• Title/Summary/Keyword: two-term approximation of the Boltzmann equation

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The study of electron transport coefficients in pure $CF_4$ by 2-term approximation of the Boltzmann equation (2항근사 볼츠만 방정식을 이용한 $CF_4$분자가스의 전자수송계수의 해석)

  • Jeon, Byung-Hoon;Ha, Sung-Chul
    • Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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    • 2001.05c
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    • pp.29-32
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    • 2001
  • We measured the electron transport coefficients(the electron drift velocity, W, and the longitudinal diffusion coefficient, $D_L$) in pure $CF_4$ over the E/N range from 0.04 Td to 250 Td by the double shutter drift tube. And these electron transport coefficients in pure $CF_4$ were calculated over the E/N range from 0.01 to 250 Td at 1 Torr by using the two-term approximation of the Boltzmann equation.

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Study on the Electron Transport Coefficient in Mixtures of $CF_4$ and Ar ($CF_4-Ar$ 혼합기체의 전자수송계수에 관한 연구)

  • Kim, Sang-Nam
    • The Transactions of the Korean Institute of Electrical Engineers P
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    • v.56 no.1
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    • pp.1-5
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    • 2007
  • Study on the electron transport coefficient in mixtures of CF4 and Ar, have been analyzed over a range of the reduced electric field strength between 0.1 and 350[Td] by the two-term approximation of the Boltzmann equation (BEq.) method and the Monte Carlo simulation (MCS). The calculations of electron swarm parameters require the knowledge of several collision cross-sections of electron beam. Thus, published momentum transfer, ionization, vibration, attachment, electronic excitation, and dissociation cross-sections of electrons for $CF_4$ and Ar, were used. The differences of the transport coefficients of electrons in $CF_4$ mixtures of Ar, have been explained by the deduced energy distribution functions for electrons and the complete collision cross-sections for electrons. The results of the Boltzmann equation and the Monte Carlo simulation have been compared with the data presented by several workers. The deduced transport coefficients for electrons agree reasonably well with the experimental and simulation data obtained by Nakamura and Hayashi. The energy distribution function of electrons in $CF_4-Ar$ mixtures shows the Maxwellian distribution for energy. That is, $f({\varepsilon})$ has the symmetrical shape whose axis of symmetry is a most probably energy. The proposed theoretical simulation techniques in this work will be useful to predict the fundamental process of charged particles and the breakdown properties of gas mixtures. A two-term approximation of the Boltzmann equation analysis and Monte Carlo simulation have been used to study electron transport coefficients.

The analysis of dependence on the gas number density in $SF_{6}$-Ar mixtures ($SF_{6}$-Ar혼합가스에서의 압력 의존도 해석)

  • 전병훈;하성철
    • Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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    • 2002.07a
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    • pp.248-251
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    • 2002
  • We measured the electron drift velocity, W, in 0.5% $SF_{6}$-Ar mixture over the E/N range from 30 Td to 300 Td and gas pressure range from 0.1 to 8 Torr by the double shutter drift tube with a variable drift distance. This coefficient in the mixture was calculated over the same E/N and gas pressure range by using the two-term approximation of the Boltzmann equation. And the measured and calculated values at different gas number density at each E/N was appreciable dependence in the results on the gas number density,

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The Dependence on the Gas Pressure in SF6 Molecular Gas (SF6분자가스의 압력 의존도)

  • Jeon, Byung-Hoon
    • Journal of the Korean Institute of Electrical and Electronic Material Engineers
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    • v.20 no.9
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    • pp.816-820
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    • 2007
  • We measured the electron drift velocity, W, in 0.5% $SF_6-Ar$ mixture over the E/N range from 30 Td to 300 Td and gas pressure range from 0.1 to 0.5 Torr by the double shutter drift tube with a variable drift distance, and calculated over the same E/N and gas pressure range by using the two-term approximation of the Boltzmann equation. The measured and calculated values at different gas pressure at each E/N was appreciable dependence in the results on the gas pressure.

The Drift Velocity of Electrons in CF4, CH4, Ar Mixtures Gas (CF4, CH4, Ar 혼합기체의 전자이동속도)

  • Kim, Sang-Nam
    • The Transactions of the Korean Institute of Electrical Engineers P
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    • v.60 no.3
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    • pp.105-109
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    • 2011
  • Drift Velocity of Electrons in pure $CF_4$, $CH_4$ and mixtures of $CF_4$ and Ar. Have been analyzed over a range of the reduced electric field strength between 0.1 and 350[Td] by the two-term approximation of the Boltzmann equation (BEq.) method and the Monte Carlo simulation (MCS). The results of the Boltzmann equation and the Monte Carlo simulation have been compared with the data presented by several workers. The deduced transport coefficients for electrons agree reasonably well with the experimental and simulation data obtained by Nakamura and Hayashi. The energy distribution function of electrons in $CF_4$-Ar mixtures shows the Maxwellian distribution for energy. That is, f(${\varepsilon}$) has the symmetrical shape whose axis of symmetry is a most probably energy. The measured results and the calculated results have been compared each other.

A Simulation of the Energy Distribution Function for Electron in CF4, CH4, Ar Gas Mixtures (시뮬레이션에 의한 CF4, CH4, Ar혼합기체(混合氣體)에서 전자(電子)에너지분포함수)

  • Kim, Sang-Nam
    • The Transactions of the Korean Institute of Electrical Engineers P
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    • v.52 no.1
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    • pp.9-13
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    • 2003
  • Energy Distribution Function in pure $CH_4$, $CF_4$ and mixtures of $CF_4$ and Ar, have been analyzed over a range of the reduced electric field strength between 0.1 and 350[Td] by the two-term approximation of the Boltzmann equation (BEq.) method and the Monte Carlo simulation (MCS). The results of the Boltzmann equation and the Monte Carlo simulation have been compared with the data presented by several workers. The deduced transport coefficients for electrons agree reasonably well with the experimental and simulation data obtained by Nakamura and Hayashi. The energy distribution function of electrons in $CF_4-Ar$ mixtures shows the Maxwellian distribution for energy. That is, $f(\varepsilon)$ has the symmetrical shape whose axis of symmetry is a most probably energy. The measured results and the calculated results have been compared each other.

The Study of Electron Transport coefficients in $SiH_4$-Ar Mixtures by Using Boltzmann Equation Analysis and Monte-Carlo Simulation (볼츠만방정식과 몬테칼로법에 의한 $SiH_4$-Ar 혼합가스의 전자수송계수에 관한 연구)

  • 하성철;전병훈
    • Journal of the Korean Institute of Electrical and Electronic Material Engineers
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    • v.14 no.2
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    • pp.169-174
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    • 2001
  • The electron transport coefficients(the electron drift velocity, W, and the longitudinal and transverse diffusion coefficient, D$_{L}$ and D$_{T}$) in SiH$_4$-Ar mixtures containing 0.5% and 5.0% monosilane were calculated over the E/N range from 0.01 to 300 Td and over the gas pressure range 0.5, 1.0 and 1.5 Torr by the time-of-flight(TOF) method of the Boltzmann equation(BE.) and Monte-Carlo simulation(MCS). The electron energy distribution function in each SiH$_4$-Ar mixtures at E/N=10 Td and L=0.2 cm, which in equilibrium region in the mean electron enregy were compared.red.

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The study on the electron transport coefficients in Neon gas by 2-tenn approximation of the Boltzmann Equation (2항근사 볼츠만 방정식을 이용한 Ne의 전자수송재수 연구)

  • Jeon, Byoung-Hoon;Ha, Sung-Chul;Song, Byoung-Doo
    • Proceedings of the KIEE Conference
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    • 2003.10a
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    • pp.236-238
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    • 2003
  • The electron transport coefficients, the electron drift velocity W, the longitudinal diffusion coefficient $ND_L$ and $D_L/\mu$, in pure Ne were calculated over the wide E/N range from 0.01 to 800 Td at 1 Torr by two-term approximation of the Boltzmann equation for determination of electron collision cross sections set and for quantitative characteristic analysis of Ne molecular gas.

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Electron Energy Distribution function in CH4 by MCS-BEq (MCS-BEq에 의한 CH4기체에서 전자에너지 분포함수)

  • Kim, Sang-Nam
    • The Transactions of the Korean Institute of Electrical Engineers P
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    • v.62 no.1
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    • pp.18-22
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    • 2013
  • This paper describes the information for quantitative simulation of weakly ionized plasma. We must grasp the meaning of the plasma state condition to utilize engineering application and to understand materials of plasma state. Using quantitative simulations of weakly ionized plasma, we can analyze gas characteristic. In this paper, the electron transport characteristic in $CH_4$ has been analysed over the E/N range 0.1~300[Td], at the 300[$_{\circ}\;K$] by the two term approximation Boltzmann equation method and Monte Carlo Simulation. Boltzmann equation method has also been used to predict swarm parameter using the same cross sections as input. The behavior of electron has been calculated to give swarm parameter for the electron energy distribution function has been analysed in $CH_4$ at E/N=10, 100 for a case of the equilibrium region in the mean energy. A set of electron collision cross section has been assembled and used in Monte Carlo simulation to predict values of swarm parameters. The result of Boltzmann equation and Monte Carlo Simulation has been compared with experimental data by Ohmori, Lucas and Carter. The swarm parameter from the swarm study are expected to sever as a critical test of current theories of low energy scattering by atoms and molecules.

Ionization and Diffusion Coefficients in CH4 Gas by Simulation (시뮬레이션에 의한 CH4 기체의 전리 및 확산계수)

  • Kim, Sang-Nam
    • The Transactions of the Korean Institute of Electrical Engineers P
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    • v.63 no.4
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    • pp.317-321
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    • 2014
  • This paper describes the information for quantitative simulation of weakly ionized plasma. We must grasp the meaning of the plasma state condition to utilize engineering application and to understand materials of plasma state. Using quantitative simulations of weakly ionized plasma, we can analyze gas characteristic. In this paper, the electron Ionization and diffusion Coefficients in $CH_4$ has been analysed over the E/N range 0.1~300[Td], at the 300[$^{\circ}K$] by the two term approximation Boltzmann equation method and Monte Carlo Simulation. Boltzmann equation method has also been used to predict swarm parameter using the same cross sections as input. The behavior of electron has been calculated to give swarm parameter for the electron energy distribution function has been analysed in $CH_4$ at E/N=10, 100 for a case of the equilibrium region in the mean energy. A set of electron collision cross section has been assembled and used in Monte Carlo simulation to predict values of swarm parameters. The result of Boltzmann equation and Monte Carlo Simulation has been compared with experimental data by Ohmori, Lucas and Carter. The swarm parameter from the swarm study are expected to sever as a critical test of current theories of low energy scattering by atoms and molecules.