Pith. sign in

REVIEW 3 major objections 5 minor 28 references

Numerical modeling of two magnetized counter-propagating weakly collisional plasma flows in arch configuration

T0 review · 3 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Two counter-streaming plasma flows in an arched magnetic field interact in two regimes, separated by the magnetic Mach number crossing unity.

desk verdict Plausible two-regime picture for a planned arch experiment, but the kinetic 'confirmation' is not dimensionless-matched and the Weibel/turbulence claims rest on a hybrid model that the authors admit cannot capture them. read the letter →

arxiv 2412.06065 v2 pith:3Y7ZFSFX submitted 2024-12-08 physics.plasm-ph

Artem V. Korzhimanov , Sergey A. Koryagin , Andrey D. Sladkov , Mikhail E. Viktorov This is my paper · ORCID
classification physics.plasm-ph
keywords magneticplasmaarchreconnectionWeibelinstabilityMachnumberE×Bdriftioncyclotronsurfacewaveshybridparticle-in-cellsimulationcollisionlessflows
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper uses numerical modeling to predict what happens when two supersonic plasma flows are injected head-on into an arched magnetic field from its two bases. It claims the interaction is governed by the magnetic Mach number $M_m = V_0/V_A$: below $M_m=1$ the flows form a quasi-stationary plasma arch that slowly expands through $\mathbf{E}\times\mathbf{B}$ drift, while above $M_m=1$ the arch breaks up through intense magnetic reconnection, plasmoid formation, and turbulence. The simulations also show filamentation of the flows from the Weibel instability and surface waves near the ion-cyclotron frequency on the arch boundaries. The modeling is deliberately matched to a planned laboratory experiment, so the paper also formulates observable signatures for each regime. A scaled fully kinetic simulation is offered as confirmation that electron kinetic effects do not overturn the hybrid picture.

What carries the argument

The central object is the arched magnetic-field configuration with a magnetic Mach number of order unity, $M_m = V_0/V_A \sim 1$, where $V_0$ is the injected flow speed and $V_A$ the Alfv\'en speed; this single control parameter sorts the dynamics into subcritical and overcritical regimes. The argument is carried by a two-dimensional hybrid simulation (kinetic ions, fluid electrons with a 10-moment pressure tensor, in the Darwin low-frequency approximation that neglects displacement current but retains inductive fields) run at experimental scales, supplemented by a fully kinetic particle-in-cell run at scaled parameters. The key mechanisms inside this machinery are the diamagnetic compression that produces the transverse electric field driving $\mathbf{E}\times\mathbf{B}$ drift; the ion-cyclotron surface wave whose growth is traced to the $T_\parallel > T_\perp$ anisotropy of the injected ions; and the Weibel instability driven by electron pressure anisotropy, with its expected strongest mode at $k \sim 1/r_{ce}$ in the external magnetic field.

What would settle it

Run the fully kinetic simulation with the hybrid run's dimensionless beam widths, $w_0/d_0 \approx 6.36$ and $w_0/r_i \approx 6.70$, instead of the $0.25$ and $0.27$ used in the scaled run, and look for the subcritical/overcritical transition; if the two-regime split disappears, the kinetic confirmation fails. In the planned laboratory experiment, ramping the coil current through $M_m = 1$ and measuring whether the arch changes from slow expansion to plasmoid-shedding turbulent breakup would settle the claim directly.

Watch

Extended reading notes

Core claim

On its own terms, the paper establishes that the collision of two magnetized counter-streaming plasma flows in an arch configuration is neither stationary nor in equilibrium, and that the magnetic Mach number separates two observable behaviors. In the subcritical regime ($M_m < 1$), the demagnetized ions and magnetized electrons form a plasma tube whose diamagnetic compression of the magnetic field induces a transverse electric field; the resulting $\mathbf{E}\times\mathbf{B}$ drift slowly pushes the arch outward, creating a diagonal null line with oppositely directed magnetic fields where reconnection proceeds too slowly to break the arch. In the overcritical regime ($M_m > 1$), the higher flow pressure drives rapid reconnection accompanied by tearing instability, detached plasmoids, and a quasi-turbulent mixing of field lines. In both regimes, the interpenetrating flows develop electron pressure anisotropy that feeds the Weibel instability and density filamentation, and the tube boundaries carry elliptically polarized surface waves near the ion-cyclotron frequency. The paper argues these effects will be visible in the planned experiment as arch-edge brightening, slow outward drift, turbulent breakup, and radio emission near the electron cyclotron frequency.

Load-bearing premise

The paper's conclusions rest on assuming that the scaled fully kinetic run, with its much narrower beam and reduced mass ratio, still represents the same physics as the full-scale hybrid run and confirms it.

Editorial extensions

If this is right

  • If the central claim is correct, the planned experiment should see a sharp change when the flow pressure crosses the magnetic pressure: a quasi-stationary arch with bright edges below $M_m=1$, and turbulent breakup with plasmoids above it.
  • The slow outward drift of the arch should be measurable with a high-speed camera, the surface waves should appear in a MHz-frequency receiver, and the turbulent reconnection should emit GHz radiation near the electron cyclotron frequency.
  • Because the regime boundary sits at $M_m\sim1$, the experiment can be tuned by varying the discharge current or the coil magnetic field to sit exactly at the transition and test the predicted threshold.
  • The Weibel filaments should appear as bright threads along the flow direction, consistent with the luminous threads already visible in the preliminary optical-glow images.
  • The scaled kinetic simulation implies that electron-scale effects strengthen filamentation but do not change the regime classification, so the computationally cheaper hybrid model can be used to plan and interpret the experiment.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A direct test the paper leaves implicit is to scan $M_m$ across unity while holding the other dimensionless parameters fixed; a clear threshold in arch-expansion speed and reconnection activity would confirm the two-regime split.
  • Because the scaled kinetic run used a much narrower beam than the hybrid run ($w_0/d_0 = 0.25$ versus $6.36$, and $w_0/r_i = 0.27$ versus $6.70$), a kinetic run that matches the hybrid dimensionless beam width would test whether the confirmation is quantitative or only qualitative.
  • The same two-regime logic may apply to solar and magnetospheric arch structures: slow reconnection below $M_m=1$ could explain persistent loops, while $M_m>1$ conditions would favor eruptive breakup.
  • Seeding the injected flows with a small initial perpendicular temperature would test whether the surface-wave growth and the subcritical/overcritical boundary shift, since the ion-cyclotron instability depends on maintaining $T_\parallel > T_\perp$.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. Korzhimanov et al. report two-dimensional numerical simulations of two counter-streaming, weakly collisional plasma flows injected along an arched external magnetic field, motivated by a planned experiment on an arc-discharge setup. The study combines full-scale hybrid simulations (the authors' AKA code, with kinetic ions and a 10-moment electron fluid) and a smaller fully kinetic particle-in-cell simulation (Smilei) at scaled parameters. The central claims are that the interaction is non-equilibrium and non-stationary, that the arch expands via E x B drift and forms a region of oppositely directed magnetic fields where reconnection occurs, that two regimes exist separated by a magnetic Mach number of order unity (slow reconnection for Mm < 1, more intense reconnection and turbulence for Mm > 1), that Weibel instability produces density filamentation, and that surface waves near the ion-cyclotron frequency are excited. The abstract, Section V, and Section VI present the two-regime split and the statement that fully kinetic modeling at scaled parameters confirmed the main conclusions of the hybrid modeling as the principal results.

Significance. If the conclusions hold, the paper provides concrete, falsifiable predictions for an experiment: two interaction regimes, arch expansion, filaments visible in optical glow, MHz-range surface waves, possible GHz-range radiation, and high-energy electrons. The study is useful because it connects a specific experimental geometry to kinetic and hybrid simulations, and it supplies a parameter table (Table I) that makes the scaling assumptions transparent. The use of two independent codes and prior validation of the AKA code on related problems are strengths. However, the significance is moderated by the admitted limitations of the hybrid electron closure for Weibel and turbulization, and by the fact that the kinetic run is not a dimensionless match to the hybrid run. These issues directly affect the load-bearing claim of kinetic confirmation.

major comments (3)
  1. [Section III and Table I] The scaling claim in Section III that 'the remaining quantities were chosen so as to preserve the main dimensionless parameters without significant changes' is contradicted by Table I. The ratios w0/d0 and w0/ri change by a factor of about 25 between the hybrid run (6.36 and 6.70) and the kinetic run (0.25 and 0.27), and w0/re changes from 670 to 4.29. The kinetic beam is therefore narrower than one ion inertial length and one ion gyroradius, whereas the hybrid beams are several ion scales wide. Since the paper's claims about Weibel filament width, tearing/reconnection geometry, and surface waves at k ~ 1/d_i depend on these ratios, the fully kinetic run is not a weakly scaled copy of the arch configuration. Section VI's statement that 'fully kinetic modeling at scaled parameters confirmed the main conclusions of the hybrid modeling' is consequently not supported by the presented comparison. The authors should either perform a kinetic run with matched dimensionless ratios or substantially qualify what the present kinetic run can confirm.
  2. [Section IV.B and IV.C] The paper itself states in Section IV.B that the hybrid code 'does not allow to investigate the turbulization as it does not resolve electron spatial scales' and in Section IV.C that Weibel instability 'cannot be correctly described in hydrodynamic approximation for electrons.' Nevertheless, the hybrid simulations are used to attribute the observed filamentation to Weibel instability and to predict turbulization in the overcritical regime. Since the kinetic confirmation is at mismatched parameters (see previous comment), the electron-kinetic aspects of the central claims—filament width, the nature of the turbulent state, and the reconnection rate—rest on hybrid electron-fluid modeling alone. The manuscript should state explicitly which conclusions are supported by the hybrid model and which require kinetic simulation, and should not present the kinetic run as a validation of these electron-kinetic effects.
  3. [Section IV and Section V] The two-regime picture is presented as a threshold at Mm ~ 1, with Section V describing the 'most interesting dynamics' at 'magnetic Mach numbers slightly greater than unity.' However, the presented hybrid runs correspond to Mm = 0.95 (subcritical, velocity V0) and Mm = 1.9 (overcritical, velocity 2V0), with no simulation at a near-critical value just above unity. The abstract and conclusions frame the Mm < 1 / Mm > 1 split and the associated 'more intense' reconnection and turbulization as demonstrated results, but the overcritical behavior is shown only at Mm = 1.9. The threshold behavior is therefore an extrapolation from two points. A scan in flow velocity around Mm = 1, or a clear statement that the near-critical regime is inferred rather than simulated, is needed to support the central claim.
minor comments (5)
  1. [Figure 10 caption] The caption reads 'initial particle concentration anf velocity of flows'; 'anf' should be 'and.'
  2. [Table I] In the kinetic column of Table I, the Alfvén velocity entry contains a stray space: '1 .05 × 109 cm/s' should be '1.05 × 10^9 cm/s.'
  3. [Equations (1)-(12)] The notation for velocity variables is inconsistent: vs and vi are used for phase-space velocity without boldface in some inline occurrences, while V_s denotes bulk velocity. Boldface should be used consistently for vector quantities in the equations and in the text.
  4. [Section III] The scaling paragraph would benefit from an explicit list of the dimensionless parameters that were intended to be preserved, rather than only a qualitative description followed by Table I. This would make it easier for the reader to see which ratios are matched and which are not.
  5. [Reference 20] Reference 20 is cited as an arXiv preprint (arXiv:2305.03539); if a peer-reviewed version exists, it should be cited instead or in addition.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular derivation chain: simulation outputs are self-contained; the kinetic scaling mismatch is a validity concern, not a circular step.

full rationale

All load-bearing claims in this paper are outputs of numerical simulations rather than consequences of fitted inputs or self-citations. The hybrid equations (Sec. III, Eqs. 5-12) are a standard 10-moment electron-fluid/kinetic-ion closure, and the observed reconnection, E x B-drift expansion, surface waves, and Weibel filamentation are presented as results of evolving these equations with the stated initial and boundary conditions; none of these quantities is used to define a parameter that is then 'predicted.' The Mm<1/Mm>1 regime split is not circular either: it is selected by the imposed flow velocity, but the paper's claim is about the difference in the nonlinear evolution, which is simulated rather than assumed. The code tests cited (Refs. 20, 22) are published validations of AKA, and the kinetic check uses the independent Smilei code, so no load-bearing step reduces to a self-citation. The one notable flaw is that the kinetic 'confirmation' (Sec. VI) is not dimensionless-matched: Table I shows w0/d0=6.36 (hybrid) vs 0.25 (kinetic) and w0/ri=6.70 vs 0.27, a factor of ~25, despite Sec. III's claim that 'the main dimensionless parameters' were preserved. The manuscript itself flags that the hybrid model cannot resolve electron spatial scales (Sec. IV.B). This mismatch is a correctness/validity limitation of the kinetic check, not a circularity, because the kinetic run is a separate computation that does not by construction reproduce the hybrid results. Therefore the paper is not circular; the appropriate concern is the strength of the kinetic validation.

Assumptions & free parameters 6 free parameters · 6 assumptions · 0 invented entities

The central claims rest on the hybrid model's electron-fluid closure, the 2D representation of the arch, the prescribed coil field, the zero-initial-temperature assumption, and the unverified scaling of the kinetic confirmation runs. No new physical entities are introduced, but the free parameters (flow velocity, density, field, beam width, mass ratio) are all chosen by hand, and the dimensionless scaling that connects the hybrid and kinetic runs is the least supported link in the chain.

free parameters (6)
  • Hybrid flow velocity V0 = 1e6 cm/s and 2e6 cm/s
    Varied across simulations to set the magnetic Mach number Mm = V0/VA around unity; the two values define the subcritical and overcritical regimes.
  • Initial density N0 = 1e16 cm^-3
    Chosen from the upper end of the experimental range (1e13-1e16 cm^-3); sets the Alfven velocity VA = B0/sqrt(mu0 mi N0) and thus Mm.
  • Magnetic field B0 at injection = 0.25 T (hybrid), 250 T (kinetic)
    Chosen to match the computed coil field in the chamber center (0.25 T) and then scaled for the kinetic run; combined with N0 and V0 it fixes Mm = 0.95.
  • Initial beam width w0 = 7.5 cm (hybrid), 0.30 cm (kinetic)
    Set near the experimental generator outlet (2 cm diameter) for hybrid and then reduced in the kinetic run; controls w0/d0, w0/ri, w0/re ratios.
  • Ion-electron mass ratio mi/me = 100 (hybrid), 16 (kinetic)
    Reduced from the physical value of about 4.9e4 for aluminum to make computations tractable; affects electron pressure evolution and electron gyroradius in both codes.
  • Kinetic flow velocity V0_kin = 1e9 cm/s
    Chosen to approach c/30 while remaining nonrelativistic; used in the scaled Smilei runs to confirm hybrid results.
assumptions (6)
  • domain assumption The Darwin (low-frequency) hybrid model with massless electrons and a 10-moment pressure tensor closure (Eqs. 5-12) adequately describes the low-frequency dynamics of the weakly collisional arch plasma, including reconnection and Weibel-like growth.
    Invoked in Section III as the basis of all hybrid runs; the paper notes corrections of order Ve,i/c but does not validate the closure against collisions or the full Vlasov-Maxwell system for this scenario.
  • domain assumption A two-dimensional slab geometry is representative of the three-dimensional arched magnetic configuration produced by two coils at a right angle.
    The hybrid and kinetic simulations are 2D (Section III), while the experimental arch is 3D (Section II); the paper does not discuss out-of-plane curvature effects or 3D instabilities.
  • domain assumption The externally imposed arched magnetic field from the separate coil calculation is correct and is the appropriate initial/background field for the simulation.
    Stated in Section III: 'The external magnetic field was considered to be given, its configuration was obtained by means of a separate electromagnetic calculation for the known geometry of real coils.' Validity of this field map is not shown.
  • domain assumption Initial electron and ion temperatures may be set to zero without changing the regime outcomes.
    Stated in Section III: 'the temperature of electrons and ions was assumed to be initially zero.' The experiment has Te about 3 eV; the role of initial thermal spread in seeding instabilities is not examined.
  • standard math The identification of the surface mode with the ion cyclotron frequency follows from the cold-plasma dispersion relation w = k V_A at k = 1/d_i.
    Used in Section IV A to connect the observed wavelength to omega_ci; this is a standard dispersion result but is applied without a direct frequency measurement in the simulation.
  • ad hoc to paper The reduced mass ratio and enhanced velocity in the kinetic simulation preserve the essential physics despite not preserving all dimensionless ratios.
    The paper claims the main dimensionless parameters are preserved (Section III) but Table I shows w0/d0 and w0/ri differ by a factor of about 25 between hybrid and kinetic runs; the confirmation argument depends on this unverified assumption.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Numerical modeling of two magnetized counter-propagating weakly collisional plasma flows in arch configuration." pith.science (2026). https://pith.science/paper/3Y7ZFSFX

@misc{pith2026241206065,
  author       = {Pith},
  title        = {Pith review of: Numerical modeling of two magnetized counter-propagating weakly collisional plasma flows in arch configuration},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/3Y7ZFSFX}},
  note         = {Machine review of arXiv:2412.06065}
}
abstract

Numerical modeling of the interaction process of two counter-streaming supersonic plasma flows with an arched magnetic field configuration in the regime of a magnetic Mach number of the order of unity $M_m \sim 1$ is carried out. The flows were launched from the bases of the arch along the direction of the magnetic field. It is shown that the interaction has non-equilibrium and non-stationary nature. It is accompanied by an expansion of the resulting magnetic plasma arch due to $E \times B$ drift with the formation of a region with oppositely directed magnetic fields, in which magnetic reconnection is observed. In the subcritical regime Mm < 1 the reconnection process is slow, and in the overcritical one Mm > 1 it is more intense and leads to plasma turbulization. Filamentation of flows due to the development of Weibel instability, as well as excitation of surface waves near the ion-cyclotron frequency on the surface of the plasma tube are also observed. The modeling was carried out for the parameters of an experiment planned for the near future, which made it possible to formulate the conditions for observing the effects discovered in the modeling.

Figures

Figures reproduced from arXiv: 2412.06065 by the authors.

Figure 1
Figure 1. An image of the experimental setup. 1, 2 – plasma sources, 3 – magnetic coils, 4 – [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Images of optical plasma glow during collision of two plasma flows at different moments [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Plasma particle concentration (left) and magnetic pressure (right) at different time [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figures from the paper (9 more)
Figure 4
Figure 4. Figure 4: z-component of electric field at times of 5 µs (left) and 60 µs (right). Arrows show the magnetic field lines. Electric field is normalized to E0 = V0B0 = 25 V/cm. As can be seen from [PITH_FULL_IMAGE:figures/full_fig_p011_4.png]
Figure 5
Figure 5. Figure 5: The same as in Fig. 3 for the case of two flows. [PITH_FULL_IMAGE:figures/full_fig_p012_5.png]
Figure 6
Figure 6. Figure 6: Local gyroradius of ions (left) and electrons (right) normalized to ion inertial length [PITH_FULL_IMAGE:figures/full_fig_p013_6.png]
Figure 7
Figure 7. Figure 7: Same as in Fig. 5 for flows with twice the speed. [PITH_FULL_IMAGE:figures/full_fig_p014_7.png]
Figure 8
Figure 8. Figure 8: z-component (left) and in-plane component (right) of the electric field at time 50 µs after the start of the calculation for two flows. Top row – for the parameters of [PITH_FULL_IMAGE:figures/full_fig_p015_8.png]
Figure 9
Figure 9. Figure 9: Ratio of the longitudinal component of the pressure tensor with respect to the magnetic [PITH_FULL_IMAGE:figures/full_fig_p016_9.png]
Figure 10
Figure 10. Figure 10: The result of fully kinetic modeling. z-component of current density (top row), the concentration of electrons (middle row) and ions (bottom row) at three time instants are shown. The current density Jz is normalized to eN0V0 (N0, V0 are initial particle concentration…
Figure 11
Figure 11. Figure 11: Ratio of the longitudinal (with respect to the magnetic field) component of the ion (left) [PITH_FULL_IMAGE:figures/full_fig_p018_11.png]
Figure 12
Figure 12. Figure 12: Local ion gyroradius at the time instant [PITH_FULL_IMAGE:figures/full_fig_p019_12.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

28 extracted references · 23 canonical work pages

  1. [1]

    Masuda , author T

    author author S. Masuda , author T. Kosugi , author H. Hara , author S. Tsuneta , \ and\ author Y. Ogawara ,\ 10.1038/371495a0 journal journal Nature \ volume 371 ,\ pages 495–497 ( year 1994 ) NoStop

    doi:10.1038/371495a0 1994

  2. [2]

    Liu ,\ 10.4236/aast.2020.52003 journal journal Advances in Aerospace Science and Technology \ volume 5 ,\ pages 45–57 ( year 2020 ) NoStop

    author author Y. Liu ,\ 10.4236/aast.2020.52003 journal journal Advances in Aerospace Science and Technology \ volume 5 ,\ pages 45–57 ( year 2020 ) NoStop

    work page arXiv 2020

  3. [3]

    Xia , author J

    author author Q. Xia , author J. T. \ Dahlin , author V. Zharkova , \ and\ author S. K. \ Antiochos ,\ 10.3847/1538-4357/ab846d journal journal The Astrophysical Journal \ volume 894 ,\ pages 89 ( year 2020 ) NoStop

    work page doi:10.3847/1538-4357/ab846d 2020

  4. [4]

    Yamada , author R

    author author M. Yamada , author R. Kulsrud , \ and\ author H. Ji ,\ 10.1103/RevModPhys.82.603 journal journal Reviews of Modern Physics \ volume 82 ,\ pages 603–664 ( year 2010 ) NoStop

    doi:10.1103/revmodphys.82.603 2010

  5. [5]

    Katz , author J

    author author N. Katz , author J. Egedal , author W. Fox , author A. Le , author J. Bonde , \ and\ author A. Vrublevskis ,\ 10.1103/PhysRevLett.104.255004 journal journal Physical Review Letters \ volume 104 ,\ pages 255004 ( year 2010 ) NoStop

    work page doi:10.1103/physrevlett.104.255004

  6. [6]

    author author S. K. P. \ Tripathi \ and\ author W. Gekelman ,\ 10.1103/PhysRevLett.105.075005 journal journal Physical Review Letters \ volume 105 ,\ pages 075005 ( year 2010 ) NoStop

    work page doi:10.1103/physrevlett.105.075005 2010

  7. [7]

    author author E. V. \ Stenson \ and\ author P. M. \ Bellan ,\ 10.1103/PhysRevLett.109.075001 journal journal Physical Review Letters \ volume 109 ,\ pages 075001 ( year 2012 ) NoStop

    work page doi:10.1103/physrevlett.109.075001 2012

  8. [8]

    author author M. E. \ Viktorov , author A. V. \ Vodopyanov , author S. V. \ Golubev , author D. A. \ Mansfeld , author A. G. \ Nikolaev , author V. P. \ Frolova , \ and\ author G. Y. \ Yushkov ,\ 10.1134/S1063785015090291 journal journal Technical Physics Letters \ volume 41 ,\ pages 901–904 ( year 2015 ) NoStop

    work page doi:10.1134/s1063785015090291

Show all 28 references
  1. [9]

    author author M. E. \ Viktorov , author D. A. \ Mansfeld , author A. V. \ Vodopyanov , author N. D. \ Kiryuhin , author S. V. \ Golubev , \ and\ author G. Y. \ Yushkov ,\ 10.1088/1361-6587/aa6c36 journal journal Plasma Physics and Controlled Fusion \ volume 59 ,\ pages 075001 ...

    doi

  2. [10]

    \ Wang , author X.-J

    author author F.-P. \ Wang , author X.-J. \ Zhang , \ and\ author W.-S. \ Duan ,\ 10.1002/ctpp.202400040 journal journal Contributions to Plasma Physics \ ( year 2024 ),\ 10.1002/ctpp.202400040 NoStop

    2024 doi

  3. [11]

    author author M. E. \ Viktorov , author S. V. \ Golubev , \ and\ author A. V. \ Vodopyanov ,\ 10.1088/1361-6587/aaf68f journal journal Plasma Physics and Controlled Fusion \ volume 61 ,\ pages 035001 ( year 2019 a ) NoStop

    2019 doi

  4. [12]

    author author M. E. \ Viktorov , author S. V. \ Golubev , \ and\ author A. V. \ Vodopyanov ,\ 10.1088/1742-6596/1400/7/077034 journal journal Journal of Physics: Conference Series \ volume 1400 ,\ pages 077034 ( year 2019 b ) NoStop

    2019 doi

  5. [13]

    author author E. S. \ Weibel ,\ 10.1103/PhysRevLett.2.83 journal journal Physical Review Letters \ volume 2 ,\ pages 83–84 ( year 1959 ) NoStop

    1959 doi

  6. [14]

    Bertrand , author D

    author author P. Bertrand , author D. Del Sarto , \ and\ author A. Ghizzo ,\ @noop title The Vlasov equation 1: history and general properties \ ( publisher ISTE Ltd / John Wiley & Sons Inc ,\ address Hoboken ,\ year 2019 ) NoStop

    2019

  7. [15]

    author author C. K. \ Birdsall \ and\ author A. B. \ Langdon ,\ @noop title Plasma physics via computer simulation ,\ Series in Plasma Physics\ ( publisher Taylor & Francis ,\ address New York, New York; London, [England] ,\ year 2004 ) NoStop

    2004

  8. [16]

    Palmroth , author U

    author author M. Palmroth , author U. Ganse , author Y. Pfau-Kempf , author M. Battarbee , author L. Turc , author T. Brito , author M. Grandin , author S. Hoilijoki , author A. Sandroos , \ and\ author S. von Alfthan ,\ 10.1007/s41115-018-0003-2 journal journal Living Reviews...

    doi

  9. [17]

    author author T. B. \ Krause , author A. Apte , \ and\ author P. J. \ Morrison ,\ 10.1063/1.2799346 journal journal Physics of Plasmas \ volume 14 ,\ pages 102112 ( year 2007 ) NoStop

    2007 doi

  10. [18]

    Hesse , author D

    author author M. Hesse , author D. Winske , \ and\ author M. M. \ Kuznetsova ,\ 10.1029/95JA01559 journal journal Journal of Geophysical Research: Space Physics \ volume 100 ,\ pages 21815–21825 ( year 1995 ) NoStop

    1995 doi

  11. [19]

    Sarrat , author D

    author author M. Sarrat , author D. Del Sarto , \ and\ author A. Ghizzo ,\ 10.1209/0295-5075/115/45001 journal journal EPL (Europhysics Letters) \ volume 115 ,\ pages 45001 ( year 2016 ) NoStop

    2016 doi

  12. [20]

    Sladkov \ and\ author A

    author author A. Sladkov \ and\ author A. Korzhimanov ,\ http://arxiv.org/abs/2305.03539 title Numerical study of weibel instability driven by anisotropic electron temperature in collisionless plasmas , \ ( year 2023 ),\ note arXiv 2305.03539 NoStop

    2023 arXiv

  13. [21]

    Sladkov , author R

    author author A. Sladkov , author R. Smets , \ and\ author A. Korzhimanov ,\ 10.1088/1742-6596/1640/1/012011 journal journal Journal of Physics: Conference Series \ volume 1640 ,\ pages 012011 ( year 2020 ) NoStop

    2020 doi

  14. [22]

    Sladkov , author R

    author author A. Sladkov , author R. Smets , author N. Aunai , \ and\ author A. Korzhimanov ,\ 10.1063/5.0052003 journal journal Physics of Plasmas \ volume 28 ,\ pages 072108 ( year 2021 ) NoStop

    2021 doi

  15. [23]

    Bolaños , author A

    author author S. Bolaños , author A. Sladkov , author R. Smets , author S. N. \ Chen , author A. Grisollet , author E. Filippov , author J.-L. \ Henares , author V. Nastasa , author S. Pikuz , author R. Riquier , author M. Safronova , author A. Severin , author M. Starodubtsev...

    doi

  16. [24]

    Burdonov , author W

    author author K. Burdonov , author W. Yao , author A. Sladkov , author R. Bonito , author S. Chen , author A. Ciardi , author A. Korzhimanov , author A. Soloviev , author M. Starodubtsev , author R. Zemskov , author S. Orlando , author M. Romanova , \ and\ author J. Fuchs ,\ 1...

    doi

  17. [25]

    Zemskov , author K

    author author R. Zemskov , author K. Burdonov , author A. Soloviev , author A. Sladkov , author A. Korzhimanov , author J. Fuchs , author D. Bisikalo , author A. Zhilkin , author M. Barkov , author A. Ciardi , author W. Yao , author M. Glyavin , author M. Morozkin , author M. ...

  18. [26]

    Sladkov , author C

    author author A. Sladkov , author C. Fegan , author W. Yao , author A. F. A. \ Bott , author S. N. \ Chen , author H. Ahmed , author E. D. \ Filippov , author R. Lelièvre , author P. Martin , author A. McIlvenny , author T. Waltenspiel , author P. Antici , author M. Borghesi ,...

    doi

  19. [27]

    Derouillat , author A

    author author J. Derouillat , author A. Beck , author F. Pérez , author T. Vinci , author M. Chiaramello , author A. Grassi , author M. Flé , author G. Bouchard , author I. Plotnikov , author N. Aunai , author J. Dargent , author C. Riconda , \ and\ author M. Grech ,\ 10.1016/...

    doi

  20. [28]

    author author R. Z. \ Sagdeev \ and\ author V. D. \ Shafranov ,\ @noop journal journal Sov. Phys. JETP \ volume 12 ,\ pages 130–132 ( year 1961 ) NoStop

    1961

Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.