CÁC THAM SỐ CHUYỂN ĐỘNG ELECTRON CỦA HỖN HỢP KHÍ XE-HE TRONG PHÓNG ĐIỆN KHÍ

In the present study, authors have calculated and analysed electron transport coefficients of Xe-He mixture gases in gas discharge using a two-term approximation of[r]

ELECTRON TRANSPORT PARAMETERS OF THE XE-HE MIXTURE GASES

IN GAS DISCHARGE

Pham Xuan Hien 1* , Tran Thanh Son 2 , and Do Anh Tuan 1

1 Hung Yen University of Technology and Education 2

Electric Power University, Ha Noi, Vietnam

SUMMARY

The physical characteristics of Xe-He mixture gases in gas discharge are very important to study light source for not only plasma display panels (PDPs) but also other industrial applications In the present study, authors have calculated and analysed electron transport coefficients of Xe-He mixture gases in gas discharge using a two-term approximation of the Boltzmann equation for energy These electron transport coefficients in Xe-He mixture gases are electron drift velocity, density-normalized longitudinal diffusion coefficient, transverse diffusion coefficient, and the Townsend first ionization

Keywords: gas discharge; mixture gas; Xe-He; electron transport coefficients

INTRODUCTION*

Plasma display panel (PDP) has been widely

used to fabricate commercial display, digital

display [1-3] Normally, these DPDs with a

size larger than 50 inches and a thickness less

than 10 cm include millions small discharge

cells [2] In each cell, a rare gas such as Xe is

often used to ignite and extinguish

successively In order to reduce the discharge

on set voltage and sustain a uniform glow

discharge, He or Ne gas is often added with

suitable mixture ratios [2] Moreover, Xe-He

and Xe-Ne mixtures allow the ionization and

avalanche effect, which are the most

important component material of panel x-ray

detectors Because of above reasons, the

physical and chemical data and applications

of these mixtures have been reported by many

authors H Lee et al [2] and ref therein

studied the characteristics of these mixtures

with different mixture ratios and suggested

the new Xe-He based gas mixture for gas

microstrip detector (GMD) structure Uchida

et al [1] have calculated and analysed the

electron swarm parameters and related

properties in Xe-He and Xe-Ne mixtures

using the Boltzmann equation analysis

However, these coefficients are still

unavailable over the wide rage of E/N values

*

Email: xuanhiendk2@gmail.com

In order to understand and study physical processes and physical characteristics of

Xe-Ne gas mixtures in gas discharge, the electron drift velocity, W, density-normalized longitudinal coefficient, NDL, density-normalized transverse coefficient, NDT, ratio

of longitudinal coefficient (DL) and electron mobility (), and Townsend first ionization coefficient (/N) in Xe-Ne mixtures were calculated in previously study [4] With the same purpose, in the present study, these coefficients for Xe-He gas mixtures in gas discharge were also calculated and analysed using the two-term approximation of Boltzmann equation for energy The results of this study, along with the results in [4] provide the better understanding for these mixtures These are useful for selecting good choices in many industrial applications using these mixtures

BOLTZMANN EQUATION FOR ENERGY The following two-term approximation of Boltzmann equation for energy, which was suggested by Tagashira [5] and successfully applied for Xe-Ne [4], BF3-Ar and BF3-SiH4

[6], TEOS-Ar and TEOS-O2 [7] mixtures, is also briefly represented The present analysis used the electron swarm method The electron transport coefficients, which include the

electron drift velocity, the density-normalized

longitudinal diffusion coefficient, the

Townsend first ionization coefficient and the

electron attachment coefficient are obtained

from electron energy distribution function

(EEDF) The EEDF can be deduced from

solution of Boltzmann’s equation In this study,

a backward prolongation technique, along with

an initial condition and input data are used for

computation The initial condition and the input

data are listed as follows:

The initial conditions are: the gas number

density N = 3.5353×1016 cm-3; the partition

ratio of the remaining energy after ionization

collision is 0.5

The input data contain electron collision cross

sections of objective gases; the temperature of

gases; ratio of E/N; max and the division

number over the range of 0-max

The relationship between the electron

transport coefficients with EEDF and electron

collision cross sections are given in

expressions (1-4)

The electron drift velocity calculated from the

solution of electron energy distribution function,

f(, E/N), of the Boltzmann equation is:

1/ 2

m 0

where  is the electron energy, m is the

electron mass, e is the elementary charge and

qm(ε) is the momentum-transfer cross section

The density-normalized longitudinal diffusion

coefficient is:

1 1

V



where V1 is the speed of the electron, qT is the

total cross section; Fn andn (n = 0, 1, 2) are,

respectively, the electron energy distributions

of various orders and their eigenvalues V1,

n

 , 0n, and An are given by

1/ 2

1

2e

m

   (2.1)

1

0 V N 1 0 q F d i 0

     (2.2)

1

T

V E

3N q



1 0n V N 1 0 q F d i n

     (2.4)

n 0 n

A F d  (2.5) where qi is the ionization cross section The Townsend first ionization coefficient is:

1/ 2

1/ 2 i I

/ N f ( , E / N) q ( )d



where I is the ionization onset energy and

qi() is the ionization cross section

The electron attachment coefficient is:

1/ 2

1/ 2 a 0



where qa() is the attachment cross section RESULTS AND DISCUSSION

It is necessary to use the consistent electron collision cross section set for both of Xe and

He atoms to reproduce the reliable electron transport coefficients in Xe-He mixtures Therefore, the electron collision cross section for Xe atom determined by Hashimoto and Nakamura [8] and He atom determined by Hayashi [9] were used throughout in this study The accuracy of the electron collision cross section set for each gas was confirmed

to be consistent with all electron transport coefficients in each pure gas For the sake of comparison and justification the validity of the sets of collision cross sections and that of two-term approximation of the Boltzmann equation, the measured electron transport coefficients in each gas have been showed in Figs 1-4 The calculated electron transport coefficients in each pure gas are in good agreement with the measurements over the wide E/N range

Electron drift velocity (W)

The results for the electron drift velocities, W,

as functions of E/N for Xe-He mixtures calculated in the E/N range 0.01 < E/N < 800

Td (1 Td = 10-17 V.cm2) by a two-term

approximation of the Boltzmann equation are

shown in Fig 1 Slight regions of the NDC

(negative differential conductivity)

phenomena in 70% and 90% Xe-He mixtures

are observed in the E/N range 0.2 < E/N < 3

Td The NDC is relatively shallow in these

cases The occurrences of these phenomena

are due to the Ramsauer-Townsend minimum

(RTM) of the elastic momentum transfer

cross sections of the Xe atom In this binary

mixtures, the values of W are suggested to be

between those of the pure gases over E/N > 1

Td and these values grow linearly over E/N >

10 Td The increased concentration of Xe

atom caused increase of electron drift velocity

characteristics of Xe-He mixtures

Figure 1 Electron drift velocity, W, as

functions of E/N for the Xe-He mixtures with

1%, 5%, 10%, 30%, 50%, 70% and 90% Xe

The solid line and symbols show present W

values calculated using a two-term

approximation of the Boltzmann equation for

the Xe-He mixtures The symbols show the

experimental values for He and Xe from [10]

Transversal Diffusion Coefficients (ND L

and ND T )

Figure 2 Transverse diffusion coefficient coefficient, NDT, as functions of E/N for the Xe-He mixtures with 1%, 5%, 10%, 30%, 50%, 70% and 90% Xe The solid line and symbols show present NDT values calculated using a two-term approximation of the Boltzmann equation for the Xe-He mixtures

Figure 3 Density-normalized longitudinal diffusion coefficient, NDL, as functions of E/N for the Xe-He mixtures with 1%, 5%, 10%, 30%, 50%, 70% and 90% Xe The solid line and symbols show present NDL values calculated using a two-term approximation of the Boltzmann equation for the Xe-He mixtures The results for the density-normalized longitudinal diffusion coefficients, NDL and transverse diffusion coefficient coefficient,

NDT, as functions of E/N for Xe-He mixtures calculated in the E/N range 0.1 < E/N < 800

Td by a two-term approximation of the Boltzmann equation are shown in Figs 2 and

3, respectively In these binary mixtures, the values of NDL and the NDT are suggested to

be between those of the pure gases over E/N

> 8 Td and E/N > 3 Td, respectively On the other hand, in Fig 3, the NDC regions are clearly indicated in NDL curves in Xe-He mixtures and the NDC region moves to the right to higher percentage of Xe

The Townsend first ionization coefficient

The first Townsend ionization coefficient, α/N, as functions of E/N for Xe-He mixtures calculated by a two-term approximation of the Boltzmann equation are shown in Figs 4 The

remarkable synergism in the Townsend first

ionization coefficient α/N is displayed in 1%,

5% and 10% Xe-He mixtures In these cases,

the values of α/N in the Xe-He mixtures

mixture are greater than those in pure Xe and

He atoms

Figure 4 Townsend first ionization

coefficient, /N as functions of E/N for the

Xe-He mixtures with 1%, 5%, 10%, 30%,

50%, 70% and 90% Xe The solid line and

symbols show present /N values calculated

using a two-term approximation of the

Boltzmann equation for the Xe-He mixtures

The solid curves show present α /N values

calculated for the pure Xe and pure He atoms

The symbols show the measured values for

Xe and He from [10], respectively

CONCLUSIONS

The electron drift velocity,

density-normalized longitudinal diffusion coefficient,

transversal diffusion coefficient, and

Townsend first ionization coefficient in the

Xe-He mixtures are calculated using a

two-term approximation of the Boltzmann

equation for the energy in the E/N range of

0.1-800 Td The NDC phenomena in these

binary gas mixtures are suggested for electron

drift velocity and density-normalized

longitudinal diffusion coefficients The

remarkable synergism in the Townsend first

ionization coefficient was also found out

REFERENCES

1 S Uchida, H Sugawara, Y Sakai, T Watanabe

and B.-H Hong, “Boltzmann equation analysis of electron swarm parameters and related properties

of Xe-He and Xe-Ne mixtures used for plasma display panels,” J Phys D: Appl Phys 33 (2000)

62–71

2 H Lee, K Lee, S Eom, H Park and J Kang,

“Simulation study of plasma display panel-based flat panel x-ray detector,” IEEE Transactions on

Nuclear Science 60.2 (2013): 908-912

3 S V Avtaeva, “Electron Parameters in Xe-Ne Mixtures,” High Temperature, 2010, Vol 48, No

3, pp 321–327

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Tươi, “Tính toán và phân tích các hệ số chuyển động của electron trong phóng điện khí của hỗn hợp khí Xe-Ne,” Tạp chí Nghiên cứu Khoa học và

Công nghệ Quân sự, Số 26, 8 – 2013, trang 66-72

5 H Tagashira, Y Sakai, and S Sakamoto, “The development of electron avalanches in argon at high E/N values II Boltzmann equation analysis,”

J Phys D, vol 10, no 7, pp 1051–1063 (May 1977)

6 Pham Xuan Hien, Byung-Hoon Jeon, and Do

Anh Tuan, “Electron Collision Cross Sections for the BF 3 Molecule and Electron Transport Coefficients in BF 3 -Ar and BF 3 -SiH 4 Mixtures,”

Journal of the Physical Society of Japan, vol 82,

no 3, pp 034301-1–8, Mar 2013

7 Do Anh Tuan and Byung-Hoon Jeon, “Electron Collision Cross Sections for the Tetraethoxysilane Molecule and Electron Transport Coefficients in Tetraethoxysilane-O 2 and Tetraethoxysilane-Ar Mixtures,” Journal of the Physical Society of

Japan, vol.81, no 6, pp 064301-1–8, Jun 2012

8 Hashimoto and Y Nakamura, Papers of Gas Discharge Technical Committee, vol ED-90-61 (Japan: IEE), 1990, as quoted in M Suzuki, T Taniguchi, N Yoshimura, and H Tagashira,

“Momentum Transfer Cross Section of Xenon Deducted from Electron Drift Velocity Data,” J

Phys D, vol 25, no 1, pp.50-56 (Jan 1992)

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TÓM TẮT

CÁC THAM SỐ CHUYỂN ĐỘNG ELECTRON CỦA HỖN HỢP KHÍ XE-HE

TRONG PHÓNG ĐIỆN KHÍ

Phạm Xuân Hiển 1* , Trần Thanh Sơn 2

, Đỗ Anh Tuấn 1

1 Trường Đại học Sư phạm Kỹ thuật Hưng Yên,

2 Trường Đại học Điện lực, Hà Nội, Việt Nam

Các đặc tính vật lý của hỗn hợp khí Xe-He trong phóng điện khí là rất quan trọng để nghiên cứu nguồn sang không chỉ cho bảng hiển thị plasma mà còn cả cho các ứng dụng công nghiệp Trong nghiên cứu này, nhóm tác giả đã tính toán và phân tích các hệ số chuyển động electron của hỗn hợp khí Xe-He trong phóng điện khí sử dụng thuật toán xấp xỉ bậc hai phương trình Boltzmann Các hệ số chuyển động electron này trong hỗn hợp khí Xe-He bao gồm vận tốc chuyển dịch electron, hệ số chuyển động ngang và dọc và hệ số ion hóa Townsend thứ nhất

Keywords: phóng điện khí; hỗn hợp khí; Xe-He; hệ số chuyển động electron

*

Email: xuanhiendk2@gmail.com