Ambipolar field role in formation of electron distribution function in gas discharge plasma

Yuan, Chengxun; Bogdanov, E. A.; Kudryavtsev, A. A.; Rabadanov, K. M.; Zhou, Zhongxiang

doi:10.1038/s41598-017-15073-6

Cited by 16 publications

(19 citation statements)

References 24 publications

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“…Such pronounced vortices, as observed in figures 1, 7 and 8, are not observed. Figure 5 shows that g(ε)=0, as it should be for a Maxwellian EEDF, according to equation (23). Thus, it follows from (17) that the stream lines must be vertical.…”

Section: Resultsmentioning

confidence: 82%

“…Therefore, from the assumption that ∂f 0 /∂r =0, it follows that E r =0. The applicability of the local approximation in the PC of a glow discharge is also discussed in [8,9,15,23,24]. Because the D-D is obtained by equating L G e to zero, the proximity to the local mode and, accordingly, the proximity of f 0 to the D-D, indicates that the terms vD e E f r z 2 2 0 e - ¶ ¶ and v V f 0 e in Γ ε are the main terms, and that the terms including E r are small supplements.…”

Section: Introductionmentioning

confidence: 99%

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Vortex electron flux and EDF nonlocality of moderate and high-pressure gas discharge plasmas

Yuan

Bogdanov

Kudryavtsev

et al. 2018

Plasma Sources Sci. Technol.

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Even at medium and high pressures, when the standard, commonly accepted in the literature as the criterion of the applicability of the local field approximation (LFA) L>λ ε , is fulfilled, the ambipolar field is shown to be dominant on the periphery of plasma, which leads to the formation of a vortex motion of electrons on the phase plane and LFA non-applicability for the solution of the Boltzmann kinetic equation. The spinning direction of the vortex depends on the behavior of the momentum transfer cross sections. In most cases, the vortex rotates counterclockwise; however, for decreasing cross-sections, a clockwise direction is possible. One manifestation of the vortexes is complex spatial profiles of the excitation rates and their constants on the periphery of the plasma volume.

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Section: Resultsmentioning

confidence: 82%

Section: Introductionmentioning

confidence: 99%

Vortex electron flux and EDF nonlocality of moderate and high-pressure gas discharge plasmas

Yuan

Bogdanov

Kudryavtsev

et al. 2018

Plasma Sources Sci. Technol.

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“…To apply the local approximation, the characteristic size of the discharge volume L (diffusion length) must exceed the electron energy relaxation length L , l e  and the value of the heating (longitudinal) field must be greater than the value of the ambipolar field: E E h a > [6][7][8][9]; that is, terms with spatial gradients in the kinetic equation can be ignored. Accordingly, use of local approximation is questionable at low and medium gas pressures when L l > e and the ambipolar field dominates at the plasma periphery, where E E a h > eventually.…”

Section: Introductionmentioning

confidence: 99%

“…Accordingly, use of local approximation is questionable at low and medium gas pressures when L l > e and the ambipolar field dominates at the plasma periphery, where E E a h > eventually. Research (see, for example, [6][7][8][9][10]) has indicated that, under these conditions, the EDF is nonlocal, and it is necessary to solve the kinetic equation with accounting for spatial variables. Therefore, using the local approximation at L l > e leads to errors [6].…”

Section: Introductionmentioning

confidence: 99%

“…Research (see, for example, [6][7][8][9][10]) has indicated that, under these conditions, the EDF is nonlocal, and it is necessary to solve the kinetic equation with accounting for spatial variables. Therefore, using the local approximation at L l > e leads to errors [6]. Overall, the problem of finding the EDF requires solving a partial differential equation, which is a computationally resource-intensive task.…”

Section: Introductionmentioning

confidence: 99%

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Influence of metastable atoms on the formation of nonlocal EDF, electron reaction rates, and transport coefficients in argon plasma

Yuan

Zhou

Yao

et al. 2019

Plasma Sources Sci. Technol.

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The influence of metastable atoms on formation of the nonlocal electron distribution function (EDF) and other characteristics of gas-discharge plasma in argon is investigated in this paper. Superelastic collisions of electrons with metastable atoms strongly affect the shape of the EDF, the behavior of reaction rate constants, and other plasma characteristics. An interesting phenomenon of EDF replication emerges with a period of excitation threshold; this effect can increase the rate constants of excitation and ionization processes by several orders of magnitude, especially at the periphery of the plasma volume. Thus, collisions between electrons and metastable atoms are important in the formation of a nonlocal EDF, and neglecting them can lead to large errors in calculations of plasma characteristics.

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A generalized electron energy probability function for inductively coupled plasmas under conditions of nonlocal electron kinetics

Mouchtouris

Kokkoris

2018

Journal of Applied Physics

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A generalized equation for the electron energy probability function (EEPF) of inductively coupled Ar plasmas is proposed under conditions of nonlocal electron kinetics and diffusive cooling. The proposed equation describes the local EEPF in a discharge and the independent variable is the kinetic energy of electrons. The EEPF consists of a bulk and a depleted tail part and incorporates the effect of the plasma potential, Vp, and pressure. Due to diffusive cooling, the break point of the EEPF is eVp. The pressure alters the shape of the bulk and the slope of the tail part. The parameters of the proposed EEPF are extracted by fitting to measure EEPFs (at one point in the reactor) at different pressures. By coupling the proposed EEPF with a hybrid plasma model, measurements in the gaseous electronics conference reference reactor concerning (a) the electron density and temperature and the plasma potential, either spatially resolved or at different pressure (10–50 mTorr) and power, and (b) the ion current density of the electrode, are well reproduced. The effect of the choice of the EEPF on the results is investigated by a comparison to an EEPF coming from the Boltzmann equation (local electron kinetics approach) and to a Maxwellian EEPF. The accuracy of the results and the fact that the proposed EEPF is predefined renders its use a reliable alternative with a low computational cost compared to stochastic electron kinetic models at low pressure conditions, which can be extended to other gases and/or different electron heating mechanisms.

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Ambipolar field role in formation of electron distribution function in gas discharge plasma

Cited by 16 publications

References 24 publications

Vortex electron flux and EDF nonlocality of moderate and high-pressure gas discharge plasmas

Vortex electron flux and EDF nonlocality of moderate and high-pressure gas discharge plasmas

Influence of metastable atoms on the formation of nonlocal EDF, electron reaction rates, and transport coefficients in argon plasma

A generalized electron energy probability function for inductively coupled plasmas under conditions of nonlocal electron kinetics

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