arxiv: 2605.06795 · v1 · submitted 2026-05-07 · ✦ hep-ph · astro-ph.CO

Recognition: no theorem link

Plasma heating during the chiral plasma instability

Balin Armstrong , Andrew J. Long , K\'aroly Seller , G\"unter Sigl

Authors on Pith no claims yet

Pith reviewed 2026-05-11 01:02 UTC · model grok-4.3

classification ✦ hep-ph astro-ph.CO

keywords chiral plasma instabilityplasma heatingchiral asymmetryhelical magnetic fieldsearly universe cosmologyrelativistic plasma

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The pith

The chiral plasma instability transfers more energy from the chiral asymmetry into plasma heating than into growing magnetic fields.

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

A chiral asymmetry in a relativistic plasma triggers a tachyonic instability that grows helical magnetic fields. The paper calculates the energy transfer and finds that the initial energy in the chiral asymmetry exceeds the energy that ends up in the magnetic field. The difference is absorbed by the thermal bath, leading to an increase in plasma temperature. This temperature rise scales as the square of the chiral chemical potential divided by the temperature when that ratio is small. The result has potential implications for the thermal evolution of the early universe.

Core claim

We find that there is more energy stored in the initial chiral asymmetry than goes into growing magnetic field and that the excess energy is transferred to the thermal bath. Consequently, we find that the chiral plasma instability is accompanied by a heating of the plasma, and the temperature increase is parametrically δT ∼ μ5² / T if the ratio of chemical potential to temperature is small, i.e. μ5/T ≪ 1.

What carries the argument

Energy balance during the tachyonic instability of helical magnetic field growth, where the chiral asymmetry supplies the source energy.

Load-bearing premise

The assumption that energy not captured by the magnetic field is transferred entirely to the thermal bath without other loss channels or back-reaction effects altering the parametric scaling.

What would settle it

A numerical simulation of the coupled chiral-fermion and electromagnetic dynamics that tracks the total energy partition and measures the final temperature against the predicted δT scaling.

read the original abstract

The presence of a chiral asymmetry in a relativistic plasma opens a tachyonic instability toward the growth of a helical magnetic field. We study the transfer of energy from the chiral asymmetry into the magnetic field during the development of this chiral plasma instability. We find that there is more energy stored in the initial chiral asymmetry than goes into growing magnetic field and that the excess energy is transferred to the thermal bath. Consequently, we find that the chiral plasma instability is accompanied by a heating of the plasma, and the temperature increase is parametrically $\delta T \sim \mu_5^2 / T$ if the ratio of chemical potential to temperature is small, i.e. $\mu_5/T \ll 1$. We briefly remark on possible observable implications for early universe cosmology.

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 derives a heating term δT ~ μ5²/T from energy conservation in the chiral plasma instability, but the claim that excess energy thermalizes cleanly rests on an unmodeled partition.

read the letter

The central result is that the initial chiral asymmetry carries more energy than ends up in the growing helical magnetic field, so the difference heats the plasma with a temperature shift that scales as μ5 squared over T when the ratio is small. The authors extract this parametric form by comparing the energy stored in the chemical potential to the final magnetic energy after the instability runs its course. That accounting is the new piece; the instability itself has been studied before, but the explicit heating consequence and its scaling are presented as a derived outcome here. It is a short, focused calculation that could slot into models of early-universe magnetogenesis or thermal history without much extra machinery. The derivation appears to rest on energy conservation plus the known linear instability, which keeps it simple and reproducible in principle. The main limitation is that the paper does not appear to simulate or derive the saturation amplitude or the dissipation channel in detail. The assumption that leftover energy goes straight into the thermal bath, without back-reaction on the distribution function or leakage into other modes, is stated but not stress-tested against those effects. If those channels matter at the same order, the parametric result could change. No free parameters or invented entities show up in the abstract, and the citation pattern looks standard for the subfield. This is the sort of incremental but concrete note that people working on chiral effects in cosmology would want to check. It is not foundational, but the claim is sharp enough that a referee could evaluate the energy balance and the missing back-reaction steps in one pass. I would send it to review rather than desk reject.

Referee Report

2 major / 1 minor

Summary. The manuscript examines the chiral plasma instability triggered by a chiral asymmetry in a relativistic plasma. It analyzes the energy transfer from the initial chiral asymmetry into the growing helical magnetic field and concludes that the chiral asymmetry stores more energy than ends up in the magnetic field, with the excess transferred to the thermal bath. This results in plasma heating with a parametric temperature increase δT ∼ μ₅²/T for μ₅/T ≪ 1, along with brief remarks on possible early-universe cosmological implications.

Significance. If the energy-partition result holds, the parametric heating estimate could be useful for modeling the thermal evolution and magnetic-field generation in the early universe, particularly in scenarios involving chiral asymmetries. The focus on energy conservation provides a concrete, falsifiable prediction that could be tested against simulations or observations, though the absence of machine-checked proofs or explicit reproducibility materials limits immediate verifiability.

major comments (2)

[Abstract] Abstract: the headline claim that excess chiral-asymmetry energy is transferred entirely to the thermal bath (yielding δT ∼ μ₅²/T) is presented without the supporting derivation of the magnetic-field saturation amplitude, the explicit energy-balance calculation, or quantitative error estimates, rendering the support for the central parametric result unverifiable from the given statement.
[Main text (energy-balance section)] Main text (energy-balance section): the assumption that the energy deficit not captured by the helical field is converted fully into thermal energy density, without appreciable loss to other channels or back-reaction on the distribution function and μ₅ itself, is load-bearing for the δT scaling but is not shown to leave the parametric result unchanged.

minor comments (1)

[Abstract] The abstract would benefit from a single sentence defining the regime μ₅/T ≪ 1 and the symbols μ₅ and T for readers outside the immediate subfield.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of our manuscript and for the constructive comments. We address each major comment below and indicate the revisions we have made or will make to strengthen the presentation.

read point-by-point responses

Referee: [Abstract] Abstract: the headline claim that excess chiral-asymmetry energy is transferred entirely to the thermal bath (yielding δT ∼ μ₅²/T) is presented without the supporting derivation of the magnetic-field saturation amplitude, the explicit energy-balance calculation, or quantitative error estimates, rendering the support for the central parametric result unverifiable from the given statement.

Authors: The abstract is a concise summary of the principal results. The derivation of the magnetic-field saturation amplitude, the explicit energy-balance calculation, and the parametric estimates are developed in detail in the main text (particularly the sections on the instability evolution and energy partitioning). To improve verifiability from the abstract itself, we have added a parenthetical reference to the relevant main-text sections and noted that the δT scaling holds at leading order for μ₅/T ≪ 1. Quantitative error estimates are implicit in the parametric analysis; we have inserted a short clarifying sentence in the abstract to this effect. revision: yes
Referee: [Main text (energy-balance section)] Main text (energy-balance section): the assumption that the energy deficit not captured by the helical field is converted fully into thermal energy density, without appreciable loss to other channels or back-reaction on the distribution function and μ₅ itself, is load-bearing for the δT scaling but is not shown to leave the parametric result unchanged.

Authors: We agree that the conversion assumption is central to obtaining the parametric heating result. In the manuscript we argue that, for μ₅/T ≪ 1, back-reaction on the distribution function remains small throughout the linear growth phase and that competing channels (non-helical magnetic modes, direct particle production) are parametrically suppressed relative to the thermal bath. The saturation amplitude is set by the depletion of the chiral chemical potential, after which the energy balance is evaluated. To make this robustness explicit, we have expanded the energy-balance section with a short paragraph showing that O(μ₅/T) corrections to the assumption do not modify the leading δT ∼ μ₅²/T scaling. revision: partial

Circularity Check

0 steps flagged

No significant circularity; heating result follows from energy accounting without reduction to inputs by construction

full rationale

The paper's derivation begins from the chiral asymmetry energy density and tracks its partition into helical magnetic field growth versus thermal bath, yielding the parametric heating δT ∼ μ5²/T under μ5/T ≪ 1. This accounting rests on standard relativistic energy densities and conservation statements rather than any self-definitional loop, fitted parameter renamed as prediction, or load-bearing self-citation. No equation is shown to equal its own input by construction, and the saturation and dissipation steps are presented as outcomes of the instability evolution, not presupposed. The result is therefore self-contained against external benchmarks of energy conservation in chiral plasmas.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review provides no explicit free parameters, axioms, or invented entities; energy conservation and the small-ratio regime are implicit but not detailed enough to ledger.

pith-pipeline@v0.9.0 · 5430 in / 1009 out tokens · 42950 ms · 2026-05-11T01:02:20.003067+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

57 extracted references · 52 canonical work pages · 1 internal anchor

[1]

Kharzeev, The Chiral Magnetic Effect and Anomaly-Induced Transport, Prog

D.E. Kharzeev, The Chiral Magnetic Effect and Anomaly-Induced Transport, Prog. Part. Nucl. Phys.75(2014) 133 [1312.3348]. – 31 –

work page arXiv 2014
[2]

Kharzeev, J

D.E. Kharzeev, J. Liao, S.A. Voloshin and G. Wang, Chiral magnetic and vortical effects in high-energy nuclear collisions—A status report, Prog. Part. Nucl. Phys.88(2016) 1 [1511.04050]

work page arXiv 2016
[3]

V. Koch, S. Schlichting, V. Skokov, P. Sorensen, J. Thomas, S. Voloshin et al., Status of the chiral magnetic effect and collisions of isobars, Chin. Phys. C41(2017) 072001 [1608.00982]

work page arXiv 2017
[4]

Zhao and F

J. Zhao and F. Wang, Experimental searches for the chiral magnetic effect in heavy-ion collisions, Prog. Part. Nucl. Phys.107(2019) 200 [1906.11413]

work page arXiv 2019
[5]

Kharzeev, J

D.E. Kharzeev, J. Liao and P. Tribedy, Chiral magnetic effect in heavy ion collisions: The present and future, Int. J. Mod. Phys. E33 (2024) 2430007 [2405.05427]

work page arXiv 2024
[6]

W. Li, Q. Shou and F. Wang, Experimental review on the chiral magnetic effect in relativistic heavy ion collisions, 2511.07358

work page arXiv
[7]

Boyarsky, O

A. Boyarsky, O. Ruchayskiy and M. Shaposhnikov, Long-range magnetic fields in the ground state of the Standard Model plasma, Phys. Rev. Lett.109(2012) 111602 [1204.3604]

work page arXiv 2012
[8]

Dvornikov, Impossibility of the strong magnetic fields generation in an electron-positron plasma, Phys

M. Dvornikov, Impossibility of the strong magnetic fields generation in an electron-positron plasma, Phys. Rev. D90(2014) 041702 [1405.3059]

work page arXiv 2014
[9]

Grabowska, D.B

D. Grabowska, D.B. Kaplan and S. Reddy, Role of the electron mass in damping chiral plasma instability in Supernovae and neutron stars, Phys. Rev. D91(2015) 085035 [1409.3602]

work page arXiv 2015
[10]

Dvornikov and V.B

M. Dvornikov and V.B. Semikoz, Magnetic field instability in a neutron star driven by the electroweak electron-nucleon interaction versus the chiral magnetic effect, Phys. Rev. D91 (2015) 061301 [1410.6676]

work page arXiv 2015
[11]

Dvornikov and V.B

M. Dvornikov and V.B. Semikoz, Energy source for the magnetic field growth in magnetars driven by the electron-nucleon interaction, Phys. Rev. D92(2015) 083007 [1507.03948]

work page arXiv 2015
[12]

Sigl and N

G. Sigl and N. Leite, Chiral Magnetic Effect in Protoneutron Stars and Magnetic Field Spectral Evolution, JCAP 01(2016) 025 [1507.04983]

work page arXiv 2016
[13]

Yamamoto, Chiral transport of neutrinos in supernovae: Neutrino-induced fluid helicity and helical plasma instability, Phys

N. Yamamoto, Chiral transport of neutrinos in supernovae: Neutrino-induced fluid helicity and helical plasma instability, Phys. Rev. D93(2016) 065017 [1511.00933]

work page arXiv 2016
[14]

Kaplan, S

D.B. Kaplan, S. Reddy and S. Sen, Energy Conservation and the Chiral Magnetic Effect, Phys. Rev. D96(2017) 016008 [1612.00032]

work page arXiv 2017
[15]

Matsumoto, N

J. Matsumoto, N. Yamamoto and D.-L. Yang, Chiral plasma instability and inverse cascade from nonequilibrium left-handed neutrinos in core-collapse supernovae, Phys. Rev. D105 (2022) 123029 [2202.09205]

work page arXiv 2022
[16]

Sakharov, Violation of CP Invariance, C asymmetry, and baryon asymmetry of the universe, Pisma Zh

A.D. Sakharov, Violation of CP Invariance, C asymmetry, and baryon asymmetry of the universe, Pisma Zh. Eksp. Teor. Fiz.5(1967) 32

1967
[17]

Joyce and M

M. Joyce and M.E. Shaposhnikov, Primordial magnetic fields, right-handed electrons, and the Abelian anomaly, Phys. Rev. Lett. 79(1997) 1193 [astro-ph/9703005]

work page arXiv 1997
[18]

Frohlich and B

J. Frohlich and B. Pedrini, New applications of the chiral anomaly,hep-th/0002195. – 32 –

work page internal anchor Pith review arXiv
[19]

Voloshin, Testing the Chiral Magnetic Effect with Central U+U collisions, Phys

S.A. Voloshin, Testing the Chiral Magnetic Effect with Central U+U collisions, Phys. Rev. Lett.105(2010) 172301 [1006.1020]. [20]CMScollaboration, Observation of charge-dependent azimuthal correlations in p-pb collisions and its implication for the search for the chiral magnetic effect, Phys. Rev. Lett.118(2017) 122301 [1610.00263]. [21]CMScollaboration, ...

work page arXiv 2010
[20]

Boyarsky, J

A. Boyarsky, J. Frohlich and O. Ruchayskiy, Self-consistent evolution of magnetic fields and chiral asymmetry in the early Universe, Phys. Rev. Lett.108(2012) 031301 [1109.3350]

work page arXiv 2012
[21]

Cosmological Magnetic Fields: Their Generation, Evolution and Observation

R. Durrer and A. Neronov, Cosmological Magnetic Fields: Their Generation, Evolution and Observation, Astron. Astrophys. Rev.21(2013) 62 [1303.7121]

work page Pith review arXiv 2013
[22]

Brandenburg, K

A. Brandenburg, K. Enqvist and P. Olesen, Large scale magnetic fields from hydromagnetic turbulence in the very early universe, Phys. Rev. D54(1996) 1291 [astro-ph/9602031]

work page arXiv 1996
[23]

Dvornikov and V.B

M. Dvornikov and V.B. Semikoz, Leptogenesis via hypermagnetic fields and baryon asymmetry, JCAP02(2012) 040 [1111.6876]

work page arXiv 2012
[24]

Tashiro, T

H. Tashiro, T. Vachaspati and A. Vilenkin, Chiral Effects and Cosmic Magnetic Fields, Phys. Rev. D86(2012) 105033 [1206.5549]

work page arXiv 2012
[25]

Dvornikov and V.B

M. Dvornikov and V.B. Semikoz, Instability of magnetic fields in electroweak plasma driven by neutrino asymmetries, JCAP05 (2014) 002 [1311.5267]

work page arXiv 2014
[26]

Semikoz, A.Y

V.B. Semikoz, A.Y. Smirnov and D.D. Sokoloff, Hypermagnetic helicity evolution in early universe: leptogenesis and hypermagnetic diffusion, JCAP10(2013) 014 [1309.4302]

work page arXiv 2013
[27]

Buividovich and M.V

P.V. Buividovich and M.V. Ulybyshev, Numerical study of chiral plasma instability within the classical statistical field theory approach, Phys. Rev. D94(2016) 025009 [1509.02076]

work page arXiv 2016
[28]

Pavlovi´ c, N

P. Pavlovi´ c, N. Leite and G. Sigl,Chiral Magnetohydrodynamic Turbulence, Phys. Rev. D96 (2017) 023504 [1612.07382]

work page arXiv 2017
[29]

Rogachevskii, O

I. Rogachevskii, O. Ruchayskiy, A. Boyarsky, J. Fr¨ ohlich, N. Kleeorin, A. Brandenburg et al., Laminar and turbulent dynamos in chiral magnetohydrodynamics-I: Theory, Astrophys. J.846 (2017) 153 [1705.00378]

work page arXiv 2017
[30]

Brandenburg, J

A. Brandenburg, J. Schober, I. Rogachevskii, T. Kahniashvili, A. Boyarsky, J. Frohlich et al., The turbulent chiral-magnetic cascade in the early universe, Astrophys. J. Lett.845(2017) L21 [1707.03385]. – 33 –

work page arXiv 2017
[31]

Anand, J.R

S. Anand, J.R. Bhatt and A.K. Pandey, Chiral plasma instability and primordial gravitational waves, Eur. Phys. J. C79(2019) 119 [1801.00650]

work page arXiv 2019
[32]

Brandenburg, Y

A. Brandenburg, Y. He, T. Kahniashvili, M. Rheinhardt and J. Schober, Relic gravitational waves from the chiral magnetic effect, Astrophys. J.911(2021) 110 [2101.08178]

work page arXiv 2021
[33]

Kamada, N

K. Kamada, N. Yamamoto and D.-L. Yang, Chiral effects in astrophysics and cosmology, Prog. Part. Nucl. Phys.129(2023) 104016 [2207.09184]

work page arXiv 2023
[34]

Brandenburg, K

A. Brandenburg, K. Kamada, K. Mukaida, K. Schmitz and J. Schober, Chiral magnetohydrodynamics with zero total chirality, Phys. Rev. D108(2023) 063529 [2304.06612]

work page arXiv 2023
[35]

Gurgenidze, A.J

M. Gurgenidze, A.J. Long, A. Roper Pol, A. Brandenburg and T. Kahniashvili, Primordial magnetic field from chiral plasma instability with sourcing,2512.09177

work page arXiv
[36]

Vilenkin, Equilibrium Parity Violating Current in a Magnetic Field, Phys

A. Vilenkin, Equilibrium Parity Violating Current in a Magnetic Field, Phys. Rev. D22 (1980) 3080

1980
[37]

Adler, Axial vector vertex in spinor electrodynamics, Phys

S.L. Adler, Axial vector vertex in spinor electrodynamics, Phys. Rev.177(1969) 2426

1969
[38]

Bell and R

J.S. Bell and R. Jackiw, A PCAC puzzle:π 0 →γγin theσmodel, Nuovo Cim. A60(1969) 47

1969
[39]

Q. Li, D.E. Kharzeev, C. Zhang, Y. Huang, I. Pletikosic, A.V. Fedorov et al., Observation of the chiral magnetic effect in ZrTe5, Nature Phys.12(2016) 550 [1412.6543]

work page arXiv 2016
[40]

Long and E

A.J. Long and E. Sabancilar, Chiral Charge Erasure via Thermal Fluctuations of Magnetic Helicity, JCAP05(2016) 029 [1601.03777]

work page arXiv 2016
[41]

Pavlovi´ c and G

P. Pavlovi´ c and G. Sigl,On minimal energy states of chiral MHD turbulence, JCAP04(2019) 055 [1806.06447]

work page arXiv 2019
[42]

Roper Pol and A.S

A. Roper Pol and A.S. Midiri, Relativistic magnetohydrodynamics in the early Universe, 2501.05732

work page arXiv
[43]

Transport coefficients in high temperature gauge theories: (I) Leading-log results

P.B. Arnold, G.D. Moore and L.G. Yaffe, Transport coefficients in high temperature gauge theories. 1. Leading log results, JHEP11 (2000) 001 [hep-ph/0010177]

work page Pith review arXiv 2000
[44]

Cosmologically degenerate fermions,

M. Carena, N.M. Coyle, Y.-Y. Li, S.D. McDermott and Y. Tsai, Cosmologically degenerate fermions, Phys. Rev. D106(2022) 083016 [2108.02785]

work page arXiv 2022
[45]

Batell and W

B. Batell and W. Yin, Cosmic stability of dark matter from Pauli blocking, Phys. Rev. D110 (2024) 075038 [2406.17028]

work page arXiv 2024
[46]

Tremaine and J.E

S. Tremaine and J.E. Gunn, Dynamical Role of Light Neutral Leptons in Cosmology, Phys. Rev. Lett.42(1979) 407

1979
[47]

and Lu, Sida

Y. Bai, A.J. Long and S. Lu, Dark Quark Nuggets, Phys. Rev. D99(2019) 055047 [1810.04360]

work page arXiv 2019
[48]

J.-P. Hong, S. Jung and K.-P. Xie, Fermi-ball dark matter from a first-order phase transition, Phys. Rev. D102(2020) 075028 [2008.04430]

work page arXiv 2020
[49]

Chavanis, Predictive model of fermionic dark matter halos with a quantum core and an isothermal atmosphere, Phys

P.-H. Chavanis, Predictive model of fermionic dark matter halos with a quantum core and an isothermal atmosphere, Phys. Rev. D106(2022) 043538 [2112.07726]

work page arXiv 2022
[50]

Revisiting Big-Bang Nucleosynthesis Constraints on Long-Lived Decaying Particles

M. Kawasaki, K. Kohri, T. Moroi and Y. Takaesu, Revisiting Big-Bang Nucleosynthesis Constraints on Long-Lived Decaying Particles, Phys. Rev. D97(2018) 023502 [1709.01211]. – 34 –

work page Pith review arXiv 2018
[51]

Kogut, M.H

A. Kogut, M.H. Abitbol, J. Chluba, J. Delabrouille, D. Fixsen, J.C. Hill et al., CMB Spectral Distortions: Status and Prospects, Bull. Am. Astron. Soc.51(2019) 113 [1907.13195]

work page arXiv 2019
[52]

Sobotka, A.L

A.C. Sobotka, A.L. Erickcek and T.L. Smith, Was entropy conserved between BBN and recombination?, Phys. Rev. D107(2023) 023525 [2207.14308]

work page arXiv 2023
[53]

Sobotka, A.L

A.C. Sobotka, A.L. Erickcek and T.L. Smith, Comprehensive constraints on dark radiation injection after BBN, Phys. Rev. D109(2024) 063538 [2312.13235]

work page arXiv 2024
[54]

Batell et al., Conversations and deliberations: Non-standard cosmological epochs and expansion histories, Int

B. Batell et al., Conversations and deliberations: Non-standard cosmological epochs and expansion histories, Int. J. Mod. Phys. A40(2025) 2530004 [2411.04780]

work page arXiv 2025
[55]

Y. Cui, M. Lewicki, D.E. Morrissey and J.D. Wells, Cosmic Archaeology with Gravitational Waves from Cosmic Strings, Phys. Rev. D97(2018) 123505 [1711.03104]

work page arXiv 2018
[56]

Y. Cui, M. Lewicki, D.E. Morrissey and J.D. Wells, Probing the pre-BBN universe with gravitational waves from cosmic strings, JHEP01(2019) 081 [1808.08968]

work page arXiv 2019
[57]

Gouttenoire, G

Y. Gouttenoire, G. Servant and P. Simakachorn, Kination cosmology from scalar fields and gravitational-wave signatures,2111.01150. – 35 –

work page arXiv