The double sheath on cathodes of discharges burning in cathode vapour

Abstract

The model of a collisionless near-cathode space-charge sheath with ionization of atoms emitted by the cathode surface is considered. Numerical calculations showed that the mathematical problem is solvable and its solution is unique. In the framework of this model, the sheath represents a double layer with a potential maximum, with the ions which are produced before the maximum returning to the cathode surface and those produced after the maximum escaping into the plasma. Numerical results are given in a form to be readily applicable in analysis of discharges burning in cathode vapour, such as vacuum arcs. In particular, the results indicate that the ion backflow coefficient in such discharges exceeds 0.5, in agreement with values extracted from the experiment.

Asymptotic theory of double layer and shielding of electric field at the edge of illuminated plasma

“…An asymptotic solution for plane geometry is given and compared with numerical results in Sec. 3. An asymptotic solution for cylindrical geometry is outlined in Sec.…”

“…The boundary condition at ξ 5 = 0 is expressed by Eq. ( 48) with C 4 = −2C 3 2 /3; we recall that not only V 5 (ξ 5 ) but also dV 5 (ξ 5 ) /dξ 5 are continuous at ξ 5 = 0 as discussed in Sec. 3.3.…”

“…The latter is particularly surprising since in all known models a near-wall space-charge sheath is bordered by a nonuniform quasi-neutral presheath where the ions going to the sheath are accelerated and the voltage drop is of the order of the electron temperature measured in volts. (We set aside cases where the ions are produced on the surface, as in Q-machines or experiments with heated cavities [2], or inside the sheath, as in near-cathode layers of discharges burning in cathode vapour [3].) Moreover, the difference between illuminated and un-illuminated regions in terms of ion momentum is in the presence or absence of ionization friction force, and the fact that the ion fluid is accelerated in the illuminated plasma, where the ionization friction force is present, and is not accelerated in the un-illuminated plasma, where the friction force is absent, is somehow counterintuitive.The above feature is extremely interesting, also from the methodological point of view; note that the classical Bohm sheath solution [4] is sufficient to describe both the sheath and the adjacent (un-illuminated) plasma in such situation.…”

Dust and powder in fusion plasmas: recent developments in theory, modeling, and experiments

“…Recall that, similar to arcing modelling (Benilov and Benilova 2010;Kaufmann et al 2017) and to plasma-wall interaction modelling (Komm et al 2017a;, the electron Q e and ion Q i heating terms do not only stand for the kinetic (dust potential dependent due to the sheath acceleration) contributions but also include chemical contributions. Denoting the collected particle fluxes by Γ e,i , for the collected electrons, we have Q chem e = A d Γ e W f , with the work function being W f ∼ 4-5 eV for most metals, that can be the dominant contribution in cold T e ∼ 1 eV detached divertor plasmas, as confirmed in Ref.…”

Field to thermo-field to thermionic electron emission: A practical guide to evaluation and electron emission from arc cathodes

“…In the model, 23 the ion flux is assumed to be formed inside the sheath as a result of ionization of neutral metal vapor emitted by the cathode; see Ref. 30 for details.…”