A Critical Review of Orificed Hollow Cathode Modeling: 0D Models

Abstract

A critical review of zero-dimensional orificed hollow cathode modeling is presented, with a focus on the validity of model assumptions, the reproducibility of model results, and the observed scaling behaviors. Complete models were capable of recreating the original results of their authors, but were generally unable to produce agreement with other experimental data. Resolution of the potential structure of the emitter sheath beyond the inclusion of the pre-sheath is attempted in only one model. In all other models it is assumed that the plasma and sheath potentials are equal, inflating the contribution of emitter ion bombardment and power deposition in the insert plasma by sheath electrons while essentially neglecting electron back-bombardment. Model results are generally sensitive to the internal neutral pressure, but neutral flow predictions do not agree with experimental data. Inconsistent property data and the inappropriate evaluation of flux terms between control volumes are pervasive, and introduce significant errors. Most models require substantial input in the form of experimental data or free parameters and cannot be used for predictive calculations.

Numerical study of a hollow cathode neutraliser by means of a zero-dimensional plasma model

“…Some approaches take into account an effective length of the emitter [19], also known as attachment length, from which the electrons are thermionically emitted. The effective length has been experimentally observed [13], however a consensus on its modeling has not been reached yet.…”

“…Electrons and ions exit the orifice downstream with energies equal to 5/2T e,o and 2T i,o , respectively, as seen from the third and fourth terms on the right hand side of equation (19). Electrons are assumed to travel along the orifice by forced convection, that is the electrons are extracted from the cathode through the orifice exit while colder electrons coming from the insert replace those hotter extracted electrons.…”

“…The plasma resistivity η in the insert volume is calculated similarly to that in the orifice section from equations ( 21), ( 22), ( 23), ( 24) and ( 25) in which the plasma and neutral gas properties must be those relative to the insert region. Within the insert volume, it is assumed that the main current flow is along the radial direction, for this reason the plasma resistivity is multiplied by the fraction r in / (4/3πr in L in ), which is the path along which the plasma flows (r in ) divided by the averaged cross section perpendicular to the radial direction, which is computed as [11,19] A in,lat S = = S A in,lat (r)dS…”

“…The first term on the right hand side of the power balance equation is the ionisation loss, where E iz is the ionisation energy. Note that the ionisation loss is in the form of surface loss rather than in the form of volumetric loss as in equation (19).…”

“…Depending on the approach, the models can predict plasma density, electron temperature, plasma potential, neutral density, power deposition on the internal surface of the cathode, emitter temperature and cathode lifetime. The reader may find a comprehensive critical review signed by Wordingham et al [19] that covers most of the zero-dimensional models proposed until today.…”