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.>
Integrity signals
Registry
Cites
Statistics
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?
Numerical tricks (enlarged vacuum permittivity, reduced ion mass, thruster size scaling) are still used in many simulations to reduce computational time.
“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]
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 · see citing works
Computer Simulation Using Particles
Hockney, R. W., & EASTWOOD, J. W. (1988) · Institute of Physics eBooks · doi:10.1887/0852743920 · Cited by 5,489 · see citing works
Computer Simulation Using Particles
Hockney, R. W., & EASTWOOD, J. W. (1988) · CRC Press eBooks · doi:10.1201/9780367806934 · Cited by 4,453 · see citing works
Plasma Physics via Computer Simulation
Birdsall, C. K., & Langdon, A. B. (2018) · CRC Press eBooks · doi:10.1201/9781315275048 · Cited by 3,766 · see citing works
Self-citationPlasma physics via computer simulation
Tajima, T. (1986) · Computer Physics Communications · doi:10.1016/0010-4655(86)90240-7 · Cited by 1,306 · see citing works
Dissipation of Currents in Ionized Media
Buneman, O. (1959) · Physical Review · doi:10.1103/physrev.115.503 · Cited by 849 · see citing works
Particle simulation of plasmas
Dawson, J. M. (1983) · Reviews of Modern Physics · doi:10.1103/revmodphys.55.403 · Cited by 786 · see citing works
Child, C. D. (1911) · Physical Review · doi:10.1103/physrevseriesi.32.492 · Cited by 738 · see citing works
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 · see citing works
Langmuir, I. (1923) · Physical Review · doi:10.1103/physrev.21.419 · Cited by 638 · see citing works
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 · see citing works
The Plasma Dispersion Function
(2005) · Series in plasma physics · doi:10.1201/9781420034684.axc · Cited by 521 · see citing works
The particle-in-cell computing method for fluid dynamics
Harlow, F. H. (1964) · Cited by 471 · see citing works
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 · see citing works
Self-citationOpal, C. B., Peterson, W. K., & Beaty, E. C. (1971) · The Journal of Chemical Physics · doi:10.1063/1.1676707 · Cited by 395 · see citing works
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 · see citing works
Bœuf, J.-P., & Marode, E. (1982) · Journal of Physics D Applied Physics · doi:10.1088/0022-3727/15/11/012 · Cited by 328 · see citing works
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 · see citing works
Dawson, J. (1962) · The Physics of Fluids · doi:10.1063/1.1706638 · Cited by 287 · see citing works
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 283 · see citing works
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 · see citing works
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 · see citing works
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 · see citing works
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 · see citing works
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 · see citing works
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 · see citing works
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 · see citing works
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 · see citing works
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 · see citing works
Self-citationTime-reversible difference procedures
Buneman, O. (1967) · Journal of Computational Physics · doi:10.1016/0021-9991(67)90056-3 · Cited by 138 · see citing works
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 · see citing works
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 · see citing works
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 · see citing works
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 · see citing works
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 · see citing works
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 · see citing works
Fry, T. C. (1921) · Physical Review · doi:10.1103/physrev.17.441 · Cited by 97 · see citing works
Computational Plasma Physics: With Applications To Fusion And Astrophysics
Tajima, T. (2019) · CERN Document Server (European Organization for Nuclear Research) · Cited by 96 · see citing works
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 · see citing works
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 · see citing works
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 · see citing works
Computer Experiment of Anomalous Diffusion
Hockney, R. W. (1966) · The Physics of Fluids · doi:10.1063/1.1761939 · Cited by 87 · see citing works
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 · see citing works
Auer, P. L., Hurwitz, H., & Kilb, R. W. (1962) · The Physics of Fluids · doi:10.1063/1.1706615 · Cited by 84 · see citing works
Tajima, T. (2018) · CRC Press eBooks · doi:10.1201/9780429501470 · Cited by 80 · see citing works
An introduction to computational physics
(1998) · Choice Reviews Online · doi:10.5860/choice.35-5142 · Cited by 77 · see citing works
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 · see citing works
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 · see citing works
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 · see citing works
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 · see citing works
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 · see citing works
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 · see citing works
Self-citationBurger, P. (1965) · Journal of Applied Physics · doi:10.1063/1.1714378 · Cited by 54 · see citing works
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 · see citing works
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 · see citing works
Theilhaber, K. S., & Birdsall, C. K. (1989) · Physics of Fluids B Plasma Physics · doi:10.1063/1.859041 · Cited by 51 · see citing works
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 · see citing works
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 · see citing works
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 · see citing works
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 · see citing works
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 · see citing works
Self-citationComputers and Their Role in the Physical Sciences
Fernbach, S., & Taub, A. H. (1970) · Cited by 39 · see citing works
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 · see citing works
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 · see citing works
Theilhaber, K. S., & Birdsall, C. K. (1989) · Physics of Fluids B Plasma Physics · doi:10.1063/1.859204 · Cited by 31 · see citing works
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 · see citing works
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 · see citing works
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 · see citing works
Lomax, R. J. (1960) · Journal of Electronics and Control · doi:10.1080/00207216008962754 · Cited by 24 · see citing works
Collisions in multi-dimensional plasma simulations
Matsuda, Y., & Okuda, H. (1975) · The Physics of Fluids · doi:10.1063/1.861092 · Cited by 22 · see citing works
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 · see citing works
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 · see citing works
Nonexistence of dc States in Low-Pressure Thermionic Converters
Burger, P. (1964) · Journal of Applied Physics · doi:10.1063/1.1713159 · Cited by 16 · see citing works
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 · see citing works
Models of Particles and Moving Media
(1971) · Elsevier eBooks · doi:10.1016/b978-0-12-224250-2.x5001-1 · Cited by 15 · see citing works
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 · see citing works
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 · see citing works
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 · see citing works
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 · see citing works
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 · see citing works
Some calculations of transients in an electronic valve
Hartree, D. R. (1950) · Applied Scientific Research Section B · doi:10.1007/bf02919956 · Cited by 10 · see citing works
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 · see citing works
The opposite-stream plasma diode
Burger, P. (1964) · NASA Technical Reports Server (NASA) · Cited by 6 · see citing works
Computer experiments in plasma physics
Buneman, O., & DUNN, D. A. (1965) · NASA Technical Reports Server (NASA) · Cited by 5 · see citing works
How to get started in particle simulation
Denavit, J., & Kruer, W. L. (1980) · Comments on plasma physics and controlled fusion · Cited by 5 · see citing works
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 · see citing works
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 · see citing works
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 · see citing works
Numerical studies of the low pressure RF plasma
Vender, D. (1990) · ANU Open Research (Australian National University) · doi:10.25911/5d6c405030bd3 · Cited by 2 · see citing works
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 · see citing works
Self-citation
Flagged first, then by citations
1 of the 91 references couldn’t be matched to a known paper.
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 · see citing works
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 · see citing works
Tutorial: Physics and modeling of Hall thrusters
Boeuf, J.-P. (2017) · Journal of Applied Physics · doi:10.1063/1.4972269 · Cited by 504 · see citing works
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 413 · see citing works
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 · see citing works
Self-citationFluid simulations of glow discharges: Effect of metastable atoms in argon
Lymberopoulos, D. P., & Economou, D. J. (1993) · Journal of Applied Physics · doi:10.1063/1.352926 · Cited by 372 · see citing works
Plasma immersion ion implantation—a fledgling technique for semiconductor processing
Chu, P. K.-H., Qin, S., Chan, C., Cheung, N. W., & Larson, L. A. (1996) · Materials Science and Engineering R Reports · doi:10.1016/s0927-796x(96)00194-5 · Cited by 346 · see citing works
Killian, T. C., Pattard, T., Pohl, T., & Rost, J. M. (2007) · Physics Reports · doi:10.1016/j.physrep.2007.04.007 · Cited by 335 · see citing works
Nanbu, K. (2000) · IEEE Transactions on Plasma Science · doi:10.1109/27.887765 · Cited by 327 · see citing works
Pancheshnyi, S., Biagi, S. F., Bordage, M., Hagelaar, G. J. M., Morgan, W. L., Phelps, A. V., & Pitchford, L. C. (2011) · Chemical Physics · doi:10.1016/j.chemphys.2011.04.020 · Cited by 321 · see citing works
Bœuf, J.-P., & Pitchford, L. C. (1995) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.51.1376 · Cited by 320 · see citing works
Particle and fluid simulations of low-temperature plasma discharges: benchmarks and kinetic effects
Kim, H. C., Iza, F., Yang, S. S., Radmilović-Radjenović, M., & Lee, J. K. (2005) · Journal of Physics D Applied Physics · doi:10.1088/0022-3727/38/19/r01 · Cited by 301 · see citing works
Tskhakaya, D., Matyash, K., Schneider, R., & Taccogna, F. (2007) · Contributions to Plasma Physics · doi:10.1002/ctpp.200710072 · Cited by 297 · see citing works
Computer Simulations of Laser Ablation of Molecular Substrates
Zhigilei, L. V., Leveugle, E., Garrison, B. J., Yingling, Y. G., & Zeifman, M. (2003) · Chemical Reviews · doi:10.1021/cr010459r · Cited by 289 · see citing works
Theory of cumulative small-angle collisions in plasmas
Nanbu, K. (1997) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.55.4642 · Cited by 255 · see citing works
Particle 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 · see citing works
Boyle, P. C., Ellingboe, A. R., & Turner, M. M. (2004) · Journal of Physics D Applied Physics · doi:10.1088/0022-3727/37/5/008 · Cited by 247 · see citing works
Collisionless electron heating in an inductively coupled discharge
Turner, M. M. (1993) · Physical Review Letters · doi:10.1103/physrevlett.71.1844 · Cited by 231 · see citing works
Kortshagen, U. R., Busch, C., & Tsendin, L. D. (1996) · Plasma Sources Science and Technology · doi:10.1088/0963-0252/5/1/001 · Cited by 212 · see citing works
Particle simulation methods for studies of low-pressure plasma sources
Donkó, Z. (2011) · Plasma Sources Science and Technology · doi:10.1088/0963-0252/20/2/024001 · Cited by 207 · see citing works
Holste, K., Dietz, P., Scharmann, S., Keil, K., Henning, T., Zschätzsch, D., Reitemeyer, M., Nauschütt, B., Kiefer, F., Kunze, F., et al. (2020) · Review of Scientific Instruments · doi:10.1063/5.0010134 · Cited by 207 · see citing works
Vahedi, V., DiPeso, G. J., Birdsall, C. K., Lieberman, M. A., & Rognlien, T. D. (1993) · Plasma Sources Science and Technology · doi:10.1088/0963-0252/2/4/006 · Cited by 207 · see citing works
Self-citationFourier transform ion cyclotron resonance (FT ICR) mass spectrometry: Theory and simulations
Николаев, Е. Н., Kostyukevich, Y., & Vladimirov, G. (2014) · Mass Spectrometry Reviews · doi:10.1002/mas.21422 · Cited by 201 · see citing works
Hysteresis and the E-to-H transition in radiofrequency inductive discharges
Turner, M. M., & Lieberman, M. A. (1999) · Plasma Sources Science and Technology · doi:10.1088/0963-0252/8/2/312 · Cited by 199 · see citing works
Graves, D. B. (1994) · IEEE Transactions on Plasma Science · doi:10.1109/27.281547 · Cited by 192 · see citing works
Pressure Heating of Electrons in Capacitively Coupled rf Discharges
Turner, M. M. (1995) · Physical Review Letters · doi:10.1103/physrevlett.75.1312 · Cited by 185 · see citing works
A PIC-MCC code for simulation of streamer propagation in air
Chanrion, O., & Neubert, T. (2008) · Journal of Computational Physics · doi:10.1016/j.jcp.2008.04.016 · Cited by 183 · see citing works
Stochastic heating in single and dual frequency capacitive discharges
Kawamura, E., Lieberman, M. A., & LICHTENBERG, A. J. (2006) · Physics of Plasmas · doi:10.1063/1.2203949 · Cited by 179 · see citing works
Nanbu, K., & Yonemura, S. (1998) · Journal of Computational Physics · doi:10.1006/jcph.1998.6049 · Cited by 176 · see citing works
Vahedi, V., Birdsall, C. K., Lieberman, M. A., DiPeso, G. J., & Rognlien, T. D. (1993) · Physics of Fluids B Plasma Physics · doi:10.1063/1.860711 · Cited by 175 · see citing works
Self-citationIon energy distribution control in single and dual frequency capacitive plasma sources
Lee, J. K., Manuilenko, О. V., Babaeva, N. Y., Kim, H. C., & Shon, J. W. (2005) · Plasma Sources Science and Technology · doi:10.1088/0963-0252/14/1/012 · Cited by 175 · see citing works
Capacitively coupled glow discharges at frequencies above 13.56 MHz
Surendra, M., & Graves, D. B. (1991) · Applied Physics Letters · doi:10.1063/1.106112 · Cited by 172 · see citing works
Electrostatic modelling of dual frequency rf plasma discharges
Boyle, P. C., Ellingboe, A. R., & Turner, M. M. (2004) · Plasma Sources Science and Technology · doi:10.1088/0963-0252/13/3/016 · Cited by 169 · see citing works
Foundations of modelling of nonequilibrium low-temperature plasmas
Alves, L. L., Bogaerts, A., Guerra, V., & Turner, M. M. (2018) · Plasma Sources Science and Technology · doi:10.1088/1361-6595/aaa86d · Cited by 166 · see citing works
Lymberopoulos, D. P., & Economou, D. J. (1995) · Journal of Research of the National Institute of Standards and Technology · doi:10.6028/jres.100.036 · Cited by 165 · see citing works
Simultaneous Potential and Circuit Solution for Two-Dimensional Bounded Plasma Simulation Codes
Vahedi, V., & DiPeso, G. J. (1997) · Journal of Computational Physics · doi:10.1006/jcph.1996.5591 · Cited by 160 · see citing works
Space and time resolved electric field measurements in helium and hydrogen RF-discharges
Czarnetzki, U., Luggenhölscher, D., & Döbele, H. F. (1999) · Plasma Sources Science and Technology · doi:10.1088/0963-0252/8/2/004 · Cited by 147 · see citing works
A self-consistent fluid model for radio-frequency discharges in SiH4–H2 compared to experiments
Nienhuis, G. J., Goedheer, W. J., Hamers, E. A. G., van Sark, W. G. J. H. M., & Bezemer, J. (1997) · Journal of Applied Physics · doi:10.1063/1.366016 · Cited by 146 · see citing works
Killian, T. C. (2007) · Science · doi:10.1126/science.1130556 · Cited by 146 · see citing works
E × B electron drift instability in Hall thrusters: Particle-in-cell simulations vs. theory
Bœuf, J.-P., & Garrigues, L. (2018) · Physics of Plasmas · doi:10.1063/1.5017033 · Cited by 143 · see citing works
Modeling of dielectric barrier discharge-induced fluid dynamics and heat transfer
Jayaraman, B., & Shyy, W. (2008) · Progress in Aerospace Sciences · doi:10.1016/j.paerosci.2007.10.004 · Cited by 141 · see citing works
Georgieva, V., Bogaerts, A., & Gijbels, R. (2004) · Physical Review E · doi:10.1103/physreve.69.026406 · Cited by 137 · see citing works
Multipactor prediction for on-board spacecraft RF equipment with the MEST software tool
Lara, J. D., Perez, F., Alfonseca, M., Galán, L., Montero, I., Roman, E., & García‐Baquero, D. R. (2006) · IEEE Transactions on Plasma Science · doi:10.1109/tps.2006.872450 · Cited by 137 · see citing works
3D PIC-MCC simulations of discharge inception around a sharp anode in nitrogen/oxygen mixtures
Teunissen, J., & Ebert, U. (2016) · Plasma Sources Science and Technology · doi:10.1088/0963-0252/25/4/044005 · Cited by 135 · see citing works
Collisionless heating in radio-frequency discharges: a review
Turner, M. M. (2009) · Journal of Physics D Applied Physics · doi:10.1088/0022-3727/42/19/194008 · Cited by 134 · see citing works
Recent Results from Studies of Electric Discharges in the Mesosphere
Neubert, T., RYCROFT, M. J., Farges, T., Blanc, E., Chanrion, O., Arnone, E., Odzimek, A., Arnold, N., Enell, C., Turunen, E., et al. (2008) · Surveys in Geophysics · doi:10.1007/s10712-008-9043-1 · Cited by 134 · see citing works
Wang, H.-Y., Jiang, W., & Wang, Y. (2010) · Plasma Sources Science and Technology · doi:10.1088/0963-0252/19/4/045023 · Cited by 132 · see citing works
Analytic model for a dual frequency capacitive discharge
Kim, H. C., Lee, J. K., & Shon, J. W. (2003) · Physics of Plasmas · doi:10.1063/1.1621000 · Cited by 132 · see citing works
Experimental and theoretical studies of cylindrical Hall thrusters
Smirnov, A. N., Raitses, Y., & Fisch, N. J. (2007) · Physics of Plasmas · doi:10.1063/1.2718522 · Cited by 129 · see citing works
Electron dynamics in low pressure capacitively coupled radio frequency discharges
Wilczek, S., Schulze, J., Brinkmann, R. P., Donkó, Z., Trieschmann, J., & Mussenbrock, T. (2020) · Journal of Applied Physics · doi:10.1063/5.0003114 · Cited by 128 · see citing works
Analytical model of a dual frequency capacitive sheath
Robiche, J., Boyle, P. C., Turner, M. M., & Ellingboe, A. R. (2003) · Journal of Physics D Applied Physics · doi:10.1088/0022-3727/36/15/311 · Cited by 128 · see citing works
Modelling N 2 –O 2 plasmas: volume and surface kinetics
Guerra, V., Tejero-del-Caz, A., Pintassilgo, C. D., & Alves, L. L. (2019) · Plasma Sources Science and Technology · doi:10.1088/1361-6595/ab252c · Cited by 126 · see citing works
Simulation benchmarks for low-pressure plasmas: Capacitive discharges
Turner, M. M., Derzsi, A., Donkó, Z., Eremin, D., Kelly, S., Lafleur, T., & Mussenbrock, T. (2013) · Repository of the Academy's Library (Library of the Hungarian Academy of Sciences) · doi:10.1063/1.4775084 · Cited by 124 · see citing works
Grubert, G. K., Becker, M. M., & Loffhagen, D. (2009) · Physical Review E · doi:10.1103/physreve.80.036405 · Cited by 120 · see citing works
Denpoh, K., & Nanbu, K. (1998) · Journal of Vacuum Science & Technology A Vacuum Surfaces and Films · doi:10.1116/1.581259 · Cited by 120 · see citing works
Vahedi, V., Birdsall, C. K., Lieberman, M. A., DiPeso, G. J., & Ronhlien, T. D. (1993) · Plasma Sources Science and Technology · doi:10.1088/0963-0252/2/4/007 · Cited by 119 · see citing works
Self-citationScaling law for direct current field emission-driven microscale gas breakdown
Venkattraman, A., & Alexeenko, A. A. (2012) · Physics of Plasmas · doi:10.1063/1.4773399 · Cited by 118 · see citing works
Particle-in-cell simulation of gas breakdown in microgaps
Radmilović-Radjenović, M., Lee, J. K., Iza, F., & Park, G. Y. (2005) · Journal of Physics D Applied Physics · doi:10.1088/0022-3727/38/6/027 · Cited by 118 · see citing works
Fundamental investigations of capacitive radio frequency plasmas: simulations and experiments
Donkó, Z., Schulze, J., Czarnetzki, U., Derzsi, A., Hartmann, P., Korolov, I., & Schüngel, E. (2012) · Plasma Physics and Controlled Fusion · doi:10.1088/0741-3335/54/12/124003 · Cited by 117 · see citing works
Kinetic properties of particle-in-cell simulations compromised by Monte Carlo collisions
Turner, M. M. (2006) · Physics of Plasmas · doi:10.1063/1.2169752 · Cited by 117 · see citing works
Anomalous sheath heating in a low pressure rf discharge in nitrogen
Turner, M. M., & Hopkins, M. B. (1992) · Physical Review Letters · doi:10.1103/physrevlett.69.3511 · Cited by 116 · see citing works
Nitschke, T., & Graves, D. B. (1994) · Journal of Applied Physics · doi:10.1063/1.358435 · Cited by 112 · see citing works
Horváth, B., Daksha, M., Korolov, I., Derzsi, A., & Schulze, J. (2017) · Plasma Sources Science and Technology · doi:10.1088/1361-6595/aa963d · Cited by 110 · see citing works
Bœuf, J.-P., & Belenguer, P. (1992) · Journal of Applied Physics · doi:10.1063/1.350666 · Cited by 109 · see citing works
Electron cross-field transport in a low power cylindrical Hall thruster
Смирнов, А. В., Raitses, Y., & Fisch, N. J. (2004) · Physics of Plasmas · doi:10.1063/1.1791639 · Cited by 109 · see citing works
Kawamura, E., Birdsall, C. K., & Vahedi, V. (2000) · Plasma Sources Science and Technology · doi:10.1088/0963-0252/9/3/319 · Cited by 108 · see citing works
Self-citationCoulomb Crystallization in Expanding Laser-Cooled Neutral Plasmas
Pohl, T., Pattard, T., & Rost, J. M. (2004) · Physical Review Letters · doi:10.1103/physrevlett.92.155003 · Cited by 107 · see citing works
Modeling and simulation of plasma etching reactors for microelectronics
Economou, D. J. (2000) · Thin Solid Films · doi:10.1016/s0040-6090(99)01056-1 · Cited by 105 · see citing works
Serikov, V. V., Kawamoto, S., & Nanbu, K. (1999) · IEEE Transactions on Plasma Science · doi:10.1109/27.799817 · Cited by 103 · see citing works
Low-pressure gas discharge modelling
Lister, G. G. (1992) · Journal of Physics D Applied Physics · doi:10.1088/0022-3727/25/12/001 · Cited by 103 · see citing works
The effect of ambipolar electric fields on the electron heating in capacitive RF plasmas
Schulze, J., Donkó, Z., Derzsi, A., Korolov, I., & Schuengel, E. (2014) · Plasma Sources Science and Technology · doi:10.1088/0963-0252/24/1/015019 · Cited by 102 · see citing works
Radiofrequency discharge benchmark model comparison
Surendra, M. (1995) · Plasma Sources Science and Technology · doi:10.1088/0963-0252/4/1/007 · Cited by 102 · see citing works
Heating Mode Transition Induced by a Magnetic Field in a Capacitive rf Discharge
Turner, M. M., Hutchinson, D. A. W., Doyle, R. A., & Hopkins, M. B. (1996) · Physical Review Letters · doi:10.1103/physrevlett.76.2069 · Cited by 102 · see citing works
2D radial-azimuthal particle-in-cell benchmark for <b>E</b> <b>×</b> <b>B</b> discharges
Villafana, W., Petronio, F., Denig, A. C., Jimenez, M. J., Eremin, D., Garrigues, L., Taccogna, F., Alvarez-Laguna, A., Boeuf, J. P., Bourdon, A., et al. (2021) · Plasma Sources Science and Technology · doi:10.1088/1361-6595/ac0a4a · Cited by 101 · see citing works
Langevin Representation of Coulomb Collisions in PIC Simulations
Manheimer, W. M., Lampe, M., & Joyce, G. (1997) · Journal of Computational Physics · doi:10.1006/jcph.1997.5834 · Cited by 101 · see citing works
Derzsi, A., Korolov, I., Schüngel, E., Donkó, Z., & Schulze, J. (2015) · Plasma Sources Science and Technology · doi:10.1088/0963-0252/24/3/034002 · Cited by 100 · see citing works
Liu, Y.-X., Schüngel, E., Korolov, I., Donkó, Z., Wang, Y., & Schulze, J. (2016) · Physical Review Letters · doi:10.1103/physrevlett.116.255002 · Cited by 99 · see citing works
Wilczek, S., Trieschmann, J., Schulze, J., Schuengel, E., Brinkmann, R. P., Derzsi, A., Korolov, I., Donkó, Z., & Mussenbrock, T. (2015) · Plasma Sources Science and Technology · doi:10.1088/0963-0252/24/2/024002 · Cited by 99 · see citing works
Spatially Averaged (Global) Model of Time Modulated High Density Chlorine Plasmas
Ashida, S., & Lieberman, M. A. (1997) · Japanese Journal of Applied Physics · doi:10.1143/jjap.36.854 · Cited by 99 · see citing works
On the reliability of low-pressure dc glow discharge modelling
Donkó, Z., Hartmann, P., & Kutasi, K. (2006) · Plasma Sources Science and Technology · doi:10.1088/0963-0252/15/2/002 · Cited by 97 · see citing works
Salabas, A., Gousset, G., & Alves, L. L. (2002) · Plasma Sources Science and Technology · doi:10.1088/0963-0252/11/4/312 · Cited by 96 · see citing works
Numerical and experimental diagnostics of rf discharges in pure and dusty argon
Belenguer, P., Blondeau, J., Boufendi, L., Toogood, M. J., Plain, A., Bouchoule, A., Laure, C., & Bœuf, J.-P. (1992) · Physical Review A · doi:10.1103/physreva.46.7923 · Cited by 95 · see citing works
Advances in modeling and simulation of vacuum electronic devices
Antonsen, T. M., Mondelli, A. A., Levush, B., Verboncoeur, J. P., & Birdsall, C. K. (1999) · Proceedings of the IEEE · doi:10.1109/5.757256 · Cited by 94 · see citing works
Self-citationeduPIC: An introductory particle based code for radio-frequency plasma simulation
Donkó, Z., Derzsi, A., Vass, M., Horváth, B., Wilczek, S., Hartmann, B., & Hartmann, P. (2021) · Plasma Sources Science and Technology · doi:10.1088/1361-6595/ac0b55 · Cited by 91 · see citing works
Wilczek, S., Trieschmann, J., Schulze, J., Schuengel, E., Brinkmann, R. P., Derzsi, A., Korolov, I., Donkó, Z., & Mussenbrock, T. (2015) · Repository of the Academy's Library (Library of the Hungarian Academy of Sciences) · Cited by 89 · see citing works
Surendra, M., & Dalvie, M. (1993) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.48.3914 · Cited by 88 · see citing works
Brandt, S., Berger, B., Schüngel, E., Korolov, I., Derzsi, A., Bruneau, B., Johnson, E. V., Lafleur, T., O’Connell, D., Koepke, M. E., et al. (2016) · Plasma Sources Science and Technology · doi:10.1088/0963-0252/25/4/045015 · Cited by 88 · see citing works
Formation of microdischarges inside a mesoporous catalyst in dielectric barrier discharge plasmas
Zhang, Y., Wang, H., Zhang, Y., & Bogaerts, A. (2017) · Plasma Sources Science and Technology · doi:10.1088/1361-6595/aa66be · Cited by 88 · see citing works
Wilczek, S., Trieschmann, J., Eremin, D., Brinkmann, R. P., Schulze, J., Schuengel, E., Derzsi, A., Korolov, I., Hartmann, P., Donkó, Z., et al. (2016) · Physics of Plasmas · doi:10.1063/1.4953432 · Cited by 87 · see citing works
Kemp, A. J., Pfund, R. E. W., & Meyer-ter-Vehn, J. (2004) · Physics of Plasmas · doi:10.1063/1.1814367 · Cited by 86 · see citing works
Kinetic phenomena in electron transport in radio-frequency fields
Petrović, Z., Raspopović, Z. M., Dujko, S., & Makabe, T. (2002) · Applied Surface Science · doi:10.1016/s0169-4332(02)00018-1 · Cited by 86 · see citing works
Self-Consistent Particle Simulation of Radio Frequency CF 4 Discharge: Effect of Gas Pressure
Denpoh, K., & Nanbu, K. (2000) · Japanese Journal of Applied Physics · doi:10.1143/jjap.39.2804 · Cited by 81 · see citing works
Николаев, Е. Н., Heeren, R. M. A., Popov, A. M., Pozdneev, A. V., & Chingin, K. (2007) · Rapid Communications in Mass Spectrometry · doi:10.1002/rcm.3234 · Cited by 81 · see citing works
A Monte Carlo simulation of ion transport at finite temperatures
Ristivojević, Z., & Petrović, Z. (2012) · Plasma Sources Science and Technology · doi:10.1088/0963-0252/21/3/035001 · Cited by 81 · see citing works
Hybrid model of a rectangular hollow cathode discharge
Donkó, Z. (1998) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.57.7126 · Cited by 81 · see citing works
Korolov, I., Leimkühler, M., Böke, M., Donkó, Z., der Gathen, V. S.-V., Bischoff, L., Hübner, G., Hartmann, P., Gans, T., Liu, Y., et al. (2020) · Journal of Physics D Applied Physics · doi:10.1088/1361-6463/ab6d97 · Cited by 80 · see citing works
Application of microscale plasma to material processing
Ito, T., Izaki, T., & Terashima, K. (2001) · Thin Solid Films · doi:10.1016/s0040-6090(00)01670-9 · Cited by 80 · see citing works
Krüger, F., Wilczek, S., Mussenbrock, T., & Schulze, J. (2019) · Plasma Sources Science and Technology · doi:10.1088/1361-6595/ab2c72 · Cited by 79 · see citing works
Capacitive discharges driven by combined dc/rf sources
Kawamura, E., Lieberman, M. A., LICHTENBERG, A. J., & Hudson, E. A. (2007) · Journal of Vacuum Science & Technology A Vacuum Surfaces and Films · doi:10.1116/1.2771561 · Cited by 78 · see citing works
The anomalous diffusion of meteor trails
Dyrud, L. P., Oppenheim, M. M., & Endt, A. F. V. (2001) · Geophysical Research Letters · doi:10.1029/2000gl012749 · Cited by 77 · see citing works
- 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 › Plasma Diagnostics and Applications
- 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