One is MU-300 from Mitsubishi heavy industries loading two racks (left), and the other is G-II from Grumman aircraft engineering Corp. For four racks (right).*

*Microgravity Experiments Using Parabolic Flights for Dusty Plasmas DOI: http://dx.doi.org/10.5772/intechopen.90530*

#### **Figure 2.**

long time to prepare and perform the microgravity experiments by the aircrafts. Pieces of information in the chapter help successors to reduce money and time and

The Japanese team experienced the missions of PK-3 plus, where the team aimed at demonstrating a critical phenomenon in dusty plasmas [12–14]. The PK-3 plus had a configuration of parallel-plate electrodes for rf (13.56 MHz) discharges. The team did microgravity experiments by aircrafts using the chamber the same as the PK-3 plus in Japan. This opportunity allowed the team to proceed to the next parabolic flight campaign for the next project of PK-4. The team built the apparatus of PK-4J whose glass tube for discharges was scaled down from the original one to load a rack system on the aircrafts for parabolic flights in Japan. The PK-4J had two phases of the microgravity experiments in Japan. The Phase 1 was dedicated to sophisticate the apparatus and acquire wide experience for the experiments using the parabolic flights. In the other, Phase 2, the behaviors of the dust particles were observed in cylindrical discharges [15], which had been preliminarily studied in numerical simulations [16, 17]. In parallel with the microgravity experiments, measuring parameters such as ion density and electron temperature in plasmas had been developed to reach comprehensive analyses of phenomena observed under

In Japan, the parabolic flights are carried out by a company, Diamond Air Service, Inc. It has two aircrafts (**Figure 1**). One is smaller than the other and equipped with two racks. The larger one has four racks. Everything for the experiments is integrated into the rack before loading on the aircraft. The whole rack is inspected that all components inside are tightly fixed and checked before flights not to electromagnetically interfere with the aircrafts during operation. The aircraft makes a condition free from gravity with a flight pattern of parabola in an airspace above the Sea of Japan or the Pacific Ocean. It takes 1 h to obtain a set of parabolas not more than 15 times a day. **Figure 2(a)** shows a graph of an altitude as a function of time corresponding to the flight pattern of the aircraft. Angles of elevation and

*Aircrafts for parabolic flights operated by DAS. There are two types of the aircrafts. One is MU-300 from Mitsubishi heavy industries loading two racks (left), and the other is G-II from Grumman aircraft engineering*

get much more scientific merit in future microgravity experiments.

**2. Microgravity experiments by parabolic flights**

**2.1 Background**

*Progress in Fine Particle Plasmas*

microgravity [18–21].

**2.2 Parabolic flights**

**Figure 1.**

**48**

*Corp. For four racks (right).*

*(a) A flight pattern of the aircraft to obtain a condition under microgravity shown by an altitude of the aircraft as a function of time. The figure shows an angle of elevation and the acceleration parallel to gravity in a unit of G which can be felt by everything onboard. Here the 1 G is equivalent to the acceleration of gravity on the earth, i.e., 9.8 m/s<sup>2</sup> . One can feel free from gravity during around 20 s in a parabola. (b) The time variations of accelerations onboard the aircraft measured in a parabolic flight. The x, y, and z are corresponding to the directions parallel to the traveling direction of the aircraft, to its wing, and to the gravity, respectively.*

accelerations to be feel onboard are also indicated on the graph. The 1 G is corresponding to the acceleration of gravity on the earth, i.e., 9.8 m/s<sup>2</sup> . To make a parabola, the aircraft rapidly accelerates and gains speed while getting the nose down between 60 and 20 s. After that, it elevates steeply while getting the nose up between 20 and 0 s and reaches the release point of an elevation of 45°, where a pilot closes the throttle. The aircraft continues flying by its inertia and makes the parabola between 0 and 20 s, where gravity is well balanced with the inertia. This is why everything onboard does not feel gravity. One can typically have a time of 20 s under microgravity during the aircraft moving up and dropping down in around 1000 m. After the parabola, the aircraft recovers speed and its altitude. Before and after the parabola, a load force normally acts on the aircraft by the acceleration less than 2 G.

**Figure 2(b)** is a graph of accelerations onboard the aircraft measured in a parabolic flight. The accelerations were detected by the directions of *x*, *y*, and *z* parallel to the traveling direction of the aircraft, to its wing, and to the gravity, respectively. The acceleration in the *z*-direction, i.e., parallel to gravity, dropped down to 0 G (μG) after an entry to parabola with 1.8 G and kept a constant stable for around 20 s. In the *y*-direction along to the wing, the acceleration was detected to be less than 4 <sup>10</sup><sup>2</sup> G and had no effect on the experiments. However, in the *x*-direction parallel to the traveling direction, the acceleration was increased when the throttle was closed at the entry. It caused a problem in a feasibility study of Phase 1 as described later.

(**Figure 3(b)**). The main tube was set along to the traveling direction of the aircraft (*x*-direction). The dust particles were illuminated on the cross section perpendicu-

The first campaign of parabolic flights in Phase 1 made it clear that the dust particles were levitated around a plasma-sheath boundary near the bottom of the main tube under gravity and moved up to the center of the tube under microgravity (**Figure 4(a)**). The cloud of the dust particles of μG seemed to elongate along the axis of the tube as a shape of a cylinder since a disk was observed on the FOV. In the next campaign, the FOV was set on the plane parallel to the axis. **Figure 4(b)** shows that the shape of the cloud was a cylinder elongating along the axis and spatial distribution of the dust clouds moved up from around the plasma-sheath boundary at 7 mm to the axial center. Under microgravity, the dust particles seem to form a bundle of thread. Furthermore, it found that the dust particles were forced to be moved by acceleration along the traveling direction. Before the entry of a parabola, they went toward the back of the aircraft. They came to flow to the front of the aircraft after the entry. This was the problem to be solved in order to precisely observe arrangements of the dust particles as mentioned above. Therefore, it was decided that the main tube was placed crossing with the traveling direction of the aircraft in Phase 2 (**Figure 3(b)**). The length of the main tube was reduced to be

*Images of the clouds of the dust particles obtained in microgravity experiments of phase 1. (a) The cloud was observed on a cross section perpendicular to the axis of the main tube. The cloud stayed around the plasmasheath boundary near the bottom of the tube under gravity (1G). Under microgravity (μG), it moved up and made a disk. (b) The scale bar shows distance from the axis. The 15 mm corresponds to the inner wall of the glass tube. The dust particles were levitated around the plasma-sheath boundary near the bottom of the tube (at 7 mm from the axis) (1G). The cloud elongated along the axis. The dust particles were distributed around the*

lar to the axis of the main tube by a laser of 532 nm in wavelength, which corresponded to a field of view (FOV) observed diagonally by a charge-coupled

*Microgravity Experiments Using Parabolic Flights for Dusty Plasmas*

*DOI: http://dx.doi.org/10.5772/intechopen.90530*

420 mm to put it in a frame of the rack on the aircraft.

device (CCD) camera.

**Figure 4.**

**51**

*axis under microgravity (μG).*

## **2.3 Methodology and design of apparatus**

PK-4 was supposed to observe dust particles in a cylindrical discharge generated inside a glass tube. The Japanese team had built the apparatus of PK-4J based on dimensions and functions of PK-4 since 2011 (**Figure 3(a)**). The glass tube was an *π*-shape chamber consisting of a main tube with an inner diameter of 30 mm and branch tubes welded onto the main. The glass tube was fixed on an optical bench as the branch tubes being perpendicular to the floor on the aircraft. A pair of electrodes was placed in the branch tubes. Plasmas were generated by a rectangular pulse voltage applied between the electrodes. The voltage was varying between 650 and 750 V peak-to-peak at 1 kHz and supplied to the electrodes out of phase. This meant that polarity between the electrodes alternated at the frequency which did not allow the dust particles to follow an electric field by the voltage. Plasma frequencies of electron and ion are much higher than the frequency of the voltage, so that they are running between the electrodes back and forth. A current around 2.0 mA was observed in the discharge. The Ar gas was fed from a port on either of the branch tubes at a flow rate of four SCCM (SCCM denotes cubic centimeter per minute at the standard conditions) and pumped down from another port closed to the feeding port. Therefore the gas flow was negligible in the main tube like a stagnant pool of the gas. It was aimed at trapping the dust particles inside the main tube without perturbation by the gas flow. The dust particles of melamine-formaldehyde were injected by a dust dispenser mounted on the branch tube. Their diameter was 2.55 μm. The amount of the dust particles was regulated by a pulse voltage driving the dispenser.

The first apparatus was used for a feasibility study of Phase 1 and tested in microgravity experiments of parabolic flights between 2011 and 2012. The size of the main tube, whose length was 550 mm, was identical to the original one of PK-4

#### **Figure 3.**

*Schematic of the apparatus of PK-4J. (a) It was developed to be loaded on a rack system of the aircraft operated by Diamond Air Service, Inc. the π-shape tube enabled to observe the dust particles in a cylindrical discharge. (b) Design of the glass tube was progressed from phase 1 to phase 2. In phase 1, the main tube had been placed parallel to the traveling direction. However, it was rotated to be perpendicular to the direction to avoid the effect of inertia by acceleration along the traveling direction of the aircraft just before entry to a parabola. In order to keep the main tube inside the rack, its length was reduced. The field of view (FOV) of the CCD camera was a cross section perpendicular to the axis of the main tube in phase 1 and changed to a plane along to the axis in phase 2.*

*Microgravity Experiments Using Parabolic Flights for Dusty Plasmas DOI: http://dx.doi.org/10.5772/intechopen.90530*

(**Figure 3(b)**). The main tube was set along to the traveling direction of the aircraft (*x*-direction). The dust particles were illuminated on the cross section perpendicular to the axis of the main tube by a laser of 532 nm in wavelength, which corresponded to a field of view (FOV) observed diagonally by a charge-coupled device (CCD) camera.

The first campaign of parabolic flights in Phase 1 made it clear that the dust particles were levitated around a plasma-sheath boundary near the bottom of the main tube under gravity and moved up to the center of the tube under microgravity (**Figure 4(a)**). The cloud of the dust particles of μG seemed to elongate along the axis of the tube as a shape of a cylinder since a disk was observed on the FOV. In the next campaign, the FOV was set on the plane parallel to the axis. **Figure 4(b)** shows that the shape of the cloud was a cylinder elongating along the axis and spatial distribution of the dust clouds moved up from around the plasma-sheath boundary at 7 mm to the axial center. Under microgravity, the dust particles seem to form a bundle of thread. Furthermore, it found that the dust particles were forced to be moved by acceleration along the traveling direction. Before the entry of a parabola, they went toward the back of the aircraft. They came to flow to the front of the aircraft after the entry. This was the problem to be solved in order to precisely observe arrangements of the dust particles as mentioned above. Therefore, it was decided that the main tube was placed crossing with the traveling direction of the aircraft in Phase 2 (**Figure 3(b)**). The length of the main tube was reduced to be 420 mm to put it in a frame of the rack on the aircraft.

#### **Figure 4.**

in the *x*-direction parallel to the traveling direction, the acceleration was increased when the throttle was closed at the entry. It caused a problem in a feasibility study

PK-4 was supposed to observe dust particles in a cylindrical discharge generated inside a glass tube. The Japanese team had built the apparatus of PK-4J based on dimensions and functions of PK-4 since 2011 (**Figure 3(a)**). The glass tube was an *π*-shape chamber consisting of a main tube with an inner diameter of 30 mm and branch tubes welded onto the main. The glass tube was fixed on an optical bench as the branch tubes being perpendicular to the floor on the aircraft. A pair of electrodes was placed in the branch tubes. Plasmas were generated by a rectangular pulse voltage applied between the electrodes. The voltage was varying between 650 and 750 V peak-to-peak at 1 kHz and supplied to the electrodes out of phase. This meant that polarity between the electrodes alternated at the frequency which did not allow the dust particles to follow an electric field by the voltage. Plasma frequencies of electron and ion are much higher than the frequency of the voltage, so that they are running between the electrodes back and forth. A current around 2.0 mA was observed in the discharge. The Ar gas was fed from a port on either of the branch tubes at a flow rate of four SCCM (SCCM denotes cubic centimeter per minute at the standard conditions) and pumped down from another port closed to the feeding port. Therefore the gas flow was negligible in the main tube like a stagnant pool of the gas. It was aimed at trapping the dust particles inside the main tube without perturbation by the gas flow. The dust particles of melamine-formaldehyde were injected by a dust dispenser mounted on the branch tube. Their diameter was 2.55 μm. The amount of

the dust particles was regulated by a pulse voltage driving the dispenser.

The first apparatus was used for a feasibility study of Phase 1 and tested in microgravity experiments of parabolic flights between 2011 and 2012. The size of the main tube, whose length was 550 mm, was identical to the original one of PK-4

*Schematic of the apparatus of PK-4J. (a) It was developed to be loaded on a rack system of the aircraft operated by Diamond Air Service, Inc. the π-shape tube enabled to observe the dust particles in a cylindrical discharge. (b) Design of the glass tube was progressed from phase 1 to phase 2. In phase 1, the main tube had been placed parallel to the traveling direction. However, it was rotated to be perpendicular to the direction to avoid the effect of inertia by acceleration along the traveling direction of the aircraft just before entry to a parabola. In order to keep the main tube inside the rack, its length was reduced. The field of view (FOV) of the CCD camera was a cross section perpendicular to the axis of the main tube in phase 1 and changed to a plane along to the axis in*

of Phase 1 as described later.

*Progress in Fine Particle Plasmas*

**Figure 3.**

*phase 2.*

**50**

**2.3 Methodology and design of apparatus**

*Images of the clouds of the dust particles obtained in microgravity experiments of phase 1. (a) The cloud was observed on a cross section perpendicular to the axis of the main tube. The cloud stayed around the plasmasheath boundary near the bottom of the tube under gravity (1G). Under microgravity (μG), it moved up and made a disk. (b) The scale bar shows distance from the axis. The 15 mm corresponds to the inner wall of the glass tube. The dust particles were levitated around the plasma-sheath boundary near the bottom of the tube (at 7 mm from the axis) (1G). The cloud elongated along the axis. The dust particles were distributed around the axis under microgravity (μG).*

In Phase 2, a laser of 660 nm in wavelength was used to illuminate the dust particles. Its light was fine-shaped as the thickness (FWHM of intensity) of 50 μm by optics to make slice images of the cloud. The laser and CCD camera were mounted on a translation stage. The stage moved to make a scan in the direction along the traveling direction (*x*-axis). The CCD of a resolution of 480 640 pixels accumulated images at 200 fps while scanning at the speed of 6.5 mm/s. The field of view was 4.3 5.8 mm<sup>2</sup> .

structure was the face-centered orthorhombic (FCO) lattice [24]. The FCO structure tends to appear rather than isotropic structures such as body-centered and face-centered cubics under the conditions that a stress works in one direction

*Microgravity Experiments Using Parabolic Flights for Dusty Plasmas*

Under microgravity (μG), the cloud moved up and the dust particles were distributed around the axis. The cylinder of the cloud got thicker than that under gravity. Its axis was exactly identical to that of the main tube. **Figure 5(c)** shows coordinates of the dust particles in a region trimmed by a rectangle (indicated by **Figure 5(a)**) as a projection along the *x*-axis. The FCO structure was never found under microgravity. The dust particles formed an assembly of linear chains elongating along the *y*-axis, i.e., the main tube [28, 29]. The electric field, whose direction is alternatively switched at 1 kHz between the electrodes, makes an ion stream along its direction. The ion stream causes the wake potential around the dust particles which makes them interact by an attractive force in addition to the Coulomb repulsive force [30–32]. Linear chains of the dust particles had normally been observed near the electrodes in rf discharges which accelerate ions in sheath [33– 35]. In the discharge of the main tube, the ion stream has two components. One is from the ions going back and forth between electrodes, and the other is from those flowing toward walls by diffusion. At the axis, the ions going through the discharge are much more than those flowing toward the walls. Therefore, the dust particles form the chains around the axis by the wake potential, when they move up from the bottom to the center of the discharge under microgravity. Regarding the wake potential, its characteristics were made clear in several experiments under gravity [34, 36, 37]. Further, microscopic dynamics for causing the wake potential, e.g., visualization of the wake potential, will be expected to be analyzed in experiments under microgravity in addition to a calculation with a classical manner [38].

An apparatus of dusty plasmas was developed for observing dust particles of cylindrical discharges in a glass tube under microgravity. It was built step by step while testing its functions and observing the dust particles on board an aircraft. In order to analyze the arrangements of the dust particles, positioning the glass tube and field of views were considered in experiments of parabolic flights. It was significant for building the apparatus to suppress an effect of acceleration in the

In the experiments, coordinates of the dust particles were recorded in conditions under gravity as well as microgravity. They were located near the plasma-sheath boundary below the axis of the glass tube and found to form staking layers in a bottom part of clouds under gravity. The layers were not an isotropic threedimensional structure such as body-centered or face-centered cubic. The FCO lattice appeared in the cloud, which seemed to be deformed by a stress in one direction originated in gravity. Switching the condition from gravity to microgravity, at first, location of the dust particles was changed around the axis. The dust particles distributing around the axis drastically changed their arrangement from the FCO structure to an assembly of linear chains. The chains were possibly formed by an attractive force from a wake potential. The wake potential was promised to be caused by streaming of the ion which was going back and forth between electrodes and driven by electric field alternative at 1 kHz. The dust particles switched dominant interaction potential from Coulomb repulsive under gravity to wake under microgravity. This was unexpected in simulations removing a term of gravity and

traveling direction of the aircraft caused around entry of a parabola.

[25–27]. Here the stress means gravity.

*DOI: http://dx.doi.org/10.5772/intechopen.90530*

**4. Concluding remarks**

**53**

## **3. Dusty plasmas under microgravity**

**Figure 5** shows spatial distributions of the dust particles observed in Phase 2, where the peak-to-peak voltage and gas pressure were set at 700 V and 33 Pa, respectively [15]. The axes of *x*, *y*, and *z* correspond to the direction in traveling, that of the wing, and that perpendicular to the floor of the aircraft, respectively. Two cylinders of the clouds for the cases under gravity (1G) and microgravity (μG) are shown the **Figure 5(a)**. Both of them elongate along the *y*-axis and seem to be tapered. In the main tube, striations appeared in the discharge. The cloud became fat in swollen parts of brighter glow. In a level flight, i.e., under gravity, the main body of the cloud was placed below the axis, and the dust particles were distributed in 4.7 ≤ *z*< 2.0 mm. The cloud of 1G consists of a shell-like structure of three layers clearly appearing in the bottom part as indicated in other experimental and theoretical studies [17, 22, 23]. The outermost shell along the arrow in **Figure 5(a)** was unfolded on a plane of the cylinder surface (**Figure 5(b)**). Coordinates of the dust particles are plotted on the plane as parameters of a circumference of the cylinder (*L*) and *y*. The dust particles arranged to make a close packed structure in 2-dimension by a Coulomb repulsive force between them. This arrangement formed the layered structure stacking in the radial direction. Another work proved that the

#### **Figure 5.**

*Spatial distributions of the dust particles observed in phase 2 (the graph was reproduced by the data from the previous paper [15]). Each dot corresponds to each coordinate of a dust particle. (a) The clouds were shown for the conditions under gravity (1G) and microgravity (μG). The x, y, and z-axes correspond to the directions in traveling, of the wing and perpendicular to the floor of the aircraft, respectively. The left graph is a crosssectional view shown as projection along the y-axis (0*≤*y*<*6 mm). The right one is a projection along to the x-axis (2*≤*x*≤*2 mm). (b) An axis of L is defined as a circumference of the outermost shell along an arrow in (a). An arrangement of the dust particles is shown on a L-y plane. (c) The coordinates of the dust particles trimmed by the rectangle shown in the figure (a) are plotted on a y-z plane as a projection along to the x-direction.*

*Microgravity Experiments Using Parabolic Flights for Dusty Plasmas DOI: http://dx.doi.org/10.5772/intechopen.90530*

structure was the face-centered orthorhombic (FCO) lattice [24]. The FCO structure tends to appear rather than isotropic structures such as body-centered and face-centered cubics under the conditions that a stress works in one direction [25–27]. Here the stress means gravity.

Under microgravity (μG), the cloud moved up and the dust particles were distributed around the axis. The cylinder of the cloud got thicker than that under gravity. Its axis was exactly identical to that of the main tube. **Figure 5(c)** shows coordinates of the dust particles in a region trimmed by a rectangle (indicated by **Figure 5(a)**) as a projection along the *x*-axis. The FCO structure was never found under microgravity. The dust particles formed an assembly of linear chains elongating along the *y*-axis, i.e., the main tube [28, 29]. The electric field, whose direction is alternatively switched at 1 kHz between the electrodes, makes an ion stream along its direction. The ion stream causes the wake potential around the dust particles which makes them interact by an attractive force in addition to the Coulomb repulsive force [30–32]. Linear chains of the dust particles had normally been observed near the electrodes in rf discharges which accelerate ions in sheath [33– 35]. In the discharge of the main tube, the ion stream has two components. One is from the ions going back and forth between electrodes, and the other is from those flowing toward walls by diffusion. At the axis, the ions going through the discharge are much more than those flowing toward the walls. Therefore, the dust particles form the chains around the axis by the wake potential, when they move up from the bottom to the center of the discharge under microgravity. Regarding the wake potential, its characteristics were made clear in several experiments under gravity [34, 36, 37]. Further, microscopic dynamics for causing the wake potential, e.g., visualization of the wake potential, will be expected to be analyzed in experiments under microgravity in addition to a calculation with a classical manner [38].

## **4. Concluding remarks**

In Phase 2, a laser of 660 nm in wavelength was used to illuminate the dust particles. Its light was fine-shaped as the thickness (FWHM of intensity) of 50 μm by optics to make slice images of the cloud. The laser and CCD camera were mounted on a translation stage. The stage moved to make a scan in the direction along the traveling direction (*x*-axis). The CCD of a resolution of 480 640 pixels accumulated images at 200 fps while scanning at the speed of 6.5 mm/s. The field of

**Figure 5** shows spatial distributions of the dust particles observed in Phase 2, where the peak-to-peak voltage and gas pressure were set at 700 V and 33 Pa, respectively [15]. The axes of *x*, *y*, and *z* correspond to the direction in traveling, that of the wing, and that perpendicular to the floor of the aircraft, respectively. Two cylinders of the clouds for the cases under gravity (1G) and microgravity (μG) are shown the **Figure 5(a)**. Both of them elongate along the *y*-axis and seem to be tapered. In the main tube, striations appeared in the discharge. The cloud became fat in swollen parts of brighter glow. In a level flight, i.e., under gravity, the main body of the cloud was placed below the axis, and the dust particles were distributed in 4.7 ≤ *z*< 2.0 mm. The cloud of 1G consists of a shell-like structure of three layers clearly appearing in the bottom part as indicated in other experimental and theoretical studies [17, 22, 23]. The outermost shell along the arrow in **Figure 5(a)** was unfolded on a plane of the cylinder surface (**Figure 5(b)**). Coordinates of the dust particles are plotted on the plane as parameters of a circumference of the cylinder (*L*) and *y*. The dust particles arranged to make a close packed structure in 2-dimension by a Coulomb repulsive force between them. This arrangement formed the layered structure stacking in the radial direction. Another work proved that the

*Spatial distributions of the dust particles observed in phase 2 (the graph was reproduced by the data from the previous paper [15]). Each dot corresponds to each coordinate of a dust particle. (a) The clouds were shown for the conditions under gravity (1G) and microgravity (μG). The x, y, and z-axes correspond to the directions in traveling, of the wing and perpendicular to the floor of the aircraft, respectively. The left graph is a crosssectional view shown as projection along the y-axis (0*≤*y*<*6 mm). The right one is a projection along to the x-axis (2*≤*x*≤*2 mm). (b) An axis of L is defined as a circumference of the outermost shell along an arrow in (a). An arrangement of the dust particles is shown on a L-y plane. (c) The coordinates of the dust particles trimmed by the rectangle shown in the figure (a) are plotted on a y-z plane as a projection along to the*

view was 4.3 5.8 mm<sup>2</sup>

*Progress in Fine Particle Plasmas*

**Figure 5.**

*x-direction.*

**52**

.

**3. Dusty plasmas under microgravity**

An apparatus of dusty plasmas was developed for observing dust particles of cylindrical discharges in a glass tube under microgravity. It was built step by step while testing its functions and observing the dust particles on board an aircraft. In order to analyze the arrangements of the dust particles, positioning the glass tube and field of views were considered in experiments of parabolic flights. It was significant for building the apparatus to suppress an effect of acceleration in the traveling direction of the aircraft caused around entry of a parabola.

In the experiments, coordinates of the dust particles were recorded in conditions under gravity as well as microgravity. They were located near the plasma-sheath boundary below the axis of the glass tube and found to form staking layers in a bottom part of clouds under gravity. The layers were not an isotropic threedimensional structure such as body-centered or face-centered cubic. The FCO lattice appeared in the cloud, which seemed to be deformed by a stress in one direction originated in gravity. Switching the condition from gravity to microgravity, at first, location of the dust particles was changed around the axis. The dust particles distributing around the axis drastically changed their arrangement from the FCO structure to an assembly of linear chains. The chains were possibly formed by an attractive force from a wake potential. The wake potential was promised to be caused by streaming of the ion which was going back and forth between electrodes and driven by electric field alternative at 1 kHz. The dust particles switched dominant interaction potential from Coulomb repulsive under gravity to wake under microgravity. This was unexpected in simulations removing a term of gravity and

an example that the microgravity condition possibly revealed a phenomenon hidden under the influence of gravity.

In microgravity experiments by parabolic flights, it is meaningful to have transition state from gravity to microgravity as well as to have microgravity only. Furthermore acceleration parallel to gravity controlled in operation of the aircraft by pilots is fascinating in precisely analyzing responses of physical phenomena to gravity. This is something that cannot be done on the ISS. The mechanism in formation of the linear chains was clearly understood in observation of the dust particles moving in the transition state where the acceleration was gradually changed. There are likely advantages to use the parabolic flights in diverse fields other than microgravity science.

The behavior of the dust particles, which are visible in an invisible ensemble of plasmas consisting of electrons and ions, clearly reflects phenomena of physics in the plasmas and makes them easily understood. Indeed a phenomenon of invisible wave might be visualized and comprehended by the dust particles. There are so much dust in the universe, pollutants in the atmosphere, cosmic dust in the interstellar, the regolith on the moon, etc. They attract much interest for investigating the origin of the universe from the point of view of natural science. Particulate matter is widely used and produced in industries. The dust particles charged in the plasmas are available for seeking ways of application and new ideas in technology. The microgravity experiments of dusty plasmas are promising to open new ideas in future science and technology. The know-how introduced in the chapter will be hopefully useful for the future.

## **Acknowledgements**

The author would like to thank Dr. Satoshi Adachi of JAXA for the technical support in experiments. Microgravity experiments were performed as an activity of the scientific working group supported by JAXA with Dr. Hiroo Totsuji (Professor Emeritus of Okayama University), Dr. Yasuaki Hayashi (Professor Emeritus of Kyoto Institute of Technology), and former students of the author's laboratory, Manami Tonouchi and Tomo Ide. The author obtained a chance to join experimental projects on the ISS when he belonged to a scientific team at Max-Planck-Institut für extraterrestrishe Physik between 2005 and 2006 in Germany. He appreciates broad-mindedness of the then supervisor of the team, Professor Gregor E. Morfill, who supported his activities in Japan.

**Author details**

Kazuo Takahashi

\*Address all correspondence to: takahash@kit.jp

*Microgravity Experiments Using Parabolic Flights for Dusty Plasmas*

*DOI: http://dx.doi.org/10.5772/intechopen.90530*

provided the original work is properly cited.

Kyoto, Japan

**55**

Faculty of Electrical Engineering and Electronics, Kyoto Institute of Technology,

© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

*Microgravity Experiments Using Parabolic Flights for Dusty Plasmas DOI: http://dx.doi.org/10.5772/intechopen.90530*

## **Author details**

an example that the microgravity condition possibly revealed a phenomenon hid-

sition state from gravity to microgravity as well as to have microgravity only. Furthermore acceleration parallel to gravity controlled in operation of the aircraft by pilots is fascinating in precisely analyzing responses of physical phenomena to gravity. This is something that cannot be done on the ISS. The mechanism in formation of the linear chains was clearly understood in observation of the dust particles moving in the transition state where the acceleration was gradually changed. There are likely advantages to use the parabolic flights in diverse fields

In microgravity experiments by parabolic flights, it is meaningful to have tran-

The behavior of the dust particles, which are visible in an invisible ensemble of plasmas consisting of electrons and ions, clearly reflects phenomena of physics in the plasmas and makes them easily understood. Indeed a phenomenon of invisible wave might be visualized and comprehended by the dust particles. There are so much dust in the universe, pollutants in the atmosphere, cosmic dust in the interstellar, the regolith on the moon, etc. They attract much interest for investigating the origin of the universe from the point of view of natural science. Particulate matter is widely used and produced in industries. The dust particles charged in the plasmas are available for seeking ways of application and new ideas in technology. The microgravity experiments of dusty plasmas are promising to open new ideas in future science and technology. The know-how introduced in the chapter will be

The author would like to thank Dr. Satoshi Adachi of JAXA for the technical support in experiments. Microgravity experiments were performed as an activity of the scientific working group supported by JAXA with Dr. Hiroo Totsuji (Professor Emeritus of Okayama University), Dr. Yasuaki Hayashi (Professor Emeritus of Kyoto Institute of Technology), and former students of the author's laboratory, Manami Tonouchi and Tomo Ide. The author obtained a chance to join experimental projects on the ISS when he belonged to a scientific team at Max-Planck-Institut für extraterrestrishe Physik between 2005 and 2006 in Germany. He appreciates broad-mindedness of the then supervisor of the team, Professor Gregor E. Morfill,

den under the influence of gravity.

*Progress in Fine Particle Plasmas*

other than microgravity science.

hopefully useful for the future.

who supported his activities in Japan.

**Acknowledgements**

**54**

Kazuo Takahashi Faculty of Electrical Engineering and Electronics, Kyoto Institute of Technology, Kyoto, Japan

\*Address all correspondence to: takahash@kit.jp

© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

## **References**

[1] Hayashi Y, Tachibana K. Observation of Coulomb-crystal formation from carbon particles grown in a methane plasma. Japanese Journal of Applied Physics. 1994;**33**:L804-L806

[2] Thomas H, Morfill GE, Demmel V. Plasma crystal: Coulomb crystallization in a dusty plasma. Physical Review Letters. 1994;**73**:652-655

[3] Chu JH, I L. Direct observation of Coulomb crystals and liquids in strongly coupled rf dusty plasmas. Physical Review Letters. 1994;**72**:4009-4012

[4] Melzer A, Trottenberg T, Piel A. Experimental determination of the charge on dust particles forming Coulomb lattices. Physics Letters A. 1994;**191**:301-308

[5] Morfill GE, Thomas HM, Konopka U, Rothermel H, Zuzic M, Ivlev A, et al. Condensed plasmas under microgravity. Physical Review Letters. 1999;**83**: 1598-1601

[6] Hayashi Y. Radial ordering of fine particles in plasma under microgravity condition. Japanese Journal of Applied Physics. 2005;**44**:1436-1440

[7] Nefedov AP, Morfill GE, Fortov VE, Thomas HM, Rothermel H, Hagl T, et al. PKE-Nefedov: Plasma crystal experiments on the international Space Station. New Journal of Physics. 2003;**5**:33

[8] Thomas HM, Morfill GE, Fortov VE, Ivlev AV, Molotkov VI, Lipaev AM, et al. Complex plasma laboratory PK-3 plus on the International Space Station. New Journal of Physics. 2008;**10**:033036

[9] Usachev A, Zobnin A, Petrov O, Fortov V, Thoma M, Kretschmer M, et al. The project "Plasmakristall-4" (PK-4) is a dusty plasma experiment in a combined dc/rf(i) discharge plasma

under microgravity conditions. Czechoslovak Journal of Physics. 2004; **54**:C639-C647

plasmas and colloidal suspensions. Physical Review E. 2011;**84**:015401(R)

2014;**31**:55-61

2011;**110**:013307

2015;**32**:320409

704-708

**80**:843-848

**57**

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*DOI: http://dx.doi.org/10.5772/intechopen.90530*

*Microgravity Experiments Using Parabolic Flights for Dusty Plasmas*

discharge plasmas under gravity and microgravity. IEEE Transaction on Plasma Sciences. 2019;**47**:4213-4218

Ohishi Y, Onodera A. Pressure-induced

[25] Fujii Y, Hase K, Hamaya N,

[26] Stoeva SI, Prasad BLV, Uma S, Stoimenov PK, Zaikovski V,

[27] Hayashi Y. Structure of a threedimensional Coulomb crystal in a fineparticle plasma. Physical Review Letters. 1999;**83**:4764-4767

[28] Ivlev AV, Thoma MH, Räth C, Joyce G, Morfill GE. Complex plasmas in external fields: The role of non-Hamiltonian interactions. Physical Review Letters. 2011;**106**:155001

[29] Dietz C, Kretschmer M, Steinmüller B, Thoma MH. Recent microgravity experiments with complex direct current plasmas. Contributions to

Plasma Physics. 2018;**58**:21-29

[30] Nambu M, Vladimirov SV, Shukla PK. Attractive forces between charged particulates in plasmas. Physical Letters A. 1995;**203**:40-42

[31] Vladimirov SV, Nambu M. Attraction of charged particulates in plasmas with finite flows. Physical Review E. 1995;**52**:R2172-R2174

69-74

[32] Ishihara O, Vladimirov SV. Wake potential of a dust grain in a plasma with ion flow. Physics of Plasmas. 1997;**4**:

[33] Takahashi K, Oishi T, Shimomai K, Hayashi Y, Nishino S. Simple hexagonal

Sorensen CM, et al. Face-centered cubic

face-centered-cubic phase of monatomic metallic iodine. Physical Review Letters. 1987;**58**:796-799

and hexagonal closed-packed nanocrystal superlattices of gold nanoparticles prepared by different methods. Journal of Physical Chemistry B. 2003;**107**:7441-7448

[18] Takahashi K, Hayashi Y, Adachi S. Measurement of electron density in complex plasmas of the PK-3 plus apparatus on the international Space Station. Journal of Applied Physics.

[19] Takahashi K, Thomas HM, Molotkov VI, Morfill GE, Adachi S. Estimation of plasma parameters in dusty plasmas for microgravity experiments. International Journal of Microgravity Science and Application.

[20] Takahashi K, Adachi S, Totsuji H. Measurement of ion density and electron temperature by double-probe method to study critical phenomena in dusty plasmas. JAXA Research and Development Report. 2015;**14-012E**:7-11

[21] Takahashi K, Lin J, Hénault M, Boufendi L. Measurements of ion density and electron temperature around voids in dusty plasmas. IEEE Transaction on Plasma Science. 2018;**46**:

[22] Mitic S, Klumov BA, Konopka U, Thoma MH, Morfill GE. Structural properties of complex plasmas in a homogeneous dc discharge. Physical Review Letters. 2008;**101**:125002

[23] Totsuji H. Behavior of dust particles in cylindrical discharges: Structure formation, mixture and void, effect of gravity. Journal of Plasma Physics. 2014;

[24] Takahashi K, Totsuji H. Structure of

Coulomb crystals in cylindrical

[10] Fortov V, Morfill G, Petrov O, Thoma M, Usachev A, Hoefner H, et al. The project 'Plasmakristall-4' (PK-4)— A new stage in investigations of dusty plasmas under microgravity conditions: First results and future plans. Plasma Physics and Controlled Fusion. 2005;**47**: B537-B549

[11] Pustylnik MY, Fink MA, Nosenko V, Antonova T, Hagl T, Thomas HM, et al. Plasmakristall-4: New complex (dusty) plasma laboratory on board the International Space Station. Review of Scientific Instruments. 2016;**87**:093505

[12] Totsuji H. Thermodynamics of strongly coupled repulsive Yukawa particles in ambient neutralizing plasma: Thermodynamic instability and the possibility of observation in fine particle plasmas. Physics of Plasmas. 2008;**15**: 072111

[13] Totsuji H. Thermodynamic instability and the critical point of fine particle (dusty) plasmas: Enhancement of density fluctuations and experimental conditions for observation. Journal of Physics A: Mathematical and Theoretical. 2009;**42**:214022

[14] Totsuji H. Possible observation of critical phenomena in fine particle (dusty, complex) plasmas. Microgravity Science and Technology. 2011;**23**: 159-167

[15] Takahashi K, Tonouchi M, Adachi S, Totsuji H. Study of cylindrical dusty plasmas in PK-4J; experiments. International Journal of Microgravity Science and Application. 2014;**31**:62-65

[16] Totsuji H, Totsuji C. Structures of Yukawa and Coulomb particles in cylinders: Simulations for fine particle *Microgravity Experiments Using Parabolic Flights for Dusty Plasmas DOI: http://dx.doi.org/10.5772/intechopen.90530*

plasmas and colloidal suspensions. Physical Review E. 2011;**84**:015401(R)

**References**

[1] Hayashi Y, Tachibana K. Observation of Coulomb-crystal formation from carbon particles grown in a methane plasma. Japanese Journal of Applied

under microgravity conditions.

**54**:C639-C647

B537-B549

072111

159-167

Czechoslovak Journal of Physics. 2004;

[11] Pustylnik MY, Fink MA, Nosenko V, Antonova T, Hagl T, Thomas HM, et al. Plasmakristall-4: New complex (dusty)

plasma laboratory on board the International Space Station. Review of Scientific Instruments. 2016;**87**:093505

[12] Totsuji H. Thermodynamics of strongly coupled repulsive Yukawa particles in ambient neutralizing plasma: Thermodynamic instability and the possibility of observation in fine particle plasmas. Physics of Plasmas. 2008;**15**:

[13] Totsuji H. Thermodynamic

Physics A: Mathematical and Theoretical. 2009;**42**:214022

instability and the critical point of fine particle (dusty) plasmas: Enhancement of density fluctuations and experimental conditions for observation. Journal of

[14] Totsuji H. Possible observation of critical phenomena in fine particle (dusty, complex) plasmas. Microgravity Science and Technology. 2011;**23**:

[15] Takahashi K, Tonouchi M, Adachi S, Totsuji H. Study of cylindrical dusty plasmas in PK-4J; experiments. International Journal of Microgravity Science and Application. 2014;**31**:62-65

[16] Totsuji H, Totsuji C. Structures of Yukawa and Coulomb particles in cylinders: Simulations for fine particle

[10] Fortov V, Morfill G, Petrov O, Thoma M, Usachev A, Hoefner H, et al. The project 'Plasmakristall-4' (PK-4)— A new stage in investigations of dusty plasmas under microgravity conditions: First results and future plans. Plasma Physics and Controlled Fusion. 2005;**47**:

[2] Thomas H, Morfill GE, Demmel V. Plasma crystal: Coulomb crystallization in a dusty plasma. Physical Review

[3] Chu JH, I L. Direct observation of Coulomb crystals and liquids in strongly coupled rf dusty plasmas. Physical Review Letters. 1994;**72**:4009-4012

[4] Melzer A, Trottenberg T, Piel A. Experimental determination of the charge on dust particles forming Coulomb lattices. Physics Letters A.

[5] Morfill GE, Thomas HM, Konopka U, Rothermel H, Zuzic M, Ivlev A, et al. Condensed plasmas under microgravity. Physical Review Letters. 1999;**83**:

[6] Hayashi Y. Radial ordering of fine particles in plasma under microgravity condition. Japanese Journal of Applied

[7] Nefedov AP, Morfill GE, Fortov VE, Thomas HM, Rothermel H, Hagl T, et al.

experiments on the international Space Station. New Journal of Physics.

[8] Thomas HM, Morfill GE, Fortov VE, Ivlev AV, Molotkov VI, Lipaev AM, et al. Complex plasma laboratory PK-3 plus on the International Space Station. New Journal of Physics. 2008;**10**:033036

[9] Usachev A, Zobnin A, Petrov O, Fortov V, Thoma M, Kretschmer M, et al. The project "Plasmakristall-4" (PK-4) is a dusty plasma experiment in a combined dc/rf(i) discharge plasma

Physics. 2005;**44**:1436-1440

PKE-Nefedov: Plasma crystal

Physics. 1994;**33**:L804-L806

*Progress in Fine Particle Plasmas*

Letters. 1994;**73**:652-655

1994;**191**:301-308

1598-1601

2003;**5**:33

**56**

[17] Totsuji H, Totsuji C, Takahashi K, Adachi S. Study of cylindrical dusty plasmas in PK-4J; Theory and simulations. International Journal of Microgravity Science and Application. 2014;**31**:55-61

[18] Takahashi K, Hayashi Y, Adachi S. Measurement of electron density in complex plasmas of the PK-3 plus apparatus on the international Space Station. Journal of Applied Physics. 2011;**110**:013307

[19] Takahashi K, Thomas HM, Molotkov VI, Morfill GE, Adachi S. Estimation of plasma parameters in dusty plasmas for microgravity experiments. International Journal of Microgravity Science and Application. 2015;**32**:320409

[20] Takahashi K, Adachi S, Totsuji H. Measurement of ion density and electron temperature by double-probe method to study critical phenomena in dusty plasmas. JAXA Research and Development Report. 2015;**14-012E**:7-11

[21] Takahashi K, Lin J, Hénault M, Boufendi L. Measurements of ion density and electron temperature around voids in dusty plasmas. IEEE Transaction on Plasma Science. 2018;**46**: 704-708

[22] Mitic S, Klumov BA, Konopka U, Thoma MH, Morfill GE. Structural properties of complex plasmas in a homogeneous dc discharge. Physical Review Letters. 2008;**101**:125002

[23] Totsuji H. Behavior of dust particles in cylindrical discharges: Structure formation, mixture and void, effect of gravity. Journal of Plasma Physics. 2014; **80**:843-848

[24] Takahashi K, Totsuji H. Structure of Coulomb crystals in cylindrical

discharge plasmas under gravity and microgravity. IEEE Transaction on Plasma Sciences. 2019;**47**:4213-4218

[25] Fujii Y, Hase K, Hamaya N, Ohishi Y, Onodera A. Pressure-induced face-centered-cubic phase of monatomic metallic iodine. Physical Review Letters. 1987;**58**:796-799

[26] Stoeva SI, Prasad BLV, Uma S, Stoimenov PK, Zaikovski V, Sorensen CM, et al. Face-centered cubic and hexagonal closed-packed nanocrystal superlattices of gold nanoparticles prepared by different methods. Journal of Physical Chemistry B. 2003;**107**:7441-7448

[27] Hayashi Y. Structure of a threedimensional Coulomb crystal in a fineparticle plasma. Physical Review Letters. 1999;**83**:4764-4767

[28] Ivlev AV, Thoma MH, Räth C, Joyce G, Morfill GE. Complex plasmas in external fields: The role of non-Hamiltonian interactions. Physical Review Letters. 2011;**106**:155001

[29] Dietz C, Kretschmer M, Steinmüller B, Thoma MH. Recent microgravity experiments with complex direct current plasmas. Contributions to Plasma Physics. 2018;**58**:21-29

[30] Nambu M, Vladimirov SV, Shukla PK. Attractive forces between charged particulates in plasmas. Physical Letters A. 1995;**203**:40-42

[31] Vladimirov SV, Nambu M. Attraction of charged particulates in plasmas with finite flows. Physical Review E. 1995;**52**:R2172-R2174

[32] Ishihara O, Vladimirov SV. Wake potential of a dust grain in a plasma with ion flow. Physics of Plasmas. 1997;**4**: 69-74

[33] Takahashi K, Oishi T, Shimomai K, Hayashi Y, Nishino S. Simple hexagonal Coulomb crystal near a deformed plasma sheath boundary in a dusty plasma. Japanese Journal of Applied Physics. 1998;**37**:6609-6614

**Chapter 4**

**Abstract**

storm in a glass tube

**1. Introduction**

**59**

Dynamic Behavior of Dust

**Keywords:** dust flow, dust fluid, bow shock, dynamic circulation,

and a swirling tea in a teacup is in the tabletop scale.

one of the examples of the case.

Experimentally observed dynamic behavior, such as a particle circulation under magnetic field, a bow shock formation in an upper stream of an obstacle, etc., will be reviewed. Dust particles confined in a cylindrical glass tube show a dynamic circulation when strong magnetic field is applied from the bottom of the tube using a permanent magnet. The circulation consists of two kinds of motions: one is a toroidal rotation around the tube axis, and the other is a poloidal rotation. Dust particles are blown upward from near the bottom of the tube against the gravity neighborhood of the tube axis. A two-dimensional supersonic flow of dust particles forms a bow shock in front of a needlelike-shaped obstacle when the flow crosses the obstacle. The slower flow passes the obstacle as a laminar flow. A streamlineshaped void where dust particles are not observed is formed around the obstacle.

The natural world is filled with fluids. Fluids present various phenomena such as waves, oscillations, vortices, etc. Scales of such phenomena vary widely. The bow shock formed near the heliopause is in the astrophysical scale, while the Great Red Spot of Jupiter is in the planetary scale, a tornado is in the earth's atmosphere scale,

It is often observed that collective behavior of individual particles can be regarded as a fluid. A complex plasma, defined as a plasma in which microparticles are embedded in the background of electrons, ions, and neutral particles, provides

In 1986, Ikezi theoretically predicted existence of a crystalized structure with small particles contained in a plasma [1]. It was in 1994 that Hayashi et al., Thomas et al., and Chu et al. separately found in their experiments that charged dust particles formed the crystalized structure in plasmas [2–4]. Since then, research on dusty plasmas has been actively conducted [5–41]. Looking back on the past, Galilei discovered in 1610 that Saturn had "ears." It was found later that the "ears" were a ring or rings by Huygens, Cassini, etc. [42]. Further later in 1856, Maxwell considered the stability of Saturn's ring and concluded that the stable Saturn's ring must consist of independent particles [43]. The interplanetary space is a plasma state dominantly filled by protons brought by the solar wind. Planetary rings like the Saturn's ring is one of the examples that ubiquitously exist in the universe.

Particles in Plasmas

*Yoshifumi Saitou and Osamu Ishihara*

[34] Takahashi K, Oishi T, Shimomai K, Hayashi Y, Nishino S. Analyses of attractive forces between particles in Coulomb crystal of dusty plasmas by optical manipulations. Physical Review E. 1998;**58**:7805-7811

[35] Ivlev AV, Morfill GE, Thomas HM, Räth C, Joyce G, Huber P, et al. First observation of electrorheological plasmas. Physical Review Letters. 2008; **100**:095003

[36] Melzer A, Schweigert VA, Piel A. Transition from attractive to repulsive forces between dust molecules in a plasma sheath. Physical Review Letters. 1999;**83**:3194-3197

[37] Chen M, Dropmann M, Zhang B, Matthews LS, Hyde TW. Ion-wake field inside a glass box. Physical Review Letters. 2016;**94**:033201

[38] Melandsø F, Goree J. Polarized supersonic plasma flow simulation for charged bodies such as dust particles and spacecraft. Physical Review E. 1995; **52**:5312-5326

## **Chapter 4**

Coulomb crystal near a deformed plasma sheath boundary in a dusty plasma. Japanese Journal of Applied

[34] Takahashi K, Oishi T, Shimomai K, Hayashi Y, Nishino S. Analyses of attractive forces between particles in Coulomb crystal of dusty plasmas by optical manipulations. Physical Review E. 1998;**58**:7805-7811

[35] Ivlev AV, Morfill GE, Thomas HM, Räth C, Joyce G, Huber P, et al. First observation of electrorheological plasmas. Physical Review Letters. 2008;

[36] Melzer A, Schweigert VA, Piel A. Transition from attractive to repulsive forces between dust molecules in a plasma sheath. Physical Review Letters.

[37] Chen M, Dropmann M, Zhang B, Matthews LS, Hyde TW. Ion-wake field inside a glass box. Physical Review

[38] Melandsø F, Goree J. Polarized supersonic plasma flow simulation for charged bodies such as dust particles and spacecraft. Physical Review E. 1995;

Physics. 1998;**37**:6609-6614

*Progress in Fine Particle Plasmas*

**100**:095003

1999;**83**:3194-3197

**52**:5312-5326

**58**

Letters. 2016;**94**:033201

## Dynamic Behavior of Dust Particles in Plasmas

*Yoshifumi Saitou and Osamu Ishihara*

## **Abstract**

Experimentally observed dynamic behavior, such as a particle circulation under magnetic field, a bow shock formation in an upper stream of an obstacle, etc., will be reviewed. Dust particles confined in a cylindrical glass tube show a dynamic circulation when strong magnetic field is applied from the bottom of the tube using a permanent magnet. The circulation consists of two kinds of motions: one is a toroidal rotation around the tube axis, and the other is a poloidal rotation. Dust particles are blown upward from near the bottom of the tube against the gravity neighborhood of the tube axis. A two-dimensional supersonic flow of dust particles forms a bow shock in front of a needlelike-shaped obstacle when the flow crosses the obstacle. The slower flow passes the obstacle as a laminar flow. A streamlineshaped void where dust particles are not observed is formed around the obstacle.

**Keywords:** dust flow, dust fluid, bow shock, dynamic circulation, storm in a glass tube

## **1. Introduction**

The natural world is filled with fluids. Fluids present various phenomena such as waves, oscillations, vortices, etc. Scales of such phenomena vary widely. The bow shock formed near the heliopause is in the astrophysical scale, while the Great Red Spot of Jupiter is in the planetary scale, a tornado is in the earth's atmosphere scale, and a swirling tea in a teacup is in the tabletop scale.

It is often observed that collective behavior of individual particles can be regarded as a fluid. A complex plasma, defined as a plasma in which microparticles are embedded in the background of electrons, ions, and neutral particles, provides one of the examples of the case.

In 1986, Ikezi theoretically predicted existence of a crystalized structure with small particles contained in a plasma [1]. It was in 1994 that Hayashi et al., Thomas et al., and Chu et al. separately found in their experiments that charged dust particles formed the crystalized structure in plasmas [2–4]. Since then, research on dusty plasmas has been actively conducted [5–41]. Looking back on the past, Galilei discovered in 1610 that Saturn had "ears." It was found later that the "ears" were a ring or rings by Huygens, Cassini, etc. [42]. Further later in 1856, Maxwell considered the stability of Saturn's ring and concluded that the stable Saturn's ring must consist of independent particles [43]. The interplanetary space is a plasma state dominantly filled by protons brought by the solar wind. Planetary rings like the Saturn's ring is one of the examples that ubiquitously exist in the universe.

Research of complex plasmas including dust particles is unique in a sense that we can chase the motion of individual dust particles by the naked eye using the visible laser light on site without time delay.

In this chapter, experimentally observed dynamic behaviors, such as a circulation of dust particles under magnetic field and a bow shock formation in an upper stream of an obstacle, will be reviewed. A two-dimensional supersonic flow of dust particles forms a bow shock in front of a needlelike-shaped obstacle when the flow passes the obstacle. The slower flow passes the obstacle as a laminar flow. A streamline-shaped void where dust particles are absent is formed around the obstacle. On the other hand, dust particles confined in a cylindrical glass tube show a three-dimensional dynamic circulation when strong enough magnetic field is applied from the bottom of the tube. The circulation consists of two kinds of motions: one is a toroidal rotation around the tube axis, and the other is a poloidal rotation. Dust particles are blown upward from near the bottom of the tube against the gravity around the tube axis.

## **2. Bow shock formation in two-dimensional dust flow**

A NASA's Spitzer Space Telescope observed a shock structure formed in front of the speedster star known as Kappa Cassiopeia in 1994 [44]. The shock is formed near the boundary between a stellar wind and interstellar medium. Another example of a shock wave can be seen around a boundary between a planetary magnetosphere and a stellar wind. These shock waves are similar to a shock excited in front of a bow of a ship cruising fast a water surface and are called a bow shock.

The bow shock is also observable in a supersonic flow of charged dust particles in a complex plasma. In this section, we will look back our experimental work on the bow shock formation [45]. Charged dust particles levitate at height where the gravity and the sheath electrostatic force acting on each particle are balanced in an experimental device on the ground. Therefore, monosized dust particles distribute and flow in an almost two-dimensional plane. An obstacle is placed in the middle of the dust flow just like the star or the planet in the solar wind or the ship on the ocean. The obstacle is a thin needlelike conducting wire and forms a potential barrier against the dust flow. The bow shock is formed when the dust flow interacts with the potential barrier.

Each dust particle is an Au-coated silica sphere of *a* ¼ 5 μm in diameter and *md* <sup>¼</sup> <sup>1</sup>*:*<sup>68</sup> � <sup>10</sup>�<sup>13</sup> kg in mass. The particles are charged to *<sup>Q</sup>* <sup>¼</sup> *Zde* <sup>¼</sup>

particles is observed and recorded with a camera placed outside the device.

**2.2 Wave modes observed in a complex plasma**

**Figure 1.**

**61**

*dust source (b).*

*Dynamic Behavior of Dust Particles in Plasmas DOI: http://dx.doi.org/10.5772/intechopen.88787*

�ð Þ� <sup>4</sup>*:*<sup>4</sup> � <sup>0</sup>*:*<sup>5</sup> <sup>10</sup><sup>4</sup>*e*, where *<sup>e</sup>* is the elementary electric charge [49]. The particles levitate near the boundary between the plasma and the sheath, whose height is approximately 8 mm above the metal plate. The dust particles are irradiated with two thin fan laser lights from the radial directions. Mie-scattered laser light from the

*Schematic drawings of the experimental glass chamber: a YCOPEX device (a) and a piezoelectric buzzer as the*

In the initial state, the dust particles are accumulated in a cylindrical piezoelectric buzzer which is placed under the metal plate and acts as a dust source. A part of the accumulated dust particles is hopped into the plasma by energizing the buzzer. The dust particles are stored in the reservoir region above the metal plate when the up-and-down gate is in condition to the up position. By tilting the entire device at angle *θ* and lowering the gate, the stocked dust particles begin moving and form the almost two-dimensional flow. The flow velocity is controlled by changing angle *θ*. The velocity reaches a terminal velocity before the particles arrive near the obstacle.

It is known that there are extremely low-frequency longitudinal wave modes in complex plasmas. Typically, one is the dust acoustic (DA) mode, and the other is

### **2.1 Experimental setup**

The schematic of the experimental device Yokohama Complex Plasma Experiment (YCOPEX) is shown in **Figure 1** [46]. Detailed description on the device and experimental setup can be seen in Ref. [45]. The device consists of a glass chamber and a flat metal plate. The size of the metal plate is 800 mm in length (*x* direction = the main flow direction) and 120 mm in width (*y* direction). The device is equipped with an up-and-down gate which is electrically controlled from outside. The up-and-down gate separates the plate into two regions: the reservoir of dust particles and the experimental region. A needlelike conducting wire is placed in the experimental region and is used as an obstacle. The potential of the obstacle is floating against the plasma potential here.

The argon gas pressure is 3.6 Pa. To avoid the drag by neutral particles or by ions [45–49], the vacuum pump and the gas feeding are stopped when the pressure reached the set value. Plasma is generated with an rf discharge of 5 W (13.56 MHz). The measured plasma parameters are *ne* <sup>5</sup> <sup>10</sup><sup>14</sup> <sup>m</sup>3, *Te* 5 eV. The plasma potential is 30 V.

*Dynamic Behavior of Dust Particles in Plasmas DOI: http://dx.doi.org/10.5772/intechopen.88787*

#### **Figure 1.**

Research of complex plasmas including dust particles is unique in a sense that we can chase the motion of individual dust particles by the naked eye using the visible

In this chapter, experimentally observed dynamic behaviors, such as a circulation of dust particles under magnetic field and a bow shock formation in an upper stream of an obstacle, will be reviewed. A two-dimensional supersonic flow of dust particles forms a bow shock in front of a needlelike-shaped obstacle when the flow passes the obstacle. The slower flow passes the obstacle as a laminar flow. A

streamline-shaped void where dust particles are absent is formed around the obstacle. On the other hand, dust particles confined in a cylindrical glass tube show a three-dimensional dynamic circulation when strong enough magnetic field is applied from the bottom of the tube. The circulation consists of two kinds of motions: one is a toroidal rotation around the tube axis, and the other is a poloidal rotation. Dust particles are blown upward from near the bottom of the tube against

A NASA's Spitzer Space Telescope observed a shock structure formed in front of the speedster star known as Kappa Cassiopeia in 1994 [44]. The shock is formed near the boundary between a stellar wind and interstellar medium. Another example of a shock wave can be seen around a boundary between a planetary magnetosphere and a stellar wind. These shock waves are similar to a shock excited in front

The bow shock is also observable in a supersonic flow of charged dust particles in a complex plasma. In this section, we will look back our experimental work on the bow shock formation [45]. Charged dust particles levitate at height where the gravity and the sheath electrostatic force acting on each particle are balanced in an experimental device on the ground. Therefore, monosized dust particles distribute and flow in an almost two-dimensional plane. An obstacle is placed in the middle of the dust flow just like the star or the planet in the solar wind or the ship on the ocean. The obstacle is a thin needlelike conducting wire and forms a potential barrier against the dust flow. The bow shock is formed when the dust flow interacts

The schematic of the experimental device Yokohama Complex Plasma Experiment (YCOPEX) is shown in **Figure 1** [46]. Detailed description on the device and experimental setup can be seen in Ref. [45]. The device consists of a glass chamber and a flat metal plate. The size of the metal plate is 800 mm in length (*x* direction = the main flow direction) and 120 mm in width (*y* direction). The device is equipped with an up-and-down gate which is electrically controlled from outside. The up-and-down gate separates the plate into two regions: the reservoir of dust particles and the experimental region. A needlelike conducting wire is placed in the experimental region and is used as an obstacle. The potential of the obstacle is

The argon gas pressure is 3.6 Pa. To avoid the drag by neutral particles or by ions

[45–49], the vacuum pump and the gas feeding are stopped when the pressure reached the set value. Plasma is generated with an rf discharge of 5 W (13.56 MHz). The measured plasma parameters are *ne* <sup>5</sup> <sup>10</sup><sup>14</sup> <sup>m</sup>3, *Te* 5 eV. The plasma

of a bow of a ship cruising fast a water surface and are called a bow shock.

**2. Bow shock formation in two-dimensional dust flow**

laser light on site without time delay.

*Progress in Fine Particle Plasmas*

the gravity around the tube axis.

with the potential barrier.

**2.1 Experimental setup**

potential is 30 V.

**60**

floating against the plasma potential here.

*Schematic drawings of the experimental glass chamber: a YCOPEX device (a) and a piezoelectric buzzer as the dust source (b).*

Each dust particle is an Au-coated silica sphere of *a* ¼ 5 μm in diameter and *md* <sup>¼</sup> <sup>1</sup>*:*<sup>68</sup> � <sup>10</sup>�<sup>13</sup> kg in mass. The particles are charged to *<sup>Q</sup>* <sup>¼</sup> *Zde* <sup>¼</sup> �ð Þ� <sup>4</sup>*:*<sup>4</sup> � <sup>0</sup>*:*<sup>5</sup> <sup>10</sup><sup>4</sup>*e*, where *<sup>e</sup>* is the elementary electric charge [49]. The particles levitate near the boundary between the plasma and the sheath, whose height is approximately 8 mm above the metal plate. The dust particles are irradiated with two thin fan laser lights from the radial directions. Mie-scattered laser light from the particles is observed and recorded with a camera placed outside the device.

In the initial state, the dust particles are accumulated in a cylindrical piezoelectric buzzer which is placed under the metal plate and acts as a dust source. A part of the accumulated dust particles is hopped into the plasma by energizing the buzzer. The dust particles are stored in the reservoir region above the metal plate when the up-and-down gate is in condition to the up position. By tilting the entire device at angle *θ* and lowering the gate, the stocked dust particles begin moving and form the almost two-dimensional flow. The flow velocity is controlled by changing angle *θ*. The velocity reaches a terminal velocity before the particles arrive near the obstacle.

#### **2.2 Wave modes observed in a complex plasma**

It is known that there are extremely low-frequency longitudinal wave modes in complex plasmas. Typically, one is the dust acoustic (DA) mode, and the other is

the dust lattice (DL) mode. The *n*-dimensional DA wave velocity, *CnD DA*, and the DL velocity, *CDL*, are given by

$$\mathbf{C}\_d = \mathfrak{u}(Z\_d, m\_d) f(\kappa), \tag{1}$$

where *Cd* <sup>¼</sup> *<sup>C</sup>nD DA* or *CDL*, and

$$
\mu(Z\_d, m\_d) = \sqrt{\frac{Z\_d^2 e^2}{\varepsilon\_0 m\_d \lambda\_{Di}}} \tag{2}
$$

The arcuate structure is the bow shock. The value of *vf* is required to exceed Mach number 1 when the bow shock is formed, where the Mach number is defined as the ratio of the flow velocity to the dust acoustic velocity. The experimentally measured velocity is 71 m*=*s Mach number ð Þ *M* ¼ 1 . It is found that the arcuate structure is distinctive when the flow is supersonic. In addition, there exists a deceleration region between the leading edge of the arcuate structure and the void as shown in **Figure 2**, that is, there is a region where the flow velocity is reduced in order to keep the flux constant around the obstacle. The presence of such a deceleration region, a subsonic flow region, between the wave front and the stagnation

The density ratio *ndp=nd*<sup>0</sup> is shown as a function of the Mach number, where *ndp* is the density in front of the stagnation point and *nd*<sup>0</sup> is the density of the upstream area. It is known that a polytropic hydrodynamic model provides criterion for the

ð Þ *M* < 1

ð Þ *M* ≥ 1

*;*

(5)

point is one of the defining features of the bow shock [50].

*Typical example of the formed bow shock. Modified from Figure 3(b) of Ref. [45].*

shock wave formation [50]:

8 >>>>><

>>>>>:

is a small deviation.

**63**

<sup>1</sup> <sup>þ</sup> *<sup>γ</sup>*�<sup>1</sup> <sup>2</sup> *<sup>M</sup>*<sup>2</sup> � �<sup>1</sup>*=*ð Þ *<sup>γ</sup>*�<sup>1</sup>

*Dynamic Behavior of Dust Particles in Plasmas DOI: http://dx.doi.org/10.5772/intechopen.88787*

where *γ* is the polytropic index.

� �ð Þ *<sup>γ</sup>*þ<sup>1</sup> *<sup>=</sup>*ð Þ *<sup>γ</sup>*�<sup>1</sup> *M*<sup>2</sup>

<sup>1</sup> <sup>þ</sup> *<sup>γ</sup>* � <sup>1</sup> 2

*M*<sup>2</sup>

A molecular-dynamics simulation code is carried out to examine the bow shock formation. The density ratio *ndp=nd*<sup>0</sup> and its spatial distribution are calculated. The simulation result on the density ratio corresponds to the numerical result of Eq. (5) with *γ* ¼ 2*:*2. The experimental result on the density ratio seems to correspond to the case of *γ* ¼ 5*=*3 (= the specific heat ratio of monoatomic gas) � 2*:*2 though there

The polytropic index found in the simulation and experimental observation may result from the fact that the significant amount of internal energy of the polytropic fluid, which consists of charged dust particles, may be stored in the background

*<sup>γ</sup>* � *<sup>γ</sup>* � <sup>1</sup> 2*M*<sup>2</sup> � ��1*=*ð Þ *<sup>γ</sup>*�<sup>1</sup>

*γ*þ1 2

**2.4 Bow shock by a simulation**

*ndp nd*<sup>0</sup> ¼

**Figure 2.**

with *ε*<sup>0</sup> the permittivity of free space, *λDi*, the ion Debye length. The function *f*ð Þ*κ* is given by

$$f(\kappa) = \begin{cases} \frac{1}{\kappa^{3/2}} & \text{for } \mathcal{C}\_{DA}^{3D} \\\frac{1}{\sqrt{2\pi\kappa^2}} & \text{for } \mathcal{C}\_{DA}^{2D} \\\sqrt{\frac{4\pi\kappa}{(\kappa^2 + 2\kappa + 2)\exp\left(-\kappa\right)}} & \text{for } \mathcal{C}\_{DL}(\kappa \gg 1) \end{cases},\tag{3}$$

where *κ* ¼ *d=λDi* with *d* as the interparticle distance [16, 19, 20]. The distance is given by

$$d = \begin{cases} \frac{\mathbf{1}}{\left(n\_d^{3D}\right)^{1/3}} & \text{for 3-D dust distribution} \\ \mathbf{1} & \text{for 2-D dust distribution} \end{cases},\tag{4}$$

where *n*<sup>3</sup>*<sup>D</sup> <sup>d</sup>* and *n*<sup>2</sup>*<sup>D</sup> <sup>d</sup>* are three- and two-dimensional dust densities, respectively.

The velocity of a wave excited in the dusty plasma, *Cd*, is measured using the time-of-flight method at *θ* ¼ 0 degree. The velocity of dust acoustic modes coincides well with the velocity of the dust lattice mode around *κ* ¼ 3 � 6. The threedimensional dust acoustic mode with velocity *C*<sup>3</sup>*<sup>D</sup> DA* is likely the candidate for the observed mode of the wave although the strict mode identification is still to be determined.

#### **2.3 Bow shock formation**

The particles flow from the reservoir region to the obstacle by changing the tilting angle *θ*. The void which has a streamline-like shape can be seen in the hatched area of **Figure 2**. The void is an area where dust particles are absent. The dust flow near the leading edge of the void is decelerated. The trajectories of dust particles are deflected toward the �*y* direction in front of the void.

The flow velocity, *vf* , in the upstream area has a constant value which is mainly determined by a balance of the gravitational force controlled by angle *θ* and the neutral drag force. The flow is almost uniform, and there is no prominent structure in the upstream area when *vf* is small. When *vf* increases, an arcuate structure where the intensity of the scattered laser light is enhanced is formed in front of the leading edge of the void. For further increase of *vf* , a curvature of the arc becomes larger. The tail of the void is extended with increasing values of *vf* .

*Dynamic Behavior of Dust Particles in Plasmas DOI: http://dx.doi.org/10.5772/intechopen.88787*

#### **Figure 2.**

the dust lattice (DL) mode. The *n*-dimensional DA wave velocity, *CnD*

*u Z*ð Þ¼ *<sup>d</sup>; md*

1

1 ffiffiffiffiffiffiffiffiffi

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4*πκ κ*ð Þ <sup>2</sup> þ 2*κ* þ 2 exp ð Þ �*κ*

*DA* or *CDL*, and

*f*ð Þ¼ *κ*

*d* ¼

*<sup>d</sup>* and *n*<sup>2</sup>*<sup>D</sup>*

**2.3 Bow shock formation**

r

1 *n*<sup>3</sup>*<sup>D</sup> d*

> 1 ffiffiffiffiffiffiffiffiffiffi *πn*<sup>2</sup>*<sup>D</sup> d*

8 >>>>>>><

>>>>>>>:

8 >>>><

>>>>:

dimensional dust acoustic mode with velocity *C*<sup>3</sup>*<sup>D</sup>*

velocity, *CDL*, are given by

*Progress in Fine Particle Plasmas*

where *Cd* <sup>¼</sup> *<sup>C</sup>nD*

*f*ð Þ*κ* is given by

given by

where *n*<sup>3</sup>*<sup>D</sup>*

determined.

**62**

*DA*, and the DL

(2)

(3)

(4)

*Cd* ¼ *u Z*ð Þ *<sup>d</sup>; md f*ð Þ*κ ,* (1)

*DA*

*DA*

*,*

*DA* is likely the candidate for the

*;*

for *CDL* ð Þ *κ* ≫ 1

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi *Z*2 *de*2 *ε*0*mdλDi*

*<sup>κ</sup>*<sup>3</sup>*=*<sup>2</sup> for *<sup>C</sup>*<sup>3</sup>*<sup>D</sup>*

<sup>2</sup>*πκ*<sup>2</sup> <sup>p</sup> for *<sup>C</sup>*<sup>2</sup>*<sup>D</sup>*

s

with *ε*<sup>0</sup> the permittivity of free space, *λDi*, the ion Debye length. The function

where *κ* ¼ *d=λDi* with *d* as the interparticle distance [16, 19, 20]. The distance is

� �<sup>1</sup>*=*<sup>3</sup> for 3 � D dust distribution

<sup>q</sup> for 2 � D dust distribution

The velocity of a wave excited in the dusty plasma, *Cd*, is measured using the time-of-flight method at *θ* ¼ 0 degree. The velocity of dust acoustic modes coincides well with the velocity of the dust lattice mode around *κ* ¼ 3 � 6. The three-

observed mode of the wave although the strict mode identification is still to be

The particles flow from the reservoir region to the obstacle by changing the tilting angle *θ*. The void which has a streamline-like shape can be seen in the hatched area of **Figure 2**. The void is an area where dust particles are absent. The dust flow near the leading edge of the void is decelerated. The trajectories of dust

The flow velocity, *vf* , in the upstream area has a constant value which is mainly determined by a balance of the gravitational force controlled by angle *θ* and the neutral drag force. The flow is almost uniform, and there is no prominent structure in the upstream area when *vf* is small. When *vf* increases, an arcuate structure where the intensity of the scattered laser light is enhanced is formed in front of the leading edge of the void. For further increase of *vf* , a curvature of the arc becomes

particles are deflected toward the �*y* direction in front of the void.

larger. The tail of the void is extended with increasing values of *vf* .

*<sup>d</sup>* are three- and two-dimensional dust densities, respectively.

*Typical example of the formed bow shock. Modified from Figure 3(b) of Ref. [45].*

The arcuate structure is the bow shock. The value of *vf* is required to exceed Mach number 1 when the bow shock is formed, where the Mach number is defined as the ratio of the flow velocity to the dust acoustic velocity. The experimentally measured velocity is 71 m*=*s Mach number ð Þ *M* ¼ 1 . It is found that the arcuate structure is distinctive when the flow is supersonic. In addition, there exists a deceleration region between the leading edge of the arcuate structure and the void as shown in **Figure 2**, that is, there is a region where the flow velocity is reduced in order to keep the flux constant around the obstacle. The presence of such a deceleration region, a subsonic flow region, between the wave front and the stagnation point is one of the defining features of the bow shock [50].

The density ratio *ndp=nd*<sup>0</sup> is shown as a function of the Mach number, where *ndp* is the density in front of the stagnation point and *nd*<sup>0</sup> is the density of the upstream area. It is known that a polytropic hydrodynamic model provides criterion for the shock wave formation [50]:

$$\frac{n\_{dp}}{n\_{d0}} = \begin{cases} \left(1 + \frac{\chi - 1}{2} M^2\right)^{1/(r-1)} & (M < 1) \\\\ \left(\frac{\chi + 1}{2}\right)^{(r+1)/(r-1)} \frac{M^2}{1 + \frac{\chi - 1}{2} M^2} \left(\chi - \frac{\chi - 1}{2M^2}\right)^{-1/(r-1)} & (M \ge 1) \end{cases},\tag{5}$$

where *γ* is the polytropic index.

#### **2.4 Bow shock by a simulation**

A molecular-dynamics simulation code is carried out to examine the bow shock formation. The density ratio *ndp=nd*<sup>0</sup> and its spatial distribution are calculated. The simulation result on the density ratio corresponds to the numerical result of Eq. (5) with *γ* ¼ 2*:*2. The experimental result on the density ratio seems to correspond to the case of *γ* ¼ 5*=*3 (= the specific heat ratio of monoatomic gas) � 2*:*2 though there is a small deviation.

The polytropic index found in the simulation and experimental observation may result from the fact that the significant amount of internal energy of the polytropic fluid, which consists of charged dust particles, may be stored in the background

plasma. The value of the complex plasma polytropic index indicates that the present complex plasma is far from isothermal (*γ* ¼ 1).

As for the spatial density distribution, the density contour plot shows the arcuate structure, and its curvature increases with increasing Mach number as seen in the experiment.

## **2.5 Bow shock formation in two-dimensional flow**

Under the polytropic process which is a quasi-static process, *<sup>p</sup>=n<sup>γ</sup>* <sup>¼</sup> *const:* and *<sup>T</sup>=n<sup>γ</sup>*�<sup>1</sup> <sup>¼</sup> *const:*, are held with the polytropic index *<sup>γ</sup>*, where *<sup>p</sup>* is the pressure, *<sup>T</sup>* is the temperature, and *n* is the density. The polytropic index means

$$\gamma = \begin{cases} 0 & \text{isobaric process} \\ 1 & \text{isothermal process} \\ \kappa\_h & \text{isentropic process} \\ & \infty & \text{isobaric process} \end{cases}, \tag{6}$$

determined by measuring the pressure ratio *pdp=pd*<sup>0</sup> or the temperature ratio

outside of the system. The first law of thermodynamics gives

heat *Q*<sup>01</sup> is added to the system for the bow shock formation.

such a dynamic motion of dust particles in a complex plasma [53].

**3. Dynamic circulation under magnetic field**

ubiquitous vortex commonly encountered in nature.

**3.1 Experimental setup**

**Figure 4.**

**65**

gravity is in the negative *z* direction.

*Schematic of tea leaves in tea stirred in a teacup.*

integrating this equation from state 0 to state 1

*Dynamic Behavior of Dust Particles in Plasmas DOI: http://dx.doi.org/10.5772/intechopen.88787*

In this polytropic process, there is a small amount of heat exchange with the

where *dQ* is a differential heat added to the system, *dU* is the differential internal energy of the system, and *CV* is the specific heat at constant volume. By

where *C<sup>γ</sup>* ¼ *CV*ð Þ *γ* � *κ =*ð Þ *γ* � 1 ð Þ >0 is the polytropic specific heat. As seen in **Figure 3**, *T*<sup>1</sup> � *T*<sup>0</sup> ¼ *Tdp* � *Td*<sup>0</sup> >0, and as a result, *Q*<sup>01</sup> >0. It is expected that the

You may watch a dynamic motion of tea leaves, set on the bottom of the teacup, by stirring the tea by a teaspoon. The tea leaves get close to the center and rise near the tea surface as illustrated in **Figure 4**. We can see a similar phenomenon in a complex plasma system. In this section, we will look back our experimental work on

The observation of particle motion in the dynamic circulation similar to the motion of the tea leaves helps to understand the simple but profound nature of the

The experiment is performed in a cylindrical glass tube as shown in **Figure 5**. Detailed explanation on the experimental setup is given in Ref. [53]. The cylindrical coordinates ð Þ *r; θ; z* are with the origin at the inner bottom of the tube, and the

The argon gas pressure is *p* ¼ 5 � 25 Pa. A geometry of the gas supply and exhaust system is configured to avoid the neutral drag force acting on the dust

*dQ* ¼ *dU* þ *pdV* ¼ *CVdT* þ *pdV,* (7)

*Q*<sup>01</sup> ¼ *C<sup>γ</sup>* ð Þ *T*<sup>1</sup> � *T*<sup>0</sup> *,* (8)

*Tdp=Td*0.

where *κ<sup>h</sup>* is the ratio of specific heat. The experimentally obtained polytropic index lies between 5*=*3 and 2.2. The value 5*=*3 is equivalent to the ratio of specific heat of ideal monoatomic gas. The bow shock forms under the almost adiabatic process. The value around 2 is suggested for the investigation on the solar wind [51, 52]. In addition, the dust flow consists of a collection of dust particles with finite size. It is hard to regard the fluid component as ideal. Hence, the polytropic index deviates from 5*=*3.

The bow shock formation is a nonisothermal process. The pressure ratio and the temperature ratio *pdp=pd*<sup>0</sup> and *Tdp=Td*<sup>0</sup> dependence on the density ratio *ndp=nd*<sup>0</sup> are given by *pdp=pd*<sup>0</sup> ¼ *ndp=nd*<sup>0</sup> � �*<sup>γ</sup>* and *Tdp=Td*<sup>0</sup> <sup>¼</sup> *ndp=nd*<sup>0</sup> � �*<sup>γ</sup>*�<sup>1</sup> , where *pdp* and *Tdp* are the pressure and temperature at the stagnation point and *pd*<sup>0</sup> and *Td*<sup>0</sup> are those at the upstream area, respectively. The results are shown in **Figure 3**. The bow shock is formed for *ndp=nd*<sup>0</sup> > 1. These results suggest that the polytropic index may be

**Figure 3.** *Expected changes in the ratios of the pressure and the temperature by the bow shock formation ndp=nd*<sup>0</sup> >*1 under the polytropic process.*

*Dynamic Behavior of Dust Particles in Plasmas DOI: http://dx.doi.org/10.5772/intechopen.88787*

plasma. The value of the complex plasma polytropic index indicates that the present

As for the spatial density distribution, the density contour plot shows the arcuate structure, and its curvature increases with increasing Mach number as seen in the

Under the polytropic process which is a quasi-static process, *<sup>p</sup>=n<sup>γ</sup>* <sup>¼</sup> *const:* and *<sup>T</sup>=n<sup>γ</sup>*�<sup>1</sup> <sup>¼</sup> *const:*, are held with the polytropic index *<sup>γ</sup>*, where *<sup>p</sup>* is the pressure, *<sup>T</sup>* is

> 0 isobaric process 1 isothermal process

where *κ<sup>h</sup>* is the ratio of specific heat. The experimentally obtained polytropic index lies between 5*=*3 and 2.2. The value 5*=*3 is equivalent to the ratio of specific heat of ideal monoatomic gas. The bow shock forms under the almost adiabatic process. The value around 2 is suggested for the investigation on the solar wind [51, 52]. In addition, the dust flow consists of a collection of dust particles with finite size. It is hard to regard the fluid component as ideal. Hence, the polytropic

The bow shock formation is a nonisothermal process. The pressure ratio and the temperature ratio *pdp=pd*<sup>0</sup> and *Tdp=Td*<sup>0</sup> dependence on the density ratio *ndp=nd*<sup>0</sup> are

� �*<sup>γ</sup>*�<sup>1</sup>

� �*<sup>γ</sup>* and *Tdp=Td*<sup>0</sup> <sup>¼</sup> *ndp=nd*<sup>0</sup>

the pressure and temperature at the stagnation point and *pd*<sup>0</sup> and *Td*<sup>0</sup> are those at the upstream area, respectively. The results are shown in **Figure 3**. The bow shock is formed for *ndp=nd*<sup>0</sup> > 1. These results suggest that the polytropic index may be

*Expected changes in the ratios of the pressure and the temperature by the bow shock formation ndp=nd*<sup>0</sup> >*1*

isentropic process isochoric process

*;*

(6)

, where *pdp* and *Tdp* are

complex plasma is far from isothermal (*γ* ¼ 1).

*Progress in Fine Particle Plasmas*

**2.5 Bow shock formation in two-dimensional flow**

*γ* ¼

the temperature, and *n* is the density. The polytropic index means

8 >>><

>>>:

*κh* ∞

experiment.

index deviates from 5*=*3.

given by *pdp=pd*<sup>0</sup> ¼ *ndp=nd*<sup>0</sup>

**Figure 3.**

**64**

*under the polytropic process.*

determined by measuring the pressure ratio *pdp=pd*<sup>0</sup> or the temperature ratio *Tdp=Td*0.

In this polytropic process, there is a small amount of heat exchange with the outside of the system. The first law of thermodynamics gives

$$dQ = dU + p dV = C\_V dT + p dV,\tag{7}$$

where *dQ* is a differential heat added to the system, *dU* is the differential internal energy of the system, and *CV* is the specific heat at constant volume. By integrating this equation from state 0 to state 1

$$Q\_{01} = C\_{\gamma} (T\_1 - T\_0),\tag{8}$$

where *C<sup>γ</sup>* ¼ *CV*ð Þ *γ* � *κ =*ð Þ *γ* � 1 ð Þ >0 is the polytropic specific heat. As seen in **Figure 3**, *T*<sup>1</sup> � *T*<sup>0</sup> ¼ *Tdp* � *Td*<sup>0</sup> >0, and as a result, *Q*<sup>01</sup> >0. It is expected that the heat *Q*<sup>01</sup> is added to the system for the bow shock formation.

## **3. Dynamic circulation under magnetic field**

You may watch a dynamic motion of tea leaves, set on the bottom of the teacup, by stirring the tea by a teaspoon. The tea leaves get close to the center and rise near the tea surface as illustrated in **Figure 4**. We can see a similar phenomenon in a complex plasma system. In this section, we will look back our experimental work on such a dynamic motion of dust particles in a complex plasma [53].

The observation of particle motion in the dynamic circulation similar to the motion of the tea leaves helps to understand the simple but profound nature of the ubiquitous vortex commonly encountered in nature.

#### **3.1 Experimental setup**

The experiment is performed in a cylindrical glass tube as shown in **Figure 5**. Detailed explanation on the experimental setup is given in Ref. [53]. The cylindrical coordinates ð Þ *r; θ; z* are with the origin at the inner bottom of the tube, and the gravity is in the negative *z* direction.

The argon gas pressure is *p* ¼ 5 � 25 Pa. A geometry of the gas supply and exhaust system is configured to avoid the neutral drag force acting on the dust

**Figure 4.** *Schematic of tea leaves in tea stirred in a teacup.*

where *h* and *z* are measured in mm. The calculated *B h*ð Þ *; z* is shown in **Figure 6**. Dust particles which are acrylic resin spheres of *a* ¼ 3 μm in diameter and *md* <sup>¼</sup> <sup>1</sup>*:*<sup>7</sup> � <sup>10</sup>�<sup>14</sup> kg in mass are supplied from a dust reservoir on the top of the glass tube. Each dust particle is charged in the plasma to *<sup>Q</sup>* � �10<sup>4</sup>*<sup>e</sup>* [49]. The particles in the experimental region are irradiated with a thin fan laser light from the radial directions. The laser sheet can be rotated around the laser axis. The scattered laser light from the particles is observed and recorded with a camera

Because of the cylindrical symmetry of the glass tube, the motion of dust particles is well observable by watching in a meridional (vertical) plane as shown in

*Typical example of the formed structure. B* ¼ *1:5 kG. Modified from Figure 2(c) of Ref. [53]).*

placed outside of the tube.

*Strength of the magnetic field at r* ¼ *0.*

*Dynamic Behavior of Dust Particles in Plasmas DOI: http://dx.doi.org/10.5772/intechopen.88787*

**Figure 6.**

**Figures 5, 7**, and **8**.

**Figure 7.**

**67**

**3.2 Behavior of dust particles in a glass cylinder**

#### **Figure 5.**

*Schematic drawing of the experimental glass tube (a) and the coordinate system (b). The structure of the dust cloud can be seen in Figures 7 and 8.*

particles in the experimental region. The plasma is produced by an rf discharge of 20 W (13.56 MHz). The electron density is � <sup>10</sup><sup>14</sup> <sup>m</sup>�3, the electron temperature is � 3 eV, and the ion temperature is estimated to be � 0*:*03 eV.

A magnetic field is applied by a cylindrical permanent magnet of 50 mm in diameter placed at a distance *h* below the powered electrode, and the magnetic field strength is controlled by adjusting the distance *h* by a jack. The strength of the magnetic field at *r* ¼ 0 is given by

$$B(h, z) \approx 0.29 \left(\frac{50}{z + h + 50}\right)^3 \text{T},\tag{9}$$

*Dynamic Behavior of Dust Particles in Plasmas DOI: http://dx.doi.org/10.5772/intechopen.88787*

**Figure 6.** *Strength of the magnetic field at r* ¼ *0.*

where *h* and *z* are measured in mm. The calculated *B h*ð Þ *; z* is shown in **Figure 6**. Dust particles which are acrylic resin spheres of *a* ¼ 3 μm in diameter and *md* <sup>¼</sup> <sup>1</sup>*:*<sup>7</sup> � <sup>10</sup>�<sup>14</sup> kg in mass are supplied from a dust reservoir on the top of the glass tube. Each dust particle is charged in the plasma to *<sup>Q</sup>* � �10<sup>4</sup>*<sup>e</sup>* [49]. The particles in the experimental region are irradiated with a thin fan laser light from the radial directions. The laser sheet can be rotated around the laser axis. The scattered laser light from the particles is observed and recorded with a camera placed outside of the tube.

## **3.2 Behavior of dust particles in a glass cylinder**

Because of the cylindrical symmetry of the glass tube, the motion of dust particles is well observable by watching in a meridional (vertical) plane as shown in **Figures 5, 7**, and **8**.

**Figure 7.** *Typical example of the formed structure. B* ¼ *1:5 kG. Modified from Figure 2(c) of Ref. [53]).*

particles in the experimental region. The plasma is produced by an rf discharge of 20 W (13.56 MHz). The electron density is � <sup>10</sup><sup>14</sup> <sup>m</sup>�3, the electron temperature is

*Schematic drawing of the experimental glass tube (a) and the coordinate system (b). The structure of the dust*

A magnetic field is applied by a cylindrical permanent magnet of 50 mm in diameter placed at a distance *h* below the powered electrode, and the magnetic field strength is controlled by adjusting the distance *h* by a jack. The strength of the

> *z* þ *h* þ 50 <sup>3</sup>

T*,* (9)

*B h*ð Þ *; <sup>z</sup>* <sup>≈</sup> <sup>0</sup>*:*<sup>29</sup> <sup>50</sup>

� 3 eV, and the ion temperature is estimated to be � 0*:*03 eV.

magnetic field at *r* ¼ 0 is given by

*cloud can be seen in Figures 7 and 8.*

*Progress in Fine Particle Plasmas*

**Figure 5.**

**66**

**3.3 MHD dust flow as a rotating fluid**

*Dynamic Behavior of Dust Particles in Plasmas DOI: http://dx.doi.org/10.5772/intechopen.88787*

The radial ambipolar diffusion is suppressed due to the electron magnetization, and the current starts to flow in an azimuthal direction in a magnetized plasma. The

> *κTe e* 1 *ne*

The rotating magnetohydrodynamics (MHD) fluid involving dust particles may

**<sup>∇</sup>***<sup>p</sup>* <sup>þ</sup> *<sup>ν</sup>***∇**<sup>2</sup>

*<sup>d</sup>* by neutral particles, and ions are in the azimuthal direction. The

*∂p <sup>∂</sup><sup>r</sup>* � *<sup>J</sup>θ<sup>B</sup>*

indicating that the centrifugal force on a dust particle is balanced by the pressure

By introducing dimensionless parameters, *vr* <sup>¼</sup> *vr=rΩ*, *<sup>v</sup><sup>θ</sup>* <sup>¼</sup> *<sup>v</sup>θ=rΩ*, *vz* <sup>¼</sup> *vz<sup>=</sup>* ffiffiffiffiffiffi

*<sup>r</sup>* � *<sup>v</sup>*<sup>2</sup>

*dv<sup>θ</sup> dz vz*

*<sup>θ</sup>* þ *vz*

*dvr dz*

We consider rotating fluid with constant angular frequency *Ω* far from the tube bottom ð Þ *z* ¼ 0 . Eqs. (11) and (12) can be solved for steady, axisymmetric flow with *v* ¼ *vr* ð Þ *; vθ; vz* in cylindrical coordinates with boundary conditions *v<sup>θ</sup>* ¼ *rΩ*, *vr* ¼ 0 at *z* ¼ ∞, and *vr* ¼ *v<sup>θ</sup>* ¼ *vz* ¼ 0 at *z* ¼ 0. We assume *J* ¼ 0*; J<sup>θ</sup>* ð Þ *;* 0 and *B* ¼ ð Þ 0*;* 0*; B* .

*v* þ

1 *mdnd*

**∇** � *v*¼0*,* (12)

*<sup>g</sup>* þ *f*

*<sup>g</sup>* is in the negative *z* direction, while the

� �*,* (13)

*ν=Ω* p . Eqs. (11) and (12) can be expressed

*,* (14)

*J* � *B* þ *f,* (11)

*<sup>d</sup>* þ *f<sup>T</sup>* þ ⋯ � � is

*νΩ* <sup>p</sup> ,

be described by the Navier-Stokes equation with the continuity equation of an

*mdnd*

thermophoretic force *f<sup>T</sup>* and the other external forces are negligible in our

where *ν* is a kinematic viscosity of the dust fluid and *f* ¼ *f*

�*rΩ*<sup>2</sup> <sup>¼</sup> <sup>1</sup>

*νΩ*<sup>3</sup> <sup>p</sup> with *<sup>z</sup>* <sup>¼</sup> *<sup>z</sup><sup>=</sup>* ffiffiffiffiffiffiffiffi

*dz*<sup>2</sup> <sup>¼</sup> <sup>2</sup>*vrv<sup>θ</sup>* <sup>þ</sup>

*dz* ¼ �2*vr*

*d*2 *vr dz*<sup>2</sup> <sup>¼</sup> <sup>1</sup> <sup>þ</sup> *<sup>v</sup>*<sup>2</sup>

8 >>>>>>><

>>>>>>>:

*d*2 *vθ*

*dvz*

*mdnd*

*∂ne ∂r*

(10)

azimuthal electric field associated with the current density is given by

*<sup>E</sup><sup>θ</sup>* <sup>¼</sup> <sup>1</sup>

mum dust angular velocity is *vθ,dust* ≈0*:*02 m*=*s, near the wall.

incompressible fluid of constant mass density:

þ *v* � **∇** � �*<sup>v</sup>* ¼ � <sup>1</sup>

an external force. The gravitational force *f*

*∂ ∂t*

experimental conditions [54].

The equilibrium condition requires

gradient and the Lorentz force.

by a set of three ordinary differential equations:

*<sup>p</sup>* <sup>¼</sup> *<sup>p</sup>=ρνΩ*, and *<sup>g</sup>* <sup>¼</sup> *<sup>g</sup><sup>=</sup>* ffiffiffiffiffiffiffiffi

**69**

drag forces *f*

*ωce* j j*τen*

In the present case, *E<sup>θ</sup>* ≈9 V*=*m because *ωce* j j*τen* ≈ 17, *κTe=e*≈ 3 eV, and ð Þ *<sup>∂</sup>ne=ne∂<sup>r</sup>* �<sup>1</sup> <sup>≈</sup><sup>2</sup> � <sup>10</sup>�<sup>2</sup> m, where *<sup>ω</sup>ce* is the electron cyclotron angular frequency, *<sup>τ</sup>en* is the mean-free-time of the electron-neutral collision, and *κ* is the Boltzmann constant. This electric field will produce the azimuthal motion of ions with angular velocity *vθ,ion* ¼ *eEθ=miνin* ≈40 m*=*s. Those ions circling around the tube axis will move dust particles resulting in a dust flow around the axis. Our observed maxi-

#### **Figure 8.**

*Schematic of dust particle motion in the meridional plane. The arrows indicate the directions of dust particle motion.*

When *B h*ð Þ ≳137*; z* ¼ 0 ≤ 0*:*006 T, the dust particles levitate a few mm above the glass bottom forming a thin disk of radius 20 mm with a dense group of particles at the rim of the disk near the outer wall. When *B* is increased, the stored dust particles near the wall moved inward to the center and formed a disk of uniformly distributed at z> 0. For *B*ð Þ¼ 17*;* 0 0*:*12 T with *p* ¼ 20 Pa, where the electrons and ions are weakly magnetized and dust particles are rotating around the axis of the tube. The radial electric field is induced by the ambipolar diffusion and the vertically applied *B* field produces *E* � *B* drift motion of plasma particles, resulting in a solid body-like azimuthal motion of dust particles with angular velocity 10 � 20 mm*=*s.

With a further increase of *B* and reached *B*ð Þ 12*;* 0 ≈0*:*15 T, the dust disk becomes the form as shown in **Figure 7**, i.e., the disk is thicker and its radius is smaller. A meridional plane reveals a spectacular movement of dust particles in the thick disk.

Typical trajectories of the spectacular particle motions are shown with arrows in **Figure 8**. There are two small poloidal rotations in the meridional plane near the edges within the thick disk, i.e., one is the clockwise rotation on the right-hand plane, and the other is the counterclockwise rotation on the left-hand plane. The particle motion in the disk as seen in a meridional plane is somewhat similar to the motion of tea leaves as shown in **Figure 4**.

The dust particles move upward against the gravity near *r* ¼ 0. Especially, a part of the particles blows up and exceeds the disk thickness. Such ascending motion of dust particles is followed by radial movement toward the outer wall and then downward. The situation that the particles gush near the top looks like fireworks. After hitting close to the tube bottom, dust particles move inward along the tube bottom. At the same time, dust particles localized near the outer edge of the disk, which do not readily approach *r*≈0, form a local circulation in the meridional plane. While dust particles move in these closed circles in a meridional plane, the dust cloud rotates around the *z* axis and forms a toroidal rotation. As a result, dust particles form a helical motion around the *z* axis. A schematic illustration of the observed movement of dust particles is something similar as shown in **Figure 4**. In addition, there is a stagnation area around *r*≈0 near the tube bottom, where a group of dust particles is not involved in the dynamic meridional rotation as shown in **Figures 4** and **5**.

## **3.3 MHD dust flow as a rotating fluid**

The radial ambipolar diffusion is suppressed due to the electron magnetization, and the current starts to flow in an azimuthal direction in a magnetized plasma. The azimuthal electric field associated with the current density is given by

$$E\_{\theta} = \frac{1}{|\alpha\_{\alpha}| \tau\_{\epsilon n}} \frac{\kappa T\_{\epsilon}}{e} \frac{1}{n\_{\epsilon}} \frac{\partial n\_{\epsilon}}{\partial r} \tag{10}$$

In the present case, *E<sup>θ</sup>* ≈9 V*=*m because *ωce* j j*τen* ≈ 17, *κTe=e*≈ 3 eV, and ð Þ *<sup>∂</sup>ne=ne∂<sup>r</sup>* �<sup>1</sup> <sup>≈</sup><sup>2</sup> � <sup>10</sup>�<sup>2</sup> m, where *<sup>ω</sup>ce* is the electron cyclotron angular frequency, *<sup>τ</sup>en* is the mean-free-time of the electron-neutral collision, and *κ* is the Boltzmann constant. This electric field will produce the azimuthal motion of ions with angular velocity *vθ,ion* ¼ *eEθ=miνin* ≈40 m*=*s. Those ions circling around the tube axis will move dust particles resulting in a dust flow around the axis. Our observed maximum dust angular velocity is *vθ,dust* ≈0*:*02 m*=*s, near the wall.

The rotating magnetohydrodynamics (MHD) fluid involving dust particles may be described by the Navier-Stokes equation with the continuity equation of an incompressible fluid of constant mass density:

$$\left(\frac{\partial}{\partial t} + \boldsymbol{\nu} \cdot \nabla\right) \boldsymbol{\nu} = -\frac{1}{m\_d n\_d} \nabla p + \nu \nabla^2 \boldsymbol{\nu} + \frac{1}{m\_d n\_d} \boldsymbol{J} \times \mathbf{B} + \boldsymbol{f},\tag{11}$$

$$\nabla \cdot \boldsymbol{\nu} = \mathbf{0},\tag{12}$$

where *ν* is a kinematic viscosity of the dust fluid and *f* ¼ *f <sup>g</sup>* þ *f <sup>d</sup>* þ *f<sup>T</sup>* þ ⋯ � � is an external force. The gravitational force *f <sup>g</sup>* is in the negative *z* direction, while the drag forces *f <sup>d</sup>* by neutral particles, and ions are in the azimuthal direction. The thermophoretic force *f<sup>T</sup>* and the other external forces are negligible in our experimental conditions [54].

We consider rotating fluid with constant angular frequency *Ω* far from the tube bottom ð Þ *z* ¼ 0 . Eqs. (11) and (12) can be solved for steady, axisymmetric flow with *v* ¼ *vr* ð Þ *; vθ; vz* in cylindrical coordinates with boundary conditions *v<sup>θ</sup>* ¼ *rΩ*, *vr* ¼ 0 at *z* ¼ ∞, and *vr* ¼ *v<sup>θ</sup>* ¼ *vz* ¼ 0 at *z* ¼ 0. We assume *J* ¼ 0*; J<sup>θ</sup>* ð Þ *;* 0 and *B* ¼ ð Þ 0*;* 0*; B* . The equilibrium condition requires

$$-r\Omega^2 = \frac{1}{m\_d n\_d} \left(\frac{\partial p}{\partial r} - J\_\theta B\right),\tag{13}$$

indicating that the centrifugal force on a dust particle is balanced by the pressure gradient and the Lorentz force.

By introducing dimensionless parameters, *vr* <sup>¼</sup> *vr=rΩ*, *<sup>v</sup><sup>θ</sup>* <sup>¼</sup> *<sup>v</sup>θ=rΩ*, *vz* <sup>¼</sup> *vz<sup>=</sup>* ffiffiffiffiffiffi *νΩ* <sup>p</sup> , *<sup>p</sup>* <sup>¼</sup> *<sup>p</sup>=ρνΩ*, and *<sup>g</sup>* <sup>¼</sup> *<sup>g</sup><sup>=</sup>* ffiffiffiffiffiffiffiffi *νΩ*<sup>3</sup> <sup>p</sup> with *<sup>z</sup>* <sup>¼</sup> *<sup>z</sup><sup>=</sup>* ffiffiffiffiffiffiffiffi *ν=Ω* p . Eqs. (11) and (12) can be expressed by a set of three ordinary differential equations:

$$\begin{cases} \frac{d^2 \overline{v}\_r}{d\overline{z}^2} = \mathbf{1} + \overline{v}\_r^2 - \overline{v}\_\theta^2 + \overline{v}\_x \frac{d\overline{v}\_r}{d\overline{z}}\\ \frac{d^2 \overline{v}\_\theta}{d\overline{z}^2} = 2\overline{v}\_r \overline{v}\_\theta + \frac{d\overline{v}\_\theta}{d\overline{z}} \overline{v}\_x\\ \frac{d\overline{v}\_x}{d\overline{z}} = -2\overline{v}\_r \end{cases} \tag{14}$$

When *B h*ð Þ ≳137*; z* ¼ 0 ≤ 0*:*006 T, the dust particles levitate a few mm above the glass bottom forming a thin disk of radius 20 mm with a dense group of particles at the rim of the disk near the outer wall. When *B* is increased, the stored dust particles near the wall moved inward to the center and formed a disk of uniformly distributed at z> 0. For *B*ð Þ¼ 17*;* 0 0*:*12 T with *p* ¼ 20 Pa, where the electrons and ions are weakly magnetized and dust particles are rotating around the axis of the tube. The radial electric field is induced by the ambipolar diffusion and the vertically applied *B* field produces *E* � *B* drift motion of plasma particles, resulting in a solid body-like

*Schematic of dust particle motion in the meridional plane. The arrows indicate the directions of dust particle*

With a further increase of *B* and reached *B*ð Þ 12*;* 0 ≈0*:*15 T, the dust disk becomes the form as shown in **Figure 7**, i.e., the disk is thicker and its radius is smaller. A meridional plane reveals a spectacular movement of dust particles in the thick disk. Typical trajectories of the spectacular particle motions are shown with arrows in **Figure 8**. There are two small poloidal rotations in the meridional plane near the edges within the thick disk, i.e., one is the clockwise rotation on the right-hand plane, and the other is the counterclockwise rotation on the left-hand plane. The particle motion in the disk as seen in a meridional plane is somewhat similar to the

The dust particles move upward against the gravity near *r* ¼ 0. Especially, a part of the particles blows up and exceeds the disk thickness. Such ascending motion of dust particles is followed by radial movement toward the outer wall and then downward. The situation that the particles gush near the top looks like fireworks. After hitting close to the tube bottom, dust particles move inward along the tube bottom. At the same time, dust particles localized near the outer edge of the disk, which do not readily approach *r*≈0, form a local circulation in the meridional plane. While dust particles move in these closed circles in a meridional plane, the dust cloud rotates around the *z* axis and forms a toroidal rotation. As a result, dust particles form a helical motion around the *z* axis. A schematic illustration of the observed movement of dust particles is something similar as shown in **Figure 4**. In addition, there is a stagnation area around *r*≈0 near the tube bottom, where a group of dust particles is not involved in the dynamic meridional rotation as shown

azimuthal motion of dust particles with angular velocity 10 � 20 mm*=*s.

motion of tea leaves as shown in **Figure 4**.

in **Figures 4** and **5**.

**68**

**Figure 8.**

*Progress in Fine Particle Plasmas*

*motion.*

supplemented by the pressure gradient equation:

$$\frac{d\overline{p}}{d\overline{z}} = \frac{d^2\overline{v}\_x}{d\overline{z}^2} - \overline{v}\_x \frac{d\overline{v}\_x}{d\overline{z}} - \overline{\overline{g}}.\tag{15}$$

path of dust particles, *L* is a representative scale length of a phenomenon, *τ<sup>p</sup>* is time scale of the evolution of the phenomenon, and *τ<sup>d</sup>* is the dust plasma period [59]. The quasi-neutrality is always kept. Typically, *lmfp* � 0.1 mm, *L* � 1 cm , *τ<sup>p</sup>* � 1 s, and *τ<sup>d</sup>* � 0*:*1 s in our experiments. Hence, the dust cloud can be treated as an MHD fluid. In water or air or other fluids, a tracer such as aluminum powder or smoke is often used for visualizing a motion of fluid elements. The tea leaves in a teacup are, of course, one of the examples of the tracer as well. This is an indirect observation of the motion because a different tracer has unique characteristics, e.g., a size or a specific weight. The uniqueness comes down to a variation in trackability of the tracer to the fluid element and affects the observation results. The various trackability may give a different result in a measurement. Schlieren imaging and shadowgraph are often used to visualize a flow, too. These methods observe a fluctuation of a density or a refractive index. The setting of the optical system, etc.

In contrast, in the dust fluid, it is possible to regard each dust particle as a fluid element itself. The particle can be visualized by illuminating using a visible laser light in experiments. The laser light suffers Mie scattering because the size of the dust particle (≲10 μm) is usually larger than the wavelength of the visible laser light (� several hundreds nm). The motion of the fluid element is directly visualized without being bothered about both the trackability and the optical precision. It is worth emphasizing that the visualization is achieved on the spot without time lag in

One of the applications of such a dust fluid is the new method to estimate the dust charge [60]. A dust particle has an electric charge *Q* in a plasma and levitates at a height where the electrostatic force due to the sheath electric field *E* and the

measure the charge of an individual dust particle, it has been hard to separate *Q* and *E* independently. In addition, the conventional measurement methods require to change the experimental setup to measure *Q* and *E*. However, by regarding the collection of dust particles as a fluid, it is possible to measure the resonant frequency of the dust fluid, i.e., the dust plasma frequency by externally applying the sinusoidal oscillation. The dust charge *QA* is calculated from the resonant frequency. The charge *QA* is an averaged charge for all dust particles present in the

In fluid dynamics, the Reynolds number is one of the important parameters. The Reynolds number is given by inertial forces ð Þ*=*ð Þ viscous forces . The Reynolds number is also important in the dust flow. There are investigations relating to the widely changed Reynolds number or the viscosity of dust fluid by the simulation methods [61, 62]. However, it is hard to observe turbulence in our experiments on the dust flow, i.e., it is expected that the Reynolds number is rather small even when *M* >1. It is clear that collective behavior of dust particles can be described as a fluid globally. The fluid picture is held where the MHD conditions are satisfied. Intrinsically, however, the dust fluid is a group consisting of independent particles. Therefore, it is expected that the complex plasma includes unique features that is peculiar to a particle system, i.e., properties that are insufficient and difficult to be described by the MHD equation or the Navier–Stokes equation. Such a situation is possible where the MHD conditions do not hold locally. In fact, a few irregular particles are observed in quite rare case. For example, there is a dust particle whose orbit is irregular and different from the others in the way like the dust particle is reflected in a larger angle with faster speed by the obstacle in the bow shock experiment. In addition, the following experiment may give another example. The schematic

of the experimental device is shown in **Figure 9(a)** [63]. The dust cloud exists under an influence of an axisymmetric nonuniform magnetic field applied by a

*<sup>g</sup>*, on the ground. In experiments to

*<sup>g</sup>* are balancing, *QE* ¼ *f*

requires high precision for these methods.

*Dynamic Behavior of Dust Particles in Plasmas DOI: http://dx.doi.org/10.5772/intechopen.88787*

experiment.

**71**

gravitational force *f*

experimental region in this case.

The set of equations is well studied as similarity solutions for the rotating fluid [55, 56]. The solution shows the presence of a stagnation point at ð Þ¼ *r; z* ð Þ 0*;* 0 and the presence of a thin boundary layer near the bottom where the fluid moves inward. Our observation shows the boundary layer 3 ffiffiffiffiffiffiffiffi *ν=Ω* p ≈ 5 mm.

As Eqs. (11) and (12) show, dust particles drift in the azimuthal direction, and the centrifugal force on a particle is given by *f <sup>C</sup>* <sup>¼</sup> *mdr* ð Þ *αΩ* <sup>2</sup> with *<sup>α</sup>*, a constant less than unity. The centrifugal force is balanced by an inward drag force by neutral particles *f dn* <sup>¼</sup> *CDπa*<sup>2</sup>*mnnnv*<sup>2</sup> *<sup>r</sup>=*8, where *CD* is a drag coefficient, *mn* is a neutral mass, *nn* is a neutral density, and *vr*ð Þ ¼ *βrΩ* is a representative radial velocity of dust particles with a constant *β* <1. The balancing equation gives the equilibrium radius as

$$r = \frac{8}{3C\_D} \frac{m\_d n\_d}{m\_n n\_n} \left(\frac{\alpha}{\beta}\right)^2 \frac{a}{2}. \tag{16}$$

Eq. (16) with *α=β* ≈0*:*03 gives an equilibrium radius of about 0.02 m, which agrees well with our experimental observation.

#### **3.4 Storm in a glass tube**

The mechanism of the meridional dust flow is understood in the following way. Initially dust particles are driven by the ion azimuthal motion caused by the radial plasma density gradient in the presence of a strong vertical magnetic field. While the MHD dust fluid forms a rotation around the tube axis, the angular velocity of dust particles near the tube bottom is reduced by the friction from the sheath plasma transition area. The friction reduces the centrifugal force. As a result, the pressure gradient force together with the Lorentz force which remains the same near the bottom generates a radial inward flow of dust particles. Because of the continuity, the radial inward motion will be compensated by an axial upward flow. Dust particles near the bottom ascend along the tube axis, where the sheath electric force pushes charged dust particles upward. When rising dust particles move outside of the sheath, the dust particles feel only the gravitational force. The ascending motion of dust particles near the axis is followed by the outward movement, and then the particles descend.

A circulation with an inward flow at the bottom has been known as a teacup phenomenon [57], also known as Einstein's tea leaves [58]. In 1926, Einstein explained that tea leaves gather in the center of the teacup when the tea is stirred as a result of a secondary, rim-to-center circulation caused by the fluid rubbing against the bottom of the cup. It is indeed observed in our complex plasma experiment that there were some levitated dust particles staying close to the bottom near the center.

## **4. Discussion: collective behavior of dust particles as a fluid**

A complex plasma is a system consisting of electrons, ions, neutral gas particles, and dust particles. The dust particles are macroparticles of nanometers to micrometers in size. In our experiments, monodisperse dust particles of 3 or 5 or 5.6 μm in diameter were used. Behavior of dust particles can be regarded as MHD fluid if *lmfp* ≪ *L*, *τ<sup>p</sup>* ≫ *τd*, and the system keeps quasi-neutrality. Here *lmfp* is the mean free

*Dynamic Behavior of Dust Particles in Plasmas DOI: http://dx.doi.org/10.5772/intechopen.88787*

supplemented by the pressure gradient equation:

*dp dz* <sup>¼</sup> *<sup>d</sup>*<sup>2</sup>

inward. Our observation shows the boundary layer 3 ffiffiffiffiffiffiffiffi

centrifugal force on a particle is given by *f*

agrees well with our experimental observation.

*f*

*dn* <sup>¼</sup> *CDπa*<sup>2</sup>*mnnnv*<sup>2</sup>

*Progress in Fine Particle Plasmas*

**3.4 Storm in a glass tube**

then the particles descend.

**70**

*vz dz*<sup>2</sup> � *vz*

The set of equations is well studied as similarity solutions for the rotating fluid [55, 56]. The solution shows the presence of a stagnation point at ð Þ¼ *r; z* ð Þ 0*;* 0 and the presence of a thin boundary layer near the bottom where the fluid moves

As Eqs. (11) and (12) show, dust particles drift in the azimuthal direction, and the

*<sup>r</sup>=*8, where *CD* is a drag coefficient, *mn* is a neutral mass, *nn* is a

*α β* � �<sup>2</sup> *a* 2

unity. The centrifugal force is balanced by an inward drag force by neutral particles

neutral density, and *vr*ð Þ ¼ *βrΩ* is a representative radial velocity of dust particles with

*mdnd mnnn*

Eq. (16) with *α=β* ≈0*:*03 gives an equilibrium radius of about 0.02 m, which

The mechanism of the meridional dust flow is understood in the following way. Initially dust particles are driven by the ion azimuthal motion caused by the radial plasma density gradient in the presence of a strong vertical magnetic field. While the MHD dust fluid forms a rotation around the tube axis, the angular velocity of dust particles near the tube bottom is reduced by the friction from the sheath plasma transition area. The friction reduces the centrifugal force. As a result, the pressure gradient force together with the Lorentz force which remains the same near the bottom generates a radial inward flow of dust particles. Because of the continuity, the radial inward motion will be compensated by an axial upward flow. Dust particles near the bottom ascend along the tube axis, where the sheath electric force pushes charged dust particles upward. When rising dust particles move outside of the sheath, the dust particles feel only the gravitational force. The ascending motion of dust particles near the axis is followed by the outward movement, and

A circulation with an inward flow at the bottom has been known as a teacup phenomenon [57], also known as Einstein's tea leaves [58]. In 1926, Einstein

explained that tea leaves gather in the center of the teacup when the tea is stirred as a result of a secondary, rim-to-center circulation caused by the fluid rubbing against the bottom of the cup. It is indeed observed in our complex plasma experiment that there were some levitated dust particles staying close to the bottom near the center.

A complex plasma is a system consisting of electrons, ions, neutral gas particles, and dust particles. The dust particles are macroparticles of nanometers to micrometers in size. In our experiments, monodisperse dust particles of 3 or 5 or 5.6 μm in diameter were used. Behavior of dust particles can be regarded as MHD fluid if *lmfp* ≪ *L*, *τ<sup>p</sup>* ≫ *τd*, and the system keeps quasi-neutrality. Here *lmfp* is the mean free

**4. Discussion: collective behavior of dust particles as a fluid**

a constant *β* <1. The balancing equation gives the equilibrium radius as

*<sup>r</sup>* <sup>¼</sup> <sup>8</sup> 3*CD* *dvz*

*dz* � *<sup>g</sup>:* (15)

*ν=Ω* p ≈ 5 mm.

*<sup>C</sup>* <sup>¼</sup> *mdr* ð Þ *αΩ* <sup>2</sup> with *<sup>α</sup>*, a constant less than

*:* (16)

path of dust particles, *L* is a representative scale length of a phenomenon, *τ<sup>p</sup>* is time scale of the evolution of the phenomenon, and *τ<sup>d</sup>* is the dust plasma period [59]. The quasi-neutrality is always kept. Typically, *lmfp* � 0.1 mm, *L* � 1 cm , *τ<sup>p</sup>* � 1 s, and *τ<sup>d</sup>* � 0*:*1 s in our experiments. Hence, the dust cloud can be treated as an MHD fluid.

In water or air or other fluids, a tracer such as aluminum powder or smoke is often used for visualizing a motion of fluid elements. The tea leaves in a teacup are, of course, one of the examples of the tracer as well. This is an indirect observation of the motion because a different tracer has unique characteristics, e.g., a size or a specific weight. The uniqueness comes down to a variation in trackability of the tracer to the fluid element and affects the observation results. The various trackability may give a different result in a measurement. Schlieren imaging and shadowgraph are often used to visualize a flow, too. These methods observe a fluctuation of a density or a refractive index. The setting of the optical system, etc. requires high precision for these methods.

In contrast, in the dust fluid, it is possible to regard each dust particle as a fluid element itself. The particle can be visualized by illuminating using a visible laser light in experiments. The laser light suffers Mie scattering because the size of the dust particle (≲10 μm) is usually larger than the wavelength of the visible laser light (� several hundreds nm). The motion of the fluid element is directly visualized without being bothered about both the trackability and the optical precision. It is worth emphasizing that the visualization is achieved on the spot without time lag in experiment.

One of the applications of such a dust fluid is the new method to estimate the dust charge [60]. A dust particle has an electric charge *Q* in a plasma and levitates at a height where the electrostatic force due to the sheath electric field *E* and the gravitational force *f <sup>g</sup>* are balancing, *QE* ¼ *f <sup>g</sup>*, on the ground. In experiments to measure the charge of an individual dust particle, it has been hard to separate *Q* and *E* independently. In addition, the conventional measurement methods require to change the experimental setup to measure *Q* and *E*. However, by regarding the collection of dust particles as a fluid, it is possible to measure the resonant frequency of the dust fluid, i.e., the dust plasma frequency by externally applying the sinusoidal oscillation. The dust charge *QA* is calculated from the resonant frequency. The charge *QA* is an averaged charge for all dust particles present in the experimental region in this case.

In fluid dynamics, the Reynolds number is one of the important parameters. The Reynolds number is given by inertial forces ð Þ*=*ð Þ viscous forces . The Reynolds number is also important in the dust flow. There are investigations relating to the widely changed Reynolds number or the viscosity of dust fluid by the simulation methods [61, 62]. However, it is hard to observe turbulence in our experiments on the dust flow, i.e., it is expected that the Reynolds number is rather small even when *M* >1.

It is clear that collective behavior of dust particles can be described as a fluid globally. The fluid picture is held where the MHD conditions are satisfied. Intrinsically, however, the dust fluid is a group consisting of independent particles. Therefore, it is expected that the complex plasma includes unique features that is peculiar to a particle system, i.e., properties that are insufficient and difficult to be described by the MHD equation or the Navier–Stokes equation. Such a situation is possible where the MHD conditions do not hold locally. In fact, a few irregular particles are observed in quite rare case. For example, there is a dust particle whose orbit is irregular and different from the others in the way like the dust particle is reflected in a larger angle with faster speed by the obstacle in the bow shock experiment.

In addition, the following experiment may give another example. The schematic of the experimental device is shown in **Figure 9(a)** [63]. The dust cloud exists under an influence of an axisymmetric nonuniform magnetic field applied by a

**Acknowledgements**

*Dynamic Behavior of Dust Particles in Plasmas DOI: http://dx.doi.org/10.5772/intechopen.88787*

Research (A) 24244094.

**Author details**

Yoshifumi Saitou<sup>1</sup>

**73**

\* and Osamu Ishihara<sup>2</sup>

\*Address all correspondence to: saitou@cc.utsunomiya-u.ac.jp

2 Chubu University, Kasugai, Aichi, Japan

provided the original work is properly cited.

1 School of Engineering, Utsunomiya University, Utsunomiya, Tochigi, Japan

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

We thank Prof. T. Kamimura and Prof. Y. Nakamura for their collaboration on the bow shock research. The work on the bow shock formation is supported by the Asian Office of Aerospace Research and Development under Grant No. AOARD 104158 and JSPS Grants-in-Aid for Scientific Research (A) under Grant No.

23244110. The work on the dynamic circulation is supported by the Asian Office of Aerospace Research and Development FA2386-12-1-4077 and JSPS Grants-in-Aid for Scientific Research (A) 23244110 and for Challenging Exploratory Research 24654188. One of the authors, Saitou, thanks Prof. Y. Hayashi for his support to the experiment using the small permanent magnet, and this work is partly supported by the Japan Society for the Promotion of Science (JSPS) Grant-in-Aid for Scientific

#### **Figure 9.**

*Schematic of the experimental device (a) and the enhanced illustration of the dust cloud (b). The arrows in (b) are the directions that the particles at the edges rotate. The magnetic field is vertically upward.*

small permanent magnet. The dust particles frequently collide with other particles surrounding it. Only the dust particles locate quite near the inner edge and the outer edge rotating along the edges as shown in **Figure 9(b)**. Excluding these edge regions, the collective motion of dust particles seems to be like a fluid. As described in the previous paragraph, the dust fluid has high viscosity. In that case, the rotating particles at the edges have to transfer their momenta to the neighboring particles and must drag the neighbors to their rotating directions. However, in the experiment, the particles do not drag their neighboring particles. It is considered that, at both edges, the dust particles behave as individual particles. Hence, the MHD conditions may be locally broken near the edges, and the particle motion there may suggest one of the particulate-like properties.

## **5. Summary and subsequent development**

It is found in our experiments that the group of dust particles collectively behaves in a similar way to a fluid. In the fast flow of *M* > 1, the bow shock is formed in front of the obstacle. Under the strong magnetic field applied with the permanent magnet, the dust fluid shows a dynamic circulation.

In addition, there is the experimental result which may suggest a particle property of the group of dust particles. It is expected that the dusty plasma or the complex plasma bridges the different nature between continuum mechanics such as fluids and kinetics of particles.

Our results have inspired other researchers in wider fields beyond plasma physics [64–76]. The followings are examples. Tiwari et al. constructed two-dimensional generalized hydrodynamic model and discussed on turbulence in a strongly coupled plasma [64]. They reported that the turbulence was able to occur at a low Reynolds number if the Weissenberg number was high. Kähler et al. derived the ion susceptibility in a partially ionized plasma [65]. Tadsen et al. reported that the dust cloud confined in a magnetized plasma was diamagnetic [66]. Gibson et al. gave an improved understanding of magnetized electron behavior in a dipole magnetic field [67]. Laishram et al. investigated the dust vortex formation in a plasma [68].

Research on dusty plasmas has a strong influence to various areas of physics as seen above. Further progress will be expected.

## **Acknowledgements**

We thank Prof. T. Kamimura and Prof. Y. Nakamura for their collaboration on the bow shock research. The work on the bow shock formation is supported by the Asian Office of Aerospace Research and Development under Grant No. AOARD 104158 and JSPS Grants-in-Aid for Scientific Research (A) under Grant No. 23244110. The work on the dynamic circulation is supported by the Asian Office of Aerospace Research and Development FA2386-12-1-4077 and JSPS Grants-in-Aid for Scientific Research (A) 23244110 and for Challenging Exploratory Research 24654188. One of the authors, Saitou, thanks Prof. Y. Hayashi for his support to the experiment using the small permanent magnet, and this work is partly supported by the Japan Society for the Promotion of Science (JSPS) Grant-in-Aid for Scientific Research (A) 24244094.

## **Author details**

small permanent magnet. The dust particles frequently collide with other particles surrounding it. Only the dust particles locate quite near the inner edge and the outer edge rotating along the edges as shown in **Figure 9(b)**. Excluding these edge regions, the collective motion of dust particles seems to be like a fluid. As described in the previous paragraph, the dust fluid has high viscosity. In that case, the rotating particles at the edges have to transfer their momenta to the neighboring particles and must drag the neighbors to their rotating directions. However, in the experiment, the particles do not drag their neighboring particles. It is considered that, at both edges, the dust particles behave as individual particles. Hence, the MHD conditions may be locally broken near the edges, and the particle motion there may

*Schematic of the experimental device (a) and the enhanced illustration of the dust cloud (b). The arrows in (b)*

*are the directions that the particles at the edges rotate. The magnetic field is vertically upward.*

It is found in our experiments that the group of dust particles collectively behaves in a similar way to a fluid. In the fast flow of *M* > 1, the bow shock is formed in front of the obstacle. Under the strong magnetic field applied with the

erty of the group of dust particles. It is expected that the dusty plasma or the complex plasma bridges the different nature between continuum mechanics such as

In addition, there is the experimental result which may suggest a particle prop-

Our results have inspired other researchers in wider fields beyond plasma physics [64–76]. The followings are examples. Tiwari et al. constructed two-dimensional generalized hydrodynamic model and discussed on turbulence in a strongly coupled plasma [64]. They reported that the turbulence was able to occur at a low Reynolds number if the Weissenberg number was high. Kähler et al. derived the ion susceptibility in a partially ionized plasma [65]. Tadsen et al. reported that the dust cloud confined in a magnetized plasma was diamagnetic [66]. Gibson et al. gave an improved understanding of magnetized electron behavior in a dipole magnetic field [67]. Laishram et al. investigated the dust vortex formation in a plasma [68].

Research on dusty plasmas has a strong influence to various areas of physics as

permanent magnet, the dust fluid shows a dynamic circulation.

suggest one of the particulate-like properties.

**5. Summary and subsequent development**

seen above. Further progress will be expected.

fluids and kinetics of particles.

**72**

**Figure 9.**

*Progress in Fine Particle Plasmas*

Yoshifumi Saitou<sup>1</sup> \* and Osamu Ishihara<sup>2</sup>

1 School of Engineering, Utsunomiya University, Utsunomiya, Tochigi, Japan

2 Chubu University, Kasugai, Aichi, Japan

\*Address all correspondence to: saitou@cc.utsunomiya-u.ac.jp

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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**Chapter 5**

*Akio Sanpei*

**1. Introduction**

**79**

**Abstract**

Dusty Plasmas

Integral Photography Technique

for Three-Dimensional Imaging of

The integral photography technique has an advantage in which instantaneous three-dimensional (3D) information of objects can be estimated from a singleexposure picture obtained from a single viewing port. Recently, the technique has come into use for scientific research in diverse fields and has been applied to observe fine particles floating in plasma. The principle of integral photography technique and a design of a light-field camera for dusty plasma experiments are reported. The important parameters of the system, dependences of the size of the imaging area, and the spatial resolution on the number of lenses, pitch, and focal length of the lens array are calculated. Designed recording and reconstruction system is tested with target particles located on known positions and found that it works well in the range of dusty plasma experiment. By applying the integral photography technique to the obtained experimental image array, the 3D positions

**Keywords:** dusty plasma, integral photography, three-dimensional reconstruction,

Fine particles immersed in plasma are charged up negatively, show threedimensional (3D) motion, and form 3D-ordered state, i.e., Coulomb crystal [1–5]. Diagnostic methods for 3D information about the positions of fine particles in a plasma have therefore been widely researched. Among the various dusty plasma experiments, 90° separated two CCD cameras with helping 3D computed tomographic reconstruction [6] and stereoscopic [7, 8] are widely used to determine the 3D position of each fine particle [9]. They require two or more detectors; however, the locations and numbers of observation ports are considerably restricted in many plasma experiment devices. Planar laser scanning technique can obtain the 3D information of particles with one CCD camera [10, 11], but it requires a little while to scan across the wide field of view. In-line holographic techniques [12] and twocolor gradient methods [13, 14] can obtain 3D position of dust particles from a single-exposed photograph taken from a direction; however, these methods require a 12 bit or higher dynamic range sensors. It is required that a technique can acquire the 3D information of a dusty plasma with a single-exposed photograph taken from

of dust particles floating in an RF plasma are identified.

particle measurements, light-field, plenoptic camera

one viewing port with a conventional dynamic range sensor.

## **Chapter 5**
