CoChat
Sign Up
Cited by 3,422Plasma Diagnostics and ApplicationsVacuum and Plasma ArcsAtomic and Molecular Physics

Solving the Boltzmann equation to obtain electron transport coefficients and rate coefficients for fluid models

Open access
Hagelaar, G J M, Pitchford, L C·2005·Plasma Sources Science and Technology
DOI 10.1088/0963-0252/14/4/011
Open this paper in CoChat — free accountOpen PDF

Abstract

Fluid models of gas discharges require the input of transport coefficients and rate coefficients that depend on the electron energy distribution function. Such coefficients are usually calculated from collision cross-section data by solving the electron Boltzmann equation (BE). In this paper we present a new user-friendly BE solver developed especially for this purpose, freely available under the name BOLSIG+, which is more general and easier to use than most other BE solvers available. The solver provides steady-state solutions of the BE for electrons in a uniform electric field, using the classical two-term expansion, and is able to account for different growth models, quasi-stationary and oscillating fields, electron–neutral collisions and electron–electron collisions. We show that for the approximations we use, the BE takes the form of a convection-diffusion continuity-equation with a non-local source term in energy space. To solve this equation we use an exponential scheme commonly used for convection-diffusion problems. The calculated electron transport coefficients and rate coefficients are defined so as to ensure maximum consistency with the fluid equations. We discuss how these coefficients are best used in fluid models and illustrate the influence of some essential parameters and approximations.

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Integrity signals

Registry

Crossref · 10.1088/0963-0252/14/4/011

Cites

34 of 34 references verified0 citation errors · 0 not checkable

Statistics

Claims the paper makes

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

  • Calculations using Bolsig+ show that the fraction of electron energy loss (e-Energy LF) in an air-breathing thruster will vary with altitude as the composition of the atmosphere that can be harvested changes.

    “Calculations using Bolsig+ [48] show that the fraction of electron energy loss (e-Energy LF) in an air-breathing thruster will vary with altitude as the composition of the atmosphere that can be harvested changes (Fig. 5C).”

    From Requirements for air-breathing electric propulsion in low-altitude orbits (2024) · cites this paper as [48]

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

The self-check needs the paper’s full text.

Cites

Flagged first, then by citations

Research works printed but not linked: 2

  1. Graves D B and Jensen K F 1986 IEEE Trans. Plasma Sci. PS-14 78
  2. Scharfetter D L and Gummel H K 1969 IEEE Trans. Electron. Devices 16 64

Cited by

Sorted by citations

Related

Authors
Hagelaar, G. J. M., & Pitchford, L. C.
Affiliations
Université Toulouse III - Paul Sabatier (FR)
ORCID
Hagelaar, G J M
Venue
Plasma Sources Science and Technology
Publisher
IOP Publishing
Published
2005-10-05
Volume
14
Issue
4
Pages
722-733
ISSN
  • 0963-0252 (ISSN-L)
  • 1361-6595
DOI
10.1088/0963-0252/14/4/011
OpenAlex
W2153357396
Cited by
3,422
References
34
Citations by year
2026: 212 · 2025: 261 · 2024: 255 · 2023: 300 · 2022: 260 · 2021: 290 · 2020: 242 · 2019: 223 · 2018: 245 · 2017: 182 · 2016: 184 · 2015: 157 · 2014: 155 · 2013: 112 · 2012: 94
FWCI
20.27
Type
journal article
Language
en
Open access
Locations
Plasma Sources Science and Technology (publishedVersion)
Topics
  • Physical Sciences › Engineering › Electrical and Electronic Engineering › Plasma Diagnostics and Applications
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Vacuum and Plasma Arcs
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Atomic and Molecular Physics
Keywords
electron Boltzmann equation, electron transport coefficients, rate constants, gas discharge, fluid model, electron energy distribution, BOLSIG+, electron-electron scattering, electron-neutral collisions, advection-diffusion equation, collision cross sections, uniform electric field

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review