Space-charge sheath with ions accelerated into the plasma

Abstract

To cite this version:M S Benilov. Space-charge sheath with ions accelerated into the plasma. Journal of Physics D: Applied Physics, IOP Publishing, 2010, 43 (17) The conventional model of near-cathode space-charge sheath with ions entering the sheath from the quasi-neutral plasma may be not applicable to discharges burning in cathode vapor, e.g., vacuum arcs, where ionization of emitted atoms may occur inside the sheath with some of the produced ions returning to the cathode and others moving into the plasma. In this connection, a simple model is considered of a sheath formed by electrons and positive ions injected into the sheath with a very low velocity and moving from the sheath into the plasma. It is shown that such sheath is possible provided that the sheath voltage is equal to or exceeds approximately 1.256kT e /e. This limitation is due to the space charge in the sheath and is in this sense analogous to the limitation of ion current in a vacuum diode expressed by the Child-Langmuir law. The ions leave a sheath and enter the plasma with a velocity equal to or exceeding approximately 1.585u B .

The double sheath on cathodes of discharges burning in cathode vapour

“…Leaving the full treatment beyond the scope of this paper, we note the following. Values of the quantities τ and Φ ∞ in the case of large α can be found with the use of results [5]: Φ ∞ = −C 1 , where C 1 ≈ 1.26 is the positive root of the transcendental equation…”

“…In was hypothesized in [5] that such maximum may appear in the model of a space-charge sheath if ionization of emitted atoms inside the sheath is taken into account. This model is illustrated by figure 1.…”

“…Most models of near-cathode layers in discharges burning in cathode vapor are based on the assumption that ionization of neutral atoms emitted by the cathode surface occurs in a quasi-neutral plasma region beyond the space-charge sheath and treat the sheath and the ionization region essentially in the same way as in discharges burning in the ambient gas; e.g., [2], [4, p. 214], [7]. This assumption was put in question in [8, p. 106] on intuitive grounds and in [5] of the basis of estimates of characteristic length scales; see also [9, figure 7.6]. Note that the conclusion [5] that this assumption may be not fulfilled is not unexpected, given very high pressures which are typical of cathode spots in discharges burning in cathode vapor and an important role that can be played by ionization in near-cathode space-charge sheaths at very high pressures [10].…”

“…This feature was studied in the work [5] by means of a simple mathematical model obtained by assuming that the ionization occurs in a narrow vicinity of the point of maximum, after which the ion flux remains constant. It was found that a solution exists provided that the sheath voltage exceeds approximately 1.256kT e /e; a limitation similar to the one expressed by the ChildLangmuir law.…”

Numerical Simulation of Transient Surface Charging of Polymer Surface under DC Corona Considering Plasma Chemistry

“…Under the electric field stress, electrons are accelerated and more new electrons are generated by the intense impact ionization reactions R 1 and R 2 with time. From Figure 2c, an obvious cathode sheath about 0.1 mm in thickness is formed, and a great number of electrons are generated at the edge of the sheath [16][17][18]. The area of the electron cloud is enlarged with the large number of electrons spreading.…”