Determination of the electron density in plasma by means of a floating double probe

Jauberteau, Jean-Louis; Jauberteau, Isabelle

doi:10.1063/1.2900579

Cited by 8 publications

(14 citation statements)

References 17 publications

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“…This condition can be used to determine the ion velocity at the sheath edge. This value is necessary to calculate the electron density at ion saturation of a negative biased Langmuir probe [3,4,5].…”

Section: Resultsmentioning

confidence: 99%

“…We show that the conditions on the ions velocity defined at the sheath edge in the case of a Maxwellian distribution cannot be used in the case of other distributions like a Druyvesteyn distribution. According to the plasma parameters, we discuss the collisionless condition used in the model, then the condition n i (χ) ≥ n e (χ) in the sheath, used to determine the ion velocity at the sheath edge [3,4,5]. All these results are correlated to previous works [3,4,6,7].…”

Section: Introductionmentioning

confidence: 94%

“…Nowadays the criterion in its initial form defined for Maxwellian electrons, is largely used to describe the sheath produced in the various kinds of cold plasmas, including also non-Maxwellian plasmas. In recent publications [2,3,4,5], authors have pointed out problems due to this error. For example, wrong results have been obtained in the case of the measurements of the electron density by means of Langmuir probe at the ion saturation in non-Maxwellian plasmas.…”

Section: Introductionmentioning

confidence: 95%

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Comments on the Bohm Criterion and on the Determination of the Ion Velocity at the Sheath Edge in Non‐Maxwellian Plasma

Jauberteau

2011

Contrib. Plasma Phys.

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International audienceThis work is devoted to the study of the Bohm criterion in the general case of the electron energy distribution function (EEDF). Investigations are performed by means of a Monte Carlo integration method. We resolve the cold fluid equation system describing the ion motion within the sheath, assuming collisionless conditions, singly charged and mono kinetic incoming ions (BOHM model). Results confirm that the limit ion velocity at the sheath edge to assure a monotone electric field with a positive charge over the entire sheath is vi ≥ (kTe/Mi) or εi ≥ 1/3 <εe > in the case of Maxwellian electrons. We show that in the case of a Druyvesteyn electron energy distribution, this limit is larger, it is εi ≥ 0.6 <εe >. The study is also extended to other distributions functions. Because of the large controversy in recent publications, concerning the boundary conditions at the sheath entrance, we discuss the collisionless conditions at the sheath edge according to the plasma parameters. It is shown that in a collisionless sheath, the condition ni(χ) ≥ ne(χ) can be used to determine the limit ion velocity at the sheath edge of the negatively biased collector (Langmuir probe for instance)

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 94%

Section: Introductionmentioning

confidence: 95%

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Comments on the Bohm Criterion and on the Determination of the Ion Velocity at the Sheath Edge in Non‐Maxwellian Plasma

Jauberteau

2011

Contrib. Plasma Phys.

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“…However, these methods are not applicable for non-Maxwellian plasmas, and the electron density values can be overestimated with a discrepancy in the density up to two orders of magnitude. [10,11] In a previous work, we gave a simple method to determine the electron density for non-Maxwellian distributions, [12] considering the equality of ion and electron current at the floating potential (at V a = 0 V). However, this method is efficient only when V p and V f are very close to each other.…”

Section: Applicationmentioning

confidence: 99%

“…The use of Equations (11) and (12) is a numerical way to determine the best adjustment between f ( e ) and f v ( e ). However, different tests performed on theoretical examples have shown that C, k, and cannot be properly determined by using Equations (11) and (12) because the solution also depends on the value of f , which is unknown. So, a third equation is needed to determine these parameters.…”

Section: Applicationmentioning

confidence: 99%

Floating double probe in non‐Maxwellian plasmas: Determination of the electron density and mean electron energy

Jauberteau

2017

Contributions to Plasma Physics

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A theoretical study of the floating double probe based on the Druyvesteyn theory is developed in the case of non-Maxwellian electron energy distribution functions (EEDFs). It is used to calculate the EEDF in the electron energy range larger than -e(V f − V p ) from the I-V double probe characteristics. V f and V p are the floating and plasma potential, respectively. The analytical distribution function corresponding to the best fit of EEDF in the energy range larger than e(V f − V p ) allows the determination of the total electron density (n e ) and the mean electron energy (< e >).The method is detailed and tested in the case of a theoretical Maxwell-Boltzmann distribution function. It is applied for experiments that are performed in expanding microwave plasmas sustained in argon. Analytical EEDFs determined by this method are compared with those measured by means of single probes under the same experimental conditions. A good agreement is observed between single and double probe measurements. Results obtained under different experimental conditions are used to define the best conditions to obtain reliable results by means of the double probe technique. KEYWORDSelectron energy distribution function, electrostatic double probe, non-Maxwellian plasma 1

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Swept Langmuir probe investigation of a time varying DC discharge

Qayyum¹,

Naseer²,

Deeba³

et al. 2021

SN Appl. Sci.

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The paper reports on the development and application of a swept Langmuir probe to characterize plasma between two disc-like electrodes. A battery was added to a probe circuit to offset against the cathode fall voltage, and to make the sweep voltage effective at the probe tip. This arrangement allowed the collection of the electron and ion parts of the probe current and the subsequent construction of time-resolved current–voltage IP(V) characteristics with a time resolution of about one millisecond. The probe collected electron current in the lower voltage region of the discharge waveform where it surmounted the cathode fall voltage, whereas the ion current was collected continuously due to an accelerating field for the ions. The results highlighted how the cathode fall voltage limits the collection of the electron and ion parts of the probe current and how to handle the problem with a series battery in the probe circuit. In addition to the swept single-probe, a triple-probe was used simultaneously to compare and validate the results.

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Determination of the electron density in plasma by means of a floating double probe

Cited by 8 publications

References 17 publications

Comments on the Bohm Criterion and on the Determination of the Ion Velocity at the Sheath Edge in Non‐Maxwellian Plasma

Comments on the Bohm Criterion and on the Determination of the Ion Velocity at the Sheath Edge in Non‐Maxwellian Plasma

Floating double probe in non‐Maxwellian plasmas: Determination of the electron density and mean electron energy

Swept Langmuir probe investigation of a time varying DC discharge

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