pith. sign in

arxiv: 2605.04293 · v2 · pith:BHBYQZLOnew · submitted 2026-05-05 · ⚛️ physics.space-ph · astro-ph.GA· astro-ph.SR· physics.geo-ph· physics.plasm-ph

Transport of electrons in tangled magnetic fields

Daniel Verscharen , Natasha Jeffrey , Anton Artemyev , Jesse T. Coburn , Matthew W. Kunz , Oreste Pezzi , Mario Riquelme , Ida Svenningsson
show 1 more author
Lynn B. Wilson III
This is my paper

Pith reviewed 2026-07-01 00:31 UTC · model grok-4.3

classification ⚛️ physics.space-ph astro-ph.GAastro-ph.SRphysics.geo-phphysics.plasm-ph
keywords electron transporttangled magnetic fieldsspace plasmagyro-centre motionwave-particle interactionscross-field diffusionheliophysicsastrophysical plasmas
0
0 comments X

The pith

Electrons follow gyro-centre paths along tangled magnetic field lines but drifts, waves, trapping and diffusion modify their transport.

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

This review establishes the basic principles of electron motion in inhomogeneous cosmic magnetic fields. When field variations exceed the electron gyro-radius, electrons remain confined to trajectories along field lines, so in-situ measurements can map magnetic connectivity. The paper reviews how turbulence and instabilities tangle the fields, how kinetic instabilities alter parallel transport, and how trapping, de-trapping, cross-field diffusion and energisation arise from inhomogeneities. It concludes that electron transport emerges from the interplay of these processes across many scales and requires combined observations and theory.

Core claim

The transport of electrons in tangled fields results from a complex interplay of plasma processes that occur on a broad range of scales. A combination of in-situ plasma measurements, remote-sensing plasma observations, and plasma theory and simulations is required to resolve this challenge to heliophysics and astrophysics.

What carries the argument

Gyro-centre trajectories along magnetic field lines, modified by gyro-centre drifts, wave-particle interactions, trapping and cross-field diffusion when field variations are large compared with the electron gyro-radius.

If this is right

  • In-situ electron measurements map out the connectivity of magnetic field lines in space plasmas.
  • Kinetic instabilities can modify or disrupt parallel electron transport along field lines.
  • Trapping and de-trapping in inhomogeneous fields alter electron paths and residence times.
  • Cross-field diffusion and energisation arise from field fluctuations and inhomogeneities.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same scale-dependent processes likely govern ion transport and cosmic-ray scattering in similar tangled fields.
  • Multi-spacecraft measurements resolving both large-scale tangling and kinetic-scale waves could quantify the relative contributions of each process.
  • Improved models of solar energetic particle propagation could incorporate the trapping and diffusion mechanisms described.

Load-bearing premise

Magnetic-field variations occur on scales large compared to the electron gyro-radius, so electrons stay confined to gyro-centre trajectories along the field lines.

What would settle it

Observation of electrons crossing field lines at rates much higher than predicted by gyro-centre motion even when field variations greatly exceed the electron gyro-radius.

read the original abstract

Cosmic magnetic fields are typically inhomogeneous and often highly tangled due to large-scale plasma flows, turbulence, and instabilities. If the variations in the magnetic field occur on scales that are large compared to the gyro-radius of the plasma electrons, the electrons are primarily confined to gyro-centre trajectories along the field lines. Therefore, in-situ electron measurements help us map out the connectivity of the magnetic field in space plasmas. Gyro-centre drifts, wave-particle interactions, trapping, and cross-field diffusion are processes related to field inhomogeneities and fluctuations; they have the potential to modify or even disrupt the transport of electrons along field lines. We introduce the basic principles of electron transport in tangled magnetic fields and review the creation of tangled fields through turbulence and instabilities as well as the modulation of parallel electron transport through kinetic instabilities. We then describe trapping and de-trapping effects in inhomogeneous magnetic fields, as well as electron diffusion and energisation across the magnetic field. The transport of electrons in tangled fields results from a complex interplay of plasma processes that occur on a broad range of scales. A combination of in-situ plasma measurements, remote-sensing plasma observations, and plasma theory and simulations is required to resolve this contemporary challenge to the fields of heliophysics and astrophysics.

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.

Referee Report

0 major / 1 minor

Summary. The manuscript is a review article that introduces the basic principles of electron transport in tangled magnetic fields in space plasmas. It states that when magnetic field variations occur on scales large compared to the electron gyro-radius, electrons follow gyro-centre trajectories along field lines, enabling in-situ measurements to map magnetic connectivity. The review covers gyro-centre drifts, wave-particle interactions, trapping, and cross-field diffusion as processes that can modify transport due to field inhomogeneities. It reviews the generation of tangled fields via turbulence and instabilities, modulation of parallel transport by kinetic instabilities, trapping/de-trapping effects, and cross-field diffusion/energization. The central conclusion is that electron transport arises from a complex multi-scale interplay of plasma processes, requiring combined in-situ measurements, remote-sensing observations, theory, and simulations to address challenges in heliophysics and astrophysics.

Significance. If the synthesis is accurate and comprehensive, the review could serve as a useful reference for connecting established plasma-physics concepts (guiding-center motion, kinetic instabilities, trapping) to applications in space plasmas. It correctly frames the guiding-center approximation as the baseline regime and emphasizes the need for multi-method studies of scale interplay, which aligns with current challenges in the field. No new derivations, datasets, or falsifiable predictions are presented, so significance rests on the organization and currency of the literature review rather than novel contributions. The manuscript ships no machine-checked proofs or reproducible code.

minor comments (1)
  1. [Abstract] Abstract: the concluding sentence on the 'complex interplay of plasma processes that occur on a broad range of scales' would benefit from one concrete example of the relevant scale ranges (e.g., gyro-radius vs. turbulence correlation length) to make the motivation more specific for readers.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of the manuscript as a useful synthesis of electron transport principles in tangled magnetic fields and for the recommendation to accept. No major comments were raised requiring point-by-point response.

Circularity Check

0 steps flagged

No significant circularity; review with no derivations or predictions

full rationale

The paper is a review synthesizing established plasma-physics principles (guiding-center motion when field variations ≫ gyro-radius, kinetic instabilities, trapping, cross-field diffusion). It presents no new derivations, predictions, or fitted quantities whose validity hinges on any single untested assumption. The cited guiding-center condition is textbook and internally consistent with the regimes addressed. No load-bearing steps reduce to self-citation chains or definitions by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

As a review paper with only the abstract available, the ledger captures the key domain assumption stated in the abstract; no free parameters or invented entities are introduced.

axioms (1)
  • domain assumption Variations in the magnetic field occur on scales large compared to the electron gyro-radius, allowing confinement to gyro-centre trajectories along field lines.
    Directly stated in the abstract as the basis for the transport description.

pith-pipeline@v0.9.1-grok · 5792 in / 1147 out tokens · 14264 ms · 2026-07-01T00:31:03.177456+00:00 · methodology

Review history (2 revisions) →

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

300 extracted references · 283 canonical work pages · 63 internal anchors

  1. [1]

    131(19):191001

    Adriani O, Akaike Y, Asano K, et al (2023) Direct Measurement of the Spectral Structure of Cosmic-Ray Electrons+Positrons in the TeV Region with CALET on the International Space Station . 131(19):191001. doi:10.1103/PhysRevLett.131.191001, https://arxiv.org/abs/2311.05916 arXiv:2311.05916 [astro-ph.HE]

    work page doi:10.1103/physrevlett.131.191001 2023

  2. [2]

    118:3407--3420

    Agapitov OV, Artemyev A, Krasnoselskikh V, et al (2013) Statistics of whistler mode waves in the outer radiation belt: Cluster STAFF-SA measurements . 118:3407--3420. doi:10.1002/jgra.50312

    work page doi:10.1002/jgra.50312 2013

  3. [3]

    J Atmosph Solar-Terr Phys 71:1647--1652

    Albert JM, Shprits YY (2009) Estimates of lifetimes against pitch angle diffusion . J Atmosph Solar-Terr Phys 71:1647--1652. doi:10.1016/j.jastp.2008.07.004

    work page doi:10.1016/j.jastp.2008.07.004 2009

  4. [4]

    In: Summers D, Mann IU, Baker DN, et al (eds) Dynamics of the Earth's Radiation Belts and Inner Magnetosphere, American Geophysical Union, doi:10.1029/2012GM001324

    Albert JM, Tao X, Bortnik J (2013) Aspects of Nonlinear Wave-Particle Interactions . In: Summers D, Mann IU, Baker DN, et al (eds) Dynamics of the Earth's Radiation Belts and Inner Magnetosphere, American Geophysical Union, doi:10.1029/2012GM001324

    work page doi:10.1029/2012gm001324 2013

  5. [5]

    Arkiv for Matematik, Astronomi och Fysik 29B:1--7

    Alfv \'e n H (1943) On the Existence of Electromagnetic-Hydrodynamic Waves . Arkiv for Matematik, Astronomi och Fysik 29B:1--7

    1943

  6. [6]

    , volume =

    Amano T, Katou T, Kitamura N, et al (2020) Observational Evidence for Stochastic Shock Drift Acceleration of Electrons at the Earth's Bow Shock . 124(6):065101. doi:10.1103/PhysRevLett.124.065101, https://arxiv.org/abs/2002.06787 arXiv:2002.06787 [astro-ph.HE]

    work page doi:10.1103/physrevlett.124.065101 2020

  7. [7]

    RevModern Plasma Phys 6(1):29

    Amano T, Matsumoto Y, Bohdan A, et al (2022) Nonthermal electron acceleration at collisionless quasi-perpendicular shocks . RevModern Plasma Phys 6(1):29. doi:10.1007/s41614-022-00093-1, https://arxiv.org/abs/2209.03521 arXiv:2209.03521 [astro-ph.HE]

    work page doi:10.1007/s41614-022-00093-1 2022

  8. [8]

    to be submitted

    Amano T, Klein KG, Niemiec J, et al (2026) Electron Energy Partition in Shocks, Magnetic Reconnection, and Turbulence . to be submitted

    2026

  9. [9]

    , archivePrefix = "arXiv", eprint =

    Amato E, Blasi P (2009) A kinetic approach to cosmic-ray-induced streaming instability at supernova shocks . 392(4):1591--1600. doi:10.1111/j.1365-2966.2008.14200.x, https://arxiv.org/abs/0806.1223 arXiv:0806.1223 [astro-ph]

    work page doi:10.1111/j.1365-2966.2008.14200.x 2009

  10. [10]

    93(A12):14383--14400

    Ambrosiano J, Matthaeus WH, Goldstein ML, et al (1988) Test particle acceleration in turbulent reconnecting magnetic fields . 93(A12):14383--14400. doi:10.1029/JA093iA12p14383

    work page doi:10.1029/ja093ia12p14383 1988

  11. [11]

    Geomagnetism and Aeronomy 4:233--242

    Andronov AA, Trakhtengerts VY (1964) Kinetic instability of the Earth's outer radiation belt . Geomagnetism and Aeronomy 4:233--242

    1964

  12. [12]

    141:5--34

    Angelopoulos V (2008) The THEMIS Mission . 141:5--34. doi:10.1007/s11214-008-9336-1

    work page doi:10.1007/s11214-008-9336-1 2008

  13. [13]

    216(5):103

    Angelopoulos V, Tsai E, Bingley L, et al (2020) The ELFIN Mission . 216(5):103. doi:10.1007/s11214-020-00721-7, https://arxiv.org/abs/2006.07747 arXiv:2006.07747 [physics.space-ph]

    work page doi:10.1007/s11214-020-00721-7 2020

  14. [14]

    219(5):37

    Angelopoulos V, Zhang XJ, Artemyev AV, et al (2023) Energetic Electron Precipitation Driven by Electromagnetic Ion Cyclotron Waves from ELFIN's Low Altitude Perspective . 219(5):37. doi:10.1007/s11214-023-00984-w, https://arxiv.org/abs/2211.15653 arXiv:2211.15653 [physics.space-ph]

    work page doi:10.1007/s11214-023-00984-w 2023

  15. [15]

    Two-component turbulence

    Arendt V, Shalchi A (2020) Detailed test-particle simulations of energetic particles interacting with magnetized plasmas I. Two-component turbulence . Adv Space Res 66(8):2001--2023. doi:10.1016/j.asr.2020.07.024

    work page doi:10.1016/j.asr.2020.07.024 2020

  16. [16]

    Armstrong JW, Rickett BJ, Spangler SR (1995) Electron Density Power Spectrum in the Local Interstellar Medium . 443:209. doi:10.1086/175515

    work page doi:10.1086/175515 1995

  17. [17]

    J Geophys Res 117(A06219):A06219

    Artemyev AV, Petrukovich AA, Nakamura R, et al (2012) Adiabatic electron heating in the magnetotail current sheet: Cluster observations and analytical models. J Geophys Res 117(A06219):A06219. doi:10.1029/2012JA017513

    work page doi:10.1029/2012ja017513 2012

  18. [18]

    Ann Geophys 31:599--624

    Artemyev AV, Mourenas D, Agapitov OV, et al (2013) Parametric validations of analytical lifetime estimates for radiation belt electron diffusion by whistler waves . Ann Geophys 31:599--624. doi:10.5194/angeo-31-599-2013

    work page doi:10.5194/angeo-31-599-2013 2013

  19. [19]

    102(3):033201

    Artemyev AV, Neishtadt AI, Vasiliev AA, et al (2020) Superfast ion scattering by solar wind discontinuities . 102(3):033201. doi:10.1103/PhysRevE.102.033201

    work page doi:10.1103/physreve.102.033201 2020

  20. [20]

    127(10):e2022JA030705

    Artemyev AV, Angelopoulos V, Zhang XJ, et al (2022) Thinning of the Magnetotail Current Sheet Inferred From Low-Altitude Observations of Energetic Electrons . 127(10):e2022JA030705. doi:10.1029/2022JA030705

    work page doi:10.1029/2022ja030705 2022

  21. [21]

    arXiv e-prints arXiv:2410.07386

    Artemyev AV, Mourenas D, Zhang XJ, et al (2024 a ) Nonlinear resonant interactions of radiation belt electrons with intense whistler-mode waves . arXiv e-prints arXiv:2410.07386. doi:10.48550/arXiv.2410.07386, https://arxiv.org/abs/2410.07386 arXiv:2410.07386 [physics.space-ph]

    work page doi:10.48550/arxiv.2410.07386 2024

  22. [22]

    129(12):2024JA033231

    Artemyev AV, Sergeev VA, Angelopoulos V, et al (2024 b ) Categorization of Electron Isotropy Boundary Patterns: ELFIN and POES Observations . 129(12):2024JA033231. doi:10.1029/2024JA033231

    work page doi:10.1029/2024ja033231 2024

  23. [23]

    Physical Review X 13(2):021014

    Arzamasskiy L, Kunz MW, Squire J, et al (2023) Kinetic Turbulence in Collisionless High- Plasmas . Physical Review X 13(2):021014. doi:10.1103/PhysRevX.13.021014, https://arxiv.org/abs/2207.05189 arXiv:2207.05189 [astro-ph.HE]

    work page doi:10.1103/physrevx.13.021014 2023

  24. [24]

    83:1531--1543

    Ashour-Abdalla M, Kennel CF (1978) Nonconvective and convective electron cyclotron harmonic instabilities . 83:1531--1543. doi:10.1029/JA083iA04p01531

    work page doi:10.1029/ja083ia04p01531 1978

  25. [25]

    , keywords =

    Auster HU, Glassmeier KH, Magnes W, et al (2008) The THEMIS Fluxgate Magnetometer . 141:235--264. doi:10.1007/s11214-008-9365-9

    work page doi:10.1007/s11214-008-9365-9 2008

  26. [26]

    Magnetohydrodynamic-Particle-in-Cell Simulations of the Cosmic-Ray Streaming Instability: Linear Growth and Quasi-linear Evolution

    Bai XN, Ostriker EC, Plotnikov I, et al (2019) Magnetohydrodynamic Particle-in-cell Simulations of the Cosmic-Ray Streaming Instability: Linear Growth and Quasi-linear Evolution . 876(1):60. doi:10.3847/1538-4357/ab1648, https://arxiv.org/abs/1902.10219 arXiv:1902.10219 [astro-ph.HE]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.3847/1538-4357/ab1648 2019

  27. [27]

    Stability, Instability, and "Backwards'' Transport in Accretion Disks"

    Balbus SA (2000) Stability, Instability, and ``Backward'' Transport in Stratified Fluids . 534(1):420--427. doi:10.1086/308732, https://arxiv.org/abs/astro-ph/9906315 arXiv:astro-ph/9906315 [astro-ph]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1086/308732 2000

  28. [28]

    Convective and Rotational Stability of a Dilute Plasma

    Balbus SA (2001) Convective and Rotational Stability of a Dilute Plasma . 562(2):909--917. doi:10.1086/323875, https://arxiv.org/abs/astro-ph/0106283 arXiv:astro-ph/0106283 [astro-ph]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1086/323875 2001

  29. [29]

    Balbus SA, Hawley JF (1991) A Powerful Local Shear Instability in Weakly Magnetized Disks. I. Linear Analysis . 376:214. doi:10.1086/170270

    work page doi:10.1086/170270 1991

  30. [30]

    Reviews of Modern Physics 70(1):1--53

    Balbus SA, Hawley JF (1998) Instability, turbulence, and enhanced transport in accretion disks . Reviews of Modern Physics 70(1):1--53. doi:10.1103/RevModPhys.70.1

    work page doi:10.1103/revmodphys.70.1 1998

  31. [31]

    Electron heat conduction in the solar wind: transition from Spitzer-H\"{a}rm to the collisionless limit

    Bale SD, Pulupa M, Salem C, et al (2013) Electron Heat Conduction in the Solar Wind: Transition from Spitzer-H \"a rm to the Collisionless Limit . 769(2):L22. doi:10.1088/2041-8205/769/2/L22, https://arxiv.org/abs/1303.0932 arXiv:1303.0932 [astro-ph.SR]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/2041-8205/769/2/l22 2013

  32. [32]

    920(2):141

    Bambic CJ, Bai XN, Ostriker EC (2021) MHD-PIC Simulations of Cosmic-Ray Scattering and Transport in Inhomogeneously Ionized Plasma . 920(2):141. doi:10.3847/1538-4357/ac0ce7, https://arxiv.org/abs/2102.11877 arXiv:2102.11877 [astro-ph.GA]

    work page doi:10.3847/1538-4357/ac0ce7 2021

  33. [33]

    Beckmann RS, Dubois Y, Pellissier A, et al (2022) AGN jets do not prevent the suppression of conduction by the heat buoyancy instability in simulated galaxy clusters . 666:A71. doi:10.1051/0004-6361/202243873, https://arxiv.org/abs/2204.12514 arXiv:2204.12514 [astro-ph.GA]

    work page doi:10.1051/0004-6361/202243873 2022

  34. [34]

    L., McClure-Griffiths, N

    Bell AR (2004) Turbulent amplification of magnetic field and diffusive shock acceleration of cosmic rays . 353(2):550--558. doi:10.1111/j.1365-2966.2004.08097.x

    work page doi:10.1111/j.1365-2966.2004.08097.x 2004

  35. [35]

    2005, MNRAS, 360, 587, doi: 10.1111/j.1365-2966.2005.09047.x

    Bell AR (2005) The interaction of cosmic rays and magnetized plasma . 358(1):181--187. doi:10.1111/j.1365-2966.2005.08774.x

    work page doi:10.1111/j.1365-2966.2005.08774.x 2005

  36. [36]

    Living Reviews in Solar Physics , keywords =

    Benz AO (2017) Flare Observations . Living Rev Solar Phys 14(1):2. doi:10.1007/s41116-016-0004-3

    work page doi:10.1007/s41116-016-0004-3 2017

  37. [37]

    908(1):45

    Bian NH, Li G (2021) Stochastic Parker Spirals in the Solar Wind . 908(1):45. doi:10.3847/1538-4357/abd39a

    work page doi:10.3847/1538-4357/abd39a 2021

  38. [38]

    247:464--472

    Binney J, Cowie LL (1981) X-ray emission from M87 - A pressure confined cooling atmosphere surrounding a low mass galaxy . 247:464--472. doi:10.1086/159055

    work page doi:10.1086/159055 1981

  39. [39]

    , keywords =

    Birmingham TJ (1984) Pitch angle diffusion in the Jovian magnetodisc . 89:2699--2707. doi:10.1029/JA089iA05p02699

    work page doi:10.1029/ja089ia05p02699 1984

  40. [40]

    Blasi P (2013) The origin of galactic cosmic rays . 21:70. doi:10.1007/s00159-013-0070-7, https://arxiv.org/abs/1311.7346 arXiv:1311.7346 [astro-ph.HE]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1007/s00159-013-0070-7 2013

  41. [41]

    29(1):012105

    Blasl KA, Nakamura TKM, Plaschke F, et al (2022) Multi-scale observations of the magnetopause Kelvin-Helmholtz waves during southward IMF . 29(1):012105. doi:10.1063/5.0067370

    work page doi:10.1063/5.0067370 2022

  42. [42]

    Astron Lett 31(8):537--545

    Bogachev SA, Somov BV (2005) Comparison of the Fermi and Betatron Acceleration Efficiencies in Collapsing Magnetic Traps . Astron Lett 31(8):537--545. doi:10.1134/1.2007030

    work page doi:10.1134/1.2007030 2005

  43. [43]

    Simulations of MHD Instabilities in Intracluster Medium Including Anisotropic Thermal Conduction

    Bogdanovi \'c T, Reynolds CS, Balbus SA, et al (2009) Simulations of Magnetohydrodynamics Instabilities in Intracluster Medium Including Anisotropic Thermal Conduction . 704(1):211--225. doi:10.1088/0004-637X/704/1/211, https://arxiv.org/abs/0905.4508 arXiv:0905.4508 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/0004-637x/704/1/211 2009

  44. [44]

    674:A220

    Bold \'u JJ, Graham DB, Morooka M, et al (2023) Langmuir waves associated with magnetic holes in the solar wind . 674:A220. doi:10.1051/0004-6361/202346100

    work page doi:10.1051/0004-6361/202346100 2023

  45. [45]

    Spectrum of magnetohydrodynamic turbulence

    Boldyrev S (2006) Spectrum of Magnetohydrodynamic Turbulence . 96(11):115002. doi:10.1103/PhysRevLett.96.115002, https://arxiv.org/abs/astro-ph/0511290 arXiv:astro-ph/0511290 [astro-ph]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevlett.96.115002 2006

  46. [46]

    141:303--341

    Bonnell JW, Mozer FS, Delory GT, et al (2008) The Electric Field Instrument (EFI) for THEMIS . 141:303--341. doi:10.1007/s11214-008-9469-2

    work page doi:10.1007/s11214-008-9469-2 2008

  47. [47]

    Particle Acceleration in Collapsing Magnetic Traps with a Braking Plasma Jet

    Borissov A, Neukirch T, Threlfall J (2016) Particle Acceleration in Collapsing Magnetic Traps with a Braking Plasma Jet . 291:1385--1404. doi:10.1007/s11207-016-0915-0, https://arxiv.org/abs/1605.06343 arXiv:1605.06343 [astro-ph.SR]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1007/s11207-016-0915-0 2016

  48. [48]

    Rev Plasma Phys 1:205

    Braginskii SI (1965) Transport Processes in a Plasma . Rev Plasma Phys 1:205

    1965

  49. [49]

    J Geophys Res (Space Phys) 113(A8):A08105

    Breech B, Matthaeus WH, Minnie J, et al (2008) Turbulence transport throughout the heliosphere . J Geophys Res (Space Phys) 113(A8):A08105. doi:10.1029/2007JA012711

    work page doi:10.1029/2007ja012711 2008

  50. [50]

    J Geophys Res 118(12):7654--7664

    Breneman A, Cattell C, Kersten K, et al (2013) STEREO and Wind observations of intense cyclotron harmonic waves at the Earth’s bow shock and inside the magnetosheath . J Geophys Res 118(12):7654--7664. doi:10.1002/2013JA019372, ://dx.doi.org/10.1002/2013JA019372

    work page doi:10.1002/2013ja019372 2013

  51. [51]

    18(3):489--502

    Brown JC (1971) The Deduction of Energy Spectra of Non-Thermal Electrons in Flares from the Observed Dynamic Spectra of Hard X-Ray Bursts . 18(3):489--502. doi:10.1007/BF00149070

    work page doi:10.1007/bf00149070 1971

  52. [52]

    W., Haverkorn, M., & Zhang, H

    Brunetti G, Lazarian A (2007) Compressible turbulence in galaxy clusters: physics and stochastic particle re-acceleration . 378(1):245--275. doi:10.1111/j.1365-2966.2007.11771.x, https://arxiv.org/abs/astro-ph/0703591 arXiv:astro-ph/0703591 [astro-ph]

    work page doi:10.1111/j.1365-2966.2007.11771.x 2007

  53. [53]

    Stochastic reacceleration of relativistic electrons by turbulent reconnection: a mechanism for cluster-scale radio emission ?

    Brunetti G, Lazarian A (2016) Stochastic reacceleration of relativistic electrons by turbulent reconnection: a mechanism for cluster-scale radio emission? 458(3):2584--2595. doi:10.1093/mnras/stw496, https://arxiv.org/abs/1603.00458 arXiv:1603.00458 [astro-ph.HE]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1093/mnras/stw496 2016

  54. [54]

    , keywords =

    Brunetti G, Vazza F (2020) Second-order Fermi Reacceleration Mechanisms and Large-Scale Synchrotron Radio Emission in Intracluster Bridges . 124(5):051101. doi:10.1103/PhysRevLett.124.051101, https://arxiv.org/abs/2001.07718 arXiv:2001.07718 [astro-ph.HE]

    work page doi:10.1103/physrevlett.124.051101 2020

  55. [55]

    2001, MNRAS, 325, 1365, doi: 10.1046/j.1365-8711.2001.04510.x

    Brunetti G, Setti G, Feretti L, et al (2001) Particle reacceleration in the Coma cluster: radio properties and hard X-ray emission . 320(3):365--378. doi:10.1046/j.1365-8711.2001.03978.x, https://arxiv.org/abs/astro-ph/0008518 arXiv:astro-ph/0008518 [astro-ph]

    work page doi:10.1046/j.1365-8711.2001.03978.x 2001

  56. [56]

    Living Reviews in Solar Physics , keywords =

    Bruno R, Carbone V (2013) The Solar Wind as a Turbulence Laboratory . Living Rev Solar Phys 10(1):2. doi:10.12942/lrsp-2013-2

    work page doi:10.12942/lrsp-2013-2 2013

  57. [57]

    I., Schawinski, K., Kaviraj, S., et al

    Bu DF, Yuan F, Stone JM (2011) Magnetothermal and magnetorotational instabilities in hot accretion flows . 413(4):2808--2814. doi:10.1111/j.1365-2966.2011.18354.x, https://arxiv.org/abs/1011.5331 arXiv:1011.5331 [astro-ph.HE]

    work page doi:10.1111/j.1365-2966.2011.18354.x 2011

  58. [58]

    I - Basic theory of trapped motion

    B \"u chner J, Zelenyi LM (1989) Regular and chaotic charged particle motion in magnetotaillike field reversals. I - Basic theory of trapped motion . J Geophys Res 94:11821--11842. doi:10.1029/JA094iA09p11821

    work page doi:10.1029/ja094ia09p11821 1989

  59. [59]

    Phys Plasmas 12:102110

    Cairns IH, McMillan BF (2005) Electron acceleration by lower hybrid waves in magnetic reconnection regions . Phys Plasmas 12:102110. doi:10.1063/1.2080567

    work page doi:10.1063/1.2080567 2005

  60. [60]

    Caprioli D, Spitkovsky A (2014 a ) Simulations of Ion Acceleration at Non-relativistic Shocks. II. Magnetic Field Amplification . 794(1):46. doi:10.1088/0004-637X/794/1/46, https://arxiv.org/abs/1401.7679 arXiv:1401.7679 [astro-ph.HE]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/0004-637x/794/1/46 2014

  61. [61]

    Caprioli D, Spitkovsky A (2014 b ) Simulations of Ion Acceleration at Non-relativistic Shocks. III. Particle Diffusion . 794(1):47. doi:10.1088/0004-637X/794/1/47, https://arxiv.org/abs/1407.2261 arXiv:1407.2261 [astro-ph.HE]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/0004-637x/794/1/47 2014

  62. [62]

    Caprioli D, Haggerty CC, Blasi P (2020) Kinetic Simulations of Cosmic-Ray-modified Shocks. II. Particle Spectra . 905(1):2. doi:10.3847/1538-4357/abbe05, https://arxiv.org/abs/2009.00007 arXiv:2009.00007 [astro-ph.HE]

    work page doi:10.3847/1538-4357/abbe05 2020

  63. [63]

    Transport of Cosmic Rays in Chaotic Magnetic Fields

    Casse F, Lemoine M, Pelletier G (2001) Transport of cosmic rays in chaotic magnetic fields . 65(2):023002. doi:10.1103/PhysRevD.65.023002, https://arxiv.org/abs/astro-ph/0109223 arXiv:astro-ph/0109223 [astro-ph]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.65.023002 2001

  64. [64]

    80(14):3077--3080

    Chandran BDG, Cowley SC (1998) Thermal Conduction in a Tangled Magnetic Field . 80(14):3077--3080. doi:10.1103/PhysRevLett.80.3077

    work page doi:10.1103/physrevlett.80.3077 1998

  65. [65]

    Alfven Wave Reflection and Turbulent Heating in the Solar Wind from 1 Solar Radius to 1 AU: an Analytical Treatment

    Chandran BDG, Hollweg JV (2009) Alfv \'e n Wave Reflection and Turbulent Heating in the Solar Wind from 1 Solar Radius to 1 AU: An Analytical Treatment . 707(2):1659--1667. doi:10.1088/0004-637X/707/2/1659, https://arxiv.org/abs/0911.1068 arXiv:0911.1068 [astro-ph.SR]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/0004-637x/707/2/1659 2009

  66. [66]

    85(4):905850409

    Chandran BDG, Perez JC (2019) Reflection-driven magnetohydrodynamic turbulence in the solar atmosphere and solar wind . 85(4):905850409. doi:10.1017/S0022377819000540, https://arxiv.org/abs/1908.00880 arXiv:1908.00880 [physics.space-ph]

    work page doi:10.1017/s0022377819000540 2019

  67. [67]

    Intermittency and Alignment in Strong RMHD Turbulence

    Chandran BDG, Schekochihin AA, Mallet A (2015) Intermittency and Alignment in Strong RMHD Turbulence . 807(1):39. doi:10.1088/0004-637X/807/1/39, https://arxiv.org/abs/1403.6354 arXiv:1403.6354 [astro-ph.SR]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/0004-637x/807/1/39 2015

  68. [68]

    International Series of Monographs on Physics, Clarendon, Oxford

    Chandrasekhar S (1961) Hydrodynamic and hydromagnetic stability . International Series of Monographs on Physics, Clarendon, Oxford

    1961

  69. [69]

    Proc R Soc London Ser A 245(1243):435--455

    Chandrasekhar S, Kaufman AN, Watson KM (1958) The Stability of the Pinch . Proc R Soc London Ser A 245(1243):435--455. doi:10.1098/rspa.1958.0094

    work page doi:10.1098/rspa.1958.0094 1958

  70. [70]

    117:A09202

    Chaston CC, Bonnell JW, Clausen L, et al (2012) Energy transport by kinetic-scale electromagnetic waves in fast plasma sheet flows . 117:A09202. doi:10.1029/2012JA017863

    work page doi:10.1029/2012ja017863 2012

  71. [71]

    30(6):062110

    Che H, Zank GP (2023) Electromagnetic electron Kelvin-Helmholtz instability . 30(6):062110. doi:10.1063/5.0150895, https://arxiv.org/abs/2503.00593 arXiv:2503.00593 [astro-ph.SR]

    work page doi:10.1063/5.0150895 2023

  72. [72]

    Springer, Cham , doi:10.1007/978-3-319-22309-4

    Chen FF (2019) Introduction to Plasma Physics and Controlled Fusion . Springer, Cham , doi:10.1007/978-3-319-22309-4

    work page doi:10.1007/978-3-319-22309-4 2019

  73. [73]

    8(11):4713--4716

    Chen L, Lin Z, White R (2001) On resonant heating below the cyclotron frequency . 8(11):4713--4716. doi:10.1063/1.1406939

    work page doi:10.1063/1.1406939 2001

  74. [74]

    Impulsive Phase Coronal Hard X-ray Sources in an X3.9 Class Solar Flare

    Chen Q, Petrosian V (2012) Impulsive Phase Coronal Hard X-Ray Sources in an X3.9 Class Solar Flare . 748(1):33. doi:10.1088/0004-637X/748/1/33, https://arxiv.org/abs/1201.1484 arXiv:1201.1484 [astro-ph.SR]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/0004-637x/748/1/33 2012

  75. [75]

    Consultants Bureau, New York

    Chirikov BV (1987) Particle dynamics in magnetic traps, vol 13, 1st edn. Consultants Bureau, New York

    1987

  76. [76]

    Effects of

    Cho H, Ryu D, Kang H (2022) Effects of Forcing on Shocks and Energy Dissipation in Interstellar and Intracluster Turbulences . 926(2):183. doi:10.3847/1538-4357/ac41cc, https://arxiv.org/abs/2111.02109 arXiv:2111.02109 [astro-ph.GA]

    work page doi:10.3847/1538-4357/ac41cc 2022

  77. [77]

    Compressible Sub-Alfvenic MHD turbulence in Low-beta Plasmas

    Cho J, Lazarian A (2002) Compressible Sub-Alfv \'e nic MHD Turbulence in Low- Plasmas . 88(24):245001. doi:10.1103/PhysRevLett.88.245001, https://arxiv.org/abs/astro-ph/0205282 arXiv:astro-ph/0205282 [astro-ph]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevlett.88.245001 2002

  78. [78]

    104:18--28

    Clark G, Paranicas C, Santos-Costa D, et al (2014) Evolution of electron pitch angle distributions across Saturn's middle magnetospheric region from MIMI/LEMMS . 104:18--28. doi:10.1016/j.pss.2014.07.004

    work page doi:10.1016/j.pss.2014.07.004 2014

  79. [79]

    J Plasma Phys 88(5):175880502

    Coburn JT, Chen CHK, Squire J (2022) A measurement of the effective mean free path of solar wind protons . J Plasma Phys 88(5):175880502. doi:10.1017/S0022377822000836, https://arxiv.org/abs/2203.12911 arXiv:2203.12911 [physics.space-ph]

    work page doi:10.1017/s0022377822000836 2022

  80. [80]

    964(1):100

    Coburn JT, Verscharen D, Owen CJ, et al (2024) The Regulation of the Solar Wind Electron Heat Flux by Wave Particle Interactions . 964(1):100. doi:10.3847/1538-4357/ad1329

    work page doi:10.3847/1538-4357/ad1329 2024

Showing first 80 references.