From Weibel seeds to collisionless dynamos beyond pair-plasmas

Ammar Hakim; Istvan Pusztai; James Juno; Jason M. TenBarge; Lise Hanebring

arxiv: 2601.10472 · v2 · submitted 2026-01-15 · ⚛️ physics.plasm-ph · astro-ph.CO

From Weibel seeds to collisionless dynamos beyond pair-plasmas

Lise Hanebring , James Juno , Ammar Hakim , Jason M. TenBarge , Istvan Pusztai This is my paper

Pith reviewed 2026-05-16 13:59 UTC · model grok-4.3

classification ⚛️ physics.plasm-ph astro-ph.CO

keywords Weibel instabilitycollisionless dynamoplasma turbulence10-moment modelmagnetic field amplificationintracluster mediummass ratio

0 comments

The pith

Simulations link Weibel instability seed fields to collisionless dynamo amplification beyond pair plasmas

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

This work uses collisionless turbulence simulations starting with unmagnetized electrons to demonstrate both the generation of magnetic seed fields through the electron Weibel instability and their subsequent amplification via dynamo processes. By adopting an ion-to-electron mass ratio of 100, the study ensures electron and ion dynamics remain sufficiently decoupled, extending beyond prior pair-plasma investigations. The 10-moment fluid model evolves full pressure tensors and employs a heat-flux closure to control pressure isotropization, which in turn sets the effective magnetic Reynolds number. Varying the closure strength reveals a shift from regimes similar to kinetic pair-plasma simulations to those exhibiting dynamo behavior akin to magnetohydrodynamics. Such an approach addresses the challenge of spanning scales in weakly collisional environments like the intracluster medium.

Core claim

The simulations capture magnetic seed generation via the electron Weibel instability and the ensuing dynamo amplification in collisionless turbulence with an ion-to-electron mass ratio of 100. The electron heat-flux closure in the 10-moment model regulates pressure isotropization and sets the magnetic Reynolds number, enabling investigation of the transition between kinetic and MHD-like regimes.

What carries the argument

The 10-moment collisionless fluid solver evolving full pressure tensors for electrons and ions, with the electron heat-flux closure that regulates isotropization and effective magnetic Reynolds number

Load-bearing premise

The chosen electron heat-flux closure accurately sets the effective magnetic Reynolds number and regulates pressure isotropization in a manner representative of the weakly collisional intracluster medium

What would settle it

A direct comparison of the magnetic field growth rates and saturation levels in these 10-moment simulations against full particle-in-cell kinetic simulations with the same mass ratio would test if the closure produces representative dynamo behavior

Figures

Figures reproduced from arXiv: 2601.10472 by Ammar Hakim, Istvan Pusztai, James Juno, Jason M. TenBarge, Lise Hanebring.

**Figure 1.** Figure 1: Magnetic field generation in the simulation with the baseline parameters. a) Time evolution of the box-integrated magnetic energy EB (solid black curve) and kinetic energy in the flows EU (dashed black), normalized to the initial value of EU . With similar line styles, contributions from the {x, y, z} components of U and B are shown in red, blue and green, respectively. The dotted line corresponds to an ex… view at source ↗

**Figure 2.** Figure 2: Time evolution during the Weibel instability phase. a) Dimensionless quantities: Pressure anisotropy of electrons (blue, ∆e) and ions (red, ∆i), normalized magnetic field energy (green, β −1 e ), and instantaneous magnetic field growth rate (purple, γB/ωp,e). b) Instantaneous magnetic growth rate spectra (γBtturn) for several time instances (color coded from blue to yellow for increasing time) across the t… view at source ↗

**Figure 3.** Figure 3: Magnitude of the magnetic field in 2-D cuts of the simulation domain, taken a) and d) at the time of the fastest magnetic growth during the Weibel phase, t/tturn = 0.038, b) and e) in the middle of the dynamo growth phase, t/tturn = 2.0, and c) and f) in the saturated phase, t/tturn = 10.0. a)-c) are cuts at x = L/2, while d)-f) are cuts at y = L/2 (the latter are morphologically similar to constant z cuts… view at source ↗

**Figure 4.** Figure 4: Magnetic field generation in simulations using k0,e/k0 = {2, 4, 8, 32}, shown in different rows. Left column: Time evolution of the box-integrated magnetic energy EB (solid black curve) and kinetic energy in the flows EU (dashed black), normalized to the initial value of EU . With similar line styles, contributions from the {x, y, z} components of U and B are shown in red, blue and green, respectively. Exp… view at source ↗

**Figure 5.** Figure 5: Dependence of damping rates on closure parameters (circle markers, main figure) and wavenumber (diamond markers, inset figure). In both of these scans, star markers correspond to the baseline case. Dashed lines indicate fitted relevant power-law behavior. a) Mass flow damping rate as a function of k0,i/k0 and k/k0. b) Magnetic field damping rate as a function of k0,e/k0 and k/k0. providing computational re… view at source ↗

**Figure 6.** Figure 6: Mass-ratio dependence of the damping rate scaling exponents, defined through the power law relations γU ∝ k αU,i 0,i k αU,e 0,e , γB ∝ k αB,i 0,i k αB,e 0,e . approximately inversely proportional to their respective closure parameter: γU ∝ k −1 0,i and γB ∝ k −1 0,e. For the flow damping, this dependence can be understood by a linearized analysis, with the assumptions that in the momentum equation the mini… view at source ↗

**Figure 7.** Figure 7: Normalized probability distributions of p⊥,e/p∥,e and β∥ at three representative time points. Left panels: time of fastest Weibel growth (t/tturn = 0.038 and t/tturn = 0.021 respectively); middle panels: t/tturn = 2.0 (kinematic dynamo phase), right panels: t/tturn = 10.0 (saturated dynamo phase). The electron closure parameter is changed from its baseline value k0,e = 1k0 (upper panels) to a negligible va… view at source ↗

read the original abstract

Bridging the spatiotemporal scales of magnetic seed field generation and subsequent dynamo amplification in the weakly collisional intracluster medium presents an extreme numerical challenge. We perform collisionless turbulence simulations with initially unmagnetized electrons that capture both magnetic seed generation via the electron Weibel instability and the ensuing dynamo amplification. Going beyond existing pair-plasma studies, we use an ion-to-electron mass ratio of 100 for which we find electron and ion dynamics are sufficiently decoupled. These simulations are enabled by the 10-moment collisionless fluid solver of Gkeyll, which evolves the full pressure tensor for all species. The electron heat-flux closure regulates pressure isotropization and effectively sets the magnetic Reynolds number. We investigate how the strength of the closure influences the transition between a regime reminiscent of previous kinetic pair-plasma simulations and a regime exhibiting dynamo behavior qualitatively similar to magnetohydrodynamics.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper runs 10-moment Gkeyll simulations at m_i/m_e=100 that capture Weibel seed generation followed by dynamo growth, but the outcome tracks the heat-flux closure strength.

read the letter

The central result is a set of collisionless turbulence runs that start from unmagnetized electrons, let the Weibel instability generate seed fields, and then show subsequent amplification that looks more like an MHD dynamo once the ions are dynamically decoupled at mass ratio 100. That mass ratio is the concrete step past existing pair-plasma work, and the 10-moment solver lets them keep the full pressure tensor while varying only the electron heat-flux closure parameter to control isotropization and effective Reynolds number. The setup is therefore a single numerical experiment that spans the micro-to-macro transition the abstract promises. The code and parameter choices are stated clearly enough that someone could reproduce the runs. The limitation is that the dynamo behavior is tied to the closure. Because the closure directly sets the magnetic Reynolds number and the rate at which pressure anisotropy is removed, the reported shift from kinetic-like to MHD-like growth could be an artifact of that modeling choice rather than a robust physical outcome. The abstract notes the regulation but does not report direct benchmarks against PIC or Vlasov data in the same driven-turbulence regime, nor does it give quantitative growth rates or saturation amplitudes. If the full paper supplies those numbers and convergence checks, the claim strengthens; otherwise the transition remains suggestive. This is useful for groups already working on intracluster-medium field amplification or on multi-fluid plasma codes. A reader who needs a practical numerical bridge between Weibel seeds and large-scale dynamos will find the mass-ratio extension worth looking at, even if the closure dependence requires follow-up. I would send it to referees rather than desk-reject; the numerical approach is concrete and the mass-ratio advance is real, so the community can evaluate the closure issue in review.

Referee Report

2 major / 1 minor

Summary. The paper performs collisionless turbulence simulations with initially unmagnetized electrons using the 10-moment fluid model in Gkeyll at ion-to-electron mass ratio 100. It captures magnetic seed generation via the electron Weibel instability followed by dynamo amplification, and examines how varying the strength of the electron heat-flux closure controls the transition between a regime resembling prior kinetic pair-plasma runs and one exhibiting MHD-like dynamo behavior.

Significance. If the results hold after validation, the work would meaningfully extend kinetic studies of Weibel seeding into the regime of decoupled ions and electrons, offering a potential bridge between microscale seed generation and large-scale dynamo amplification in weakly collisional astrophysical plasmas such as the intracluster medium.

major comments (2)

[Abstract and closure description] Abstract and § on the 10-moment closure: the statement that the heat-flux closure “regulates pressure isotropization and effectively sets the magnetic Reynolds number” is load-bearing for the central claim of a physical transition, yet the manuscript supplies no first-principles derivation or side-by-side benchmark against Vlasov/PIC data in the same driven-turbulence regime; without such evidence the reported dynamo behavior risks being an artifact of the chosen closure parameters.
[Results on mass-ratio scan] Results on m_i/m_e = 100: the assertion that “electron and ion dynamics are sufficiently decoupled” at this mass ratio underpins the extension beyond pair-plasma studies, but the text does not report quantitative diagnostics (e.g., separate electron/ion energy spectra, timescale ratios, or cross-species correlation functions) that would confirm decoupling across the simulated range of closure strengths.

minor comments (1)

[Abstract] The abstract supplies no numerical values for the varied closure strength, achieved Reynolds numbers, or any convergence metrics, which would help readers assess robustness at first reading.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thoughtful and constructive report. The comments highlight important points regarding validation of the closure and confirmation of species decoupling. We address each major comment below and will revise the manuscript to strengthen the presentation while preserving the core results.

read point-by-point responses

Referee: Abstract and § on the 10-moment closure: the statement that the heat-flux closure “regulates pressure isotropization and effectively sets the magnetic Reynolds number” is load-bearing for the central claim of a physical transition, yet the manuscript supplies no first-principles derivation or side-by-side benchmark against Vlasov/PIC data in the same driven-turbulence regime; without such evidence the reported dynamo behavior risks being an artifact of the chosen closure parameters.

Authors: The heat-flux closure in the 10-moment model is a standard component of the Gkeyll fluid solver, derived from moment closures that approximate kinetic effects by controlling the rate of pressure isotropization (see prior references on the model). The observed transition in dynamo behavior with varying closure strength is a direct outcome of the simulations and reflects how the effective magnetic Reynolds number is modulated within this framework. We acknowledge that a dedicated first-principles derivation is not repeated here and that side-by-side Vlasov/PIC benchmarks in the identical driven-turbulence setup are absent. In revision we will expand the closure section with additional physical motivation drawn from the literature, explicitly state the model assumptions, and add a limitations paragraph noting that full kinetic validation in this regime is left for future work. This addresses the concern without altering the reported findings. revision: partial
Referee: Results on m_i/m_e = 100: the assertion that “electron and ion dynamics are sufficiently decoupled” at this mass ratio underpins the extension beyond pair-plasma studies, but the text does not report quantitative diagnostics (e.g., separate electron/ion energy spectra, timescale ratios, or cross-species correlation functions) that would confirm decoupling across the simulated range of closure strengths.

Authors: We agree that explicit quantitative diagnostics would better substantiate the decoupling claim. In the revised manuscript we will add panels and analysis showing separate electron and ion energy spectra, timescale ratios (including electron-to-ion response time comparisons), and cross-species correlation functions evaluated across the explored closure strengths. These additions will confirm that at m_i/m_e = 100 the species remain dynamically decoupled throughout the runs. revision: yes

Circularity Check

0 steps flagged

No circularity: results follow from explicit simulation parameters and closure choice

full rationale

The paper reports outcomes of direct numerical simulations in the 10-moment Gkeyll solver with stated initial conditions, mass ratio m_i/m_e=100, and an explicit electron heat-flux closure. No derivation reduces a claimed prediction to a quantity fitted from the same run, no uniqueness theorem is invoked via self-citation, and no ansatz is smuggled through prior work. The transition between Weibel-seeded and dynamo-like regimes is presented as a numerical finding controlled by the chosen closure strength, without any self-referential redefinition of inputs as outputs.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the validity of the 10-moment collisionless fluid closure for electrons and ions at mass ratio 100 and on the assumption that varying the heat-flux closure strength produces physically meaningful changes in magnetic Reynolds number.

free parameters (1)

heat-flux closure strength
The parameter is varied to control pressure isotropization and the effective magnetic Reynolds number; its specific values are not given in the abstract.

axioms (1)

domain assumption The 10-moment collisionless fluid solver of Gkeyll accurately evolves the full pressure tensor for electrons and ions at mass ratio 100.
The entire study is built on this numerical model; no independent verification is mentioned.

pith-pipeline@v0.9.0 · 5463 in / 1379 out tokens · 48124 ms · 2026-05-16T13:59:42.152707+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

The electron heat-flux closure regulates pressure isotropization and effectively sets the magnetic Reynolds number... ∂qjkl,α/∂xl = k0,α vth,α/√2 (pjk,α − pα δjk)
IndisputableMonolith/Foundation/AlexanderDuality.lean alexander_duality_circle_linking unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

We perform collisionless turbulence simulations... mass ratio of 100... 10-moment collisionless fluid solver of Gkeyll

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
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contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

12 extracted references · 12 canonical work pages

[1]

D., Kasper, J

Bale, S. D., Kasper, J. C., Howes, G. G., Quataert, E., Salem, C. & Sundkvist, D.2009 Magnetic fluctuation power near proton temperature anisotropy instability thresholds in the solar wind.Phys. Rev. Lett.103, 211101. Barbour, Nathaniel, Dorland, William, Abel, Ian G. & Landreman, Matt2025 From Weibel seeds to collisionless dynamos beyond pair-plasmas17 M...

work page 2009
[2]

Gallow ay, D. J. & Proctor, M. R. E.1992 Numerical calculations of fast dynamos in smooth velocity fields with realistic diffusion.Nature356(6371), 691–693. Gary, S Peter1993Cambridge atmospheric and space science series: Theory of space plasma microinstabilities. Cambridge, England: Cambridge University Press. Govoni, Federica & Feretti, Luigina2004 Magn...

work page doi:10.1142/s0218271804005080 1992
[3]

& Perkins, Francis W.1990 Fluid moment models for landau damping with application to the ion-temperature-gradient instability.Phys

Hammett, Gregory W. & Perkins, Francis W.1990 Fluid moment models for landau damping with application to the ion-temperature-gradient instability.Phys. Rev. Lett. 64, 3019–3022. Helander, P., Strumik, M. & Schekochihin, A. A.2016 Constraints on dynamo action in plasmas.Journal of Plasma Physics82(6), 905820601. Huang, Ziyu, Dong, Chuanfei & W ang, Liang20...

work page 1990
[4]

Kato, Tsunehiko N.2005Saturationmechanismoftheweibelinstabilityinweaklymagnetized plasmas.Physics of Plasmas12(8), 080705. 18L. Hanebring, J. Juno, A. Hakim, J. M. TenBarge, I. Pusztai Kato, Tsunehiko N. & Takabe, Hideaki2008 Nonrelativistic collisionless shocks in unmagnetized electron-ion plasmas.The Astrophysical Journal681(2), L93. Komarov, S., Scheko...

work page 2018
[5]

& Hara, K.2025 Ten-moment fluid modeling of the weibel instability

Kuldinow, D.A. & Hara, K.2025 Ten-moment fluid modeling of the weibel instability. Journal of Plasma Physics91(2), E66. Kulsrud, Russell M. & Zweibel, Ellen G.2008 On the origin of cosmic magnetic fields. Reports on Progress in Physics71(4), 046901. Kunz, Matthew W., Schekochihin, Alexander A. & Stone, James M.2014 Firehose and mirror instabilities in a c...

work page 2025
[6]

LeVeque, Randall J.1997 Wave propagation algorithms for multidimensional hyperbolic systems.Journal of Computational Physics131(2), 327–353

Larmor, J.1919 Possible rotational origin of magnetic fields of sun and earth.Engineering Review108, 461ff. LeVeque, Randall J.1997 Wave propagation algorithms for multidimensional hyperbolic systems.Journal of Computational Physics131(2), 327–353. Liu, Zhuo, Zhou, Muni & Loureiro, Nuno F.2025 Suppression of inverse magnetic energy transfer in collisionle...

work page 1919
[7]

& Kamionkowski, Marc2006 Cluster magnetic fields from large-scale structure and galaxy cluster shocks.The Astrophysical Journal 642(1), L1

Medvedev, Mikhail V., Sil v a, Luis O. & Kamionkowski, Marc2006 Cluster magnetic fields from large-scale structure and galaxy cluster shocks.The Astrophysical Journal 642(1), L1. Mikhailovskii, A. B.1980 Oscillations of an isotropic relativistic plasma.Plasma Physics 22(2),

work page 1980
[8]

2017 Simulations of anti-parallel reconnection using a nonlocal heat flux closure.Physics of Plasmas24(8), 082112

Ng, Jonathan, Hakim, Ammar, Bhattacharjee, A., Stanier, Adam & Daughton, W. 2017 Simulations of anti-parallel reconnection using a nonlocal heat flux closure.Physics of Plasmas24(8), 082112. Ng, Jonathan, Hakim, A., W ang, L. & Bhattacharjee, A.2020 An improved ten-moment closure for reconnection and instabilities.Physics of Plasmas27(8), 082106. Porter, ...

work page 2017
[9]

Pucci, F., Viviani, M., V alentini, F., Lapenta, G., Matthaeus, W. H. & Ser vidio, S.2021 Turbulent magnetogenesis in a collisionless plasma.The Astrophysical Journal Letters922(1), L18. Pusztai, Istv án, Juno, James, Brandenburg, Axel, TenBarge, Jason M., Hakim, Ammar, Francisquez, Manaure & Sundström, Andréas2020 Dynamo in weakly collisional nonmagnetiz...

work page doi:10.1073/pnas.1525194113 2021
[10]

M., Loureiro, N

Schoeffler, K. M., Loureiro, N. F., Fonseca, R. A. & Sil v a, L. O.2014 Magnetic-field generation and amplification in an expanding plasma.Phys. Rev. Lett.112, 175001. Schubert, G. & Soderlund, K.M.2011 Planetary magnetic fields: Observations and models. Physics of the Earth and Planetary Interiors187(3), 92–108, special Issue: Planetary Magnetism, Dynamo...

work page 2014
[11]

& Germaschewski, K.2015 Comparison of multi-fluid moment models with particle-in-cell simulations of collisionless magnetic reconnection.Physics of Plasmas22(1), 012108

W ang, Liang, Hakim, Ammar H., Bhattacharjee, A. & Germaschewski, K.2015 Comparison of multi-fluid moment models with particle-in-cell simulations of collisionless magnetic reconnection.Physics of Plasmas22(1), 012108. W ang, Liang, Hakim, Ammar H., Ng, Jonathan, Dong, Chuanfei & Germaschewski, Kai2020 Exact and locally implicit source term solvers for mu...

work page doi:10.1073/pnas.2119831119 2015
[12]

A., Allen, S

Zhura vlev a, I., Churazov, E., Schekochihin, A. A., Allen, S. W., Vikhlinin, A. & Werner, N.2019 Suppressed effective viscosity in the bulk intergalactic plasma.Nature Astronomy3(9), 832–837

work page 2019

[1] [1]

D., Kasper, J

Bale, S. D., Kasper, J. C., Howes, G. G., Quataert, E., Salem, C. & Sundkvist, D.2009 Magnetic fluctuation power near proton temperature anisotropy instability thresholds in the solar wind.Phys. Rev. Lett.103, 211101. Barbour, Nathaniel, Dorland, William, Abel, Ian G. & Landreman, Matt2025 From Weibel seeds to collisionless dynamos beyond pair-plasmas17 M...

work page 2009

[2] [2]

Gallow ay, D. J. & Proctor, M. R. E.1992 Numerical calculations of fast dynamos in smooth velocity fields with realistic diffusion.Nature356(6371), 691–693. Gary, S Peter1993Cambridge atmospheric and space science series: Theory of space plasma microinstabilities. Cambridge, England: Cambridge University Press. Govoni, Federica & Feretti, Luigina2004 Magn...

work page doi:10.1142/s0218271804005080 1992

[3] [3]

& Perkins, Francis W.1990 Fluid moment models for landau damping with application to the ion-temperature-gradient instability.Phys

Hammett, Gregory W. & Perkins, Francis W.1990 Fluid moment models for landau damping with application to the ion-temperature-gradient instability.Phys. Rev. Lett. 64, 3019–3022. Helander, P., Strumik, M. & Schekochihin, A. A.2016 Constraints on dynamo action in plasmas.Journal of Plasma Physics82(6), 905820601. Huang, Ziyu, Dong, Chuanfei & W ang, Liang20...

work page 1990

[4] [4]

Kato, Tsunehiko N.2005Saturationmechanismoftheweibelinstabilityinweaklymagnetized plasmas.Physics of Plasmas12(8), 080705. 18L. Hanebring, J. Juno, A. Hakim, J. M. TenBarge, I. Pusztai Kato, Tsunehiko N. & Takabe, Hideaki2008 Nonrelativistic collisionless shocks in unmagnetized electron-ion plasmas.The Astrophysical Journal681(2), L93. Komarov, S., Scheko...

work page 2018

[5] [5]

& Hara, K.2025 Ten-moment fluid modeling of the weibel instability

Kuldinow, D.A. & Hara, K.2025 Ten-moment fluid modeling of the weibel instability. Journal of Plasma Physics91(2), E66. Kulsrud, Russell M. & Zweibel, Ellen G.2008 On the origin of cosmic magnetic fields. Reports on Progress in Physics71(4), 046901. Kunz, Matthew W., Schekochihin, Alexander A. & Stone, James M.2014 Firehose and mirror instabilities in a c...

work page 2025

[6] [6]

LeVeque, Randall J.1997 Wave propagation algorithms for multidimensional hyperbolic systems.Journal of Computational Physics131(2), 327–353

Larmor, J.1919 Possible rotational origin of magnetic fields of sun and earth.Engineering Review108, 461ff. LeVeque, Randall J.1997 Wave propagation algorithms for multidimensional hyperbolic systems.Journal of Computational Physics131(2), 327–353. Liu, Zhuo, Zhou, Muni & Loureiro, Nuno F.2025 Suppression of inverse magnetic energy transfer in collisionle...

work page 1919

[7] [7]

& Kamionkowski, Marc2006 Cluster magnetic fields from large-scale structure and galaxy cluster shocks.The Astrophysical Journal 642(1), L1

Medvedev, Mikhail V., Sil v a, Luis O. & Kamionkowski, Marc2006 Cluster magnetic fields from large-scale structure and galaxy cluster shocks.The Astrophysical Journal 642(1), L1. Mikhailovskii, A. B.1980 Oscillations of an isotropic relativistic plasma.Plasma Physics 22(2),

work page 1980

[8] [8]

2017 Simulations of anti-parallel reconnection using a nonlocal heat flux closure.Physics of Plasmas24(8), 082112

Ng, Jonathan, Hakim, Ammar, Bhattacharjee, A., Stanier, Adam & Daughton, W. 2017 Simulations of anti-parallel reconnection using a nonlocal heat flux closure.Physics of Plasmas24(8), 082112. Ng, Jonathan, Hakim, A., W ang, L. & Bhattacharjee, A.2020 An improved ten-moment closure for reconnection and instabilities.Physics of Plasmas27(8), 082106. Porter, ...

work page 2017

[9] [9]

Pucci, F., Viviani, M., V alentini, F., Lapenta, G., Matthaeus, W. H. & Ser vidio, S.2021 Turbulent magnetogenesis in a collisionless plasma.The Astrophysical Journal Letters922(1), L18. Pusztai, Istv án, Juno, James, Brandenburg, Axel, TenBarge, Jason M., Hakim, Ammar, Francisquez, Manaure & Sundström, Andréas2020 Dynamo in weakly collisional nonmagnetiz...

work page doi:10.1073/pnas.1525194113 2021

[10] [10]

M., Loureiro, N

Schoeffler, K. M., Loureiro, N. F., Fonseca, R. A. & Sil v a, L. O.2014 Magnetic-field generation and amplification in an expanding plasma.Phys. Rev. Lett.112, 175001. Schubert, G. & Soderlund, K.M.2011 Planetary magnetic fields: Observations and models. Physics of the Earth and Planetary Interiors187(3), 92–108, special Issue: Planetary Magnetism, Dynamo...

work page 2014

[11] [11]

& Germaschewski, K.2015 Comparison of multi-fluid moment models with particle-in-cell simulations of collisionless magnetic reconnection.Physics of Plasmas22(1), 012108

W ang, Liang, Hakim, Ammar H., Bhattacharjee, A. & Germaschewski, K.2015 Comparison of multi-fluid moment models with particle-in-cell simulations of collisionless magnetic reconnection.Physics of Plasmas22(1), 012108. W ang, Liang, Hakim, Ammar H., Ng, Jonathan, Dong, Chuanfei & Germaschewski, Kai2020 Exact and locally implicit source term solvers for mu...

work page doi:10.1073/pnas.2119831119 2015

[12] [12]

A., Allen, S

Zhura vlev a, I., Churazov, E., Schekochihin, A. A., Allen, S. W., Vikhlinin, A. & Werner, N.2019 Suppressed effective viscosity in the bulk intergalactic plasma.Nature Astronomy3(9), 832–837

work page 2019