The DOI matches its Crossref record; 90 of the 91 references it cites were found in a registry or an index.
Particle-in-cell charged-particle simulations, plus Monte Carlo collisions with neutral atoms, PIC-MCC
Abstract
Many-particle charged-particle plasma simulations using spatial meshes for the electromagnetic field solutions, particle-in-cell (PIC) merged with Monte Carlo collision (MCC) calculations, are coming into wide use for application to partially ionized gases. The author emphasizes the development of PIC computer experiments since the 1950s starting with one-dimensional (1-D) charged-sheet models, the addition of the mesh, and fast direct Poisson equation solvers for 2-D and 3-D. Details are provided for adding the collisions between the charged particles and neutral atoms. The result is many-particle simulations with many of the features met in low-temperature collision plasmas; for example, with applications to plasma-assisted materials processing, but also related to warmer plasmas at the edges of magnetized fusion plasmas.>
Overview
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
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?
In the citing paper
“Nevertheless, numerical tricks (e.g. enlarged vacuum permittivity and/or reduction of ion mass or thruster size scaling) are still used in many simulations to reduce the computational time (see Refs. 59-64 for E × B thrusters, and Refs. 65-67 for PATs).”
From Plasma propulsion modeling with particle-based algorithms (2023) · cites this paper as [59]
Citations
Cites
Physics of Fully Ionized Gases
Spitzer, L., & Seeger, R. J. (1963) · American Journal of Physics · doi:10.1119/1.1969155 · Cited by 5,665
Computer Simulation Using Particles
Hockney, R. W., & EASTWOOD, J. W. (1988) · Institute of Physics eBooks · doi:10.1887/0852743920 · Cited by 5,489
Computer Simulation Using Particles
Hockney, R. W., & EASTWOOD, J. W. (1988) · CRC Press eBooks · doi:10.1201/9780367806934 · Cited by 4,603
Plasma Physics via Computer Simulation
Birdsall, C. K., & Langdon, A. B. (2018) · CRC Press eBooks · doi:10.1201/9781315275048 · Cited by 3,851
Self-citationPlasma physics via computer simulation
Tajima, T. (1986) · Computer Physics Communications · doi:10.1016/0010-4655(86)90240-7 · Cited by 1,341
Dissipation of Currents in Ionized Media
Buneman, O. (1959) · Physical Review · doi:10.1103/physrev.115.503 · Cited by 849
Particle simulation of plasmas
Dawson, J. M. (1983) · Reviews of Modern Physics · doi:10.1103/revmodphys.55.403 · Cited by 786
Child, C. D. (1911) · Physical Review · doi:10.1103/physrevseriesi.32.492 · Cited by 738
A Fast Direct Solution of Poisson's Equation Using Fourier Analysis
Hockney, R. W. (1965) · Journal of the ACM · doi:10.1145/321250.321259 · Cited by 684
Langmuir, I. (1923) · Physical Review · doi:10.1103/physrev.21.419 · Cited by 638
A binary collision model for plasma simulation with a particle code
Takizuka, T., & Abe, H. (1977) · Journal of Computational Physics · doi:10.1016/0021-9991(77)90099-7 · Cited by 588
The Plasma Dispersion Function
(2005) · Series in plasma physics · doi:10.1201/9781420034684.axc · Cited by 521
The particle-in-cell computing method for fluid dynamics
Harlow, F. H. (1964) · Cited by 471
Simultaneous Potential and Circuit Solution for 1D Bounded Plasma Particle Simulation Codes
Verboncoeur, J. P., Alves, M. V., Vahedi, V., & Birdsall, C. K. (1993) · Journal of Computational Physics · doi:10.1006/jcph.1993.1034 · Cited by 464
Self-citationOpal, C. B., Peterson, W. K., & Beaty, E. C. (1971) · The Journal of Chemical Physics · doi:10.1063/1.1676707 · Cited by 395
P3M3DP—The three-dimensional periodic particle-particle/ particle-mesh program
EASTWOOD, J. W., Hockney, R. W., & Lawrence, D. N. (1980) · Computer Physics Communications · doi:10.1016/0010-4655(80)90052-1 · Cited by 366
Bœuf, J.-P., & Marode, E. (1982) · Journal of Physics D Applied Physics · doi:10.1088/0022-3727/15/11/012 · Cited by 328
Numerical Simulation of the Weibel Instability in One and Two Dimensions
Morse, R. L., & Nielson, C. W. (1971) · The Physics of Fluids · doi:10.1063/1.1693518 · Cited by 303
Self-consistent model of a direct-current glow discharge: Treatment of fast electrons
Surendra, M., Graves, D. B., & Jellum, G. M. (1990) · Physical Review A · doi:10.1103/physreva.41.1112 · Cited by 290
Dawson, J. (1962) · The Physics of Fluids · doi:10.1063/1.1706638 · Cited by 287
Calculation of distribution functions by exploiting the stability of the steady state
Rees, H. D. (1969) · Journal of Physics and Chemistry of Solids · doi:10.1016/0022-3697(69)90018-3 · Cited by 270
Clouds-in-clouds, clouds-in-cells physics for many-body plasma simulation
Birdsall, C. K., & Fuss, D. (1969) · Journal of Computational Physics · doi:10.1016/0021-9991(69)90058-8 · Cited by 261
Self-citationParticle simulations of radio-frequency glow discharges
Surendra, M., & Graves, D. B. (1991) · IEEE Transactions on Plasma Science · doi:10.1109/27.106808 · Cited by 255
Monte Carlo simulation of ion motion in drift tubes
Lin, S., & Bardsley, J. N. (1977) · The Journal of Chemical Physics · doi:10.1063/1.433988 · Cited by 232
Numerical modeling of low-pressure RF plasmas
Vender, D., & Boswell, R. (1990) · IEEE Transactions on Plasma Science · doi:10.1109/27.57527 · Cited by 222
Numerical Simulation of Warm Two-Beam Plasma
Morse, R. L., & Nielson, C. W. (1969) · The Physics of Fluids · doi:10.1063/1.1692361 · Cited by 201
Effects of the spatial grid in simulation plasmas
Langdon, A. B. (1970) · Journal of Computational Physics · doi:10.1016/0021-9991(70)90024-0 · Cited by 188
Electron Dynamics of Diode Regions
Birdsall, C. K., Bridges, W. B., & Simpson, J. A. (1967) · Physics Today · doi:10.1063/1.3033997 · Cited by 168
Self-citationTheory of Plasma Simulation Using Finite-Size Particles
LANGDON, A. B., & Birdsall, C. K. (1970) · The Physics of Fluids · doi:10.1063/1.1693209 · Cited by 166
Self-citationTime-reversible difference procedures
Buneman, O. (1967) · Journal of Computational Physics · doi:10.1016/0021-9991(67)90056-3 · Cited by 138
Electron heating in low-pressure rf glow discharges
Surendra, M., Graves, D. B., & Morey, I. J. (1990) · Applied Physics Letters · doi:10.1063/1.102604 · Cited by 137
P3M3DP-the three-dimensional periodic particle-particle/particle-mesh program
EASTWOOD, J. W., Hockney, R. W., & Lawrence, D. N. (1984) · Computer Physics Communications · doi:10.1016/s0010-4655(84)82783-6 · Cited by 124
Self-consistent simulation of a parallel-plate rf discharge
Boswell, R., & Morey, I. J. (1988) · Applied Physics Letters · doi:10.1063/1.99327 · Cited by 115
Collisions in a Plasma of Finite-Size Particles
Okuda, H., & Birdsall, C. K. (1970) · The Physics of Fluids · doi:10.1063/1.1693210 · Cited by 100
Self-citationSpace-Charge Instabilities in Electron Diodes and Plasma Converters
Birdsall, C. K., & Bridges, W. B. (1961) · Journal of Applied Physics · doi:10.1063/1.1728361 · Cited by 99
Self-citationCalculation of steady state distribution functions by exploiting stability
Rees, H. D. (1968) · Physics Letters A · doi:10.1016/0375-9601(68)90251-x · Cited by 98
Fry, T. C. (1921) · Physical Review · doi:10.1103/physrev.17.441 · Cited by 97
Computational Plasma Physics: With Applications To Fusion And Astrophysics
Tajima, T. (2019) · CERN Document Server (European Organization for Nuclear Research) · Cited by 96
Electromagnetic and Relativistic Plasma Simulation Models
LANGDON, A. B., & Lasinski, B. F. (1976) · Methods in computational physics · doi:10.1016/b978-0-12-460816-0.50014-2 · Cited by 95
Nonphysical noises and instabilities in plasma simulation due to a spatial grid
Okuda, H. (1972) · Journal of Computational Physics · doi:10.1016/0021-9991(72)90048-4 · Cited by 91
Time-Dependent Computer Analysis of Electron—Wave Interaction in Crossed Fields
Yu, S., Kooyers, G. P., & Buneman, O. (1965) · Journal of Applied Physics · doi:10.1063/1.1714528 · Cited by 88
Computer Experiment of Anomalous Diffusion
Hockney, R. W. (1966) · The Physics of Fluids · doi:10.1063/1.1761939 · Cited by 87
One-Dimensional Model of a Lorentz Plasma
Shanny, R. A., Dawson, J. M., & Greene, J. M. (1967) · The Physics of Fluids · doi:10.1063/1.1762273 · Cited by 84
Auer, P. L., Hurwitz, H., & Kilb, R. W. (1962) · The Physics of Fluids · doi:10.1063/1.1706615 · Cited by 84
Tajima, T. (2018) · CRC Press eBooks · doi:10.1201/9780429501470 · Cited by 80
An introduction to computational physics
(1998) · Choice Reviews Online · doi:10.5860/choice.35-5142 · Cited by 77
A one-dimensional collisional model for plasma-immersion ion implantation
Vahedi, V., Lieberman, M. A., Alves, M. V., Verboncoeur, J. P., & Birdsall, C. K. (1991) · Journal of Applied Physics · doi:10.1063/1.348774 · Cited by 72
Self-citationNumerical Experiments with a Plasma Model
Eldridge, O. C., & Feix, M. R. (1963) · The Physics of Fluids · doi:10.1063/1.1706746 · Cited by 71
Electron sub-cycling in particle simulation of plasma
Adam, J. C., Servenière, A. G., & LANGDON, A. B. (1982) · Journal of Computational Physics · doi:10.1016/0021-9991(82)90076-6 · Cited by 67
One-Dimensional Plasma Model at Thermodynamic Equilibrium
Eldridge, O. C., & Feix, M. R. (1962) · The Physics of Fluids · doi:10.1063/1.1724476 · Cited by 65
Low Mach Number Magnetic Compression Waves in a Collision-Free Plasma
Auer, P. L., Hurwitz, H., & Kilb, R. W. (1961) · The Physics of Fluids · doi:10.1063/1.1706455 · Cited by 56
Space-Charge Instabilities in Electron Diodes. II
Bridges, W. B., & Birdsall, C. K. (1963) · Journal of Applied Physics · doi:10.1063/1.1729100 · Cited by 54
Self-citationBurger, P. (1965) · Journal of Applied Physics · doi:10.1063/1.1714378 · Cited by 54
Monte Carlo Calculation of Noise Near the Potential Minimum of a High-Frequency Diode
Tien, P. K., & Moshman, J. (1956) · Journal of Applied Physics · doi:10.1063/1.1722543 · Cited by 53
Kinetic theory for fluctuations and noise in computer simulation of plasma
LANGDON, A. B. (1979) · The Physics of Fluids · doi:10.1063/1.862452 · Cited by 52
Theilhaber, K. S., & Birdsall, C. K. (1989) · Physics of Fluids B Plasma Physics · doi:10.1063/1.859041 · Cited by 51
Self-citationComputational plasma physics with applications to fusion and astrophysics
Mense, A. T., & Frankel, J. I. (1989) · Annals of Nuclear Energy · doi:10.1016/0306-4549(89)90064-9 · Cited by 51
Sheath voltage ratio for asymmetric rf discharges
Alves, M. V., Lieberman, M. A., Vahedi, V., & Birdsall, C. K. (1991) · Journal of Applied Physics · doi:10.1063/1.348436 · Cited by 47
Self-citationThe optimization of particle calculations in 2 and 3 dimensions
Boris, J. P., & Roberts, K. V. (1969) · Journal of Computational Physics · doi:10.1016/0021-9991(69)90020-5 · Cited by 41
Dispersion relation for computer-simulated plasmas
Lindman, E. L. (1970) · Journal of Computational Physics · doi:10.1016/0021-9991(70)90049-5 · Cited by 41
Multi-scale particle-in-cell plasma simulation
Friedman, A., Parker, S., Ray, S., & Birdsall, C. K. (1991) · Journal of Computational Physics · doi:10.1016/0021-9991(91)90265-m · Cited by 41
Self-citationComputers and Their Role in the Physical Sciences
Fernbach, S., & Taub, A. H. (1970) · Cited by 39
Thermal Relaxation in One- and Two-Dimensional Plasma Models
MONTGOMERY, D. C., & Nielson, C. W. (1970) · The Physics of Fluids · doi:10.1063/1.1693081 · Cited by 39
Computer experiments on ion-beam neutralization with initially cold electrons
DUNN, D. A., & Ho, I. (1963) · AIAA Journal · doi:10.2514/3.2171 · Cited by 33
Theilhaber, K. S., & Birdsall, C. K. (1989) · Physics of Fluids B Plasma Physics · doi:10.1063/1.859204 · Cited by 31
Self-citationVerification of Theory for Plasma of Finite-Size Particles
Okuda, H. (1972) · The Physics of Fluids · doi:10.1063/1.1694076 · Cited by 28
Sheet-Current Plasma Model for Ion-Cyclotron Waves
Hasegawa, A., & Birdsall, C. K. (1964) · The Physics of Fluids · doi:10.1063/1.1711064 · Cited by 27
Self-citationAn orbit averaged particle code
Cohen, B. I., Brengle, T. A., Conley, D. B., & Freis, R. P. (1980) · Journal of Computational Physics · doi:10.1016/0021-9991(80)90011-x · Cited by 26
Lomax, R. J. (1960) · Journal of Electronics and Control · doi:10.1080/00207216008962754 · Cited by 24
Collisions in multi-dimensional plasma simulations
Matsuda, Y., & Okuda, H. (1975) · The Physics of Fluids · doi:10.1063/1.861092 · Cited by 22
Two-dimensional computer experiments on ion- beam neutralization
Wadhwa, R. P., Buneman, O., & Brauch, D. F. (1965) · AIAA Journal · doi:10.2514/3.3057 · Cited by 19
Computer Experiments on the Randomization of Electrons in a Collisionless Plasma
Burger, P., DUNN, D. A., & Halsted, A. S. (1965) · The Physics of Fluids · doi:10.1063/1.1761194 · Cited by 18
Nonexistence of dc States in Low-Pressure Thermionic Converters
Burger, P. (1964) · Journal of Applied Physics · doi:10.1063/1.1713159 · Cited by 16
Excitation of ion oscillations by beam-plasma interaction
Vermeer, A., Matitti, T., Hopman, H. J., & Kistemaker, J. (1967) · Plasma Physics · doi:10.1088/0032-1028/9/3/301 · Cited by 16
Models of Particles and Moving Media
(1971) · Elsevier eBooks · doi:10.1016/b978-0-12-224250-2.x5001-1 · Cited by 15
FINITE-SIZE PARTICLE PHYSICS APPLIED TO PLASMA SIMULATION.
Birdsall, C. K., Langdon, A. B., & Okuda, H. (1970) · OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) · Cited by 14
Self-citationCharacteristics of Noise in a Two-Dimensional Computer Plasma
Hockney, R. W. (1968) · The Physics of Fluids · doi:10.1063/1.1692116 · Cited by 13
Heating of magnetized plasmas by a large-amplitude low-frequency electric field
Chen, L., & Birdsall, C. K. (1973) · The Physics of Fluids · doi:10.1063/1.1694291 · Cited by 13
Self-citationElastic Collisions in Simulating One-Dimensional Plasma Diodes on the Computer
Burger, P. (1967) · The Physics of Fluids · doi:10.1063/1.1762162 · Cited by 11
Stability and application of an orbit-averaged magneto-inductive particle code
Cohen, B. I., & Freis, R. P. (1982) · Journal of Computational Physics · doi:10.1016/0021-9991(82)90109-7 · Cited by 10
Some calculations of transients in an electronic valve
Hartree, D. R. (1950) · Applied Scientific Research Section B · doi:10.1007/bf02919956 · Cited by 10
FAST NUMERICAL PROCEDURES FOR COMPUTER EXPERIMENTS ON RELATIVISTIC PLASMAS.
Buneman, O. (1969) · OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) · Cited by 10
The opposite-stream plasma diode
Burger, P. (1964) · NASA Technical Reports Server (NASA) · Cited by 6
Computer experiments in plasma physics
Buneman, O., & DUNN, D. A. (1965) · NASA Technical Reports Server (NASA) · Cited by 5
How to get started in particle simulation
Denavit, J., & Kruer, W. L. (1980) · Comments on plasma physics and controlled fusion · Cited by 5
Simultaneous Potential and Circuit Solution for Bounded Plasma Particle Simulation Codes,
Verboncoeur, J. P., Alves, M. V., & Vahedi, V. (1990) · doi:10.21236/ada233507 · Cited by 5
A relativistic Monte Carlo binary collision model for use in plasma particle simulation codes
Procassini, R. J., Birdsall, C. K., Morse, E., & Cohen, B. I. (1987) · Unknown eBooks · Cited by 4
Self-citationThe DIPSI computer code user's manual
Procassini, R. J., & Cohen, B. I. (1992) · OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) · Cited by 2
Numerical studies of the low pressure RF plasma
Vender, D. (1990) · ANU Open Research (Australian National University) · doi:10.25911/5d6c405030bd3 · Cited by 2
Birdsall, C. K., Langdon, A. B., McKee, C. F., Okuda, H., & Wong, D. Y. (1969) · OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) · Cited by 1
Self-citation
Flagged first, then by citations
1 of the 91 references couldn’t be matched to a known paper.
Research works printed but not linked: 17
- procassini, 1990, The TESS computer code user's manual
- dawson, 1962, Some investigations of plasma instabilities in one-dimensional plasmas
- 10.1063/1.1692361 · DOI
- buneman, 1968, Relativistic Plasmas, 205
- langdon, 1970, Nonphysical modifications to oscillations, fluctuations, and collisions due to space-time differencing, Proc 4th Conf Num Sim Plasmas, 467
- langdon, 1976, Meth Comput Phys, 16, 327
- langdon, 1967, Investigations of a sheet model for a bounded plasma field and radiation, Proc 4th Conf Num Sim Plasmas, 39
- hockney, 1970, Plasma Physics, 9, 135
- birdsall, 1970, Plasma Physics, 9, 241
- 1985, Multiple Time Scales
- boardman, 1980, Applied Physics, 4, 355
- boris, 1970, Relativistic plasma simulation-optimization of a hybrid code, Proc 4th Conf Num Sim Plasmas, 3
- surendra, 0, Particle simulations of radiofrequency glow discharges, IEEE Trans Plasma Sci
- 1970, Plasma Physics, 9
- 1976, Plasma Physics, 16
- birdsall, 1968, Cloud-in-cell computer experiments in two and three dimensions, Proc 4th Conf Num Sim Plasmas
- hockney, 1963, Quart Res Rev, 1
Cited by
Sorted by citations
Vahedi, V., & Surendra, M. (1995) · Computer Physics Communications · doi:10.1016/0010-4655(94)00171-w · Cited by 1,065
Physics and technology of magnetron sputtering discharges
Guðmundsson, J. T. (2020) · Plasma Sources Science and Technology · doi:10.1088/1361-6595/abb7bd · Cited by 536
Tutorial: Physics and modeling of Hall thrusters
Boeuf, J.-P. (2017) · Journal of Applied Physics · doi:10.1063/1.4972269 · Cited by 504
DIRECT SIMULATION MONTE CARLO: Recent Advances and Applications
Oran, E. S., Oh, C. K., & Cybyk, B. Z. (1998) · Annual Review of Fluid Mechanics · doi:10.1146/annurev.fluid.30.1.403 · Cited by 418
Ion energy distributions in rf sheaths; review, analysis and simulation
Kawamura, E., Vahedi, V., Lieberman, M. A., & Birdsall, C. K. (1999) · Plasma Sources Science and Technology · doi:10.1088/0963-0252/8/3/202 · Cited by 383
Self-citation
Metadata
- Authors
- Birdsall, C. K.
- Affiliations
- University of California, Berkeley (US)
- Corresponding author
- Birdsall, C.K.
- Venue
- IEEE Transactions on Plasma Science
- Published
- 1991-04
- Volume
- 19
- Issue
- 2
- Pages
- 65-85
- ISSN
- 0093-3813 (ISSN-L)
- OpenAlex
- W2165215367
- Cited by
- 1,363
- References
- 91
- Citations by year
- 2026: 40 · 2025: 67 · 2024: 48 · 2023: 51 · 2022: 46 · 2021: 68 · 2020: 44 · 2019: 42 · 2018: 66 · 2017: 53 · 2016: 40 · 2015: 52 · 2014: 50 · 2013: 42 · 2012: 40
- FWCI
- 26.44
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- IEEE Transactions on Plasma Science (publishedVersion)
- Topics
- Physical Sciences › Engineering › Electrical and Electronic Engineering › Low-Pressure Plasma Processing and Diagnostics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Dust and Plasma Wave Phenomena
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Magnetic confinement fusion research
- Keywords
- particle-in-cell simulation, Monte Carlo collisions, partially ionized plasma, Poisson solver
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
