On simplifying approaches to the solution of the Boltzmann equation in spatially inhomogeneous plasmas

Kortshagen, Uwe R.; Busch, C.; Tsendin, L. D.

doi:10.1088/0963-0252/5/1/001

Cited by 194 publications

(173 citation statements)

References 71 publications

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“…This means that the charged particles are typically not in either spatial or temporal equilibrium with the electric and magnetic fields in the plasma, and this is a major cause of theoretical difficulty in understanding radio-frequency discharges, or indeed low-pressure discharges more generally. Under these conditions, the particle kinetics are said to be "non-local" [5,6]. At the level of electron kinetics, for example, this means that an electron travelling at the typical thermal speed may move a distance comparable with the plasma size during one period of the driving frequency, without experiencing a collision.…”

Section: Introductionmentioning

confidence: 99%

Collisionless heating in radio-frequency discharges: a review

Turner¹

2009

J. Phys. D: Appl. Phys.

121

117

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Abstract. Radio-frequency discharges are practically and scientifically interesting. A practical understanding of such discharges requires, among other things, a quantitative appreciation of the mechanisms involved in heating electrons, since this heating is the proximate cause of the ionization that sustains the plasma. When these discharges are operated at sufficiently low pressure, collisionless electron heating can be an important and even the dominant mechanism. Since the low pressure regime is important for many applications, understanding collisionless heating is both theoretically and practically important. This review is concerned with the state of theoretical knowledge of collisionless heating in both inductive and capacitive discharges.

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Section: Introductionmentioning

confidence: 99%

Collisionless heating in radio-frequency discharges: a review

Turner¹

2009

J. Phys. D: Appl. Phys.

121

117

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“…Although the electron energy distribution can be rigorously obtained by a direct solution of the Boltzmann equation [18], the balance equation between volume ionization and surface loss of the charged particles is presently used as it is a simple and powerful method for determining the electron temperature [19]. In addition, it has been extended to generalized electron energy distributions [20]; no comparison with experiments has yet been reported.…”

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confidence: 99%

Electron Energy Distribution of a Current-Free Double Layer: Druyvesteyn Theory and Experiments

et al. 2011

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Electron energy distributions upstream of a current-free double layer (CFDL) contained in a lowcollisional plasma are modeled and compared with experimental results. The experimentally observed electron energy probability functions (EEPFs) with a depleted tail above the energy corresponding to the potential drop of the CFDL can be well approximated by a Druyvesteyn distribution function. Theoretical effective electron temperatures for the Druyvesteyn distribution are in good agreement with the values obtained from the experimental EEPFs over the range of pressure where the CFDL is observed.

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“…The nonlocal approach has been successfully applied to the self-consistent kinetic modelling of various low-pressure discharges: the capacitively coupled plasmas [28][29][30][31], the inductively coupled plasmas [32][33][34][35], the dc discharges [36,37], the afterglow [38], and the surface-wave discharges [39]. Additional references can be found in reviews [40][41][42].…”

Section: Self-consistent System Of Equations For a Kinetic Descrimentioning

confidence: 99%

Landau damping and anomalous skin effect in low-pressure gas discharges: Self-consistent treatment of collisionless heating

2004

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In low-pressure discharges, where the electron mean free path is larger or comparable with the discharge length, the electron dynamics is essentially nonlocal. Moreover, the electron energy distribution function (EEDF) deviates considerably from a Maxwellian. Therefore, an accurate kinetic description of the low-pressure discharges requires knowledge of the nonlocal conductivity operator and calculation of the non-Maxwellian EEDF. The previous treatments made use of simplifying assumptions: a uniform density profile and a Maxwellian EEDF. In the present study a self-consistent system of equations for the kinetic description of nonlocal, nonuniform, nearly collisionless plasmas of low-pressure discharges is reported. It consists of the nonlocal conductivity operator and the averaged kinetic equation for calculation of the non-Maxwellian EEDF. This system was applied to the calculation of collisionless heating in capacitively and inductively coupled plasmas. In particular, the importance of accounting for the nonuniform plasma density profile for computing the current density profile and the EEDF is demonstrated. The enhancement of collisionless heating due to the bounce resonance between the electron motion in the potential well and the external rf electric field is investigated. It is shown that a nonlinear and self-consistent treatment is necessary for the correct description of collisionless heating.

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On simplifying approaches to the solution of the Boltzmann equation in spatially inhomogeneous plasmas

Cited by 194 publications

References 71 publications

Collisionless heating in radio-frequency discharges: a review

Collisionless heating in radio-frequency discharges: a review

Electron Energy Distribution of a Current-Free Double Layer: Druyvesteyn Theory and Experiments

Landau damping and anomalous skin effect in low-pressure gas discharges: Self-consistent treatment of collisionless heating

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