On the electron energy distribution function in a Hall-type thruster

Fedotov, Vitalij; Ivanov, А.А.; Guerrini, G.; Vesselovzorov, A. N.; Bacal, M.

doi:10.1063/1.873700

Cited by 33 publications

(12 citation statements)

References 3 publications

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“…Physical collisions with the thruster and mirroring events in the sheath lead to some azimuthal homogenization near the exit plane. The spatially resolved electron energy distribution functions indicate that in some regions of the near-field, the distributions are multipeaked, though more dramatically so than those indicated in the probe measurements of Fedotov et al [30]. The effect of potential fluctuations on smoothing these distributions will be the subject of future research.…”

Section: Discussion and Summarymentioning

confidence: 70%

Single particle simulations of electron transport in the near-field of Hall thrusters

Smith¹,

Cappelli²

2010

J. Phys. D: Appl. Phys.

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The results of 3D, single particle electron trajectory calculations are presented for the near-field of a laboratory E × B Hall plasma thruster. For a prescribed static magnetic and electric field distribution, single electrons are launched and tracked from a simulated cathode. Collisions with external thruster surfaces are accounted for; however, field fluctuations are disregarded. Bulk statistics including the channel to beam electron current ratio, electron lifetimes and spatial distributions of the number density, mean energy, energy distributions, velocity distributions and velocity component ratios are catalogued. For conditions typical of a moderate power Hall thruster, the mean lifetime of electrons in the domain of axial scale length, L = 0.3 m, is approximately 120 ns. Electrons which eventually enter the channel are found to strike the thruster ∼10 3 times as frequently as electrons which exit the domain in the plume. For the static E and B field distributions used in this study, the channel to beam current ratio is found to be on the order of 0.1 and the velocity ratio, V E /V E×B , over the channel has a mean of ∼0.5, with higher values driven largely by collisions with the thruster indicating the importance of such events in driving transport into the channel.

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Section: Discussion and Summarymentioning

confidence: 70%

Single particle simulations of electron transport in the near-field of Hall thrusters

Smith¹,

Cappelli²

2010

J. Phys. D: Appl. Phys.

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“…(1) mathematically manageable. Expressions for the EEDF have been derived in Fedotov et al (1999), Shagayda (2012) and Shagayda and Tarasov (2017) neglecting the electronwall collision. The first have interpreted the EEDF as a beam-plasma electron distribution function with electron beam energy of several tens of eV.…”

Section: Boltzmann Solver Models and Electron Energy Distribution Funmentioning

confidence: 99%

Latest progress in Hall thrusters plasma modelling

Taccogna

Garrigues

2019

Rev. Mod. Plasma Phys.

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In the last thirty years, numerical models have revealed different physical mechanisms involved in the Hall thruster functioning leading to a bridge between analytical prediction / empirical intuition and experiments. For this reason, modeling effort is continuously increasing in the domain of Hall Thrusters. Two basic approaches exist: one based on fluid/hybrid simulation where the distribution of electrons is assumed Maxwellian and the plasma inside the thruster, considered as quasineutral, is described with macroscopic quantities (density, velocity and energy); the second approach is based on kinetic description for charged particles where no approximation is made for the distribution of particles. Fluid or hybrid approaches offer the advantage of demanding low run times and computational resources. They are very useful to perform parametric studies but actually the anomalous phenomena responsible for electron transport across the magnetic field barrier have not been selfconsistently modeled. Kinetic approach is able to better capture phenomena originating on the Debye scale length like the lateral sheaths, ExB electron drift instability, important to explain the anomalous electron transport, but it requires very long run times. For this latter, the progress in computer science offers the advantage to describe conditions more and more close to the thruster operation. In this review, we will present the two approaches emphasizing on numerical schemes used with assumptions and approximations and on main results obtained. Future directions on the Hall thruster modeling will finally outlined.

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“…4 The topic of thermodynamic non-equilibrium transport of electrons in Hall thrusters has been subjected to broad investigation in the electric propulsion community, from the theoretical, experimental and numerical perspectives. [7][8][9][10][11][12] In the operating conditions of interest for Hall thrusters, Coulomb collisions are often negligible compared to collisions with the neutral background. 3 a) Electronic mail: Author to whom correspondence should be addressed: stefano.boccelli@polimi.it b) Electronic mail: fgiro059@uottawa.ca c) Electronic mail: thierry.magin@vki.ac.be d) Electronic mail: groth@utias.utoronto.ca e) Electronic mail: james.mcdonald@uottawa.ca For high values of the Hall parameter, when the electron cyclotron frequency is much higher than the frequency of electron collisions with background neutrals, one can show that the trochoid motion of electrons in the crossed E and B fields gives rise to a ring-shaped velocity distribution function (VDF) centered around the drift velocity, u d = E/B.…”

Section: Introductionmentioning

confidence: 99%

“…9 In terms of the energy distribution function (EDF), two peaks become clearly visible, one associated with the portion of the trajectory with minimum velocity and one with the fast portion of the trochoid. 7,8 Considering the presence of electron-neutral collisions, ionizing reactions also affect the shape of the distribution function by attenuating the high-energy region and producing a population of colder secondary electrons. 9,13 In contrast, elastic collisions with background neutrals randomize the velocities, and thus tend to make the distribution isotropic.…”

Section: Introductionmentioning

confidence: 99%

A 14-moment maximum-entropy description of electrons in crossed electric and magnetic fields

Boccelli,

Giroux,

Magin

et al. 2021

Preprint

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A 14-moment maximum-entropy system of equations is applied to the description of non-equilibrium electrons in crossed electric and magnetic fields and in the presence of low collisionality, characteristic of lowtemperature plasma devices. The flexibility of this formulation is analyzed through comparison with analytical results for steady-state non-equilibrium velocity distribution functions and against particle-based solutions of the time-dependent kinetic equation. Electric and magnetic source terms are derived for the 14-moment equations, starting from kinetic theory. A simplified BGK-like collision term is formulated to describe the collision of electrons with background neutrals, accounting for the large mass disparity and for energy exchange. An approximated expression is proposed for the collision frequency, to include the effect of the electrons drift velocity, showing good accuracy in the considered conditions. The capabilities of the proposed 14-moment closure to capture accurately non-equilibrium behaviour of electrons for space homogeneous problems under conditions representative of those found in Hall thrusters is demonstrated.

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On the electron energy distribution function in a Hall-type thruster

Cited by 33 publications

References 3 publications

Single particle simulations of electron transport in the near-field of Hall thrusters

Single particle simulations of electron transport in the near-field of Hall thrusters

Latest progress in Hall thrusters plasma modelling

A 14-moment maximum-entropy description of electrons in crossed electric and magnetic fields

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