Collisionless ion modeling in Hall thrusters: Analytical axial velocity distribution function and heat flux closures

Boccelli, Stefano; Charoy, Thomas; Laguna, Alejandro Alvarez; Chabert, Pascal; Bourdon, Anne; Magin, Thierry

doi:10.1063/5.0006258

Cited by 6 publications

(7 citation statements)

References 35 publications

(49 reference statements)

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“…On the other hand, reproducing central moments is much more difficult due to the strong non-equilibrium caused by the low collisionality. This can be confirmed by looking at the VDFs for this problem, previously reported in [6]. The Euler predictions for all tracked central moments, the pressure, heat flux and fourth-order moment r, are rather inaccurate, while the maximum-entropy method manages to reproduce values that are much more accurate, if compared to the PIC kinetic solution.…”

Section: Under Review -Under Review -Under Review Comparison Of the R...supporting

confidence: 70%

“…Our first test case considers the one-dimensional axial acceleration of ions along the thruster centerline. This case was previously described in [6], where it is referred to as "test case B". We wish to compare the maximum-entropy modelling against a kinetic solution, and we select the Particle-in-Cell (PIC) simulations of [38,39].…”

Section: Under Review -Under Review -Under Review 3 Test Case I: Axia...mentioning

confidence: 99%

“…On the other hand, as ions leave the thruster channel and enter the plume, charge exchange (CEX) and momentum exchange (MEX) ion-neutral collisions play an increasingly important role [5]. In either case, the ion collision frequency is typically relatively small: under the effects of the accelerating electric field and of the ionization source terms, the ion velocity distribution function (VDF) often assumes non-equilibrium shapes [6,7,8].…”

Section: Introductionmentioning

confidence: 99%

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14-moment maximum-entropy modelling of collisionless ions for Hall thruster discharges

Boccelli¹,

McDonald²,

Magin³

2022

Preprint

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Ions in Hall thruster devices are often characterized by a low collisionality. In the presence of acceleration fields and azimuthal electric field waves this results in strong deviations from thermodynamic equilibrium, which requires one to employ kinetic descriptions. This work investigates the application of the 14-moment maximum-entropy model to this problem. This method consists in a set of 14 PDEs that describe the density, momentum, pressure tensor components, heat flux and fourth-order moment of the gas. The method is applied to the ion dynamics and its accuracy is assessed against the kinetic solution. Three test cases are considered: a purely axial acceleration problem, the problem of ion-wave trapping and finally the evolution of ions in the axial-azimuthal plane.Only ions are considered in this work, since the goal is providing a direct comparison of different methods. The coupling with electrons is thus removed by prescribing reasonable values of the electric field. The maximum-entropy system appears to be a robust and accurate option for the considered test cases, bringing significant improvements over the simpler pressureless gas models or the Euler equations for gas dynamics.

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Section: Under Review -Under Review -Under Review Comparison Of the R...supporting

confidence: 70%

Section: Under Review -Under Review -Under Review 3 Test Case I: Axia...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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14-moment maximum-entropy modelling of collisionless ions for Hall thruster discharges

Boccelli¹,

McDonald²,

Magin³

2022

Preprint

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“…We denote by = the frequency at which a given neutral particle is hit by a fast-moving ion. We consider an ion density ≈ 10 18 m −3 , a cross-section ≈ 5 × 10 −19 m 2 and an ion velocity ≈ 10 km/s (ions are created at a low velocity and typically accelerate up to, say, 15 − 20 km/s, see for example [24]), giving…”

Section: A Effect Of Ionization and Ion-neutral Interactions On The Dsmc Fieldsmentioning

confidence: 99%

“…We denote by 𝜈 𝑛𝑖 = 𝑛 𝑖 𝜎 𝑛𝑖 𝑉 𝑖 the frequency at which a given neutral particle is hit by a fast-moving ion. We consider an ion density 𝑛 𝑖 ≈ 10 18 m −3 , a cross-section 𝜎 𝑛𝑖 ≈ 5 × 10 −19 m 2 and an ion velocity 𝑉 𝑖 ≈ 10 km/s (ions are created at a low velocity and typically accelerate up to, say, 15 − 20 km/s, see for example [24]), giving 𝜏 𝑛𝑖 ≡ 𝜈 −1 𝑛𝑖 ≈ 2 × 10 −4 s. The residence time of a neutral particle inside the channel can be roughly estimated as 𝜏 𝑛 ≈ 𝐿 tc /𝑉 𝑛 , with 𝐿 tc = 0.025 m and 𝑉 𝑛 ≈ 100 m/s, such that 𝜏 𝑛 ≈ 1.5 × 10 −4 s. From this simplified analysis, the mean ion-neutral collision time and the neutral transit time appear comparable 𝜏 𝑛𝑖 ≈ 𝜏 𝑛 . Therefore, ion-neutral collisions are not the predominant contribution PREPRINThttps://doi.org/10.2514/1.B38346 to the problem, but completely neglecting them, as we do in the present work, is a strong assumption, that should be relaxed in a future work.…”

Section: A Effect Of Ionization and Ion-neutral Interactions On The D...mentioning

confidence: 99%

Numerical Investigation of Reversed Gas-Feed Configurations for Hall Thrusters

Boccelli

Magin

Frezzotti

2021

Journal of Propulsion and Power

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A reversed gas feed configuration for Hall thrusters is proposed and studied numerically. As an alternative to standard direct injection, we investigate the effect of injecting the propellant near the channel exit and directing it backwards, towards the anode. The resulting neutral density and average velocity fields are studied with the Direct Simulation Monte Carlo method for both cold and warm anode conditions. The residence time of neutral particles inside the channel and in the ionization region is computed using a test-particle Monte Carlo method.The computations indicate that the reversed injection allows for increasing the mass utilization efficiency of a standard feed configuration from 2-5% to a maximum of 20-30% depending on the initial efficiency.

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14-moment maximum-entropy modeling of collisionless ions for Hall thruster discharges

2022

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Ions in Hall effect thrusters are often characterized by a low collisionality. In the presence of acceleration fields and azimuthal electric field waves, this results in strong deviations from thermodynamic equilibrium, introducing kinetic effects. This work investigates the application of the 14-moment maximum-entropy model to this problem. This method consists in a set of 14 partial differential equations (PDEs) for the density, momentum, pressure tensor components, heat flux vector, and fourth-order moment associated with the particle velocity distribution function. The model is applied to the study of collisionless ion dynamics in a Hall thruster-like configuration, and its accuracy is assessed against different models, including the Vlasov kinetic equation. Three test cases are considered: a purely axial acceleration problem, the problem of ion-wave trapping, and finally the evolution of ions in the axial-azimuthal plane. Most of this work considers ions only, and the coupling with electrons is removed by prescribing reasonable values of the electric field. This allows us to obtain a direct comparison among different ion models. However, the possibility to run self-consistent plasma simulations is also briefly discussed, considering quasi-neutral or multi-fluid models. The maximum-entropy system appears to be a robust and accurate option for the considered test cases. The accuracy is improved over the simpler pressureless gas model (cold ions) and the Euler equations for gas dynamics, while the computational cost shows to remain much lower than direct kinetic simulations.

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Collisionless ion modeling in Hall thrusters: Analytical axial velocity distribution function and heat flux closures

Cited by 6 publications

References 35 publications

14-moment maximum-entropy modelling of collisionless ions for Hall thruster discharges

14-moment maximum-entropy modelling of collisionless ions for Hall thruster discharges

Numerical Investigation of Reversed Gas-Feed Configurations for Hall Thrusters

14-moment maximum-entropy modeling of collisionless ions for Hall thruster discharges

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