Integral Photography Technique for Three-Dimensional Imaging of Dusty Plasmas

*Akio Sanpei*

## **Abstract**

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 of dust particles floating in an RF plasma are identified.

**Keywords:** dusty plasma, integral photography, three-dimensional reconstruction, particle measurements, light-field, plenoptic camera

## **1. Introduction**

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 one viewing port with a conventional dynamic range sensor.

The "integral photography technique" [15] is known as a principle used in naked eye 3D display and in commercial refocus cameras. Such refocus camera is also called as "plenoptic camera" or "light-field camera." It provides 3D imaging technologies based on a small lens array or a pinhole array to capture light rays from slightly different directions. This technique has an advantage in which instantaneous 3D information of objects can be estimated from a single-exposure picture obtained from a single viewing port.

**2.1 Recording system for dusty plasma experiments**

*DOI: http://dx.doi.org/10.5772/intechopen.88865*

*Integral Photography Technique for Three-Dimensional Imaging of Dusty Plasmas*

through each lens of the array to 2D image points (*X*(*i*, *<sup>j</sup>*)

*z*-plane create blurred spots on the sensor.

*for various l values between the lens and a sensor [26].*

follows:

**Figure 2.**

**Figure 3.**

**81**

*image array [26].*

In this section, it is shown how to design a recording system for dusty plasma experiments. **Figure 2** shows a schematic of relationship among lens array, detector, and imaging area on the recording system. The Cartesian (*x*, *y*, *z*) coordinate axes are indicated in the lower right corner of the figure. Rays are projected directly onto the sensor after passing through the lens array, which is placed at *z* = 0. Therefore, 3D spatial point of light source, i.e., the position of a dust particle, is projected

The array of projected images on the sensor is called as "elemental image array." The considerable parameters of the lens array are the number of lenses, lens pitch, and focal length. In the following discussion, we deal only with convex lens array. The focal length *F* of a convex lens array is calculated from the lens law as

> *<sup>F</sup>* <sup>¼</sup> *Ll L* þ *l*

between the lens array and the sensor. **Figure 3** shows *F* dependence on *L* with three values of *l*. The most suitable value of *F* can be determined by changing the experimental configuration. Particles located at misaligned positions from focused

*The schematic of relationship among the small lens array, the detector, and the imaging area of the recording system. Rays are projected directly onto the sensor after passing through the lens array to form an elemental*

*Focal length F of a convex lens array plotted as a function of the distance L between the object and the lens array*

where *L* is the distance between the object and the lens array and *l* is the distance

, *Y*(*i*, *<sup>j</sup>*)

*,* (1)

) on the detector.

Recently, the integral photography technique has come into use for scientific research in diverse fields. Example applications are particle tracking for velocimetry [16–19], microscopy measurement [20, 21], spray imaging [22], etc. In the research filed of plasma, 3D reconstructions of positions of particles levitating in a plasma have been demonstrated using commercial light-field Lytro cameras [23], and the time evolution of dusty plasmas has been measured using a commercial light-field Raytrix camera [24]. An open-ended plenoptic camera, which is constructed with a lens array and a typical reflex CMOS camera, obtained the 3D positions of dust particles in a radio-frequency (RF) plasma [25, 26]. Dual-filter plenoptic imaging system has been applied to observe lithium pellets in a high-temperature plasma [27].

In this chapter, the principle, design, and experimental results of the integral photography technique for 3D imaging of dusty plasmas will be presented.

## **2. Principle of the integral photography analysis**

**Figure 1** shows a schematic of recording and 3D reconstruction system with integral photography for dusty plasma experiment. A small lens array is placed in front of the particles levitating in a plasma to obtain an array of projected image. The rays emerging from 3D objects, i.e., scattering light rays from dusts pass through the small lens array and are captured on a sensor device. A 3D spatial point of object that is a position of a dust particle should be projected to twodimensional (2D) image points (*X*(*i*, *<sup>j</sup>*) , *Y*(*i*, *<sup>j</sup>*) ) through each (*i*, *j*)th lens of the array on a detector. The 3D reconstruction is then carried out computationally by creating inverse propagating rays within a virtual system similar to the recorded one.

#### **Figure 1.**

*Schematic of recording and 3D reconstruction system with the integral photography technique: (A) object, (B) lens array, (C) array of projected images on the detector, (D) virtual lens array, and (E and E*<sup>0</sup> *) virtual observation planes [25].*

*Integral Photography Technique for Three-Dimensional Imaging of Dusty Plasmas DOI: http://dx.doi.org/10.5772/intechopen.88865*

## **2.1 Recording system for dusty plasma experiments**

In this section, it is shown how to design a recording system for dusty plasma experiments. **Figure 2** shows a schematic of relationship among lens array, detector, and imaging area on the recording system. The Cartesian (*x*, *y*, *z*) coordinate axes are indicated in the lower right corner of the figure. Rays are projected directly onto the sensor after passing through the lens array, which is placed at *z* = 0. Therefore, 3D spatial point of light source, i.e., the position of a dust particle, is projected through each lens of the array to 2D image points (*X*(*i*, *<sup>j</sup>*) , *Y*(*i*, *<sup>j</sup>*) ) on the detector. The array of projected images on the sensor is called as "elemental image array."

The considerable parameters of the lens array are the number of lenses, lens pitch, and focal length. In the following discussion, we deal only with convex lens array. The focal length *F* of a convex lens array is calculated from the lens law as follows:

$$F = \frac{Ll}{L+l},\tag{1}$$

where *L* is the distance between the object and the lens array and *l* is the distance between the lens array and the sensor. **Figure 3** shows *F* dependence on *L* with three values of *l*. The most suitable value of *F* can be determined by changing the experimental configuration. Particles located at misaligned positions from focused *z*-plane create blurred spots on the sensor.

#### **Figure 2.**

The "integral photography technique" [15] is known as a principle used in naked

Recently, the integral photography technique has come into use for scientific research in diverse fields. Example applications are particle tracking for velocimetry [16–19], microscopy measurement [20, 21], spray imaging [22], etc. In the research filed of plasma, 3D reconstructions of positions of particles levitating in a plasma have been demonstrated using commercial light-field Lytro cameras [23], and the time evolution of dusty plasmas has been measured using a commercial light-field Raytrix camera [24]. An open-ended plenoptic camera, which is constructed with a lens array and a typical reflex CMOS camera, obtained the 3D positions of dust particles in a radio-frequency (RF) plasma [25, 26]. Dual-filter plenoptic imaging system has been applied to observe lithium pellets in a high-temperature

In this chapter, the principle, design, and experimental results of the integral

**Figure 1** shows a schematic of recording and 3D reconstruction system with integral photography for dusty plasma experiment. A small lens array is placed in front of the particles levitating in a plasma to obtain an array of projected image. The rays emerging from 3D objects, i.e., scattering light rays from dusts pass through the small lens array and are captured on a sensor device. A 3D spatial point of object that is a position of a dust particle should be projected to two-

, *Y*(*i*, *<sup>j</sup>*)

*Schematic of recording and 3D reconstruction system with the integral photography technique: (A) object, (B) lens array, (C) array of projected images on the detector, (D) virtual lens array, and (E and E*<sup>0</sup>

on a detector. The 3D reconstruction is then carried out computationally by creating inverse propagating rays within a virtual system similar to the

) through each (*i*, *j*)th lens of the array

*) virtual*

photography technique for 3D imaging of dusty plasmas will be presented.

**2. Principle of the integral photography analysis**

dimensional (2D) image points (*X*(*i*, *<sup>j</sup>*)

eye 3D display and in commercial refocus cameras. Such refocus camera is also called as "plenoptic camera" or "light-field camera." It provides 3D imaging technologies based on a small lens array or a pinhole array to capture light rays from slightly different directions. This technique has an advantage in which instantaneous 3D information of objects can be estimated from a single-exposure picture

obtained from a single viewing port.

*Progress in Fine Particle Plasmas*

plasma [27].

recorded one.

**Figure 1.**

**80**

*observation planes [25].*

*The schematic of relationship among the small lens array, the detector, and the imaging area of the recording system. Rays are projected directly onto the sensor after passing through the lens array to form an elemental image array [26].*

#### **Figure 3.**

*Focal length F of a convex lens array plotted as a function of the distance L between the object and the lens array for various l values between the lens and a sensor [26].*

In order to make an efficient recording system, the configuration of the CMOS sensor must be considered. The number of lenses in the array should be a multiple of the aspect ratio of the CMOS sensor. In addition, the lens pitch must take into account the size of the imaging area. After passing through the lens, rays are projected onto the sensor directly. If we assume that rays from a given dust particle are projected onto all elemental images, the limit of the imaging area is calculated using straight lines passing through the center of the outermost lens

$$(\boldsymbol{x}, \boldsymbol{y}, \boldsymbol{z}) = \left(\boldsymbol{x}, p\left(\boldsymbol{n}\_{\mathcal{Y}} - \mathbf{1}\right)/2, \mathbf{0}\right) \tag{2}$$

**2.2 Reconstruction of 3D position of light source**

*DOI: http://dx.doi.org/10.5772/intechopen.88865*

of the particle.

easily calculated as

where *X*ð Þ *<sup>i</sup>;<sup>j</sup>*

0 (*X*(*i*, *<sup>j</sup>*)

intensity *I*

**83**

*center; <sup>Y</sup>*ð Þ *<sup>i</sup>;<sup>j</sup>*

, *Y*(*i*, *<sup>j</sup>*)

*I x*ð Þ¼ *; y; z*

**Figure 1**, is scanned along *z*-axis.

To extract the positions of projected particles (*X*(*i*, *<sup>j</sup>*)

*Integral Photography Technique for Three-Dimensional Imaging of Dusty Plasmas*

virtual observation plane located on *z* from a point (*X*(*i*, *<sup>j</sup>*)

*pz* ¼ �

*qz* ¼ �

P *i* P *j I*

where *r* is the distance between (*X*(*i*, *<sup>j</sup>*)

image array, a subtraction technique is applied together with the color and profile thresholds. Background image is subtracted from obtained experimental image to reduce background noises such as the reflection of the laser light from the wall of the vacuum vessel. Then, the color space of the subtracted image is converted from RGB to "Lab" scale [28]. To obtain bright pixels colored with irradiating laser from the image, the threshold values of "*L*" and "*a*," which depend on the experimental configurations, were considered. For example, by analyzing the dust experiment shown in the Section 3.3 (see **Figure 9**), pixels with "*L*" values greater than 110 out of 255 and "*a*" values less than 110 out of 255 are used. Filtering with the geometrical features of the luminance distribution patch on pixels was also applied to detect the positions of dust particles from noise. The luminance centroid of each luminance distribution patch was estimated, and it was treated as the position

Using the observed elemental image array, the 3D image of particle distribution is reconstructed in the computer. The light path arriving at the point (*pz*, *qz*) on a

(*i*, *j*)th lens on the elemental image array is calculated with ray tracing according to geometrical information, such as distance from lens array to detector and focal length of lenses. If the thin lens approximation can be applied, (*pz*, *qz*) on giving *z* is

*<sup>l</sup>* <sup>þ</sup> *<sup>X</sup>*ð Þ *<sup>i</sup>;<sup>j</sup>*

*<sup>l</sup>* <sup>þ</sup> *<sup>Y</sup>*ð Þ *<sup>i</sup>;<sup>j</sup>*

<sup>0</sup> *<sup>X</sup>*ð Þ *<sup>i</sup>;<sup>j</sup> ; <sup>Y</sup>*ð Þ *<sup>i</sup>;<sup>j</sup>* � �*G*ð Þ *<sup>i</sup>;<sup>j</sup> <sup>X</sup>*ð Þ *<sup>i</sup>;<sup>j</sup> ; <sup>Y</sup>*ð Þ *<sup>i</sup>;<sup>j</sup>* � � cos <sup>2</sup>*α=r*<sup>2</sup>

*<sup>X</sup>*ð Þ *<sup>i</sup>;<sup>j</sup>* � *<sup>X</sup>*ð Þ *<sup>i</sup>;<sup>j</sup> center* � � � *<sup>z</sup>*

*<sup>Y</sup>*ð Þ *<sup>i</sup>;<sup>j</sup>* � *<sup>Y</sup>*ð Þ *<sup>i</sup>;<sup>j</sup> center* � � � *<sup>z</sup>*

Luminosity *I*(*x*, *y*, *z*) of 3D light-field is estimated as a summation of light

P *i* P *j*

whether (*i*, *j*)th lenslet exists in a field of view or not defined as

) over all (*i*, *j*)th lenses [25, 29, 30] as

, *Y*(*i*, *<sup>j</sup>*)

the angle between the optical axis and the incident ray. *G*(*i*, *<sup>j</sup>*) is a function indicating

*<sup>G</sup>*ð Þ *<sup>i</sup>;<sup>j</sup>* <sup>¼</sup> <sup>1</sup>*, if X*ð Þ *; <sup>Y</sup>* <sup>∈</sup>lenslet <sup>0</sup>*,* otherwise �

A target light source should locate on where *I*(*x*, *y*, *z*) shows the extremal value with respect to *z*, i.e., at convergent points of the rays. To detect the positions of dust particles, therefore, the virtual observation plane, indicated as E and E<sup>0</sup> in

*center* � � is the center of the (*i*, *<sup>j</sup>*)th lens.

, *Y*(*i*, *<sup>j</sup>*)

, *Y*(*i*, *<sup>j</sup>*)

*<sup>G</sup>*ð Þ *<sup>i</sup>;<sup>j</sup> <sup>X</sup>*ð Þ *<sup>i</sup>;<sup>j</sup> ; <sup>Y</sup>*ð Þ *<sup>i</sup>;<sup>j</sup>* � � *,* (12)

) and the position (*x*, *y*, *z*) and *α* is

(13)

) from the elemental

) corresponding to

*center* (10)

*center* (11)

and through pixels on the edges of the sensor area corresponding to the outermost lens

$$f\_{\mathbf{x}}(\mathbf{x}, \mathbf{y}, \mathbf{z}) = (\mathbf{x}, H/2, -l), \text{ (x}, H(n\_{\mathbf{y}} - \mathbf{2})/2, -l). \tag{3}$$

Here, *n* is the number of lenses along a given axis, the subscript "*y*" denotes the direction of the *y*-axis, *H* is the length of the CMOS sensor in the *y*-axis, and *p* is the lens pitch. Furthermore, the limits for the plane perpendicular to the *z*-axis are expressed as

$$y\_1 = p\frac{n\_\mathcal{\mathcal{V}} - 1}{2} - L\frac{H - (n\_\mathcal{\mathcal{V}} - 1)p}{2l},\tag{4}$$

$$y\_2 = p\frac{n\_\mathcal{y} - 1}{2} + \frac{L}{l} \left\{ p\frac{n\_\mathcal{y} - 1}{2} - \frac{H}{n\_\mathcal{y}} \left(\frac{n\_\mathcal{y} - 2}{2}\right) \right\}.\tag{5}$$

In the same manner, the limits for the *z*-axis of the imaging area are expressed as

$$z\_1 = \frac{n\_\text{y} - 1}{2} p \times \frac{2n\_\text{y}l}{(n\_\text{y} - 2)H - n\_\text{y}(n\_\text{y} - 1)p},\tag{6}$$

$$z\_2 = \frac{n\_\mathcal{\mathcal{Y}} - 1}{2} p \times \frac{2l}{H - (n\_\mathcal{\mathcal{Y}} - 1)p}. \tag{7}$$

The number *nx* of lenses along the *x*-direction is calculated from *ny* using the aspect ratio of the CMOS sensor. Then we can design *p* and *n* from experimental requirement of *L* and the size of the imaging area using above equations.

An uncertainty in the reconstructed image will be attributed to the spatial resolution of an elemental image on CMOS sensor [24]. The length *h* of a side of a pixel on the CMOS sensor produces uncertainties in the plane perpendicular to the *z*-axis as

$$\frac{hL}{l} \tag{8}$$

and along the *z*-axis itself as

$$\frac{hL}{2l} \times \frac{\left(n\_\text{y} - \mathbf{1}\right)\left(L + l\right)}{H} . \tag{9}$$

The above equation indicates that the large ratio of distances *L*/*l* and finite size of a pixel on the CMOS sensor cause a relatively large uncertainty along the *z*-axis.

## **2.2 Reconstruction of 3D position of light source**

In order to make an efficient recording system, the configuration of the CMOS sensor must be considered. The number of lenses in the array should be a multiple of the aspect ratio of the CMOS sensor. In addition, the lens pitch must take into account the size of the imaging area. After passing through the lens, rays are projected onto the sensor directly. If we assume that rays from a given dust particle are projected onto all elemental images, the limit of the imaging area is calculated

and through pixels on the edges of the sensor area corresponding to the outer-

Here, *n* is the number of lenses along a given axis, the subscript "*y*" denotes the direction of the *y*-axis, *H* is the length of the CMOS sensor in the *y*-axis, and *p* is the lens pitch. Furthermore, the limits for the plane perpendicular to the *z*-axis are

> *ny* � 1 <sup>2</sup> � *<sup>H</sup> ny*

In the same manner, the limits for the *z*-axis of the imaging area are expressed as

ð Þ¼ *<sup>x</sup>; <sup>y</sup>; <sup>z</sup> <sup>x</sup>; p ny* � <sup>1</sup> *<sup>=</sup>*2*;* <sup>0</sup> (2)

ð Þ¼ *<sup>x</sup>; <sup>y</sup>; <sup>z</sup>* ð Þ *<sup>x</sup>; <sup>H</sup>=*2*;* �*<sup>l</sup> , x; H ny* � <sup>2</sup> *<sup>=</sup>*2*;* �*<sup>l</sup> :* (3)

*<sup>H</sup>* � *ny* � <sup>1</sup> *<sup>p</sup>*

2*nyl ny* � <sup>2</sup> *<sup>H</sup>* � *ny ny* � <sup>1</sup> *<sup>p</sup>*

> 2*l <sup>H</sup>* � *ny* � <sup>1</sup> *<sup>p</sup>*

*ny* � 2 2

<sup>2</sup>*<sup>l</sup> ,* (4)

*:* (5)

*,* (6)

*:* (7)

*<sup>l</sup>* (8)

*<sup>H</sup> :* (9)

using straight lines passing through the center of the outermost lens

*y*<sup>1</sup> ¼ *p*

*<sup>z</sup>*<sup>1</sup> <sup>¼</sup> *ny* � <sup>1</sup>

<sup>2</sup> *<sup>p</sup>* �

*<sup>z</sup>*<sup>2</sup> <sup>¼</sup> *ny* � <sup>1</sup>

*hL* 2*l* �

<sup>2</sup> *<sup>p</sup>* �

requirement of *L* and the size of the imaging area using above equations.

The number *nx* of lenses along the *x*-direction is calculated from *ny* using the aspect ratio of the CMOS sensor. Then we can design *p* and *n* from experimental

An uncertainty in the reconstructed image will be attributed to the spatial resolution of an elemental image on CMOS sensor [24]. The length *h* of a side of a pixel on the CMOS sensor produces uncertainties in the plane perpendicular to the

*hL*

*ny* � <sup>1</sup> ð Þ *<sup>L</sup>* <sup>þ</sup> *<sup>l</sup>*

The above equation indicates that the large ratio of distances *L*/*l* and finite size of a pixel on the CMOS sensor cause a relatively large uncertainty along the *z*-axis.

*ny* � 1 2 þ

*y*<sup>2</sup> ¼ *p*

*ny* � 1 <sup>2</sup> � *<sup>L</sup>*

> *L <sup>l</sup> <sup>p</sup>*

most lens

*Progress in Fine Particle Plasmas*

expressed as

*z*-axis as

**82**

and along the *z*-axis itself as

To extract the positions of projected particles (*X*(*i*, *<sup>j</sup>*) , *Y*(*i*, *<sup>j</sup>*) ) from the elemental image array, a subtraction technique is applied together with the color and profile thresholds. Background image is subtracted from obtained experimental image to reduce background noises such as the reflection of the laser light from the wall of the vacuum vessel. Then, the color space of the subtracted image is converted from RGB to "Lab" scale [28]. To obtain bright pixels colored with irradiating laser from the image, the threshold values of "*L*" and "*a*," which depend on the experimental configurations, were considered. For example, by analyzing the dust experiment shown in the Section 3.3 (see **Figure 9**), pixels with "*L*" values greater than 110 out of 255 and "*a*" values less than 110 out of 255 are used. Filtering with the geometrical features of the luminance distribution patch on pixels was also applied to detect the positions of dust particles from noise. The luminance centroid of each luminance distribution patch was estimated, and it was treated as the position of the particle.

Using the observed elemental image array, the 3D image of particle distribution is reconstructed in the computer. The light path arriving at the point (*pz*, *qz*) on a virtual observation plane located on *z* from a point (*X*(*i*, *<sup>j</sup>*) , *Y*(*i*, *<sup>j</sup>*) ) corresponding to (*i*, *j*)th lens on the elemental image array is calculated with ray tracing according to geometrical information, such as distance from lens array to detector and focal length of lenses. If the thin lens approximation can be applied, (*pz*, *qz*) on giving *z* is easily calculated as

$$p\_z = -\frac{\left(X^{(i,j)} - X\_{center}^{(i,j)}\right) \times z}{l} + X\_{center}^{(i,j)}\tag{10}$$

$$q\_x = -\frac{\left(Y^{(i,j)} - Y\_{center}^{(i,j)}\right) \times z}{l} + Y\_{center}^{(i,j)}\tag{11}$$

where *X*ð Þ *<sup>i</sup>;<sup>j</sup> center; <sup>Y</sup>*ð Þ *<sup>i</sup>;<sup>j</sup> center* � � is the center of the (*i*, *<sup>j</sup>*)th lens.

Luminosity *I*(*x*, *y*, *z*) of 3D light-field is estimated as a summation of light intensity *I* 0 (*X*(*i*, *<sup>j</sup>*) , *Y*(*i*, *<sup>j</sup>*) ) over all (*i*, *j*)th lenses [25, 29, 30] as

$$I(\mathbf{x}, y, z) = \frac{\sum\_{i} \sum\_{j} I'(\mathbf{X}^{(ij)}, \mathbf{Y}^{(ij)}) \mathbf{G}\_{(ij)}(\mathbf{X}^{(ij)}, \mathbf{Y}^{(ij)}) \cos^2 a/r^2}{\sum\_{i} \sum\_{j} \mathbf{G}\_{(ij)}(\mathbf{X}^{(ij)}, \mathbf{Y}^{(ij)})},\tag{12}$$

where *r* is the distance between (*X*(*i*, *<sup>j</sup>*) , *Y*(*i*, *<sup>j</sup>*) ) and the position (*x*, *y*, *z*) and *α* is the angle between the optical axis and the incident ray. *G*(*i*, *<sup>j</sup>*) is a function indicating whether (*i*, *j*)th lenslet exists in a field of view or not defined as

$$G\_{(i,j)} = \begin{cases} \mathbf{1}, & \text{if } (X, Y) \in \text{lenslet} \\ \mathbf{0}, & \text{otherwise} \end{cases} \tag{13}$$

A target light source should locate on where *I*(*x*, *y*, *z*) shows the extremal value with respect to *z*, i.e., at convergent points of the rays. To detect the positions of dust particles, therefore, the virtual observation plane, indicated as E and E<sup>0</sup> in **Figure 1**, is scanned along *z*-axis.

## **3. Experimental setup and results**

## **3.1 Estimation of measurement parameters for a dusty plasma experiment**

In order to determine the parameters of multi-convex lens array for a dusty plasma experiment, we adjusted the side of the imaging area and *L* to be approximately 5 and 80 mm, respectively. The commercial, standard reflex camera (D810, Nikon) was applied as the CMOS sensor. The sensor has dimensions of 36 � 24 mm<sup>2</sup> and *h* = 1/205 mm. Due to the geometrical limit of the camera D810, the distance *l* must be more than 65 mm. Rays are projected onto the CMOS sensor directly after passing through the lens array. Subsequently, *F* is estimated as 35 mm from Eq. (1). The number *n* of lenses is inversely proportional to *p* and to the size of a lens. Because of the increased number of tracing rays, an increase in *n* increases the resolution; however, the number of pixels illuminated by each lens decreases. For a lens array including (*nx*, *ny*)=9 � 6 lenses, *p* is led as 2.2 mm and the D810 camera has 818 � 818 square pixels for each lens. The imaging area for the plane perpendicular to the *z*-axis lies between *y*<sup>1</sup> = �2.5 mm and *y*<sup>2</sup> = 2.423 mm, as estimated from Eqs. (4) and (5). The area of the measurable plane is a function of the position *z* of virtual plane, and it is maximized to be approximately 24 mm<sup>2</sup> at *z* = 80 mm. Regarding the *z*-axis, the imaging area lies between *z*<sup>1</sup> = 143 mm and *z*<sup>2</sup> = 55 mm, as estimated from Eqs. (6) and (7). **Table 1** shows the parameters of the designed multi-convex lens array and those of the recording system.

A picture of the designed lens array using acrylic plastic is shown in **Figure 4**. The rim around the periphery facilitates the holding of the array. **Figure 5** shows a sample image obtained with the designed lens array system. The object appears as a single green circle with �1 mm of diameter which is located on *z* = 80 mm.

### **3.2 Reconstruction of known target light sources**

Developed recording and reconstruction system has been tested using target light sources located on known positions. In this test experiment, the typical exposure time of the camera is 1/400 s. The elemental image array obtained with the system was stored in a computer as 10 bits of data. In addition to the position (*X*(*i*, *<sup>j</sup>*) , *Y*(*i*, *<sup>j</sup>*) ) of the particles identified in each elemental images, the intensity *I* 0 (*X*(*i*, *<sup>j</sup>*) , *Y*(*i*, *<sup>j</sup>*) ) for each particle is recorded as well. Then *I*(*x*, *y*, *z*) on a virtual observation plane located on *z* is calculated according to Eq. (12). The position of the maxima of the brightness of the light-field *I*(*x*, *y*, *z*) determines the *z*, which represents the depth of particles. After calibrating the apparent pixel sizes on the images to the real

**Figure 5.**

**Figure 6.**

**85**

*squares and closed circles, respectively [26].*

**Figure 4.**

*lenses have the same F value of 35 mm [26].*

*DOI: http://dx.doi.org/10.5772/intechopen.88865*

*the CMOS sensor.*

*Sample image obtained with the designed lens array system. Single green circles are recorded as 9 6 circles on*

*Top view of reconstruction result for the test data. The target and reconstructed data are indicated by open*

*Photograph of the designed lens array. It includes 9 6 convex spherical lenses with rectangular boundaries. All*

*Integral Photography Technique for Three-Dimensional Imaging of Dusty Plasmas*


#### **Table 1.**

*Parameters of multi-convex lens array and the recording system for dusty plasma experiment with the CMOS camera D810.*

*Integral Photography Technique for Three-Dimensional Imaging of Dusty Plasmas DOI: http://dx.doi.org/10.5772/intechopen.88865*

#### **Figure 4.**

**3. Experimental setup and results**

*Progress in Fine Particle Plasmas*

**3.1 Estimation of measurement parameters for a dusty plasma experiment**

multi-convex lens array and those of the recording system.

**3.2 Reconstruction of known target light sources**

*Y*(*i*, *<sup>j</sup>*)

*Y*(*i*, *<sup>j</sup>*)

**Table 1.**

**84**

*camera D810.*

In order to determine the parameters of multi-convex lens array for a dusty plasma experiment, we adjusted the side of the imaging area and *L* to be approximately 5 and 80 mm, respectively. The commercial, standard reflex camera (D810, Nikon) was applied as the CMOS sensor. The sensor has dimensions of 36 � 24 mm<sup>2</sup> and *h* = 1/205 mm. Due to the geometrical limit of the camera D810, the distance *l* must be more than 65 mm. Rays are projected onto the CMOS sensor directly after passing through the lens array. Subsequently, *F* is estimated as 35 mm from Eq. (1). The number *n* of lenses is inversely proportional to *p* and to the size of a lens. Because of the increased number of tracing rays, an increase in *n* increases the resolution; however, the number of pixels illuminated by each lens decreases. For a lens array including (*nx*, *ny*)=9 � 6 lenses, *p* is led as 2.2 mm and the D810 camera has 818 � 818 square pixels for each lens. The imaging area for the plane perpendicular to the *z*-axis lies between *y*<sup>1</sup> = �2.5 mm and *y*<sup>2</sup> = 2.423 mm, as estimated from Eqs. (4) and (5). The area of the measurable plane is a function of the position *z* of virtual plane, and it is maximized to be approximately 24 mm<sup>2</sup> at *z* = 80 mm. Regarding the *z*-axis, the imaging area lies between *z*<sup>1</sup> = 143 mm and *z*<sup>2</sup> = 55 mm, as estimated from Eqs. (6) and (7). **Table 1** shows the parameters of the designed

A picture of the designed lens array using acrylic plastic is shown in **Figure 4**. The rim around the periphery facilitates the holding of the array. **Figure 5** shows a sample image obtained with the designed lens array system. The object appears as a

Developed recording and reconstruction system has been tested using target light sources located on known positions. In this test experiment, the typical exposure time of the camera is 1/400 s. The elemental image array obtained with the system was stored in a computer as 10 bits of data. In addition to the position (*X*(*i*, *<sup>j</sup>*)

) for each particle is recorded as well. Then *I*(*x*, *y*, *z*) on a virtual observation plane located on *z* is calculated according to Eq. (12). The position of the maxima of the brightness of the light-field *I*(*x*, *y*, *z*) determines the *z*, which represents the depth of particles. After calibrating the apparent pixel sizes on the images to the real

*Parameters of multi-convex lens array and the recording system for dusty plasma experiment with the CMOS*

) of the particles identified in each elemental images, the intensity *I*

**Parameter Value** *F* 35 mm (convex) *nx* � *ny* 9 � 6 Size of a lens 2.2 � 2.2 mm<sup>2</sup> Pixels per lens 818 � 818 pixels *l* ≥65 mm Working area on *<sup>x</sup>*�*<sup>y</sup>* plane at *<sup>z</sup>* = 80 mm �24 mm<sup>2</sup> Working range of *z* from lens array 55–143 mm

single green circle with �1 mm of diameter which is located on *z* = 80 mm.

*Photograph of the designed lens array. It includes 9 6 convex spherical lenses with rectangular boundaries. All lenses have the same F value of 35 mm [26].*

#### **Figure 5.**

,

0 (*X*(*i*, *<sup>j</sup>*) , *Sample image obtained with the designed lens array system. Single green circles are recorded as 9 6 circles on the CMOS sensor.*

#### **Figure 6.**

*Top view of reconstruction result for the test data. The target and reconstructed data are indicated by open squares and closed circles, respectively [26].*

scales of the dust particle cloud, the absolute (*x*, *y*, *z*) coordinates can be determined.

In **Figure 6**, the 3D positions of the known target and reconstructed particles are marked by open squares and closed circles, respectively. In this test experiment, the optical axis is set along the *z*-axis, the multi-convex lens array is located at *z* = 0, and *l* is set to be 77 mm. Mechanical setting errors cause 30 μm of the error bars for the target data points. The error bars of the reconstructed data points are determined according to the pixel dimensions of the recording system. From Eqs. (8) and (9), the uncertainties for the *x*- (*y*-) and *z*-directions are estimated as 6 and 108 μm, respectively. The relative error between the positions of the target and reconstructed data fits into the known range. Therefore it is concluded that the developed recording and reconstruction system works well in the range of dusty plasma experiment.

## **3.3 Apply to dusty plasma experiment**

Finally, the developed system is applied to a dusty plasma comprising monodiverse polymer spheres (diameter = 6.5 μm) floating in a horizontal, parallelplate RF plasma. **Figures 7** and **8** show a photograph and schematic of the experimental setup. A piezoelectric vibrator is contained in an RF electrode as the injector of fine particles into a plasma. A grounded counter electrode is positioned at the upper side of the 13.56-MHz-powered electrode at the distance of 14 mm. Fine particles levitate in the plasma generated between the electrodes. A solid-state laser, which radiates light of 532 nm in wavelength, 4 mm in diameter, and 10 mW in radiation power, was used in our experiment to observe fine particles in the plasma using scattered laser light.

The lens array and the CMOS sensor were located at a side port of the chamber with a distance of *l* = 65 mm to obtain the elemental image array. An enlarged

experimentally obtained elemental image array from above experimental device is shown in **Figure 9**. This figure shows roughly 3 � 2 elements out of the 9 � 6 elements captured by the CMOS camera. Each image element is recorded with approximately 818 � 818 square pixels on the sensor. Scattered light from the dust particles levitating in the RF plasma appears as green dots, and slightly different elemental images result from parallax differences. As shown in **Figure 9**, only five dust particles floated in the plasma in this experiment. They oscillated vertically in the field of view and did not form any ordered array. The 3D positions of particles determined from **Figure 9** are shown in **Table 2** and **Figure 10**. Note that the *z*-axis

*Roughly 3* � *2 elements are enlarged from experimentally obtained array of 54 elemental images after subtraction of a background image. The green dots indicate the presence of dust particles. Each image element is*

*recorded with approximately 818* � *818 square pixels [26].*

*Schematic of experimental setup (not to scale). (A) 13.56 MHz RF source, (B) dust source, (C and C*<sup>0</sup>

*Integral Photography Technique for Three-Dimensional Imaging of Dusty Plasmas*

*powered and grounded electrode respectively, (D) illuminating laser (10 mW at 532 nm), (E) dust particles in*

*)*

**Figure 8.**

**Figure 9.**

**87**

*plasma, (F) lens array, (G) CMOS sensor.*

*DOI: http://dx.doi.org/10.5772/intechopen.88865*

is along the optical axis and value of *z* is the distance from the lens array.

**Figure 10(a)** shows a bird's-eye view of the reconstructed distribution. Green dots indicate the 3D positions of the levitating dusts, and cross symbols indicate the projected position on the *x*�*y* plane with *z* = 90 mm. The *x*�*y* distribution of dust particles in **Figure 10(c)** agrees with the observed configuration of dust particles in **Figure 9**. From the reconstructed image, we can recognize that particles are

#### **Figure 7.**

*A photograph of experimental setup. Plasma is generated inside of an octagonal pillar shape chamber shown in the center of the figure. Designed lens array is located between the chamber, and the camera is shown in right-hand side of the figure.*

*Integral Photography Technique for Three-Dimensional Imaging of Dusty Plasmas DOI: http://dx.doi.org/10.5772/intechopen.88865*

#### **Figure 8.**

scales of the dust particle cloud, the absolute (*x*, *y*, *z*) coordinates can be deter-

respectively. The relative error between the positions of the target and

reconstructed data fits into the known range. Therefore it is concluded that the developed recording and reconstruction system works well in the range of dusty

Finally, the developed system is applied to a dusty plasma comprising monodiverse polymer spheres (diameter = 6.5 μm) floating in a horizontal, parallelplate RF plasma. **Figures 7** and **8** show a photograph and schematic of the experimental setup. A piezoelectric vibrator is contained in an RF electrode as the injector of fine particles into a plasma. A grounded counter electrode is positioned at the upper side of the 13.56-MHz-powered electrode at the distance of 14 mm. Fine particles levitate in the plasma generated between the electrodes. A solid-state laser, which radiates light of 532 nm in wavelength, 4 mm in diameter, and 10 mW in radiation power, was used in our experiment to observe fine particles in the plasma

The lens array and the CMOS sensor were located at a side port of the chamber

with a distance of *l* = 65 mm to obtain the elemental image array. An enlarged

*A photograph of experimental setup. Plasma is generated inside of an octagonal pillar shape chamber shown in the center of the figure. Designed lens array is located between the chamber, and the camera is shown in*

In **Figure 6**, the 3D positions of the known target and reconstructed particles are marked by open squares and closed circles, respectively. In this test experiment, the optical axis is set along the *z*-axis, the multi-convex lens array is located at *z* = 0, and *l* is set to be 77 mm. Mechanical setting errors cause 30 μm of the error bars for the target data points. The error bars of the reconstructed data points are determined according to the pixel dimensions of the recording system. From Eqs. (8) and (9), the uncertainties for the *x*- (*y*-) and *z*-directions are estimated as 6 and 108 μm,

mined.

plasma experiment.

*Progress in Fine Particle Plasmas*

using scattered laser light.

**Figure 7.**

**86**

*right-hand side of the figure.*

**3.3 Apply to dusty plasma experiment**

*Schematic of experimental setup (not to scale). (A) 13.56 MHz RF source, (B) dust source, (C and C*<sup>0</sup> *) powered and grounded electrode respectively, (D) illuminating laser (10 mW at 532 nm), (E) dust particles in plasma, (F) lens array, (G) CMOS sensor.*

#### **Figure 9.**

*Roughly 3* � *2 elements are enlarged from experimentally obtained array of 54 elemental images after subtraction of a background image. The green dots indicate the presence of dust particles. Each image element is recorded with approximately 818* � *818 square pixels [26].*

experimentally obtained elemental image array from above experimental device is shown in **Figure 9**. This figure shows roughly 3 � 2 elements out of the 9 � 6 elements captured by the CMOS camera. Each image element is recorded with approximately 818 � 818 square pixels on the sensor. Scattered light from the dust particles levitating in the RF plasma appears as green dots, and slightly different elemental images result from parallax differences. As shown in **Figure 9**, only five dust particles floated in the plasma in this experiment. They oscillated vertically in the field of view and did not form any ordered array. The 3D positions of particles determined from **Figure 9** are shown in **Table 2** and **Figure 10**. Note that the *z*-axis is along the optical axis and value of *z* is the distance from the lens array. **Figure 10(a)** shows a bird's-eye view of the reconstructed distribution. Green dots indicate the 3D positions of the levitating dusts, and cross symbols indicate the projected position on the *x*�*y* plane with *z* = 90 mm. The *x*�*y* distribution of dust particles in **Figure 10(c)** agrees with the observed configuration of dust particles in **Figure 9**. From the reconstructed image, we can recognize that particles are


with pinhole ultraviolet or soft X-ray detector [39–41], instead of lenslet array for

*Integral Photography Technique for Three-Dimensional Imaging of Dusty Plasmas*

*DOI: http://dx.doi.org/10.5772/intechopen.88865*

The integral photography technique is useful for 3D observation of dusty plasmas. This technique has an advantage in which instantaneous 3D information of objects can be estimated from a single-exposure picture obtained from a single viewing port. The principle of integral photography technique and its analytical method has been explained in detail. A design of a light-field camera for dusty plasma experiments has been 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. Then, the recording and reconstruction system has been 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 of dust particles floating in an RF plasma are

The author appreciates Prof. Y. Hayashi and Prof. Y. Awatsuji of Kyoto Institute of Technology for fruitful suggestions from the perspective of researches for the dusty plasma and the integral photography technique, respectively. The author also thanks Prof. S. Masamune of Chubu University and Prof. H. Himura of Kyoto Institute of Technology for the comments on this study. Finally, the author would like to thank Mr. K. Tokunaga of Kyoto Institute of Technology for experimental assistance. This research is partly supported by JSPS KAKENHI Grant Numbers

It is still unclear how many dust particles can be counted by the system using the integral photography technique because many parameters trade off against each other. Well-designed optical and recording systems are required to identify the 3D positions for a large number of particles. The defocusing effect of objects is another considerable problem. The effect makes the positions of objects on sensor difficult to identify, and uncertainties in the reconstructed image may increase. In order to avoid such a problem, some commercial light-field cameras mount different *F* lens arrays simultaneously. Moreover, subpixel analyses, modern particle detection, and interpolation algorithms would enable the achievement of enhanced

visible light.

accuracy [42, 43].

**5. Conclusions**

identified.

**89**

**Acknowledgements**

15K05364, 18K18750, and 24244094.

**Table 2.**

x*,* y*, and* z *coordinates in mm of each particle, as determined from Figure 9.*

#### **FIgure 10.**

*(a) Bird's-eye view. Cross symbols indicate projected position of the xy plane with z = 90 mm. (b) Projection of the xz plane. (c) Projection of the xy plane. Each panel shows the reconstructed positions of the levitating particles, as obtained from Figure 9. Dust are randomly distributed between z = 88.4 and 89.8 mm, which are the distance from the lens array [26].*

randomly distributed between *z* = 88.4 and 89.8 mm, which are the distance from the lens array. The mean distance among particles is estimated approximately 780 μm.

## **4. Expected future of the integral photography technique for plasma measurement**

The integral photography technique has great potential of versatile applications for plasma measurement. With the help of Mie-scattering ellipsometry technique [31, 32], it would bring information about the size of particles in addition to sixdimensional information about position and velocity. Combined with intrinsic fluorescence spectroscopy [33], specification of dust's materials will be available not only for standard polymer but also for unusual target such as microorganisms [34, 35]. Moreover, deconvolution techniques [36, 37] will extend the integral photography to determine 3D distribution of spatially continuous light sources [38]. 3D information of bremsstrahlung emissivity distribution should be obtained

*Integral Photography Technique for Three-Dimensional Imaging of Dusty Plasmas DOI: http://dx.doi.org/10.5772/intechopen.88865*

with pinhole ultraviolet or soft X-ray detector [39–41], instead of lenslet array for visible light.

It is still unclear how many dust particles can be counted by the system using the integral photography technique because many parameters trade off against each other. Well-designed optical and recording systems are required to identify the 3D positions for a large number of particles. The defocusing effect of objects is another considerable problem. The effect makes the positions of objects on sensor difficult to identify, and uncertainties in the reconstructed image may increase. In order to avoid such a problem, some commercial light-field cameras mount different *F* lens arrays simultaneously. Moreover, subpixel analyses, modern particle detection, and interpolation algorithms would enable the achievement of enhanced accuracy [42, 43].

## **5. Conclusions**

The integral photography technique is useful for 3D observation of dusty plasmas. This technique has an advantage in which instantaneous 3D information of objects can be estimated from a single-exposure picture obtained from a single viewing port. The principle of integral photography technique and its analytical method has been explained in detail. A design of a light-field camera for dusty plasma experiments has been 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. Then, the recording and reconstruction system has been 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 of dust particles floating in an RF plasma are identified.

## **Acknowledgements**

The author appreciates Prof. Y. Hayashi and Prof. Y. Awatsuji of Kyoto Institute of Technology for fruitful suggestions from the perspective of researches for the dusty plasma and the integral photography technique, respectively. The author also thanks Prof. S. Masamune of Chubu University and Prof. H. Himura of Kyoto Institute of Technology for the comments on this study. Finally, the author would like to thank Mr. K. Tokunaga of Kyoto Institute of Technology for experimental assistance. This research is partly supported by JSPS KAKENHI Grant Numbers 15K05364, 18K18750, and 24244094.

randomly distributed between *z* = 88.4 and 89.8 mm, which are the distance from the lens array. The mean distance among particles is estimated approximately 780 μm.

*(a) Bird's-eye view. Cross symbols indicate projected position of the xy plane with z = 90 mm. (b) Projection of the xz plane. (c) Projection of the xy plane. Each panel shows the reconstructed positions of the levitating particles, as obtained from Figure 9. Dust are randomly distributed between z = 88.4 and 89.8 mm, which are*

*x y z* 0.4226 0.7535 88.542 0.2322 0.2773 88.950 0.1896 0.4043 89.676 0.3075 0.3272 88.860 0.6975 0.1367 89.540

x*,* y*, and* z *coordinates in mm of each particle, as determined from Figure 9.*

**4. Expected future of the integral photography technique for plasma**

The integral photography technique has great potential of versatile applications for plasma measurement. With the help of Mie-scattering ellipsometry technique [31, 32], it would bring information about the size of particles in addition to sixdimensional information about position and velocity. Combined with intrinsic fluorescence spectroscopy [33], specification of dust's materials will be available not only for standard polymer but also for unusual target such as microorganisms [34, 35]. Moreover, deconvolution techniques [36, 37] will extend the integral photography to determine 3D distribution of spatially continuous light sources [38]. 3D information of bremsstrahlung emissivity distribution should be obtained

**measurement**

*the distance from the lens array [26].*

**FIgure 10.**

**88**

**Table 2.**

*Progress in Fine Particle Plasmas*

*Progress in Fine Particle Plasmas*

## **Author details**

Akio Sanpei Kyoto Institute of Technology, Kyoto, Japan

\*Address all correspondence to: sanpei@kit.ac.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.

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PhysRevLett.73.652

2001. p. 49

10.1063/1.1755705

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*Integral Photography Technique for Three-Dimensional Imaging of Dusty Plasmas*

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*Progress in Fine Particle Plasmas*

Kyoto Institute of Technology, Kyoto, Japan

provided the original work is properly cited.

\*Address all correspondence to: sanpei@kit.ac.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,

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[25] Sanpei A, Takao N, Kato Y, Hayashi Y. Initial result of threedimensional reconstruction of dusty plasma through integral photography technique. IEEE Transactions on Plasma Science. 2016;**44**:508. Available from: https://ieeexplore.ieee.org/abstract/

[26] Sanpei A, Tokunaga K, Hayashi Y. Design of an open-ended plenoptic camera for three-dimensional imaging of dusty plasmas. Japanese Journal of Applied Physics. 2017;**56**:080305. DOI:

[27] Sun Z, Baldwin JK, Wei X, Wang Z, Jiansheng H, Maingi R, et al. Initial results and designs of dual-filter and plenoptic imaging for high-temperature plasmas. The Review of Scientific Instruments. 2018;**89**(10):E112. DOI:

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**95**

opalescence.

**Chapter 6**

**Abstract**

Carbon Dioxide

*Tsuyohito Ito and Kazuo Terashima*

coupled plasmas because of the properties of media.

barrier discharge, dusty plasmas in dense fluids

**1. Introduction**

Dusty Plasmas in Supercritical

Dusty plasmas, which are systems comprising plasmas and dust particles, have emerged in various fields such as astrophysics and semiconductor processes. The fine particles possibly form ordered structures, namely, plasma crystals, which have been extensively studied as a model to observe statistical phenomena. However, the structures of the plasma crystals in ground-based experiments are two-dimensional (2D) because of the anisotropy induced by gravity. Microgravity experiments successfully provided opportunities to observe the novel phenomena hidden by gravity. The dusty plasmas generated in supercritical fluids (SCFs) are proposed herein as a means for realizing a pseudo-microgravity environment for plasma crystals. SCF has a high and controllable density; therefore, the particles in SCF can experience pseudo-microgravity conditions with the aid of buoyancy. In this chapter, a study on the particle charging and the formation of the plasma crystals in supercritical CO2, the realization of a pseudo-microgravity environment, and the outlook for the dusty plasmas in SCF are introduced. Our studies on dusty plasmas in SCF not only provide the pseudo-microgravity conditions but also open a novel field of strongly

**Keywords:** plasma crystal, supercritical fluid, pseudo-microgravity, surface dielectric

The dynamics of statistical phenomena, such as phase transitions and wave propagation, and kinetic phenomena, such as the motion of dislocations in a crystal, are difficult to observe because atoms are too small. For a long time, many models have been developed that imitate crystal structures and can be observed with an optical microscope. For example, in 1947, Bragg, who established X-ray diffraction, and Nye reported the bubble model to understand the dynamics of dislocations [1]. The most extensively studied system is probably a charged particle system. For example, colloidal crystals, ordered structures of microparticles in colloidal dispersion, were developed [2]. Colloidal crystals have been studied not only as a model of crystal structure but also for application to optical materials [3]. Interparticle distances are close to the wavelength of visible light, which results in

Dusty plasmas or fine particle plasmas, a system composed of dust particles and plasmas, have also been extensively studied as a model of crystal structure. In 1986,

*Yasuhito Matsubayashi, Noritaka Sakakibara,* 

## **Chapter 6**

## Dusty Plasmas in Supercritical Carbon Dioxide

*Yasuhito Matsubayashi, Noritaka Sakakibara, Tsuyohito Ito and Kazuo Terashima*

## **Abstract**

Dusty plasmas, which are systems comprising plasmas and dust particles, have emerged in various fields such as astrophysics and semiconductor processes. The fine particles possibly form ordered structures, namely, plasma crystals, which have been extensively studied as a model to observe statistical phenomena. However, the structures of the plasma crystals in ground-based experiments are two-dimensional (2D) because of the anisotropy induced by gravity. Microgravity experiments successfully provided opportunities to observe the novel phenomena hidden by gravity. The dusty plasmas generated in supercritical fluids (SCFs) are proposed herein as a means for realizing a pseudo-microgravity environment for plasma crystals. SCF has a high and controllable density; therefore, the particles in SCF can experience pseudo-microgravity conditions with the aid of buoyancy. In this chapter, a study on the particle charging and the formation of the plasma crystals in supercritical CO2, the realization of a pseudo-microgravity environment, and the outlook for the dusty plasmas in SCF are introduced. Our studies on dusty plasmas in SCF not only provide the pseudo-microgravity conditions but also open a novel field of strongly coupled plasmas because of the properties of media.

**Keywords:** plasma crystal, supercritical fluid, pseudo-microgravity, surface dielectric barrier discharge, dusty plasmas in dense fluids

## **1. Introduction**

The dynamics of statistical phenomena, such as phase transitions and wave propagation, and kinetic phenomena, such as the motion of dislocations in a crystal, are difficult to observe because atoms are too small. For a long time, many models have been developed that imitate crystal structures and can be observed with an optical microscope. For example, in 1947, Bragg, who established X-ray diffraction, and Nye reported the bubble model to understand the dynamics of dislocations [1]. The most extensively studied system is probably a charged particle system. For example, colloidal crystals, ordered structures of microparticles in colloidal dispersion, were developed [2]. Colloidal crystals have been studied not only as a model of crystal structure but also for application to optical materials [3]. Interparticle distances are close to the wavelength of visible light, which results in opalescence.

Dusty plasmas or fine particle plasmas, a system composed of dust particles and plasmas, have also been extensively studied as a model of crystal structure. In 1986, Ikezi theoretically predicted that microparticles (diameter, 0.3–30 μm) embedded in a commonly used plasma processing possibly form an ordered structure or plasma crystal [4]. Microparticles inside the plasma become negatively charged because of the higher mobility of electrons. The charged particles exert a repulsive Coulombic force on each other. Plasma crystals can be formed when the interparticle electrostatic potential exceeds the kinetic energy of particles. A good measure for the formation of plasma crystals is a Coulomb coupling parameter *Γ*. *Γ* is defined as a ratio of the electrostatic potential energy to the kinetic energy of particles. The plasma with *Γ* > 1 is defined as a strongly coupled plasma [5], and Monte Carlo simulation suggests that an ordered structure can be formed when *Γ* > 170 [6].

In 1994, three independent groups simultaneously reported the experimental observation of plasma crystals [7–9]. However, these crystal structures were strongly affected by gravity. Because the electric field in a plasma sheath can compensate for gravity, the structure of plasma crystals can be maintained in a sheath region. Such compression in a direction of gravitational force gives plasma crystals a two-dimensional (2D) structure. To eliminate the gravitational anisotropy, microgravity experiments using the International Space Station and a sounding rocket have been conducted and provided three-dimensional (3D) plasma crystals [10]. The 3D plasma crystals in microgravity experiments show some new phenomena, such as an unexpected void structure and various crystal structures (fcc, bcc, and hcp) [11]. Such microgravity experiments give promising results; however, they are time-consuming and costly. To overcome the time and cost issues, a groundbased "microgravity" experiment is greatly needed. Previously, several concepts have been proposed. Applying thermophoretic force was reported as an effective approach to cancel gravity [12, 13]. The shell structure of dust particles, "Coulomb balls," was found. Another approach is the magnetic field. It was reported that the magnetic field applied on super-paramagnetic particles can compensate for the gravity [14]. In the case of colloidal dispersion, gravity affects the crystal structures in a similar manner. Microgravity experiments were conducted as is for dusty plasmas, which revealed that the crystal structure under microgravity is basically random stacking of hexagonally close-packed planes alone and suggested that fcc, which is often observed in ground-based experiments, is induced by gravity [15]. Buoyancy is employed to compensate for gravity in ground-based experiments [16]. Buoyancy can be tuned by changing the ratio of H2O and D2O; the density of media can be matched to that of microparticles.

In the present study, buoyancy in supercritical fluids (SCFs) is proposed as a means for compensating for gravity in dusty plasmas. SCF is a state of matter whose temperature and pressure exceed those of the critical point (*T*c, *P*c), as described in **Figure 1**. The critical point is the end point of the vapor pressure curve, above which it is impossible to distinguish whether the phase is gas or liquid, and the phase is defined as SCF. SCF has liquid-like solubility, high density, and gas-like low viscosity. Owing to such unique properties, SCF has been applied to fabrication processes of such materials as aerogels and nanoparticles [17]. The critical temperature *T*c varies with molecules. CO2 and Xe are frequently used as SCF media, because they have *T*c near room temperature, 304 and 290 K, respectively. The critical pressure *P*c of each medium is 7.38 and 5.84 MPa, respectively; therefore, temperature control by a water cooling/heating system, and the application of pressure by a pump can provide SCF states of CO2 and Xe. The properties of SCF that are significant for the application to dusty plasmas are density and viscosity. **Figure 2a** shows the dependence of the density of CO2, Xe, and typical liquid (H2O and ethanol) on pressure. The temperatures of Xe and CO2 are their own *T*c, and those of water and ethanol are set to room temperature (293 K). The densities of H2O and ethanol show little change against pressure. Meanwhile, those of CO2 and

**97**

microgravity condition.

*Dusty Plasmas in Supercritical Carbon Dioxide DOI: http://dx.doi.org/10.5772/intechopen.88768*

T*-*P *phase diagram of a matter focusing around the critical point.*

*respectively (the values were obtained from the NIST database [25]).*

**Figure 1.**

**Figure 2.**

Xe successively increase with increasing pressure and reach or exceed those of typical liquids above *P*c, where they become SCF. This means that controllable buoyancy can be applied to microparticles in SCF, which possibly results in the realization of pseudo-microgravity conditions for dusty plasmas. **Figure 2b** shows the dependence of the viscosity of each medium on pressure. Despite the large density of SCF, the viscosities are only one-tenth those of typical liquids. Therefore, microparticles in SCF experience little viscous drag, which delays reaching a condition of thermal equilibrium, as is observed in colloidal dispersion [18]. Therefore, SCFs are considered to be attractive media suitable for the generation of dusty plasmas in a pseudo-

*Dependences of the density (a) and the viscosity (b) of Xe, CO2, H2O, and ethanol on pressure: the temperatures of the former two and the latter two are set to their own* T*c and room temperature (293 K),* 

The generation of nonthermal plasmas in SCF is challenging, because the pressure is so high that applying higher voltage is necessary based on Paschen's law. The discharge plasmas in SCFs have been successfully generated by employing electrodes with a gap on the order of micrometers [19]. The possibilities of the plasmas in SCF for application to carbon nanomaterial syntheses and unique phenomena, such as a large decrease of breakdown voltage near the critical point, were shown [20]. For application to the generation of dusty plasmas, surface dielectric barrier discharge (DBD) in the field-emitting regime was employed [21]. The breakdown voltages of CO2 for the discharges in the "standard regime," in which electrons are

*Dusty Plasmas in Supercritical Carbon Dioxide DOI: http://dx.doi.org/10.5772/intechopen.88768*

#### **Figure 1.**

*Progress in Fine Particle Plasmas*

Ikezi theoretically predicted that microparticles (diameter, 0.3–30 μm) embedded in a commonly used plasma processing possibly form an ordered structure or plasma crystal [4]. Microparticles inside the plasma become negatively charged because of the higher mobility of electrons. The charged particles exert a repulsive Coulombic force on each other. Plasma crystals can be formed when the interparticle electrostatic potential exceeds the kinetic energy of particles. A good measure for the formation of plasma crystals is a Coulomb coupling parameter *Γ*. *Γ* is defined as a ratio of the electrostatic potential energy to the kinetic energy of particles. The plasma with *Γ* > 1 is defined as a strongly coupled plasma [5], and Monte Carlo simulation

In 1994, three independent groups simultaneously reported the experimental

In the present study, buoyancy in supercritical fluids (SCFs) is proposed as a means for compensating for gravity in dusty plasmas. SCF is a state of matter whose temperature and pressure exceed those of the critical point (*T*c, *P*c), as described in **Figure 1**. The critical point is the end point of the vapor pressure curve, above which it is impossible to distinguish whether the phase is gas or liquid, and the phase is defined as SCF. SCF has liquid-like solubility, high density, and gas-like low viscosity. Owing to such unique properties, SCF has been applied to fabrication processes of such materials as aerogels and nanoparticles [17]. The critical temperature *T*c varies with molecules. CO2 and Xe are frequently used as SCF media, because they have *T*c near room temperature, 304 and 290 K, respectively. The critical pressure *P*c of each medium is 7.38 and 5.84 MPa, respectively; therefore, temperature control by a water cooling/heating system, and the application of pressure by a pump can provide SCF states of CO2 and Xe. The properties of SCF that are significant for the application to dusty plasmas are density and viscosity. **Figure 2a** shows the dependence of the density of CO2, Xe, and typical liquid (H2O and ethanol) on pressure. The temperatures of Xe and CO2 are their own *T*c, and those of water and ethanol are set to room temperature (293 K). The densities of H2O and ethanol show little change against pressure. Meanwhile, those of CO2 and

observation of plasma crystals [7–9]. However, these crystal structures were strongly affected by gravity. Because the electric field in a plasma sheath can compensate for gravity, the structure of plasma crystals can be maintained in a sheath region. Such compression in a direction of gravitational force gives plasma crystals a two-dimensional (2D) structure. To eliminate the gravitational anisotropy, microgravity experiments using the International Space Station and a sounding rocket have been conducted and provided three-dimensional (3D) plasma crystals [10]. The 3D plasma crystals in microgravity experiments show some new phenomena, such as an unexpected void structure and various crystal structures (fcc, bcc, and hcp) [11]. Such microgravity experiments give promising results; however, they are time-consuming and costly. To overcome the time and cost issues, a groundbased "microgravity" experiment is greatly needed. Previously, several concepts have been proposed. Applying thermophoretic force was reported as an effective approach to cancel gravity [12, 13]. The shell structure of dust particles, "Coulomb balls," was found. Another approach is the magnetic field. It was reported that the magnetic field applied on super-paramagnetic particles can compensate for the gravity [14]. In the case of colloidal dispersion, gravity affects the crystal structures in a similar manner. Microgravity experiments were conducted as is for dusty plasmas, which revealed that the crystal structure under microgravity is basically random stacking of hexagonally close-packed planes alone and suggested that fcc, which is often observed in ground-based experiments, is induced by gravity [15]. Buoyancy is employed to compensate for gravity in ground-based experiments [16]. Buoyancy can be tuned by changing the ratio of H2O and D2O; the density of media

suggests that an ordered structure can be formed when *Γ* > 170 [6].

can be matched to that of microparticles.

**96**

T*-*P *phase diagram of a matter focusing around the critical point.*

#### **Figure 2.**

*Dependences of the density (a) and the viscosity (b) of Xe, CO2, H2O, and ethanol on pressure: the temperatures of the former two and the latter two are set to their own* T*c and room temperature (293 K), respectively (the values were obtained from the NIST database [25]).*

Xe successively increase with increasing pressure and reach or exceed those of typical liquids above *P*c, where they become SCF. This means that controllable buoyancy can be applied to microparticles in SCF, which possibly results in the realization of pseudo-microgravity conditions for dusty plasmas. **Figure 2b** shows the dependence of the viscosity of each medium on pressure. Despite the large density of SCF, the viscosities are only one-tenth those of typical liquids. Therefore, microparticles in SCF experience little viscous drag, which delays reaching a condition of thermal equilibrium, as is observed in colloidal dispersion [18]. Therefore, SCFs are considered to be attractive media suitable for the generation of dusty plasmas in a pseudomicrogravity condition.

The generation of nonthermal plasmas in SCF is challenging, because the pressure is so high that applying higher voltage is necessary based on Paschen's law. The discharge plasmas in SCFs have been successfully generated by employing electrodes with a gap on the order of micrometers [19]. The possibilities of the plasmas in SCF for application to carbon nanomaterial syntheses and unique phenomena, such as a large decrease of breakdown voltage near the critical point, were shown [20]. For application to the generation of dusty plasmas, surface dielectric barrier discharge (DBD) in the field-emitting regime was employed [21]. The breakdown voltages of CO2 for the discharges in the "standard regime," in which electrons are

dominantly provided by ionizations, increase with increasing pressure, while it was found that field emission plays a major role in generating discharges under high pressure, which results in discharges with breakdown voltages as low as 2 kV. The surface DBD in the field-emitting regime is considered to be suitable for the generation of dusty plasmas in SCF, because the discharge with such low breakdown voltages possibly generates less heat and causes less damage to microparticles and electrodes.

In this chapter, a study on dusty plasmas in supercritical CO2 (scCO2) is introduced. In Section 2, the first report on the generation of dusty plasmas in SCF, on the formation of plasma crystals in scCO2, and on the estimation of the particle charges is described [22]. Section 3 covers the realization of a pseudo-microgravity environment for dusty plasmas in scCO2 and the 3D arrangement of particles [23]. In Section 4, the outlook for dusty plasmas in SCF, which includes the further applications of pseudo-microgravity conditions and the comparisons with other strongly coupled plasmas, is briefly discussed.

## **2. Motion of particles in dusty plasmas generated in scCO2**

The particle motion in dusty plasmas generated in scCO2 was analyzed. The particles were electrically charged by the surface DBD in the field-emitting regime and showed the formation of an ordered structure above the electrodes. The analysis of the equation of motion revealed that the charge of a particle was on the order of −104 to −105 *e* C (*e*: elementary charge). The kinetic energy of a particle was estimated by recording the motion with a high-speed camera. The estimated Coulomb coupling parameter was 102 –104 , from which the formation of strongly coupled plasmas was confirmed.

## **2.1 Experimental approach**

**Figure 3** shows a schematic diagram of the experimental setup for the generation of the dusty plasmas in scCO2. As shown in **Figure 3a**, CO2 pressurized by a high-pressure pump with a cooling circuit was introduced into the high-pressure chamber. The temperature inside the chamber was controlled by a water cooling/ heating system. The temperature and pressure of CO2 were 304.1–305.8 K and 0.10–8.33 MPa, respectively, which includes gaseous, liquid, and SCF states of CO2. High voltages of up to 10 kVp-p with a frequency of 0.1–10 kHz were applied to the electrode. The microparticles (divinylbenzene resin; diameter, 30.0 μm; density, 1.19 g cm<sup>−</sup><sup>3</sup> ) were placed on the etched region of the electrodes before applying voltages. The density of the particles was larger than that of CO2 in this experimental condition; therefore, a pseudo-microgravity condition could not be achieved. The interest of this study is the charging and the motion of the particles in scCO2. The motion of microparticles was observed by an optical microscope through a sapphire window under light-emitting diode (LED) illumination, as shown in **Figure 3b**. The high-speed camera was employed for the detection of the fast motion with frame rates up to 1000 fps. The motion in the direction of gravitational force was observed through a mirror. **Figure 3c** shows the detailed structure of the electrodes. The upper, powered electrode consists of a Cu film deposited on polyimide film, etched in a linear fashion, and closed by Ag pastes to confine particles. This rectangular region is referred to as the "etched region." The thicknesses of the Cu films and polyimide films were 30 and 20 μm, respectively. Ag paste was deposited on the reverse side and connected to the grounded chamber.

**99**

**Figure 3.**

**Figure 4.**

*Dusty Plasmas in Supercritical Carbon Dioxide DOI: http://dx.doi.org/10.5772/intechopen.88768*

**2.2 Generation of dusty plasmas in scCO2**

white, which might be derived from atomic emission.

*1 atm (c) (adapted from [22], © IOP Publishing Ltd., all rights reserved).*

**Figure 4** shows photos of the electrodes and the plasmas generated with them without microparticles placed. **Figure 4a** shows photos of the electrodes whose etching width was 670 μm. **Figure 4b** shows the plasmas generated in scCO2 in the field-emitting regime. The red luminescence is consistent with the previous optical emission spectroscopy measurement, which suggests that this is induced by electron-neutral bremsstrahlung [24]. **Figure 4c** shows the plasmas generated at atmospheric pressure in the standard regime, whose luminescence was blue or

*Images of electrodes (a), surface DBD in field-emitting regime in scCO2 (b), and in standard-regime in CO2 at* 

*Schematic of the experimental setup for the generation of the dusty plasmas in scCO2: (a) top view, (b) side* 

*view, and (c) the electrodes (adapted from [22], © IOP Publishing Ltd., all rights reserved).*

In the experiments with particles, the particles in the etched region of the electrodes started to move intensely near the electrode surface when the voltage of ~3.0 kVp-p with a frequency of 10 kHz was applied, while many particles adhered to the Cu film and the Ag pastes, as shown in **Figure 5**. The moving particles were possibly electrically charged and accelerated by the AC electric field. When the frequency was decreased to 1 kHz, several particles floated above the electrodes, as shown **Figure 6**. **Figure 6a** shows the top view, where it is confirmed that the

*Dusty Plasmas in Supercritical Carbon Dioxide DOI: http://dx.doi.org/10.5772/intechopen.88768*

#### **Figure 3.**

*Progress in Fine Particle Plasmas*

coupled plasmas, is briefly discussed.

to −105

coupled plasmas was confirmed.

**2.1 Experimental approach**

density, 1.19 g cm<sup>−</sup><sup>3</sup>

the grounded chamber.

Coulomb coupling parameter was 102

and electrodes.

order of −104

dominantly provided by ionizations, increase with increasing pressure, while it was found that field emission plays a major role in generating discharges under high pressure, which results in discharges with breakdown voltages as low as 2 kV. The surface DBD in the field-emitting regime is considered to be suitable for the generation of dusty plasmas in SCF, because the discharge with such low breakdown voltages possibly generates less heat and causes less damage to microparticles

In this chapter, a study on dusty plasmas in supercritical CO2 (scCO2) is introduced. In Section 2, the first report on the generation of dusty plasmas in SCF, on the formation of plasma crystals in scCO2, and on the estimation of the particle charges is described [22]. Section 3 covers the realization of a pseudo-microgravity environment for dusty plasmas in scCO2 and the 3D arrangement of particles [23]. In Section 4, the outlook for dusty plasmas in SCF, which includes the further applications of pseudo-microgravity conditions and the comparisons with other strongly

The particle motion in dusty plasmas generated in scCO2 was analyzed. The particles were electrically charged by the surface DBD in the field-emitting regime and showed the formation of an ordered structure above the electrodes. The analysis of the equation of motion revealed that the charge of a particle was on the

was estimated by recording the motion with a high-speed camera. The estimated

**Figure 3** shows a schematic diagram of the experimental setup for the generation of the dusty plasmas in scCO2. As shown in **Figure 3a**, CO2 pressurized by a high-pressure pump with a cooling circuit was introduced into the high-pressure chamber. The temperature inside the chamber was controlled by a water cooling/ heating system. The temperature and pressure of CO2 were 304.1–305.8 K and 0.10–8.33 MPa, respectively, which includes gaseous, liquid, and SCF states of CO2. High voltages of up to 10 kVp-p with a frequency of 0.1–10 kHz were applied to the electrode. The microparticles (divinylbenzene resin; diameter, 30.0 μm;

–104

applying voltages. The density of the particles was larger than that of CO2 in this experimental condition; therefore, a pseudo-microgravity condition could not be achieved. The interest of this study is the charging and the motion of the particles in scCO2. The motion of microparticles was observed by an optical microscope through a sapphire window under light-emitting diode (LED) illumination, as shown in **Figure 3b**. The high-speed camera was employed for the detection of the fast motion with frame rates up to 1000 fps. The motion in the direction of gravitational force was observed through a mirror. **Figure 3c** shows the detailed structure of the electrodes. The upper, powered electrode consists of a Cu film deposited on polyimide film, etched in a linear fashion, and closed by Ag pastes to confine particles. This rectangular region is referred to as the "etched region." The thicknesses of the Cu films and polyimide films were 30 and 20 μm, respectively. Ag paste was deposited on the reverse side and connected to

*e* C (*e*: elementary charge). The kinetic energy of a particle

) were placed on the etched region of the electrodes before

, from which the formation of strongly

**2. Motion of particles in dusty plasmas generated in scCO2**

**98**

*Schematic of the experimental setup for the generation of the dusty plasmas in scCO2: (a) top view, (b) side view, and (c) the electrodes (adapted from [22], © IOP Publishing Ltd., all rights reserved).*

**Figure 4.**

*Images of electrodes (a), surface DBD in field-emitting regime in scCO2 (b), and in standard-regime in CO2 at 1 atm (c) (adapted from [22], © IOP Publishing Ltd., all rights reserved).*

## **2.2 Generation of dusty plasmas in scCO2**

**Figure 4** shows photos of the electrodes and the plasmas generated with them without microparticles placed. **Figure 4a** shows photos of the electrodes whose etching width was 670 μm. **Figure 4b** shows the plasmas generated in scCO2 in the field-emitting regime. The red luminescence is consistent with the previous optical emission spectroscopy measurement, which suggests that this is induced by electron-neutral bremsstrahlung [24]. **Figure 4c** shows the plasmas generated at atmospheric pressure in the standard regime, whose luminescence was blue or white, which might be derived from atomic emission.

In the experiments with particles, the particles in the etched region of the electrodes started to move intensely near the electrode surface when the voltage of ~3.0 kVp-p with a frequency of 10 kHz was applied, while many particles adhered to the Cu film and the Ag pastes, as shown in **Figure 5**. The moving particles were possibly electrically charged and accelerated by the AC electric field. When the frequency was decreased to 1 kHz, several particles floated above the electrodes, as shown **Figure 6**. **Figure 6a** shows the top view, where it is confirmed that the

**Figure 5.** *Image of the particles moving near the electrode surface.*

particles aligned at the center of the etched region. The particles showed motion along the electrode edge, whose direction is indicated in **Figure 6a**. **Figure 6b** shows the side view. The particles were levitated at a height of 500 μm or more above the electrode surface. These phenomena could be observed in the condition of high-pressure gaseous, liquid, and supercritical CO2. It was considered that the particles levitated after the applied frequency was lowered, because the particles are likely to follow the AC electric fields with lower frequency, which is discussed in detail later.

## **2.3 Numerical simulations of the particle motion**

The equation of motion of charged particles in scCO2 shown below was numerically solved:

$$m\frac{\text{d}^2x}{\text{d}t^2} = -mg + \rho Vg - k\frac{\text{d}x}{\text{d}t} + QE(x)\sin 2\pi ft\tag{1}$$

**101**

**Figure 6.**

**Figure 7.**

*Publishing Ltd., all rights reserved).*

which its sign becomes inverted.

charge and peak voltage *QU* is 1.5 × 105

*from [22], © IOP Publishing Ltd., all rights reserved).*

*Dusty Plasmas in Supercritical Carbon Dioxide DOI: http://dx.doi.org/10.5772/intechopen.88768*

the *x*-*z*-plane, and it is assumed for the calculation that the *y*-direction is infinitely extended. The position of interest is *x* = 0, where the particles aligned in the experiments. **Figure 8** shows the electric field along the *z*-direction *E*(*z*) at *x* = 0. However the applied voltage is large, the absolute value of *E*(*z*) is the highest at the electrode surface, and *E*(*z*) becomes 0 at a certain height from the electrode surface, above

*Contour map of the calculated electric potential near the electrodes with the applied voltage of 5 kV (adapted* 

*Images of particles aligned above the electrodes: (a) top view and (b) side view (adapted from [22], © IOP* 

The time evolution of the height from the electrode surface of the charged particle is shown in **Figure 9**. The condition is scCO2, where the pressure is

, product of particle

*e* C kV, and applied frequency is 1.0 kHz.

8.07 MPa, temperature is 305.8 K, density is 0.641 g cm<sup>−</sup><sup>3</sup>

where *m* is the particle mass, *z* is the height of the particle from the electrode surface, *t* is the time, *g* is the gravitational constant, *ρ* is the mass density of CO2, *V* is the volume of the particle, *k* = 6*πηr* is the viscous drag coefficient, *η* is the viscosity of CO2 and was obtained from the NIST database [25], *r* is the radius of the particle, *Q* is the particle charge, *E*(*z*) is the electric field along *z*, and *f* is the applied frequency. *E*(*z*) was obtained from the derivative of the electric potential calculated with the finite-element method using freely available software [26]. **Figure 7** shows the contour map of the electric potential near the electrodes with an applied voltage of 5 kV. Here, *z* is defined as the opposite direction of the gravitational force so that z = 0 corresponds to the electrode surface (the surface of the polyimide film in the etched region); *x* and *y* are defined as the direction parallel to the electrode surface, as indicated in **Figure 6**. **Figure 7** is the cross-sectional view of the electrodes in

*Dusty Plasmas in Supercritical Carbon Dioxide DOI: http://dx.doi.org/10.5772/intechopen.88768*

#### **Figure 6.**

*Progress in Fine Particle Plasmas*

particles aligned at the center of the etched region. The particles showed motion along the electrode edge, whose direction is indicated in **Figure 6a**. **Figure 6b** shows the side view. The particles were levitated at a height of 500 μm or more above the electrode surface. These phenomena could be observed in the condition of high-pressure gaseous, liquid, and supercritical CO2. It was considered that the particles levitated after the applied frequency was lowered, because the particles are likely to follow the AC electric fields with lower frequency, which is discussed

The equation of motion of charged particles in scCO2 shown below was numeri-

where *m* is the particle mass, *z* is the height of the particle from the electrode surface, *t* is the time, *g* is the gravitational constant, *ρ* is the mass density of CO2, *V* is the volume of the particle, *k* = 6*πηr* is the viscous drag coefficient, *η* is the viscosity of CO2 and was obtained from the NIST database [25], *r* is the radius of the particle, *Q* is the particle charge, *E*(*z*) is the electric field along *z*, and *f* is the applied frequency. *E*(*z*) was obtained from the derivative of the electric potential calculated with the finite-element method using freely available software [26]. **Figure 7** shows the contour map of the electric potential near the electrodes with an applied voltage of 5 kV. Here, *z* is defined as the opposite direction of the gravitational force so that z = 0 corresponds to the electrode surface (the surface of the polyimide film in the etched region); *x* and *y* are defined as the direction parallel to the electrode surface, as indicated in **Figure 6**. **Figure 7** is the cross-sectional view of the electrodes in

\_ d*z*

<sup>d</sup>*<sup>t</sup>* <sup>+</sup> *QE*(*z*) sin2*ft* (1)

= −*mg* + *Vg* − *k*

**100**

in detail later.

**Figure 5.**

cally solved:

*m*

**2.3 Numerical simulations of the particle motion**

*Image of the particles moving near the electrode surface.*

d2 \_*z* d *t* 2

*Images of particles aligned above the electrodes: (a) top view and (b) side view (adapted from [22], © IOP Publishing Ltd., all rights reserved).*

#### **Figure 7.**

*Contour map of the calculated electric potential near the electrodes with the applied voltage of 5 kV (adapted from [22], © IOP Publishing Ltd., all rights reserved).*

the *x*-*z*-plane, and it is assumed for the calculation that the *y*-direction is infinitely extended. The position of interest is *x* = 0, where the particles aligned in the experiments. **Figure 8** shows the electric field along the *z*-direction *E*(*z*) at *x* = 0. However the applied voltage is large, the absolute value of *E*(*z*) is the highest at the electrode surface, and *E*(*z*) becomes 0 at a certain height from the electrode surface, above which its sign becomes inverted.

The time evolution of the height from the electrode surface of the charged particle is shown in **Figure 9**. The condition is scCO2, where the pressure is 8.07 MPa, temperature is 305.8 K, density is 0.641 g cm<sup>−</sup><sup>3</sup> , product of particle charge and peak voltage *QU* is 1.5 × 105 *e* C kV, and applied frequency is 1.0 kHz.

**Figure 8.**

*Electric field along* z*-direction for each applied voltage at x = 0, which is indicated by the dotted line in*  **Figure 7** *(adapted from [22], © IOP Publishing Ltd., all rights reserved).*

Three types of initial condition were tried for the calculation. The first one was the particle on the electrode surface (*z* = 0), the second was the particle at the potential valley (*Ez* = 0), and the last was the particle staying far from the electrode surface (*z* = 3 mm). Whichever initial condition was used, the particle settled at a certain *z* after enough time passed. **Figure 10** shows the magnified graph of the particle position with the initial condition *z* = 0. The particle moves upward very rapidly and reaches the maximum height within 10 ms. After that, it moves downward and settles at *z* between 650 and 660 μm. The inset shows the particle motion after the settlement. The particle shows oscillation with an amplitude of 5 μm and a period of 1 ms. The frequency of this oscillation corresponds to the applied AC frequency. This oscillation is too small and fast to visualize in the scale of **Figure 9**.

## **2.4 Estimation of charge and coulomb coupling parameter**

The equilibrium positions of the particle were plotted against the product of the particle charge and the applied peak voltage *QU* for each AC frequency, as shown in **Figure 11**. The condition is the same as the calculation shown in **Figure 9** except for *QU*. The error bars indicate the oscillation amplitudes. The equilibrium height increases with increasing *QU* and lowering the AC frequency. A higher *QU* means stronger electric fields applied on the particle. The particle is likely to follow the AC field with a lower frequency, which is also confirmed by the fact that the oscillation amplitudes are larger for the lower frequency. The experimental result that the particles levitated after the lowering of the AC frequency can be explained by this analysis. The plots in **Figure 11** have important implications for the particle charge. In fact, the particle charges can be estimated from the measured height of the particle from the electrode surface. The range of the particle charge estimated from the experimental results was on the order of (104 –105 )*e* C. The particle charge is reported to be (1–3) × 103 *e* C with the orbital motion limited theory [27], (103 –105 )*e* C with the analysis of particle motion [28], and on the order of 106 *e* C with Faraday cup measurement [29]. Therefore, the estimated particle charge is considered to be of a reasonable order. These analyses lack the information on the sign of the particle charges, although it is a common understanding that particles in a discharge plasma get negatively charged because

**103**

**Figure 9.**

**Figure 10.**

*Publishing Ltd., all rights reserved).*

from the electrodes by field emission.

*Dusty Plasmas in Supercritical Carbon Dioxide DOI: http://dx.doi.org/10.5772/intechopen.88768*

of the higher mobility of electrons. Therefore, DC offset was applied to clarify the sign. **Figure 12** shows the changes of the particle positions with DC offset. When negative bias was applied, the particle moved downward. Meanwhile, the particle moved upward with the positive offset. This behavior is consistent with the numerical simulation results for the negatively charged particle, as shown **Figure 13**. The average position of the particle is 820 μm with the applied offset of +50 V and 656 μm without offset. It is considered that the particles get negatively charged by the discharges in scCO2 because of the flux of the electrons emitted

*Magnified graph of* **Figure 9** *for the initial position of electrode surface (data adapted from [22]).*

*Calculated time evolution of the height of charged particle for each initial position (adapted from [22], © IOP* 

The kinetic energy of a particle was estimated with high-speed imaging. The motion along the *y*-direction is shown in **Figure 6a**. The movie was recorded with a frame rate of 125 fps and a duration of 3.848 s. **Figure 6a** is captured from this movie. The velocities of three particles were in the range of (1.4–2.1) × 102 μm s<sup>−</sup><sup>1</sup>

,

#### **Figure 9.**

*Progress in Fine Particle Plasmas*

the scale of **Figure 9**.

**Figure 8.**

Three types of initial condition were tried for the calculation. The first one was the particle on the electrode surface (*z* = 0), the second was the particle at the potential valley (*Ez* = 0), and the last was the particle staying far from the electrode surface (*z* = 3 mm). Whichever initial condition was used, the particle settled at a certain *z* after enough time passed. **Figure 10** shows the magnified graph of the particle position with the initial condition *z* = 0. The particle moves upward very rapidly and reaches the maximum height within 10 ms. After that, it moves downward and settles at *z* between 650 and 660 μm. The inset shows the particle motion after the settlement. The particle shows oscillation with an amplitude of 5 μm and a period of 1 ms. The frequency of this oscillation corresponds to the applied AC frequency. This oscillation is too small and fast to visualize in

*Electric field along* z*-direction for each applied voltage at x = 0, which is indicated by the dotted line in* 

The equilibrium positions of the particle were plotted against the product of the particle charge and the applied peak voltage *QU* for each AC frequency, as shown in **Figure 11**. The condition is the same as the calculation shown in **Figure 9** except for *QU*. The error bars indicate the oscillation amplitudes. The equilibrium height increases with increasing *QU* and lowering the AC frequency. A higher *QU* means stronger electric fields applied on the particle. The particle is likely to follow the AC field with a lower frequency, which is also confirmed by the fact that the oscillation amplitudes are larger for the lower frequency. The experimental result that the particles levitated after the lowering of the AC frequency can be explained by this analysis. The plots in **Figure 11** have important implications for the particle charge. In fact, the particle charges can be estimated from the measured height of the particle from the electrode surface. The range of the particle charge estimated from the experimental results was on the order of

)*e* C. The particle charge is reported to be (1–3) × 103

–105

estimated particle charge is considered to be of a reasonable order. These analyses lack the information on the sign of the particle charges, although it is a common understanding that particles in a discharge plasma get negatively charged because

*e* C with the orbital

)*e* C with the analysis of particle motion [28],

*e* C with Faraday cup measurement [29]. Therefore, the

**2.4 Estimation of charge and coulomb coupling parameter**

**Figure 7** *(adapted from [22], © IOP Publishing Ltd., all rights reserved).*

**102**

(104 –105

motion limited theory [27], (103

and on the order of 106

*Calculated time evolution of the height of charged particle for each initial position (adapted from [22], © IOP Publishing Ltd., all rights reserved).*

**Figure 10.** *Magnified graph of* **Figure 9** *for the initial position of electrode surface (data adapted from [22]).*

of the higher mobility of electrons. Therefore, DC offset was applied to clarify the sign. **Figure 12** shows the changes of the particle positions with DC offset. When negative bias was applied, the particle moved downward. Meanwhile, the particle moved upward with the positive offset. This behavior is consistent with the numerical simulation results for the negatively charged particle, as shown **Figure 13**. The average position of the particle is 820 μm with the applied offset of +50 V and 656 μm without offset. It is considered that the particles get negatively charged by the discharges in scCO2 because of the flux of the electrons emitted from the electrodes by field emission.

The kinetic energy of a particle was estimated with high-speed imaging. The motion along the *y*-direction is shown in **Figure 6a**. The movie was recorded with a frame rate of 125 fps and a duration of 3.848 s. **Figure 6a** is captured from this movie. The velocities of three particles were in the range of (1.4–2.1) × 102 μm s<sup>−</sup><sup>1</sup> ,

#### **Figure 11.**

*Equilibrium position of the particle against the product of particle charge and applied peak voltage QU (© IOP Publishing Ltd., all rights reserved).*

#### **Figure 12.**

*Change in the height of the particle by applying DC offset.*

from which the kinetic energy was (1.8–4.5) × 104 K. Assuming that the interparticle distance was 700 mm and the particle charges were −(104 –105 )*e* C, this system had a Coulomb coupling parameter on the order of 102 –104 and is considered to be a strongly coupled plasma.

To the authors' knowledge, this is the first report on the formation of strongly coupled dusty plasmas in a dense medium. Almost all the reports employ RF plasmas in a vacuum to generate dusty plasmas. There are a few reports on the strongly coupled dusty plasmas generated in thermal plasmas under atmospheric pressure, where CeO2 particles get positively charged by the thermal emission of electrons [30]. No other studies on the generation of dusty plasmas in a dense medium, such as high-pressure gas, liquid, and SCF, have been reported. Furthermore, this study is the first report on the formation of plasma crystals using DBD. Conventional plasma crystals have been formed in DC or RF glow discharge with metallic electrodes. DBD, which is usually employed for generating low-temperature plasmas under relatively high pressure, such as atmospheric-pressure plasmas, has not been used for plasma crystals up to now.

**105**

*Dusty Plasmas in Supercritical Carbon Dioxide DOI: http://dx.doi.org/10.5772/intechopen.88768*

**3. Pseudo-microgravity environment for dusty plasmas in scCO2**

*Time evolution of the height of the particle with and without DC offset (© IOP Publishing Ltd., all rights* 

was analyzed by the estimation of the Coulomb coupling parameter.

particles employed were lighter. Their mass density was 0.5 g cm<sup>−</sup><sup>3</sup>

**3.1 Experimental approach**

**Figure 13.**

*reserved).*

The charging of particles by discharge in scCO2 was clarified, and the particle charges were successfully estimated, as shown in the previous section. However, the microparticles used in Section 2 were so heavy that the pseudo-microgravity environment was hardly realized. In this section, lighter resin particles were used. Compensation for gravitational force by buoyancy was confirmed by controlling the balance between gravitational force and buoyancy, suggesting the formation of a microgravity environment for dusty plasmas in scCO2. The formation behavior

The experimental setup and the simulation method were basically the same as in Section 2. The width of the etched region of the upper electrodes was 2.7 mm. The

tal conditions were *mg* > *ρVg* for condition (a); *mg* ~ *ρVg* for conditions (b), (c), and (d); and *mg* < *ρVg* for condition (e) as shown in **Figure 14**. The density of CO2 for each condition is shown in **Figure 14**. The temperature was set to 31.7–32.1°C, slightly higher than the critical temperature of CO2 (31.1°C). Condition (a) has a pressure of 6.92 MPa, where CO2 is gaseous, and its density is lower than that of the

particle. CO2 is a supercritical condition in conditions (b), (c), (d), and (e).

**3.2 Generation of dusty plasmas in scCO2 with varying density of media**

The particles were also arranged in the *x-y* (horizontal)-plane, as shown in **Figure 16**, which confirmed the 3D arrangement of particles resulting from the

As in the previous section, several particles got levitated and trapped above the electrodes after the AC frequency was decreased. The applied AC voltage was 5 kVp-p, and the frequency was initially 10 kHz and decreased to 155 Hz. **Figure 15i** is the side view of the particle arrangement with condition (a). The particles formed a single-layer structure. However, when the CO2 density was controlled in condition (c), particles were arranged in the gravitational direction, as shown in **Figure 15ii**.

. The experimen-

*Progress in Fine Particle Plasmas*

**104**

from which the kinetic energy was (1.8–4.5) × 104

*Change in the height of the particle by applying DC offset.*

strongly coupled plasma.

**Figure 12.**

**Figure 11.**

*IOP Publishing Ltd., all rights reserved).*

used for plasma crystals up to now.

had a Coulomb coupling parameter on the order of 102

ticle distance was 700 mm and the particle charges were −(104

To the authors' knowledge, this is the first report on the formation of strongly coupled dusty plasmas in a dense medium. Almost all the reports employ RF plasmas in a vacuum to generate dusty plasmas. There are a few reports on the strongly coupled dusty plasmas generated in thermal plasmas under atmospheric pressure, where CeO2 particles get positively charged by the thermal emission of electrons [30]. No other studies on the generation of dusty plasmas in a dense medium, such as high-pressure gas, liquid, and SCF, have been reported. Furthermore, this study is the first report on the formation of plasma crystals using DBD. Conventional plasma crystals have been formed in DC or RF glow discharge with metallic electrodes. DBD, which is usually employed for generating low-temperature plasmas under relatively high pressure, such as atmospheric-pressure plasmas, has not been

*Equilibrium position of the particle against the product of particle charge and applied peak voltage QU (©* 

K. Assuming that the interpar-

)*e* C, this system

and is considered to be a

–105

–104

**Figure 13.** *Time evolution of the height of the particle with and without DC offset (© IOP Publishing Ltd., all rights reserved).*

## **3. Pseudo-microgravity environment for dusty plasmas in scCO2**

The charging of particles by discharge in scCO2 was clarified, and the particle charges were successfully estimated, as shown in the previous section. However, the microparticles used in Section 2 were so heavy that the pseudo-microgravity environment was hardly realized. In this section, lighter resin particles were used. Compensation for gravitational force by buoyancy was confirmed by controlling the balance between gravitational force and buoyancy, suggesting the formation of a microgravity environment for dusty plasmas in scCO2. The formation behavior was analyzed by the estimation of the Coulomb coupling parameter.

## **3.1 Experimental approach**

The experimental setup and the simulation method were basically the same as in Section 2. The width of the etched region of the upper electrodes was 2.7 mm. The particles employed were lighter. Their mass density was 0.5 g cm<sup>−</sup><sup>3</sup> . The experimental conditions were *mg* > *ρVg* for condition (a); *mg* ~ *ρVg* for conditions (b), (c), and (d); and *mg* < *ρVg* for condition (e) as shown in **Figure 14**. The density of CO2 for each condition is shown in **Figure 14**. The temperature was set to 31.7–32.1°C, slightly higher than the critical temperature of CO2 (31.1°C). Condition (a) has a pressure of 6.92 MPa, where CO2 is gaseous, and its density is lower than that of the particle. CO2 is a supercritical condition in conditions (b), (c), (d), and (e).

## **3.2 Generation of dusty plasmas in scCO2 with varying density of media**

As in the previous section, several particles got levitated and trapped above the electrodes after the AC frequency was decreased. The applied AC voltage was 5 kVp-p, and the frequency was initially 10 kHz and decreased to 155 Hz. **Figure 15i** is the side view of the particle arrangement with condition (a). The particles formed a single-layer structure. However, when the CO2 density was controlled in condition (c), particles were arranged in the gravitational direction, as shown in **Figure 15ii**. The particles were also arranged in the *x-y* (horizontal)-plane, as shown in **Figure 16**, which confirmed the 3D arrangement of particles resulting from the

compensation of the gravity. It was observed that some particles exchanged their positions with their neighbors. Furthermore, the structure is not periodic—in other words, it is liquid-like. The particles formed a single- or double-layer structure with condition (e), as shown in **Figure 15iii**. Of all the experimental conditions, 3D structures were formed in the pseudo-microgravity conditions (b), (c), and (d). The window of the density of CO2 for the formation of 3D plasma crystals was found to be ±0.2 g cm<sup>−</sup><sup>3</sup> compared with that of the particles.

The particles showed oscillation in the gravitational direction with a frequency equal to the applied AC frequency. In condition (c), the particles staying above and below the dashed line indicated in **Figure 15ii** showed oscillations antiphase to each other, the amplitudes of which were 20 and 60 μm, respectively.

## **3.3 Numerical simulations for pseudo-microgravity condition**

To analyze the motion of a particle in the experimental conditions, Eq. (1), explained in the previous section, was applied. The initial position of the particle was set to *z* = 0. The particle charge was assumed to be −7 × 104 *e* C based on the results explained in the previous section. **Figure 17** shows the calculated time evolution of a particle for each density of CO2. The particle starts to move upward after *t* = 0 and reaches a steady height in all conditions. The inset shows the magnified graph with the particles staying at a steady position. The steady height increases with increasing CO2 density and approaches the position where the electric field is zero at any time with *ρVg* approaching *mg*. Additionally, the particles oscillate with applied AC frequency. The oscillation amplitude was smaller when *mg* = *ρVg* than in any other condition.

## **3.4 Estimation of Coulomb coupling parameter**

For the estimation of the Coulomb coupling parameter, the kinetic energies of both the oscillation and thermal motion of the particles were taken into consideration, instead of the thermal energy. The latter was assumed to be the same as the temperature of the chamber because of the small heat generation in the surface DBD in the field-emitting regime [24]. The oscillation energy was calculated as *mA*<sup>2</sup> (2*πf*) 2 /2 on the supposition that the oscillation is harmonic, where *A* is the

#### **Figure 14.**

*Dependence of CO2 density on pressure: the density of the particle is indicated by the red broken line, and the experimental conditions (a)–(e) are plotted (reprinted from [23], with the permission of AIP Publishing).*

**107**

**Figure 16.**

*AIP Publishing).*

**Figure 15.**

oscillation amplitude of a particle. The dependence of the oscillation amplitude on CO2 density is shown in **Figure 18a**. The amplitude has the minimum value when *mg* = *ρVg*, as suggested in **Figure 17**. The calculated oscillation energy was in the range of 9.4 × 10<sup>−</sup>24–3.4 × 10−15 J, while the thermal random motion energy

*Top view of the trapped particles with the condition of mg = ρVg (reprinted from [23], with the permission of* 

*Side view of the trapped particles above the electrodes with the condition of mg > ρVg (i), mg = ρVg (ii), and* 

*mg < ρVg (iii) (reprinted from [23], with the permission of AIP Publishing).*

*Dusty Plasmas in Supercritical Carbon Dioxide DOI: http://dx.doi.org/10.5772/intechopen.88768* *Dusty Plasmas in Supercritical Carbon Dioxide DOI: http://dx.doi.org/10.5772/intechopen.88768*

#### **Figure 15.**

*Progress in Fine Particle Plasmas*

found to be ±0.2 g cm<sup>−</sup><sup>3</sup>

compensation of the gravity. It was observed that some particles exchanged their positions with their neighbors. Furthermore, the structure is not periodic—in other words, it is liquid-like. The particles formed a single- or double-layer structure with condition (e), as shown in **Figure 15iii**. Of all the experimental conditions, 3D structures were formed in the pseudo-microgravity conditions (b), (c), and (d). The window of the density of CO2 for the formation of 3D plasma crystals was

 compared with that of the particles. The particles showed oscillation in the gravitational direction with a frequency equal to the applied AC frequency. In condition (c), the particles staying above and below the dashed line indicated in **Figure 15ii** showed oscillations antiphase to each

To analyze the motion of a particle in the experimental conditions, Eq. (1), explained in the previous section, was applied. The initial position of the particle was

explained in the previous section. **Figure 17** shows the calculated time evolution of a particle for each density of CO2. The particle starts to move upward after *t* = 0 and reaches a steady height in all conditions. The inset shows the magnified graph with the particles staying at a steady position. The steady height increases with increasing CO2 density and approaches the position where the electric field is zero at any time with *ρVg* approaching *mg*. Additionally, the particles oscillate with applied AC frequency. The oscillation amplitude was smaller when *mg* = *ρVg* than in any other condition.

For the estimation of the Coulomb coupling parameter, the kinetic energies of both the oscillation and thermal motion of the particles were taken into consideration, instead of the thermal energy. The latter was assumed to be the same as the temperature of the chamber because of the small heat generation in the surface DBD in the field-emitting regime [24]. The oscillation energy was calculated as

/2 on the supposition that the oscillation is harmonic, where *A* is the

*Dependence of CO2 density on pressure: the density of the particle is indicated by the red broken line, and the experimental conditions (a)–(e) are plotted (reprinted from [23], with the permission of AIP Publishing).*

*e* C based on the results

other, the amplitudes of which were 20 and 60 μm, respectively.

**3.3 Numerical simulations for pseudo-microgravity condition**

set to *z* = 0. The particle charge was assumed to be −7 × 104

**3.4 Estimation of Coulomb coupling parameter**

**106**

**Figure 14.**

*mA*<sup>2</sup>

(2*πf*) 2 *Side view of the trapped particles above the electrodes with the condition of mg > ρVg (i), mg = ρVg (ii), and mg < ρVg (iii) (reprinted from [23], with the permission of AIP Publishing).*

#### **Figure 16.**

*Top view of the trapped particles with the condition of mg = ρVg (reprinted from [23], with the permission of AIP Publishing).*

oscillation amplitude of a particle. The dependence of the oscillation amplitude on CO2 density is shown in **Figure 18a**. The amplitude has the minimum value when *mg* = *ρVg*, as suggested in **Figure 17**. The calculated oscillation energy was in the range of 9.4 × 10<sup>−</sup>24–3.4 × 10−15 J, while the thermal random motion energy

#### **Figure 17.**

*Calculated time evolution of the height of the particle with each CO2 density (reprinted from [23], with the permission of AIP Publishing).*

#### **Figure 18.**

*Dependence of the amplitude of the oscillation of the particle (a) and the Coulomb coupling parameter (b) (reprinted from [23], with the permission of AIP Publishing).*

was 4.2 × 10<sup>−</sup>21 J. The particle charge and the interparticle distance are assumed to be −7 × 104 *e* C and 250 μm, respectively. **Figure 18b** shows the dependence of the Coulomb coupling parameter on CO2 density. The coupling parameter shows the maximum value when *mg* = *ρVg* because of the suppression of the oscillation energy. The coupling parameter is possibly enhanced with the aid of the gravity compensation by buoyancy. The calculated Coulomb coupling parameter for condition (c), which is the closest to the condition with *mg* = *ρVg* in this study, is less than the previously reported criterion for the transition from liquid to solid (*Γ* > 170) [31–33], which is consistent with the observation of liquid-like behavior.

**109**

*Dusty Plasmas in Supercritical Carbon Dioxide DOI: http://dx.doi.org/10.5772/intechopen.88768*

**4. Outlook for dusty plasmas in SCF**

The pseudo-microgravity conditions for dusty plasmas provide the opportunity to study collective phenomena without any anisotropy. **Figure 19** summarizes this study and shows its further application, as discussed below. Microgravity experiments using huge, expensive pieces of apparatus, such as a space station, largely limit the number of experimental trials. Therefore, some exciting discoveries have

One of the unexplored phenomena is the rotation of a particle on its own axis, which was suggested by Sato at a workshop held at Tohoku University in 2014 [34]. Before going into details, the similarity between dusty plasma physics and solid-state physics should be considered. It is useful for finding novel phenomena in dusty plasmas to learn from solid-state physics. The idea of plasma crystals is similar to that of strongly correlated electron systems in a solid. In commonly used plasmas, ions and electrons have a large kinetic energy (=0.01–1 eV) and small interparticle electrostatic energy owing to small particle charge and large interparticle distance (low number density), which results in a very small Coulomb coupling parameter. Therefore, strongly coupled plasmas (*Γ* > 1) can hardly be realized. The introduction of dust particles changes that situation. The particles collect many electrons and have a large electric charge. In addition, they have a large mass to prevent acceleration and small kinetic energy, which results in a large Coulomb coupling parameter and possible realization of strongly coupled plasmas. Meanwhile, electron-electron interaction has great importance in the field of solid-state physics. The conducting electrons in a simple metal, such as Cu and Al, have no or weak interactions between electrons and can move freely. Some transition metal oxides and rare-earth oxides possibly show the localization of electrons and insulating behavior because of large electrostatic repulsion between electrons, even if they have a partially filled electron band in a simple band picture. The so-called Mott insulator shows various phenomena, such as a metal-insulator transition, magnetic transition, and superconducting transition with or without applying temperature change, chemical doping, and so on. Mott insulators have been one of the most extensively studied subjects [35]. There seem to be similarities between dusty plasmas and a strongly correlated electron system, given that, in both cases, novel ordered phases appear with strengthening of the interactions, which was considered to be ignorable. Some of the exciting phenomena observed in a strongly correlated electron system possibly emerge in

One of the examples might be the rotation of a particle on its own axis, which is like the spin of an electron. The positions of particles in dusty plasmas have been successfully tracked; however, there are no reports on their rotation to the authors' knowledge. It may be difficult to observe because the particle size is small (several tens of micrometers at largest). Larger particles are likely to sink because they are heavy. However, particle size does not matter in microgravity experiments. Using millimeter-sized particles possibly reveals the details of particle motion. The pseudo-microgravity condition can also make experiments with larger particles possible, because particle size does not matter so long as the density of the media is

The applicability of heavier particles in microgravity experiments provides opportunities to use functional oxide or metal particles. Many studies on dusty plasmas employ resin particles, which possess no notable functional properties except for lightness. Using functional particles might make dusty plasmas

**4.1 Pseudo-microgravity condition**

dusty plasmas in a similar manner.

matched to that of the particle.

been possibly missed.

*Progress in Fine Particle Plasmas*

**108**

be −7 × 104

**Figure 18.**

**Figure 17.**

*permission of AIP Publishing).*

was 4.2 × 10<sup>−</sup>21 J. The particle charge and the interparticle distance are assumed to

*Dependence of the amplitude of the oscillation of the particle (a) and the Coulomb coupling parameter* 

*Calculated time evolution of the height of the particle with each CO2 density (reprinted from [23], with the* 

Coulomb coupling parameter on CO2 density. The coupling parameter shows the maximum value when *mg* = *ρVg* because of the suppression of the oscillation energy. The coupling parameter is possibly enhanced with the aid of the gravity compensation by buoyancy. The calculated Coulomb coupling parameter for condition (c), which is the closest to the condition with *mg* = *ρVg* in this study, is less than the previously reported criterion for the transition from liquid to solid (*Γ* > 170) [31–33],

which is consistent with the observation of liquid-like behavior.

*(b) (reprinted from [23], with the permission of AIP Publishing).*

*e* C and 250 μm, respectively. **Figure 18b** shows the dependence of the

## **4. Outlook for dusty plasmas in SCF**

## **4.1 Pseudo-microgravity condition**

The pseudo-microgravity conditions for dusty plasmas provide the opportunity to study collective phenomena without any anisotropy. **Figure 19** summarizes this study and shows its further application, as discussed below. Microgravity experiments using huge, expensive pieces of apparatus, such as a space station, largely limit the number of experimental trials. Therefore, some exciting discoveries have been possibly missed.

One of the unexplored phenomena is the rotation of a particle on its own axis, which was suggested by Sato at a workshop held at Tohoku University in 2014 [34]. Before going into details, the similarity between dusty plasma physics and solid-state physics should be considered. It is useful for finding novel phenomena in dusty plasmas to learn from solid-state physics. The idea of plasma crystals is similar to that of strongly correlated electron systems in a solid. In commonly used plasmas, ions and electrons have a large kinetic energy (=0.01–1 eV) and small interparticle electrostatic energy owing to small particle charge and large interparticle distance (low number density), which results in a very small Coulomb coupling parameter. Therefore, strongly coupled plasmas (*Γ* > 1) can hardly be realized. The introduction of dust particles changes that situation. The particles collect many electrons and have a large electric charge. In addition, they have a large mass to prevent acceleration and small kinetic energy, which results in a large Coulomb coupling parameter and possible realization of strongly coupled plasmas. Meanwhile, electron-electron interaction has great importance in the field of solid-state physics. The conducting electrons in a simple metal, such as Cu and Al, have no or weak interactions between electrons and can move freely. Some transition metal oxides and rare-earth oxides possibly show the localization of electrons and insulating behavior because of large electrostatic repulsion between electrons, even if they have a partially filled electron band in a simple band picture. The so-called Mott insulator shows various phenomena, such as a metal-insulator transition, magnetic transition, and superconducting transition with or without applying temperature change, chemical doping, and so on. Mott insulators have been one of the most extensively studied subjects [35]. There seem to be similarities between dusty plasmas and a strongly correlated electron system, given that, in both cases, novel ordered phases appear with strengthening of the interactions, which was considered to be ignorable. Some of the exciting phenomena observed in a strongly correlated electron system possibly emerge in dusty plasmas in a similar manner.

One of the examples might be the rotation of a particle on its own axis, which is like the spin of an electron. The positions of particles in dusty plasmas have been successfully tracked; however, there are no reports on their rotation to the authors' knowledge. It may be difficult to observe because the particle size is small (several tens of micrometers at largest). Larger particles are likely to sink because they are heavy. However, particle size does not matter in microgravity experiments. Using millimeter-sized particles possibly reveals the details of particle motion. The pseudo-microgravity condition can also make experiments with larger particles possible, because particle size does not matter so long as the density of the media is matched to that of the particle.

The applicability of heavier particles in microgravity experiments provides opportunities to use functional oxide or metal particles. Many studies on dusty plasmas employ resin particles, which possess no notable functional properties except for lightness. Using functional particles might make dusty plasmas

functional: susceptible to a magnetic field using magnetic particles [36], photocatalytic using photocatalyst particles, and so on. Such functional dusty plasmas are attractive as a functional fluid whose flow and reactivity can be controlled by a magnetic field or light irradiation. In addition, functional particles, such as magnetic or ferroelectric ones, are expected to show the interparticle interaction via such properties. Such interaction yields intentionally introduced anisotropy, which possibly causes the emergence of the crystal structures that still have not been observed in dusty plasmas or novel phase transitions.

## **4.2 Dusty plasmas in dense media**

Another aspect of dusty plasmas in SCF is a density of media higher than in dusty plasmas in vacuum and lower than or comparable to that in colloidal dispersion. In colloidal dispersion, interparticle interaction is mediated via solvent flow, unlike in the case of dusty plasmas, where particles interact directly with each other via electrostatic force. Dusty plasmas in SCF are considered to be placed at the transient region, as shown in **Figure 20**. Changes of the mode of the interactions might be observable in dusty plasmas in SCF.

In this study, the existence of electrons and ions in the region of trapped particles and their screening effects were ignored. That region is somewhat far from surface

**Figure 19.**

*Overview and further application of this study.*

#### **Figure 20.**

*Interparticle interaction modes in dusty plasmas in vacuum, colloidal dispersion, and the transient region, dusty plasmas in SCF.*

**111**

*Dusty Plasmas in Supercritical Carbon Dioxide DOI: http://dx.doi.org/10.5772/intechopen.88768*

**5. Conclusion**

**Acknowledgements**

encouragement.

**Conflict of interest**

The authors declare no conflict of interest.

DBD; therefore, there seem to be few electrons and ions when SCF is taken as a high-pressure gas, because their lifetime is too short under high pressure owing to frequent collisions. However, SCF also has a liquid-like characteristic. Solvated ions in a liquid have a long lifetime, and it was reported that electrons generated by discharge plasmas can be solvated [37]. The lifetime of ions and electrons in SCF is possibly so long that they can reach where the particles stay. The behaviors of the electrons and ions in plasmas generated in SCF are still not fully understood. Further analysis of the interparticle interaction in dusty plasmas in SCF could serve as a probe to clarify it.

Plasma crystals, realized in dusty plasmas, provide opportunities to study statistical phenomena and lattice dynamics in a crystal. However, in ground-based experiments, gravity imposes a large anisotropy on plasma crystals, which results in their 2D structure. This study on the dusty plasmas in SCF aimed at overcoming the problems caused by gravity that hinder research on dusty plasmas. The particles were successfully electrically charged by the surface DBD in scCO2. The estimation of the particle charge and the analysis of the particle motion confirmed the formation of strongly coupled plasmas. With the density of scCO2 matched to that of particles, which means a pseudo-microgravity condition for the particles, 3D-ordered structures were successfully formed. The pseudo-microgravity conditions provide opportunities to find novel phenomena and to develop functional dusty plasmas. In addition, the dusty plasmas in SCF can be considered as the intermediate phase between dusty plasmas in vacuum and colloidal dispersion. SCF is left largely unexplored with regard to the media for the generation of strongly coupled plasmas. Our pioneering works has been opening a novel field of strongly coupled plasmas.

This work was supported financially by a Grant-in-Aid for Scientific Research on Innovative Areas (Frontier Science of Interactions between Plasmas and Nanointerfaces, Grant No. 21110002) and the Grant-in-Aid for Challenging Exploratory Research (Grant No. 15K13389) from the Ministry of Education, Culture, Sports, Science, and Technology (MEXT) of Japan. We would like to thank Sekisui Chemical Co., Ltd. for providing us the fine resin particles (HB-2051) used in this study. One of the authors of this chapter, K.T., would like to give special thanks to Professor O. Ishihara (Chubu University) for his valuable suggestions and

*Dusty Plasmas in Supercritical Carbon Dioxide DOI: http://dx.doi.org/10.5772/intechopen.88768*

DBD; therefore, there seem to be few electrons and ions when SCF is taken as a high-pressure gas, because their lifetime is too short under high pressure owing to frequent collisions. However, SCF also has a liquid-like characteristic. Solvated ions in a liquid have a long lifetime, and it was reported that electrons generated by discharge plasmas can be solvated [37]. The lifetime of ions and electrons in SCF is possibly so long that they can reach where the particles stay. The behaviors of the electrons and ions in plasmas generated in SCF are still not fully understood. Further analysis of the interparticle interaction in dusty plasmas in SCF could serve as a probe to clarify it.

## **5. Conclusion**

*Progress in Fine Particle Plasmas*

functional: susceptible to a magnetic field using magnetic particles [36], photocatalytic using photocatalyst particles, and so on. Such functional dusty plasmas are attractive as a functional fluid whose flow and reactivity can be controlled by a magnetic field or light irradiation. In addition, functional particles, such as magnetic or ferroelectric ones, are expected to show the interparticle interaction via such properties. Such interaction yields intentionally introduced anisotropy, which possibly causes the emergence of the crystal structures that still have not been

Another aspect of dusty plasmas in SCF is a density of media higher than in dusty plasmas in vacuum and lower than or comparable to that in colloidal dispersion. In colloidal dispersion, interparticle interaction is mediated via solvent flow, unlike in the case of dusty plasmas, where particles interact directly with each other via electrostatic force. Dusty plasmas in SCF are considered to be placed at the transient region, as shown in **Figure 20**. Changes of the mode of the interactions

In this study, the existence of electrons and ions in the region of trapped particles and their screening effects were ignored. That region is somewhat far from surface

*Interparticle interaction modes in dusty plasmas in vacuum, colloidal dispersion, and the transient region,* 

observed in dusty plasmas or novel phase transitions.

**4.2 Dusty plasmas in dense media**

might be observable in dusty plasmas in SCF.

*Overview and further application of this study.*

**110**

**Figure 20.**

**Figure 19.**

*dusty plasmas in SCF.*

Plasma crystals, realized in dusty plasmas, provide opportunities to study statistical phenomena and lattice dynamics in a crystal. However, in ground-based experiments, gravity imposes a large anisotropy on plasma crystals, which results in their 2D structure. This study on the dusty plasmas in SCF aimed at overcoming the problems caused by gravity that hinder research on dusty plasmas. The particles were successfully electrically charged by the surface DBD in scCO2. The estimation of the particle charge and the analysis of the particle motion confirmed the formation of strongly coupled plasmas. With the density of scCO2 matched to that of particles, which means a pseudo-microgravity condition for the particles, 3D-ordered structures were successfully formed. The pseudo-microgravity conditions provide opportunities to find novel phenomena and to develop functional dusty plasmas. In addition, the dusty plasmas in SCF can be considered as the intermediate phase between dusty plasmas in vacuum and colloidal dispersion. SCF is left largely unexplored with regard to the media for the generation of strongly coupled plasmas. Our pioneering works has been opening a novel field of strongly coupled plasmas.

## **Acknowledgements**

This work was supported financially by a Grant-in-Aid for Scientific Research on Innovative Areas (Frontier Science of Interactions between Plasmas and Nanointerfaces, Grant No. 21110002) and the Grant-in-Aid for Challenging Exploratory Research (Grant No. 15K13389) from the Ministry of Education, Culture, Sports, Science, and Technology (MEXT) of Japan. We would like to thank Sekisui Chemical Co., Ltd. for providing us the fine resin particles (HB-2051) used in this study. One of the authors of this chapter, K.T., would like to give special thanks to Professor O. Ishihara (Chubu University) for his valuable suggestions and encouragement.

## **Conflict of interest**

The authors declare no conflict of interest.

*Progress in Fine Particle Plasmas*

## **Author details**

Yasuhito Matsubayashi1 \*, Noritaka Sakakibara<sup>2</sup> , Tsuyohito Ito2 and Kazuo Terashima2

1 Advanced Coating Technology Research Center, National Institute of Advanced Industrial Science and Technology, Tsukuba, Ibaraki, Japan

2 Department of Advanced Materials Science, Graduate School of Frontier Sciences, The University of Tokyo, Chiba, Japan

\*Address all correspondence to: y-matsubayashi@aist.go.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.

**113**

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*Dusty Plasmas in Supercritical Carbon Dioxide DOI: http://dx.doi.org/10.5772/intechopen.88768*

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[17] Cansell F, Chevalier B, Demourgues A, Etourneau J, Even C, Pessey V, et al. Supercritical fluid processing: A new route for materials synthesis. Journal of Materials

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**Author details**

Kazuo Terashima2

Yasuhito Matsubayashi1

\*, Noritaka Sakakibara<sup>2</sup>

Industrial Science and Technology, Tsukuba, Ibaraki, Japan

\*Address all correspondence to: y-matsubayashi@aist.go.jp

Sciences, The University of Tokyo, Chiba, Japan

provided the original work is properly cited.

1 Advanced Coating Technology Research Center, National Institute of Advanced

© 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,

2 Department of Advanced Materials Science, Graduate School of Frontier

, Tsuyohito Ito2

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Section 3

Generation of Nanoparticles

Section 3
