The formation of a plasma sheath with secondary electron emission†

Anderson, N.

doi:10.1080/00207217208938304

Cited by 9 publications

(10 citation statements)

References 1 publication

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“…On the other hand the electron emission coefficient γ e has values between 0.4 and 1.6 for many metals and for energies of impacting electrons up to several keV. Because γ i is usually much smaller than γ e many authors [4,5,8] simply ignore γ i . In this paper both are taken into account.…”

Section: Basic Assumptions and The Poisson Equationmentioning

confidence: 99%

Fluid Model of a Sheath Formed in Front of an Electron Emitting Electrode Immersed in a Plasma with Two Electron Temperatures

Gyergyek

Čerček

2005

Contrib. Plasma Phys.

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The formation of a sheath in front of a negatively biased electrode (collector) that emits electrons is studied by a one-dimensional fluid model. Electron and ion emission coefficients are introduced in the model. It is assumed that the electrode is immersed in a plasma that contains energetic electrons. The electron velocity distribution function is assumed to be a sum of two Maxwellian distributions with two different temperatures, while the ions and the emitted electrons are assumed to be monoenergetic. The condition for zero electric field at the collector is derived. Using this equation the dependence of electron and ion critical emission coefficients on various parameters -like the ratio between the hot and cool electron density, the ratio between hot and cool electron temperature and the initial velocity of secondary electrons -is calculated for a floating collector. A modification of the Bohm criterion due to the presence of hot and emitted electrons is also given. The transition between space charge limited and temperature limited electron emission for a current-carrying collector is also analyzed. The critical potential, where this transition occurs, is calculated as a function of several parameters like the Richardson emission current, the ratio between the hot and cool electron density, the ratio between hot and cool electron temperature and the initial velocity of secondary electrons.

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Section: Basic Assumptions and The Poisson Equationmentioning

confidence: 99%

Fluid Model of a Sheath Formed in Front of an Electron Emitting Electrode Immersed in a Plasma with Two Electron Temperatures

Gyergyek

Čerček

2005

Contrib. Plasma Phys.

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“…The model presented in section 2 offers a possibility for a quantitative test of whether a given solution of the model equations is physically acceptable or not. The function g( , S ), defined in (32), is proportional to the square of the electric field (d /dz) 2 in the sheath as a function of potential . Since g( , S ) is proportional to the square of the electric field, it should be positive for all between C and S in the sheath.…”

Section: Positive Square Of Electric Fieldmentioning

confidence: 99%

“…Many studies of sheath formation in front of electron emitting electrodes can also be found [31][32][33][34][35][36][37][38][39][40][41][42][43], as this subject also has great practical importance. Attempts to study the effects of the energetic and emitted electrons to the sheath formation simultaneously [44] can also be found in the literature.…”

Section: Introductionmentioning

confidence: 99%

Sheath structure in front of an electron emitting electrode immersed in a two-electron temperature plasma: a fluid model and numerical solutions of the Poisson equation

Gyergyek

Jurčič-Zlobec

Čerček

et al. 2009

Plasma Sources Sci. Technol.

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A one-dimensional fluid model of sheath formation in front of a large, planar, floating, electron emitting electrode (collector) immersed in a two-electron temperature plasma is presented. For certain values of the parameters the Bohm criterion is triple valued. Three methods to select the correct Bohm velocity are compared. The simplest is to find the parameters, where the floating potentials that correspond to the high and to the low Bohm velocity are equal. But sometimes-when the electron emission is small-such parameters cannot be found. The second method is the 'maximum positive ion flux criterion', proposed recently by Fernández Palop et al (2002 J. Appl. Phys. 91 2587), for electronegative plasmas. In this work it is modified for a two-electron temperature plasma with emitted electrons and applied successfully. This method is sometimes-when the electron emission from the collector is increased-not applicable because the positive ion flux as a function of potential has only 1 maximum. The third method is a numerical solution of the Poisson equation. The transition from the low to the high Bohm velocity occurs at the parameters where the numerically found space charge density profile indicates the formation of a double layer in the sheath. These parameters are always identical to the parameters found with the maximum positive ion flux method, when the latter can be applied. The 'shooting method' for the correct determination of electric field at the collector is presented. This method reveals the existence of regular and irregular numerical solutions of the Poisson equation. The irregular solutions of the Poisson equation fulfill only one of the two sheath edge conditions and they correspond to the solutions of the fluid model, that are not physically acceptable. The parameters, where the numerical solutions of the Poisson equation become irregular, are identical to those found with the 'positive square of electric field' test, which is also presented.

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“…Here, T e is the plasma electron temperature and μ m i /m e is the ion-electron mass ratio. The study of the emissive sheath has been persistently developed since then, and a range of emissive sheath theories have been proposed [6][7][8][9]. For a strongly emissive surface, a space-charge limited (SCL) sheath with a nonmonotonic potential profile is formed when γ e exceeds a certain critical value [10].…”

Section: Introductionmentioning

confidence: 99%

“…supposing 𝑅 𝑝 ≫ 𝜆 𝑒𝑠 . Equation (6) indicates that SEE is dictated by two characteristic lengths: 𝛾 𝑒0 = 1 if the mean free path to create a SE equals to its escape mean free path, 𝛾 𝑒0 < 1 if SEs vanish quicker than their creation during the transport to the surface, vice versa.…”

mentioning

confidence: 99%

Vlasov simulation of the emissive plasma sheath with energy-dependent secondary emission coefficient and improved modeling for dielectric charging effects

et al. 2022

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A one-dimensional Vlasov–Poisson simulation code is employed to investigate the plasma sheath considering electron-induced secondary electron emission (SEE) and backscattering. The SEE coefficient is commonly treated as constant in a range of plasma simulations; here, an improved SEE model of a charged dielectric wall is constructed, which includes the wall charging effect on the SEE coefficient and the energy dependency of the SEE coefficient. Pertinent algorithms to implement the previously mentioned SEE model in plasma simulation are studied in detail. It is found that the SEE coefficient increases with the amount of negative wall charges, which in turn reduces the emissive sheath potential. With an energy-dependent SEE coefficient, the sheath potential is a nonlinear function of the plasma electron temperature, as opposed to the linear relation predicted by the classic emissive sheath theory. Simulation combining both wall-charging effect and SEE coefficient’ energy dependency suggests that the space-charged limited sheath is formed at high plasma electron temperature levels, where both sheath potential and surface charging saturate. Additionally, different algorithms to implement the backscattering in the kinetic simulation are tested and compared. Converting backscattered electrons to secondary electrons via an effective SEE coefficient barely affects the sheath properties. The simulation results are shown to be commensurate with the upgraded sheath theory predictions.

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The formation of a plasma sheath with secondary electron emission†

Cited by 9 publications

References 1 publication

Fluid Model of a Sheath Formed in Front of an Electron Emitting Electrode Immersed in a Plasma with Two Electron Temperatures

Fluid Model of a Sheath Formed in Front of an Electron Emitting Electrode Immersed in a Plasma with Two Electron Temperatures

Sheath structure in front of an electron emitting electrode immersed in a two-electron temperature plasma: a fluid model and numerical solutions of the Poisson equation

Vlasov simulation of the emissive plasma sheath with energy-dependent secondary emission coefficient and improved modeling for dielectric charging effects

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