Cutoff effects of electron velocity distribution to the properties of plasma parameters near the plasma-sheath boundary

Jelić, N.

doi:10.1063/1.3659022

Cited by 7 publications

(14 citation statements)

References 17 publications

(16 reference statements)

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“…The obtained results are in very good agreement with the model of Jelić [2] made for cold ion source in collision free plasma model. This gives a hope that the code could be used also for the studies of sheath formation in the presence of warm ion sources [19][20][21] and/or magnetic field [22][23][24], where at the moment we are still lacking reliable theoretical models.…”

Section: Discussionsupporting

confidence: 89%

“…For smaller potential drops (up to approximately 0.5 V) the results of the simulation are even in relatively good quantitative agreement with the model [2] for the electron flow velocity U 1 and for the electron temperature kT 1 . For the electron density the quantitative agreement between our simulations and the model [2] is not so perfect, but nevertheless our simulations and the model [2] both indicate rather strong deviation of the electron density from the Boltzmann distribution, especially for small potential drops between the plasma and the electrode. If the electron flow velocity profiles are compared it can be noticed that in the model (Fig.…”

Section: Comparison With the Model Of Jelić [2]supporting

confidence: 66%

“…At the end of this section we compare the results of our simulations to the analytical model of Jelić [2]. It is convenient to present the profiles of various plasma parameters, like particle density, temperature, flow velocity etc.…”

Section: Comparison With the Model Of Jelić [2]mentioning

confidence: 98%

“…Some time ago Andrews and Varey [1] presented a study of the sheath formation in front of an electrode close to the plasma potential, where they have taken into account the effects of the cutoff of the electron velocity distribution function. More recently Jelić [2] has extended this study to both -plasma and sheath region. Analytic expressions for the moments of the electron velocity distribution function have been derived.…”

Section: Introductionmentioning

confidence: 97%

“…We also present modifications of the code that were made in order to achieve a small potential drop between the plasma and the electrode and in the same time preserve the Maxwellian velocity distribution of electrons. At the end of this section the simulation results are compared to the analytical results of Jelić [2]. In the last section conclusions are presented.…”

Section: Introductionmentioning

confidence: 98%

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Potential Formation in Front of an Electrode Close to the Plasma Potential Studied by PIC Simulation

Gyergyek

Kovačič

2014

Contrib. Plasma Phys.

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Potential formation in front of an electrode that has the potential which is close to the plasma potential is studied by particle-in-cell (PIC) simulations. The code BIT1 [D. Tskhakaya, R. Schneider, J. Comp. Phys., 225, 829 (2007)] is used for this purpose. It is shown that this code is very appropriate for our analysis because of its ability to create charged particles by uniform volume production in the entire system and to maintain in the same time the Maxwellian electron velocity distribution function prescribed in the input file. It turns out that some modifications of the code are necessary in order to achieve small sheath potential drops and to detect the cutoff in the electron velocity distribution function. The modifications of the code are described. The small sheath potential drop is achieved by introducing a finite reflectivity of the electrons at the left electrode, while the expected cutoffs of the electron velocity distribution function are found by tracking the reflected electrons as separate particle species. The simulation results are compared to the theoretical model of Jelić [N. Jelić, Phys. Plasmas, 18, 113504 (2011)]. The matching is very good and this is a sign that the PIC simulations are very appropriate tool for the analysis of this type of problems.

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Section: Discussionsupporting

confidence: 89%

Section: Comparison With the Model Of Jelić [2]supporting

confidence: 66%

Section: Comparison With the Model Of Jelić [2]mentioning

confidence: 98%

Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 98%

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Potential Formation in Front of an Electrode Close to the Plasma Potential Studied by PIC Simulation

Gyergyek

Kovačič

2014

Contrib. Plasma Phys.

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Effect of two-temperature electrons distribution on an electrostatic plasma sheath

Xiang

Gan

et al. 2013

Physics of Plasmas

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A magnetized collisionless plasma sheath containing two-temperature electrons is studied using a one-dimensional model in which the low-temperature electrons are described by Maxwellian distribution (MD) and high-temperature electrons are described by truncated Maxwellian distribution (TMD). Based on the ion wave approach, a modified sheath criterion including effect of TMD caused by high-temperature electrons energy above the sheath potential energy is established theoretically. The model is also used to investigate numerically the sheath structure and energy flux to the wall for plasmas parameters of an open divertor tokamak-like. Our results show that the profiles of the sheath potential, two-temperature electrons and ions densities, high-temperature electrons and ions velocities as well as the energy flux to the wall depend on the high-temperature electrons concentration, temperature, and velocity distribution function associated with sheath potential. In addition, the results obtained in the high-temperature electrons with TMD as well as with MD sheaths are compared for the different sheath potential.

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Introduction to the theory and application of a unified Bohm criterion for arbitrary-ion-temperature collision-free plasmas with finite Debye lengths

et al. 2018

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At present, identifying and characterizing the common plasma–sheath edge (PSE) in the conventional fluid approach leads to intrinsic oversimplifications, while the kinetic one results in unusable over-generalizations. In addition, none of these approaches can be justified in realistic plasmas, i.e., those which are characterized by non-negligible Debye lengths and a well-defined non-negligible ion temperature. In an attempt to resolve this problem, we propose a new formulation of the Bohm criterion [D. Bohm, The Characteristics of Electrical Discharges in Magnetic Fields (McGraw-Hill, New York, 1949)], which is here expressed in terms of fluid, kinetic, and electrostatic-pressure contributions. This “unified” Bohm criterion consists of a set of two equations for calculating the ion directional energy (i.e., the mean directional velocity) and the plasma potential at the common PSE, and is valid for arbitrary ion-to-electron temperature ratios. It turns out to be exact at any point of the quasi-neutral plasma provided that the ion differential polytropic coefficient function (DPCF) of Kuhn et al. [Phys. Plasmas 13, 013503 (2006)] is employed, with the advantage that the DPCF is an easily measurable fluid quantity. Moreover, our unified Bohm criterion holds in plasmas with finite Debye lengths, for which the famous kinetic criterion formulated by Harrison and Thompson [Proc. Phys. Soc. 74, 145 (1959)] fails. Unlike the kinetic criterion in the case of negligible Debye length, the kinetic contribution to the unified Bohm criterion, arising due to the presence of negative and zero velocities in the ion velocity distribution function, can be calculated separately from the fluid term. This kinetic contribution disappears identically at the PSE, yielding strict equality of the ion directional velocity there and the ion sound speed, provided that the latter is formulated in terms of the present definition of DPCFs. The numerical values of these velocities are found for the Tonks–Langmuir collision-free, plane-parallel discharge model [Phys. Rev. 34, 876 (1929)], however, with the ion-source temperature extended here from the original (zero) value to arbitrary high ones. In addition, it turns out, that the charge-density derivative (in the potential “space”) with respect to the potential exhibits two characteristic points, i.e., potentials, namely the points of inflection and maximum of that derivative (in the potential space), which stay “fixed” at their respective potentials independent of the Debye length until it is kept fairly small. Plasma quasi-neutrality appears well satisfied up to the first characteristic point/potential, so we identify that one as the plasma edge (PE). Adopting the convention that the sheath is a region characterized by considerable electrostatic pressure (energy density), we identify the second characteristic point/potential as the sheath edge (SE). Between these points, the charge density increases from zero to a finite value. Thus, the interval between the PE and SE, with the “fixed” width (in the potential “space”) of about one third of the electron temperature, will be named the plasma–sheath transition (PST). Outside the PST, the electrostatic-pressure term and its derivatives turn out to be nearly identical with each other, independent of the particular values of the ion temperature and Debye length. In contrast, an increase in Debye lengths from zero to finite values causes the location of the sonic point/potential (laying inside the PST) to shift from the PE (for vanishing Debye length) towards the SE, while at the same time, the absolute value of the corresponding ion-sound velocity slightly decreases. These shifts turn out to be manageable with employing the mathematical concept of the plasma-to-sheath transition (different from, but related to our natural PST concept), resulting in approximate, but sufficiently reliable semi-analytic expressions, which are functions of the ion temperature and Debye length.

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Cutoff effects of electron velocity distribution to the properties of plasma parameters near the plasma-sheath boundary

Cited by 7 publications

References 17 publications

Potential Formation in Front of an Electrode Close to the Plasma Potential Studied by PIC Simulation

Potential Formation in Front of an Electrode Close to the Plasma Potential Studied by PIC Simulation

Effect of two-temperature electrons distribution on an electrostatic plasma sheath

Introduction to the theory and application of a unified Bohm criterion for arbitrary-ion-temperature collision-free plasmas with finite Debye lengths

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