arxiv: 2605.04437 · v1 · submitted 2026-05-06 · 🌌 astro-ph.SR · physics.plasm-ph

Recognition: unknown

Nonlinear steepening of a fast magnetoacoustic wave in the vicinity of a coronal magnetic null point

Andrea Costa, Mariana C\'ecere, Valery M. Nakariakov, Yu Zhong

Pith reviewed 2026-05-08 17:19 UTC · model grok-4.3

classification 🌌 astro-ph.SR physics.plasm-ph

keywords fast magnetoacoustic wavesmagnetic null pointsnonlinear steepeningwave dissipationsolar coronasympathetic flareswave refraction

0 comments

The pith

Fast magnetoacoustic waves steepen nonlinearly and dissipate before reaching a coronal magnetic null point.

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

The paper models the travel of a fast magnetoacoustic wave from an impulsive source toward a magnetic null point in a potential field with uniform plasma density and temperature. The wave moves across the local field along the configuration bisector. The drop in fast wave speed near the null refracts the wave overall, but the central segment stays plane. This speed reduction strengthens the wave's nonlinear distortion, so the front can break and dissipate energy at a finite distance from the null rather than arriving intact. The result bears on how waves might drive sympathetic flares without direct null-point contact.

Core claim

The incoming fast wave approaches the null point along the bisector of the magnetic configuration, i.e., across the local field. The fast-speed non-uniformity around the null point causes the refraction of the incident fast wave. However, the segment of the incoming wave which approaches the null point is locally plane. The decrease in the fast speed towards the null point amplifies the nonlinear deformation of the incoming wave. Hence, the fast wave can become subject to nonlinear dissipation at a distance from the null point and not reach it.

What carries the argument

The non-uniform fast magnetoacoustic speed, which decreases toward the null and amplifies nonlinear deformation of the incoming wave.

If this is right

Wave energy can be deposited through shock formation away from the null point.
Nonlinear deformation can override linear refraction in setting the wave's final fate.
Sympathetic flare models must include possible dissipation of incoming waves before they reach a null.
The distance of dissipation depends on the initial wave amplitude and the magnetic geometry.

Where Pith is reading between the lines

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

Realistic density or temperature gradients could shift the dissipation distance either inward or outward.
The same speed-gradient mechanism may operate in other coronal magnetic structures that lack a true null.
Higher-resolution observations of wave fronts approaching active-region nulls could measure the predicted pre-null steepening.

Load-bearing premise

The equilibrium plasma density and temperature are taken to be constant, so all non-uniformity in wave speed arises from the magnetic field geometry alone.

What would settle it

A numerical simulation or coronal observation that tracks wave amplitude and shows a discontinuity forming at a clear distance before the wave reaches the modeled null point.

Figures

Figures reproduced from arXiv: 2605.04437 by Andrea Costa, Mariana C\'ecere, Valery M. Nakariakov, Yu Zhong.

**Figure 1.** Figure 1: The equilibrium null-point magnetic field configuration (left panel). The magnetic separatrices (dash-dot lines) and the β ≈ 1 equipartition layer (red circle) are demonstrated. A shaded circular region outside the null point indicates the location of the initial pulse. The Alfvén speed (CA) and fast wave speed (Cf) dependence on the distance (r) from the null-point (right panel). The paper is organised as… view at source ↗

**Figure 2.** Figure 2: Evolution of a locally-plane linear fast wave approaching a null point along a magnetic bisector in the decreasing s direction, i.e., from right to left. The figure shows the perpendicular component of the velocity, normalised to the local fast speed at the instants of time τ = 0.13 (top), τ = 0.64 (middle), and τ = 1.41 (bottom). The parameter β0 = 0.2. where β0 = C 2 s /C2 A0. Eq. (3.4) could be solved a… view at source ↗

**Figure 3.** Figure 3: Comparison of the amplitude of a locally-plane linear fast wave approaching a null point along a magnetic bisector, obtained in the WKB approximation (curve) and numerically with the full equation (circles). The parameter β0 = 0.2. hand side terms in Eq. (3.4), reducing it to ∂ 2V ∂τ 2 − β0 + s 2 ∂ 2V ∂s2 = 0. (3.5) A solution to Eq. (3.5) that describes a wave propagating in the negative s direction i… view at source ↗

**Figure 4.** Figure 4: Perturbations of the density in a fast wave pulse excited by a remote localised source, approaching a 2D magnetic null point. The red circle indicates the CA = Cs distance. The snapshots are taken at the instants of time, indicated in the grey inlets. excited waves are magnetoacoustic and hence perturb the density of the plasma. Gradually, the initially circular, in the 2D geometry, fast wave front experie… view at source ↗

**Figure 5.** Figure 5: Evolution of the shape of the fast wave pulse with the distance from the null point. The left and right columns show, respectively, the perpendicular velocity and that velocity normalised to the local fast speed. The initial pulse has the width w0 = 2 Mm, and the amplitude 20 km s−1 (upper row), 80 km s−1 (middle row) and 160 km s−1 (bottom row). The red and blue curves demonstrate the perturbation of the … view at source ↗

**Figure 6.** Figure 6: The dependence of the relative amplitude of a fast wave pulse as it approaches a magnetic null point along a magnetic bisector for different initial amplitudes A0 (left) and widths w0 (right). Each curve is normalised to its initial amplitude. The vertical axis is plotted on a logarithmic scale. The red and blue vertical lines mark the initial position R0 and the predicted steepening distance Rsf from the … view at source ↗

**Figure 7.** Figure 7: Normalised steepening distance d from magnetic null point as a function of the initial amplitudes A0 (left) and widths w0 (right) in log-log plots. The slanted lines indicate the power-law fits obtained for different A0 and w0 combinations. the fast wave pulse with an initially circular wave front is subject to refraction caused by the non-uniformity of the fast speed, turning the wave front towards the nu… view at source ↗

read the original abstract

The interaction of a fast magnetoacoustic wave with a magnetic null point is studied in the context of the sympathetic flare phenomenon. Attention is paid to steepening the wave caused by the finite-amplitude effects in a non-uniform plasma environment. The null point is modelled by a potential magnetic configuration without a guiding field. The equilibrium plasma density and temperature are taken to be constant. The fast wave is excited by an impulsive point source outside the distance at which the local Alfv\'en and sound speeds are equal to each other. The incoming fast wave approaches the null point along the bisector of the magnetic configuration, i.e., across the local field. The fast-speed non-uniformity around the null point causes the refraction of the incident fast wave. However, the segment of the incoming wave, which approaches the null point is locally plane. The decrease in the fast speed towards the null point amplifies the nonlinear deformation of the incoming wave. Hence, the fast wave can become subject to nonlinear dissipation at a distance from the null point and not reach it.

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 shows nonlinear steepening from refraction makes a fast wave dissipate before reaching the null in a uniform-density 2D potential-field model.

read the letter

The main point is that in this setup a fast magnetoacoustic wave refracts toward the null but steepens nonlinearly and dissipates at a finite distance short of it. The drop in fast speed near the null amplifies the nonlinear term on the locally planar segment of the front, so the wave never arrives intact. This is scoped to constant equilibrium density and temperature, a potential 2D null without guide field, and an impulsive source outside the equipartition surface. Within those limits the logic holds without internal contradiction. The stress-test note is right on that score. The concrete outcome—that dissipation occurs away from the null—is the piece that is not just a restatement of earlier linear refraction studies. By freezing density and temperature the authors isolate the purely magnetic contribution to the speed gradient, which is a clean choice for highlighting the mechanism. The bisector launch and planar-segment detail also make the steepening easy to track. That is the part the paper does well. The constant-density assumption is the clearest limitation. Real coronal plasma has strong stratification that would add competing refraction and possibly shift the dissipation distance. The 2D potential field is another idealization; adding a guide field or moving to a force-free null would change the topology and the fast-speed profile. If the full text lacks resolution checks or a direct comparison to the linear limit, that would be a minor but real gap in the numerical evidence. The abstract alone does not show those details, so the soundness score in the reader report is understandable, but the model itself does not appear to hide any circularity or fitting. This is a paper for people working on MHD wave damping or sympathetic flare triggering who already know the linear null-point literature. A reader who wants a specific, falsifiable prediction about where energy is deposited would find it useful. It is not broad enough for a general audience but is focused enough to be worth referee time. I would send it to peer review. The central claim is internally consistent, the setup is deliberate, and the result supplies a concrete dissipation channel that can be tested in follow-up simulations with stratification or in 3D.

Referee Report

2 major / 2 minor

Summary. The paper studies the nonlinear steepening of a fast magnetoacoustic wave near a coronal magnetic null point modeled as a 2D potential field without guide field, with constant density and temperature. An impulsive source excites the wave outside the c_s = v_A surface, and the wave approaches along the bisector. Due to refraction from the non-uniform fast speed, the wave's locally planar segment steepens nonlinearly, leading to dissipation before reaching the null point. This is linked to sympathetic flare phenomena.

Significance. If the result holds, it demonstrates that nonlinear effects can cause fast waves to dissipate at a distance from null points due to magnetic geometry alone, which could explain limited wave propagation in the corona and has implications for energy dissipation and flare initiation. The constant density/temperature assumption is a deliberate choice to isolate geometry effects, and the scoping to the model avoids overgeneralization.

major comments (2)

The manuscript does not describe the numerical scheme, grid resolution, artificial dissipation terms, or any convergence tests and comparisons to linear theory. Without these, it is impossible to confirm that the reported steepening and dissipation distance arise from the physical nonlinear term rather than numerical effects. This directly bears on the central claim in the abstract.
No analytical estimate of the nonlinear steepening length (based on local fast-speed gradient and wave amplitude) is provided to compare against the simulated dissipation distance. This leaves the mechanism of amplification of the nonlinear deformation (due to the decrease in fast speed) unverified quantitatively.

minor comments (2)

The abstract would benefit from a single sentence summarizing the numerical approach and key parameters (e.g., wave amplitude relative to local fast speed).
Figure captions should explicitly state the plotted quantities (velocity perturbation, density, etc.) and color scales to improve clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive assessment of our work and the constructive major comments. We address each point below and will revise the manuscript to incorporate the requested details and analysis.

read point-by-point responses

Referee: The manuscript does not describe the numerical scheme, grid resolution, artificial dissipation terms, or any convergence tests and comparisons to linear theory. Without these, it is impossible to confirm that the reported steepening and dissipation distance arise from the physical nonlinear term rather than numerical effects. This directly bears on the central claim in the abstract.

Authors: We agree that the numerical methodology section is insufficiently detailed and that this information is essential to substantiate the physical nature of the steepening. In the revised manuscript we will add a dedicated subsection describing the MHD numerical scheme (including the solver, spatial and temporal discretization, and boundary conditions), the grid resolution and domain configuration, the form and coefficients of any artificial dissipation terms, results of convergence tests performed at multiple resolutions, and direct comparisons of the nonlinear runs against the corresponding linear solutions. These additions will confirm that the reported dissipation distance is produced by the physical nonlinear term. revision: yes
Referee: No analytical estimate of the nonlinear steepening length (based on local fast-speed gradient and wave amplitude) is provided to compare against the simulated dissipation distance. This leaves the mechanism of amplification of the nonlinear deformation (due to the decrease in fast speed) unverified quantitatively.

Authors: We accept that a quantitative analytical estimate would strengthen the verification of the proposed mechanism. In the revised manuscript we will derive and present an estimate for the nonlinear steepening length that incorporates the local gradient of the fast magnetoacoustic speed and the initial wave amplitude. This estimate will be compared directly with the dissipation distance measured in the simulations, thereby confirming that the decrease in fast speed is responsible for amplifying the nonlinear deformation. revision: yes

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper performs forward modeling of an impulsive fast magnetoacoustic wave in a 2D potential null-point field with constant equilibrium density and temperature. The refraction, local planar segment, and nonlinear steepening follow directly from the MHD equations under the stated geometry and source location outside the c_s = v_A surface. No fitted parameters are relabeled as predictions, no self-citation chain supplies the central mechanism, and the conclusion that dissipation can occur before the null is reached is a direct consequence of the model assumptions rather than a self-definitional reduction. The derivation chain is self-contained against the external MHD framework.

Axiom & Free-Parameter Ledger

0 free parameters · 3 axioms · 0 invented entities

The model rests on standard MHD equations plus two domain simplifications stated in the abstract; no free parameters or new entities are introduced in the summary.

axioms (3)

standard math Ideal MHD equations govern the plasma dynamics
Implicit background framework for all magnetoacoustic wave studies.
domain assumption Potential magnetic field configuration without guiding field
Explicitly stated modeling choice for the null point.
domain assumption Equilibrium density and temperature are spatially constant
Explicit simplification that isolates magnetic-field-induced non-uniformity of the fast speed.

pith-pipeline@v0.9.0 · 5497 in / 1278 out tokens · 55255 ms · 2026-05-08T17:19:06.472815+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

39 extracted references · 36 canonical work pages

[1]

2002 Statistical Evidence for Sympathetic Flares.Astrophys

Moon YJ, Choe GS, Park YD, Wang H, Gallagher PT, Chae J, Yun HS, Goode PR. 2002 Statistical Evidence for Sympathetic Flares.Astrophys. J.574, 434–439. (10.1086/340945)

work page doi:10.1086/340945 2002
[2]

2015 A Statistical Study of Distant Consequences of Large Solar Energetic Events.Solar Phys.290, 2943–2950

Schrijver CJ, Higgins PA. 2015 A Statistical Study of Distant Consequences of Large Solar Energetic Events.Solar Phys.290, 2943–2950. (10.1007/s11207-015-0785-x)

work page doi:10.1007/s11207-015-0785-x 2015
[4]

Astronomy and Astrophysics , author =

Guité LS, Strugarek A, Charbonneau P. 2025 Flaring together: A preferred angular separation between sympathetic flares on the Sun.Astron. Astrophys.694, A74. (10.1051/0004-6361/202452381)

work page doi:10.1051/0004-6361/202452381 2025
[5]

2007 Global Coronal Mass Ejections.Astrophys

Zhukov AN, Veselovsky IS. 2007 Global Coronal Mass Ejections.Astrophys. J. Lett664, L131–L134. (10.1086/520928)

work page doi:10.1086/520928 2007
[6]

2017 The Interaction of Successive Coronal Mass Ejections: A Review.Solar Phys.292, 64

Lugaz N, Temmer M, Wang Y, Farrugia CJ. 2017 The Interaction of Successive Coronal Mass Ejections: A Review.Solar Phys.292, 64. (10.1007/s11207-017-1091-6)

work page doi:10.1007/s11207-017-1091-6 2017
[7]

2009 Driving major solar flares and eruptions: A review.Advances in Space Research43, 739–755

Schrijver CJ. 2009 Driving major solar flares and eruptions: A review.Advances in Space Research43, 739–755. (10.1016/j.asr.2008.11.004)

work page doi:10.1016/j.asr.2008.11.004 2009
[8]

2025 Avalanching Together: A Model for Sympathetic Flaring.Solar Phys.300, 82

Guité LS, Charbonneau P, Strugarek A. 2025 Avalanching Together: A Model for Sympathetic Flaring.Solar Phys.300, 82. (10.1007/s11207-025-02501-4)

work page doi:10.1007/s11207-025-02501-4 2025
[9]

2011 A Model for Magnetically Coupled Sympathetic Eruptions.Astrophys

Török T, Panasenco O, Titov VS, Mikić Z, Reeves KK, Velli M, Linker JA, De Toma G. 2011 A Model for Magnetically Coupled Sympathetic Eruptions.Astrophys. J. Lett739, L63. (10.1088/2041-8205/739/2/L63)

work page doi:10.1088/2041-8205/739/2/l63 2011
[10]

2016 A Numerical Study of Long-range Magnetic Impacts during Coronal Mass Ejections.Astrophys

Jin M, Schrijver CJ, Cheung MCM, DeRosa ML, Nitta NV, Title AM. 2016 A Numerical Study of Long-range Magnetic Impacts during Coronal Mass Ejections.Astrophys. J.820,

2016
[11]

(10.3847/0004-637X/820/1/16)

work page doi:10.3847/0004-637x/820/1/16
[12]

, keywords =

Nakariakov VM, Foullon C, Verwichte E, Young NP. 2006 Quasi-periodic modulation of solar and stellar flaring emission by magnetohydrodynamic oscillations in a nearby loop. Astron. Astrophys.452, 343–346. (10.1051/0004-6361:20054608) 14royalsocietypublishing.org/journal/rsta Phil. Trans. R. Soc0000000

work page doi:10.1051/0004-6361:20054608 2006
[13]

2006 Anomalous resistivity of current-driven isothermal plasmas due to phase space structuring.Physics of Plasmas13, 082304

Büchner J, Elkina N. 2006 Anomalous resistivity of current-driven isothermal plasmas due to phase space structuring.Physics of Plasmas13, 082304. (10.1063/1.2209611)

work page doi:10.1063/1.2209611 2006
[14]

2022 Direct observations of anomalous resistivity and diffusion in collisionless plasma

Graham DB, Khotyaintsev YV, André M, Vaivads A, Divin A, Drake JF, Norgren C, Le Contel O, Lindqvist PA, Rager AC, Gershman DJ, Russell CT, Burch JL, Hwang KJ, Dokgo K. 2022 Direct observations of anomalous resistivity and diffusion in collisionless plasma. Nature Communications13, 2954. (10.1038/s41467-022-30561-8)

work page doi:10.1038/s41467-022-30561-8 2022
[15]

B., Cozzani, G., Khotyaintsev, Y

Graham DB, Cozzani G, Khotyaintsev YV, Wilder VD, Holmes JC, Nakamura TKM, Büchner J, Dokgo K, Richard L, Steinvall K, Norgren C, Chen LJ, Ji H, Drake JF, Stawarz JE, Eriksson S. 2025 The Role of Kinetic Instabilities and Waves in Collisionless Magnetic Reconnection.Space Sci. Rev.221, 20. (10.1007/s11214-024-01133-7)

work page doi:10.1007/s11214-024-01133-7 2025
[16]

1994 What is the Condition for Fast Magnetic Reconnection?

Yokoyama T, Shibata K. 1994 What is the Condition for Fast Magnetic Reconnection?. Astrophys. J. Lett436, L197. (10.1086/187666)

work page doi:10.1086/187666 1994
[17]

2011, Living Reviews in Solar Physics, 8, 6, doi: 10.12942/lrsp-2011-6

Shibata K, Magara T. 2011 Solar Flares: Magnetohydrodynamic Processes.Living Reviews in Solar Physics8, 6. (10.12942/lrsp-2011-6)

work page doi:10.12942/lrsp-2011-6 2011
[18]

2024 A comparative study of resistivity models for simulations of magnetic reconnection in the solar atmosphere

Færder ØH, Nóbrega-Siverio D, Carlsson M. 2024 A comparative study of resistivity models for simulations of magnetic reconnection in the solar atmosphere. II. Plasmoid formation. Astron. Astrophys.683, A95. (10.1051/0004-6361/202348046)

work page doi:10.1051/0004-6361/202348046 2024
[19]

2006 Transition-Region Explosive Events: Reconnection Modulated by p-Mode Waves.Solar Phys.238, 313–327

Chen PF, Priest ER. 2006 Transition-Region Explosive Events: Reconnection Modulated by p-Mode Waves.Solar Phys.238, 313–327. (10.1007/s11207-006-0215-1)

work page doi:10.1007/s11207-006-0215-1 2006
[20]

2011 Slow Magnetoacoustic Waves in Two-ribbon Flares

Nakariakov VM, Zimovets IV. 2011 Slow Magnetoacoustic Waves in Two-ribbon Flares. Astrophys. J. Lett730, L27. (10.1088/2041-8205/730/2/L27)

work page doi:10.1088/2041-8205/730/2/l27 2011
[21]

J.,873, 2, 126

Kumar P, Nakariakov VM, Cho KS. 2017 Quasi-periodic Radio Bursts Associated with Fast-mode Waves near a Magnetic Null Point.Astrophys. J.844, 149. (10.3847/1538- 4357/aa7d53)

work page doi:10.3847/1538- 2017
[22]

2021 Quasi-Periodic Pulsations in Solar and Stellar Flares: A Review of Underpinning Physical Mechanisms and Their Predicted Observational Signatures.Space Sci

Zimovets IV, McLaughlin JA, Srivastava AK, Kolotkov DY, Kuznetsov AA, Kupriyanova EG, Cho IH, Inglis AR, Reale F, Pascoe DJ, Tian H, Yuan D, Li D, Zhang QM. 2021 Quasi-Periodic Pulsations in Solar and Stellar Flares: A Review of Underpinning Physical Mechanisms and Their Predicted Observational Signatures.Space Sci. Rev.217,

2021
[23]

(10.1007/s11214-021-00840-9)

work page doi:10.1007/s11214-021-00840-9
[24]

2004 MHD wave propagation in the neighbourhood of a two- dimensional null point.Astron

McLaughlin JA, Hood AW. 2004 MHD wave propagation in the neighbourhood of a two- dimensional null point.Astron. Astrophys.420, 1129–1140. (10.1051/0004-6361:20035900)

work page doi:10.1051/0004-6361:20035900 2004
[25]

Rev.158, 205–236

McLaughlinJA,HoodAW,deMoortelI.2011ReviewArticle:MHDWavePropagationNear Coronal Null Points of Magnetic Fields.Space Sci. Rev.158, 205–236. (10.1007/s11214-010- 9654-y)

work page doi:10.1007/s11214-010-
[26]

2006 MHD mode coupling in the neighbourhood of a 2D null point.Astron

McLaughlin JA, Hood AW. 2006 MHD mode coupling in the neighbourhood of a 2D null point.Astron. Astrophys.459, 641–649. (10.1051/0004-6361:20065558)

work page doi:10.1051/0004-6361:20065558 2006
[27]

2016 Slow-Mode MHD Wave Penetration into a Coronal Null Point due to the Mode Transmission.Solar Phys.291, 3185–3193

Afanasyev AN, Uralov AM. 2016 Slow-Mode MHD Wave Penetration into a Coronal Null Point due to the Mode Transmission.Solar Phys.291, 3185–3193. (10.1007/s11207-016- 0899-9)

work page doi:10.1007/s11207-016- 2016
[28]

2017 Magnetoacoustic Waves in a Stratified Atmosphere with a Magnetic Null Point.Astrophys

Tarr LA, Linton M, Leake J. 2017 Magnetoacoustic Waves in a Stratified Atmosphere with a Magnetic Null Point.Astrophys. J.837, 94. (10.3847/1538-4357/aa5e4e)

work page doi:10.3847/1538-4357/aa5e4e 2017
[29]

2024 Wave transformations near a coronal magnetic null point.Astron

Yadav N, Keppens R. 2024 Wave transformations near a coronal magnetic null point.Astron. Astrophys.681, A43. (10.1051/0004-6361/202347417)

work page doi:10.1051/0004-6361/202347417 2024
[30]

2024 Direct imaging of magnetohydrodynamic wave mode conversion near a 3D null point on the sun.Nature Communications15, 2667

Kumar P, Nakariakov VM, Karpen JT, Cho KS. 2024 Direct imaging of magnetohydrodynamic wave mode conversion near a 3D null point on the sun.Nature Communications15, 2667. (10.1038/s41467-024-46736-4)

work page doi:10.1038/s41467-024-46736-4 2024
[31]

2009 Nonlinear fast magnetoacoustic wave propagation in the neighbourhood of a 2D magnetic X-point: oscillatory reconnection

McLaughlin JA, De Moortel I, Hood AW, Brady CS. 2009 Nonlinear fast magnetoacoustic wave propagation in the neighbourhood of a 2D magnetic X-point: oscillatory reconnection. Astron. Astrophys.493, 227–240. (10.1051/0004-6361:200810465)

work page doi:10.1051/0004-6361:200810465 2009
[33]

2012 Modelling the Propagation of a Weak Fast-Mode MHD Shock Wave near a 2D Magnetic Null Point Using Nonlinear Geometrical Acoustics.Solar Phys.280, 561–574

Afanasyev AN, Uralov AM. 2012 Modelling the Propagation of a Weak Fast-Mode MHD Shock Wave near a 2D Magnetic Null Point Using Nonlinear Geometrical Acoustics.Solar Phys.280, 561–574. (10.1007/s11207-012-0022-9)

work page doi:10.1007/s11207-012-0022-9 2012
[34]

2013 Nonlinear Alfvén wave dynamics at a 2D magnetic null point: ponderomotive force.Astron

Thurgood JO, McLaughlin JA. 2013 Nonlinear Alfvén wave dynamics at a 2D magnetic null point: ponderomotive force.Astron. Astrophys.555, A86. (10.1051/0004-6361/201321338)

work page doi:10.1051/0004-6361/201321338 2013
[35]

2018 High frequency generation in the corona: Resonant cavities.Astron

Santamaria IC, Van Doorsselaere T. 2018 High frequency generation in the corona: Resonant cavities.Astron. Astrophys.611, A10. (10.1051/0004-6361/201731016) 15royalsocietypublishing.org/journal/rsta Phil. Trans. R. Soc0000000

work page doi:10.1051/0004-6361/201731016 2018
[36]

2008 3D MHD Coronal Oscillations about a Magnetic Null Point: Application of WKB Theory.Solar Phys.251, 563–587

McLaughlin JA, Ferguson JSL, Hood AW. 2008 3D MHD Coronal Oscillations about a Magnetic Null Point: Application of WKB Theory.Solar Phys.251, 563–587. (10.1007/s11207-007-9107-2)

work page doi:10.1007/s11207-007-9107-2 2008
[37]

Asgariet al.[KiDS], Astron

Sahade A, Cécere M, Sieyra MV, Krause G, Cremades H, Costa A. 2022 Pseudostreamer influence on flux rope evolution.Astron. Astrophys.662, A113. (10.1051/0004- 6361/202243618)

work page doi:10.1051/0004- 2022
[38]

1974Linear and Nonlinear Waves

Whitham GB. 1974Linear and Nonlinear Waves. John Wiley & Sons. (10.1002/9781118032954)

work page doi:10.1002/9781118032954
[39]

2010 FLASH: Adaptive Mesh Hydrodynamics Code for Modeling Astrophysical Thermonuclear Flashes

Fryxell B, Olson K, Ricker P, Timmes FX, Zingale M, Lamb DQ, MacNeice P, Rosner R, Truran JW, Tufo H. 2010 FLASH: Adaptive Mesh Hydrodynamics Code for Modeling Astrophysical Thermonuclear Flashes. Astrophysics Source Code Library, record ascl:1010.082

2010
[40]

2012 On the Nature and Genesis of EUV Waves: A Synthesis of Observations from SOHO, STEREO, SDO, and Hinode (Invited Review).Solar Phys.281, 187–222

Patsourakos S, Vourlidas A. 2012 On the Nature and Genesis of EUV Waves: A Synthesis of Observations from SOHO, STEREO, SDO, and Hinode (Invited Review).Solar Phys.281, 187–222. (10.1007/s11207-012-9988-6)

work page doi:10.1007/s11207-012-9988-6 2012
[41]

1987 Current Loop Coalescence Model of Solar Flares.Astrophys

Tajima T, Sakai J, Nakajima H, Kosugi T, Brunel F, Kundu MR. 1987 Current Loop Coalescence Model of Solar Flares.Astrophys. J.321, 1031. (10.1086/165694)

work page doi:10.1086/165694 1987