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

Abstract

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)

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

“…However, the large difference between the electron density values calculated by integrating over EEDF and using the classical method is probably partly due to an error (10)) corresponding to the best adjustment (thin black) is also shown on ion velocity at the sheath edge depending on the low-energy part of the EEDF. [14] This is equal to √ kT e M i only in the case of a Maxwellian distribution.…”

“…So, a third equation is needed to determine these parameters. Considering the equality between the ion and electron flux impinging on an elementary probe area in the case of homogeneous plasmas and isotropic EEDF, the equality between the absolute value of the ion and the electron current collected at the floating potential [14] can be written as…”

“…The demonstration is given in Ref. [14] . It correlates the floating potential to the ion current collected.…”

“…, and kT e is determined using the semi-logarithm equation ln [2,7] The results are also compared with the electron density (n es ) and mean energy ( es ) determined by means of single probes (using Equations (14) and (15)) located at the same place as the double probes in plasma. The relative errors on the electron density and mean energy values have been calculated using the Student statistic law for a set of 13 experiments.…”

Time evolution of the electron energy distribution function in pulsed microwave magnetoplasma in H2

“…3 The steady state is typically obtained 40 ls after the ignition. As shown in Figures 7 and 8, the EEDF is composed of two components, which can be fitted using the generalized Maxwell distribution form [32][33][34][35] f e e ð Þ ¼ C ffiffiffiffi e e p exp À e e a k ! ;…”