Effect of atoms evaporated from the anode on the structure of the vacuum arc space charge sheath
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MPERATURE PLASMA
Effect of Atoms Evaporated from the Anode on the Structure of the Vacuum Arc Space Charge Sheath Ya. I. Londer and K. N. Ul’yanov AllRussian Electrotechnical Institute, Krasnokazarmennya ul. 12, Moscow, 111250 Russia email: j.londer@mtunet.ru, [email protected] Received July 24, 2013; in final form, October 3, 2013
Abstract—The structure of the anode space charge sheath of a vacuum arc is studied with allowance for the dependence of the negative anode fall on the ratio of the directed electron velocity v0 to the electron thermal velocity vT for different values of the flux density of atoms evaporated from the anode. Poisson’s equation for the sheath potential is solved taking into account the electron space charge, fast cathode ions, and slow ions produced due to the ionization of atoms evaporated from the anode. The kinetic equation for atoms and slow anode ions is solved with allowance for ionization in the collision integral. Analytic solutions for the velocity distribution functions of atoms and slow ions and the density of slow ions are obtained. It is shown that the flux of slow ions substantially affects the spatial distribution of the electric field E(z) in the sheath. As the flux density increases, the nonmonotonic dependence E(z) transforms into a monotonic one and the sheath nar rows. For a given flux of evaporated atoms Πa, the increase in the ratio of the directed electron velocity to the electron thermal velocity leads again to a nonmonotonic dependence E(z). As z increases, the electric field first increases, passes through the maximum, decreases, passes through the minimum Emin, and then again increases toward the anode. There is a limiting value of the ratio (v0/vT)* at which Emin(z) vanishes. At v 0 / vT > (v 0 / vT )*, the condition for the existence of a steadystate sheath is violated and the profiles of the field and potential in the sheath become oscillating. The dependence of (v0/vT)* on the flux density of evap orated atoms Πa is obtained. It is shown that the domain of existence of steadystate solutions in the sheath broadens with increasing Πa. DOI: 10.1134/S1063780X14030076
1. INTRODUCTION In [1], the anode region of the electric discharge was theoretically studied taking into account the dependences of the negative anode fall on the ratio v 0 /vT . In that work, Poisson’s equation in the anode sheath was solved with allowance for the electron and ion space charges for different values of v 0 /vT , the electric field E(0), the space charge density ρ ( 0) , and the ion velocity Vi ( 0) at the sheath–plasma boundary. It was shown that, at certain values of E * ( 0) , ρ* ( 0) , (v 0 /vT )*, and Vi* ( 0), the electric field in the sheath vanishes at a point lying inside the sheath. For v 0 /vT > (v 0 /vT )*, there are no steadystate solutions in the sheath. A similar situation takes place if E ( 0) < E * ( 0), ρ ( 0) < ρ* ( 0) , or Vi ( 0) < Vi* ( 0). In [1], the domain of existence of steadystate solutions in the anode sheath of a lowpressure electric discharge was
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