Scaling Relationships for the Total Pressure in Orificed Hollow Cathodes

Taunay, Pierre-Yves; Wordingham, Christopher J.; Choueiri, Edgar Y.

doi:10.2514/6.2019-4246

Cited by 3 publications

(9 citation statements)

References 28 publications

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“…We make the following assumptions: Our first assumption is justified in the insert region of cathodes with a small orifice-to-insert diameter ratio (i.e. most orificed hollow cathodes) [36]. The Knudsen number is generally less than 1 for those cathodes.…”

Section: Assumptionsmentioning

confidence: 99%

“…Through a dimensional and statistical analysis of experimental data, the study in [36] showed that the gasdynamic and plasma effects can account for most of the variation in the total pressure within hollow cathodes. We therefore neglect the effect of viscosity on the total pressure gradient.…”

Section: Assumptionsmentioning

confidence: 99%

“…L eff πr 2 c (ν ei + ν en ) , (36) where ν ei and ν en are the electron-ion and electron-neutral collision frequencies, respectively. We use the conservation of charge (equation ( 29)) to eliminate the thermionic current terms from the electron energy equation.…”

Section: Insert Regionmentioning

confidence: 99%

“…We have shown in [36] that the empirical relationships developed in [30][31][32][33][34][35] do not generalize to other cathodes and that the assumptions of isentropic, isothermal, or viscous Poiseuille flow are invalid in the flow regime in which cathodes operate. The empirical relationship we proposed in [36] covers available data from the literature but may not generalize to new designs unless they are similar to cathodes included in the analysis used to derive the relationship. It is also limited by its data-driven approach which does not explain the physical phenomena governing the total pressure in orificed hollow cathodes.…”

Section: Introductionmentioning

confidence: 99%

“…Multiple approaches exist to estimate the total pressure, many of which are used within the context of a zero-dimensional cathode model: empirical relationships, designed for a mercury hollow cathode [30][31][32][33][34][35] or based on the available data from the literature [36], isentropic [37] or isothermal [38,39] flow approaches, Poiseuille flow theory [29,40,41], a modification of Poiseuille flow theory [42,43], and an 'equivalent temperature' or modified specific gas constant taking into account the ionization fraction [38,39,44,45]. We have shown in [36] that the empirical relationships developed in [30][31][32][33][34][35] do not generalize to other cathodes and that the assumptions of isentropic, isothermal, or viscous Poiseuille flow are invalid in the flow regime in which cathodes operate. The empirical relationship we proposed in [36] covers available data from the literature but may not generalize to new designs unless they are similar to cathodes included in the analysis used to derive the relationship.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Physics of thermionic, orificed hollow cathodes: I. Theory and experimental validation

Taunay¹,

Wordingham²,

Choueiri³

2022

Plasma Sources Sci. Technol.

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A model aimed at illuminating the physics of thermionic, orificed hollow cathodes is developed and validated with experimental data. The model is intended to describe the variation of total (neutrals, ions, and electrons) static pressure with controllable parameters. That pressure must be properly evaluated because it influences important plasma parameters in the cathode such as the attachment length and the electron temperature, which directly impact the lifetime of thermionic inserts. The model, which combines a zero-dimensional approach to the conservation of energy and momentum for the combined plasma-neutral fluid and a charge-exchange-limited ambipolar diffusion model, allows for the computation of all plasma quantities, including the total fluid pressure. The model depends on the operating conditions (discharge current and mass flow rate), cathode geometry, and the gas species, along with two non-controllable parameters: the neutral gas temperature and the sheath potential. Total pressure data at up to 307 A of cathode discharge current were obtained experimentally and were used, along with data from the literature, to validate the model. Good agreement is obtained for all quantities. The model is used in a companion paper to clarify the role of magnetic and gasdynamic pressure in the scaling of total pressure, to derive scaling laws applicable to thermionic, orificed hollow cathodes, and to propose novel cathode design rules.

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Section: Assumptionsmentioning

confidence: 99%

Section: Assumptionsmentioning

confidence: 99%

Section: Insert Regionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Physics of thermionic, orificed hollow cathodes: I. Theory and experimental validation

Taunay¹,

Wordingham²,

Choueiri³

2022

Plasma Sources Sci. Technol.

View full text Add to dashboard Cite

show abstract

Physics of thermionic orificed hollow cathodes: II. Scaling laws and design rules

Taunay¹,

Wordingham²,

Choueiri³

2022

Plasma Sources Sci. Technol.

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Scaling laws for the total pressure, electron temperature, and attachment length within orificed hollow cathodes are derived from a theoretical zero-dimensional model combined with a charge-exchange-limited ambipolar diffusion model. These quantities are critical as they control the operational life of thermionic hollow cathode inserts. The underlying models were delineated and evaluated experimentally in a companion paper (Part 1). In the present paper, scaling laws are derived from first principles for the total pressure, and from a semi-analytical approach for the electron temperature and attachment length. The total pressure is found to scale with the sum of the square of the mass flow rate multiplied by a weak function of discharge current, and with the square of the discharge current. This scaling can be physically interpreted as due to the relative importance of the Lorentz force density and the gasdynamic pressure. Both electron temperature and attachment length are found to vary inversely with the neutral gas pressure-cathode diameter product. The predicted emission length is found to be between 0.6–1.4 times the insert radius for the experimental data considered, to scale weakly with the pressure-diameter product for P d ≥ 2 Torr-cm, and to be nearly independent of the orifice diameter. The analysis suggests that the diffusion-dominated nature of the insert plasma can account for the scaling of the emission length. A general cathode design rule is formulated based on the results of the analysis: insert diameter should be chosen such that the attachment length is similar to the insert length to minimize the emission current density.

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Solution of Orifice Hollow Cathode Plasma Model Equations by Means of Particle Swarm Optimization

Coppola,

Panelli,

Battista

2024

Preprint

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Orificed Hollow Cathodes are electric devices necessary for the functioning of common plasma thrusters for space applications. From their reliability mainly depends the success of a spacecraft’s mission equipped by electric propulsion. The development of plasma models is crucial in the evaluation of plasma properties within the cathodes that are difficult to measure due to the small dimensions. Many models, based on non-linear system of plasma equations, have been proposed in the open literature. These are solved commonly by means of iterative procedures. This paper investigates the possibility to solve them by means of Particle Swarm Optimization method. The results of the validation tests confirm the expected trends for all the unknowns; the confidence bound of the discharge current as function of mass flow rate is very narrow (2÷5V), moreover the results match very well the experimental data except at the lowest mass flow rate (0.08mg/s) and discharge current (1A), where the computations underpredict the discharge current to the utmost by 40%; the highest data dispersion regards the plasma density in the emitter region (± 20 % of the average value) and the wall temperatures (± 50K respect to the average values) of orifice and insert; those of the others variables are very tiny.

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Scaling Relationships for the Total Pressure in Orificed Hollow Cathodes

Cited by 3 publications

References 28 publications

Physics of thermionic, orificed hollow cathodes: I. Theory and experimental validation

Physics of thermionic, orificed hollow cathodes: I. Theory and experimental validation

Physics of thermionic orificed hollow cathodes: II. Scaling laws and design rules

Solution of Orifice Hollow Cathode Plasma Model Equations by Means of Particle Swarm Optimization

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