Analytical model of a longitudinal hollow cathode discharge

Abstract

This paper presents a simple analytical model of a longitudinal hollow cathode discharge used in metal vapor lasers. The model describes the principle relations between the voltage, current, plasma density, and the axial structure of the discharge. Contrary to standard DC discharges, this discharge does not require electron multiplication in the cathode fall to produce ions, but rather to satisfy the electron energy balance. A self-sustainment condition is obtained from the energy balance per electron-ion pair. From this, it follows that there is a maximum voltage at which the cathode fall thickness tends to zero and the current density tends asymptotically to infinity. The discharge develops axial non-uniformity and an axial electric field in order to evacuate the created electrons to the anode, such that the characteristic time for transport losses is the same for electrons as for ions. The axial profiles of the current density, plasma density, and potential are obtained from the electron continuity equation. It is shown that additional energy absorption from the axial field, similar to electron heating in DC positive columns, modifies the self-sustainment condition and thus leads to a shift in the voltage-current characteristic, depending on the cathode length.Confidential: not for distribution.

Monte Carlo simulation of electron kinetics in a hollow cathode discharge

“…The uid model calculates the spatial density distribution of various discharge species, the mean electron energy and the electrostatic potential. The results of the MD2D model are found to agree well with experimental and analytical observation [3,4,5].…”

“…For the simulation of the HCD setup, we impose the radial and axial electric field components obtained from the uid model. The axial electric field component has an important role for the electron transport to the anode [5]. The secondary electron emission from the wall is simulated by a continuous injection of electrons from the cathode wall at a rate of 1×10 14 electrons/s.…”

“…The electrons which have reached the inner part of the HC start to absorb energy from the axial electric field, which is accelerating them in the direction of the anode. The influence of the axial field is discussed in [5]. The EEDFs show high concentration of highly energetic electrons that are more abundant in the outer regions of the discharge and, due to the presence of strong discharge.…”

Pressure effect on a tandem hollow cathode discharge in argon

“…9,10,[24][25][26][27] Since the 1990s, the hybrid model was developed for the two dimensional simulation on the hollow cathode discharges; Donko and Bogaerts et al carried out the two-dimensional hybrid simulation on the rectangular hollow cathode discharge as well as the segmented cylindrical hollow cathode discharges. [28][29][30][31] In more recent years, the numerical simulations, including the fluid model, 32-34 the particle-in-cell/ Monte-Carlo model, [35][36][37] the global (volume-averaged) model, 38,39 as well as the analytical model, 40 were developed with growing interests for the hollow cathode discharges in various regimes. Among these models, the fluid model is a fast and less computationally expensive way to provide a reasonable insight into the qualitative trends for the hollow cathode discharges in many occasions.…”

The use of hollow cathodes in deposition processes: A critical review

“…The generated secondary electrons have energies of only a few eV and therefore do not contribute to the production of additional electrons or ions, or to the excitation of atoms; furthermore, they remain within the central region of the cathode since they are repelled by the electric fields of the pre-sheath and sheath. A number of authors,[23,[138][139][140][141] have proposed that the high-energy pendulum electrons cause ionization within the sheath such that the generated secondary electrons are accelerated by the cathode sheath to sufficiently high energies to cause additional ionization events. This idea has often been the basis of the superlinear relation between the production of electrons and the applied voltage, which is required to explain the very large currents observed for the HCD state.…”