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Driving solar coronal MHD simulations on high-performance computers

T0 review · 3 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read This paper claims that the scalability bottleneck of observationally driven coronal MHD simulations—serialized boundary-condition transforms and data I/O—can be removed, improving scaling by more than an order of magnitude.

desk verdict Useful methods paper with a real new boundary condition, but the '>10x scalability' headline conflates FFT-only benchmarks with IO gains. read the letter →

arxiv 1908.08557 v1 pith:YAHYQ5IX submitted 2019-08-22 astro-ph.SR physics.comp-phphysics.plasm-phphysics.space-ph

Philippe-A. Bourdin (Space Research Institute , Austrian Academy of Sciences , Graz/Austria) This is my paper · ORCID
classification astro-ph.SRphysics.comp-phphysics.plasm-phphysics.space-ph
keywords solarcoronacoronalheatingmagnetohydrodynamicshigh-performancecomputingparallelfastFouriertransformHDF5I/OboundaryconditionsPencilCode
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper claims that the computing bottleneck that previously limited observationally driven magnetohydrodynamic models of the solar corona can be broken. For the code used in the study, boundary conditions that required a serial Fourier transform and data I/O that either stored redundant ghost cells or serialized writing were replaced by parallel FFT remapping and HDF5/MPI-2 monolithic file output. In a hard-scaling test the optimized code follows near-ideal scaling from 16 to 1024 cores and improves efficiency by more than an order of magnitude. The motivation is that realistic, active-region-scale coronal models can then be run within a typical research-project timeframe, making it possible to test nanoflare and wave-turbulence heating theories against observed magnetograms.

What carries the argument

The load-bearing machinery is the parallelization of the boundary-condition FFT and of file I/O, together with the new inverted potential-field extrapolation. The FFT parallelization collects data along one horizontal direction, lets one half of the processors send while the other half receives, and then transposes with as many communication cycles as there are subdomains along x, so the Fourier transform used for the potential-field boundary condition no longer idles the majority of cores. The HDF5 and MPI-2 I/O modules write monolithic snapshots with the inner ghost cells removed, avoiding thousands of simultaneous small-file requests and reducing storage needs by roughly a third relative to fully distributed output. The inverted potential-field extrapolation prescribes horizontal magnetic-field components at and below the photosphere through an extrapolation that concentrates flux with depth, approximating the subphotospheric pressure increase while still allowing non-vertical field near the surface.

What would settle it

Run the same hard-scaling comparison on a current HPC system at a fixed global grid size, measuring CPU time per timestep per meshpoint from 16 to more than 1024 cores with the old and new boundary-condition and I/O modules; if the optimized version is not more than an order of magnitude faster at the largest core counts, the scalability claim is not general. A second check is to inspect the ghost-layer field beneath the photosphere in a test run and verify that flux bundles narrow and flux density increases with depth as the inverted potential-field extrapolation prescribes.

Watch

Extended reading notes

Core claim

The central claim, stated on the paper's own terms, is that a set of boundary conditions and input/output strategies can remove the serial bottlenecks that once kept a coronal MHD model of an active region from scaling efficiently beyond a few hundred processors. The potential-field extrapolation at the top boundary is parallelized by a two-cycle data-remapping FFT, and snapshot I/O is made collective per layer or moved to monolithic HDF5 files that omit redundant inner ghost cells. As a result, a hard-scaling test from 16 to 1024 cores shows the optimized version tracking near-ideal scaling, with the paper reporting a scalability improvement of more than one order of magnitude. The same work introduces a novel photospheric magnetic-field boundary condition: an inverted potential-field extrapolation that makes magnetic flux bundles narrow and intensify with depth below the photosphere, allowing observed horizontal granular motions to advect field-line footpoints while remaining consistent with the observed magnetograms.

Load-bearing premise

The quantitative scaling gain is measured on a single retired 2012-era supercomputer with a particular parallel file system and no repeated runs, so the claim that the gain is more than an order of magnitude assumes that benchmark reflects modern HPC hardware and typical workloads.

Editorial extensions

If this is right

  • Observationally driven coronal MHD models can use more than a thousand cores efficiently, making active-region simulations with tens of millions of grid points feasible within a typical project timescale.
  • Because the new photospheric boundary accepts horizontal magnetic fields, granular motions can shuffle field-line footpoints, enabling direct tests of the Parker braiding and nanoflare picture.
  • Monolithic HDF5 snapshots reduce storage and allow frequent checkpointing, so long-duration runs with dense time output become practical for studying coronal heating statistics.
  • The reduced artificial currents at the lower boundary allow lower magnetic diffusivity, meaning the observationally driven footpoint motions keep more of their intended effect on the coronal field.
  • The parallel FFT and I/O strategies should also benefit other boundary conditions and diagnostics that rely on two-dimensional Fourier transforms in grid-based MHD codes.

Reading between the lines

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

  • The two-cycle send-first/receive-first remapping scheme is general enough that it could be ported to other grid-based plasma simulations whose boundary conditions require global spectral transforms; the same pattern would transfer to any pencil- or block-decomposed domain.
  • The order-of-magnitude scaling number was measured on a single, now-retired 2012-era system with an old parallel file system, so the quantitative gain on contemporary machines with different interconnect and I/O hardware could be larger or smaller—a modern re-benchmark would be needed to confirm the exact factor.
  • The inverted potential-field extrapolation is a deliberately softened approximation of the real subphotospheric pressure stratification (contrast reduced to one fifth of the scale-height value), so its main risk is a systematic error in horizontal fields near the lower boundary; a comparison against a convection-zone model with realistic pressure stratification would quantify that error.
  • Because the paper omits photospheric electric fields in the driving, a testable extension would be to include them and check whether the Poynting flux and coronal heating statistics change appreciably.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. The paper describes a collection of methods for making observationally driven solar coronal MHD simulations with the Pencil Code scale to thousands of processors. The components include a photospheric granulation driver, local correlation tracking, nudging of the observed magnetic field, a new photospheric magnetic-field boundary condition based on an inverted potential-field extrapolation, chromospheric Newtonian cooling, closed upper-boundary conditions with a swamp region, a massively parallel FFT for potential-field boundary conditions, and new IO strategies including MPI-2 and parallel HDF5. The central quantitative claim is that these optimizations improve scalability by more than an order of magnitude, enabling the use of over a thousand processors more efficiently than the original code.

Significance. If the scalability claim holds, the paper provides a practical and valuable capability: coronal MHD models of active regions could be run in substantially shorter wall-clock time, making observationally driven simulations of coronal heating feasible on contemporary HPC resources. The manuscript is also useful as a code-level description of parallel FFT and IO strategies in a widely used open-source code, and the observation-driven boundary conditions are of interest to the solar physics community. The benchmark evidence, however, is narrow: a single hard-scaling test on a decommissioned system, with the headline improvement attributed in the abstract to both boundary conditions and IO while the displayed scaling curve measures only the FFT. The physical novelty of the photospheric boundary condition is also asserted without quantitative validation. The contribution is real but the central quantitative claim needs to be made commensurate with the evidence.

major comments (3)
  1. [Abstract; Section 6; Figure 12; Table 1] The abstract's statement that "scalability is improved by more than one order of magnitude through the HPC-friendly boundary conditions and IO strategies" is not supported by the measurements as presented. Figure 12 is a hard-scaling curve of CPU time per timestep per meshpoint, which by construction excludes snapshot IO, and its caption attributes the improvement to the massive-parallel FFT. Table 1 shows that the new IO modules (mpi2, hdf5) are not faster than the distributed module at the tested configuration (8–9 s versus 2 s for a full snapshot). Thus the evidence supports an improvement from the parallel FFT, not from IO, and the abstract's attribution should be revised or supported by end-to-end scaling measurements that include IO.
  2. [Figure 12; Table 1; Section 5.2] The quantitative order-of-magnitude claim rests on a single hard-scaling test on the JuRoPA system, whose hardware and Lustre filesystem are described by the paper itself as outdated and decommissioned. No repeated runs, error bars, or tests on a second system are reported. Because the claim is intended to generalize to "thousands of processors," the lack of robustness evidence is a correctness risk. At minimum, the paper should state explicitly that the quoted improvement is machine- and filesystem-specific; ideally, it should show variance across runs or a second benchmark on a modern system.
  3. [Section 6; Figure 12] The metric used for the scaling claim is inconsistent between text and figure. Section 6 refers to a "comparison plot for the total runtime," whereas Figure 12's y-axis is "CPU time per timestep per meshpoint." Also, the hard-scaling setup is not fully specified: the problem size, grid decomposition, number of timesteps, and whether boundary-condition FFTs are included in the timed region are not stated. Without this information, the reader cannot determine what exactly improved by an order of magnitude or how to reproduce the measurement.
minor comments (4)
  1. [Section 2.4] The photospheric boundary condition depends on a manually chosen reduction of the contrast increase to one fifth of the pressure-scale-height value (fbcz_bot = 0.2). The paper acknowledges a "slight error" from this choice, but provides no sensitivity test or quantitative comparison with observed photospheric/chromospheric structure; a brief sensitivity study would strengthen the physical claim.
  2. [Table 1] The table's "red entries" are not identifiable in the printed text; please mark the relevant cells explicitly. Also, because the "distributed" module has the lowest raw write time (2 s), the advantage of the new modules should be framed as scalability and reduced storage overhead rather than raw speed at this configuration.
  3. [Figure 12] The x-axis labels appear truncated ("102416" in place of "1024"), and it is not clear whether 16 cores was included. Please correct the axis labels and specify the full set of processor counts used.
  4. [Various locations] There are several typos and minor language issues: "consitency" (Section 2.1), "coaling" (Section 2.1), "velodity" (Section 2.3 footnote), "decomissioned" (Section 5.2), "adaptice" (Section 6), "amplitues" (Section 6), "loosing" (Section 5.3), and "There number of ghost layers" (Figure 8 caption). A careful proofread is recommended.

Circularity Check

1 steps flagged · score 2.0 of 10

Mild circularity only in the presentation of flux-bundle narrowing; the main HPC scaling benchmark is an independent engineering measurement.

  1. self definitional [Abstract and Section 2.4 (Magnetic-field extrapolation)]
    "We present a novel boundary condition for non-vertical magnetic fields in the photosphere, where we approach the realistic pressure increase below the photosphere. With that, magnetic flux bundles become narrower with depth and the flux density increases accordingly. ... In order to mimic the increase in atmospheric and magnetic pressure in the solar interior below the photosphere, we use an inverted potential-field extrapolation that concentrates any magnetic flux bundles with depth, which leads to a reduction of the diameter and an increase of the amplitude of those flux bundles."

    The abstract presents the flux-bundle narrowing as a consequence of the new boundary condition, but Section 2.4 states that the boundary condition was itself constructed to produce that narrowing: the inverted potential-field extrapolation is chosen so that flux bundles shrink with depth. Thus the reported behavior is an imposed property of the ansatz, not an independent prediction or derived result. This is a mild self-definitional presentation issue; it does not affect the paper's separate, benchmark-based scalability claims.

full rationale

The paper's central quantitative claim is a scalability improvement of more than one order of magnitude, supported by a hard-scaling comparison in Figure 12 and IO timings in Table 1. That is an engineering benchmark comparing code versions before and after optimization, not a fitted parameter or a self-referential derivation, so it does not exhibit circularity. The caveats about the decommissioned JuRoPA system and the 2012 Lustre filesystem are hardware-representativeness concerns, not circularity. The only mild circularity is in the presentation of the photospheric magnetic-field boundary condition: the abstract lists flux bundles becoming narrower with depth as an outcome, while the method section explicitly designs the inverted potential-field extrapolation to concentrate magnetic flux with depth. The narrowing is therefore built into the construction rather than derived from the MHD equations or from observation. No load-bearing self-citation chain was found: citations to Bourdin et al. (2013) and related work are used as external comparisons or prior context, not to define the present results. Overall, the main methods contribution is self-contained and independently benchmarked; the circularity score reflects only the minor definitional presentation of the boundary-condition effect.

Assumptions & free parameters 8 free parameters · 5 assumptions · 0 invented entities

The central scalability claim does not depend on a fitted physical law, so the free-parameter burden is mostly numerical and modeling choices: the one-fifth contrast reduction, granulation driver amplitudes and timescales, nudging rates, and swamp diffusivities. The physical axioms are standard solar MHD modeling assumptions plus two specific shortcuts: inverted potential-field extrapolation below the photosphere and omission of electric fields in the driving. No new physical entities are introduced; the swamp regions are numerical devices rather than invented entities.

free parameters (8)
  • Photospheric magnetic contrast reduction factor = 0.2 (one fifth)
    Set in Section 2.4 to one fifth of the true pressure-scale-height contrast to avoid checkerboard artifacts in the ghost cells; the paper states this introduces an error in horizontal field components below the surface.
  • Granulation velocity amplitude v0 = 1.028 km/s
    Chosen in Section 2.3 to mimic typical observed granular flows; central to the granulation driver.
  • Granule lifetime Tgran = 5 min
    Typical observed granule lifetime used as the baseline in the driver.
  • Vorticity amplification factor frot = 5
    Chosen so that inter-granular lane speeds reach about 8 km/s; the paper says 'We choose frot = 5'.
  • Photospheric velocity nudging rate tau_u = 0.5 s^-1
    Inverse decay half-time in equation (5), chosen as a model parameter for the granulation and LCT driving.
  • Chromospheric Newtonian cooling rate tau_t = 0.5 s^-1
    Inverse decay half-time in equation (10), chosen for the temperature nudging in the chromosphere.
  • Mass diffusivity D_rho = 8.0e6 m^2/s
    Global constant diffusivity in density, introduced for numerical stability; the paper notes it causes a small mass transport into the simulation box.
  • Swamp diffusivities (eta_s, chi_s, rho_s) = not specified in text
    Height-dependent artificial diffusivities for magnetic field, heat, and mass near the top boundary; parameters are referenced but numeric values are not given in the paper.
assumptions (5)
  • domain assumption Ideal MHD equations with Spitzer heat conduction and no radiative transfer in the corona adequately describe the simulated plasma.
    The Pencil Code solves these equations; the paper's validation argument is the match with observations claimed in Bourdin et al. (2013), not a demonstration inside this paper.
  • ad hoc to paper The magnetic field below the photosphere can be represented by an inverted potential-field extrapolation even though the plasma there is not force free.
    Section 2.4 introduces this extrapolation and then modifies it with a factor of one fifth, admitting an error in horizontal field components below the surface.
  • domain assumption The upper boundary field is nearly potential, so a potential-field extrapolation with exponential contrast smoothing is appropriate.
    Section 4.2 states this assumption; currents at the boundary are then handled with artificial swamp diffusivity.
  • domain assumption Omitting photospheric electric fields in the driving does not significantly change the coronal magnetic field and heating.
    Section 2.2 explicitly omits these electric fields and justifies it by a claimed good match from prior work.
  • domain assumption Flux balancing the observed magnetograms to zero net flux does not significantly change the model's field geometry.
    Section 2.1 argues that missed connectivity is minor, without a quantitative sensitivity test.

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Cite this review

Pith. "Pith review of Driving solar coronal MHD simulations on high-performance computers." pith.science (2026). https://pith.science/paper/YAHYQ5IX

@misc{pith2026190808557,
  author       = {Pith},
  title        = {Pith review of: Driving solar coronal MHD simulations on high-performance computers},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YAHYQ5IX}},
  note         = {Machine review of arXiv:1908.08557}
}
read the original abstract

The quality of today's research is often tightly limited to the available computing power and scalability of codes to many processors. For example, tackling the problem of heating the solar corona requires a most realistic description of the plasma dynamics and the magnetic field. Numerically solving such a magneto-hydrodynamical (MHD) description of a small active region (AR) on the Sun requires millions of computation hours on current high-performance computing (HPC) hardware. The aim of this work is to describe methods for an efficient parallelization of boundary conditions and data input/output (IO) strategies that allow for a better scaling towards thousands of processors (CPUs). The Pencil Code is tested before and after optimization to compare the performance and scalability of a coronal MHD model above an AR. We present a novel boundary condition for non-vertical magnetic fields in the photosphere, where we approach the realistic pressure increase below the photosphere. With that, magnetic flux bundles become narrower with depth and the flux density increases accordingly. The scalability is improved by more than one order of magnitude through the HPC-friendly boundary conditions and IO strategies. This work describes also the necessary nudging methods to drive the MHD model with observed magnetic fields from the Sun's photosphere. In addition, we present the upper and lower atmospheric boundary conditions (photospheric and towards the outer corona), including swamp layers to diminish perturbations before they reach the boundaries. Altogether, these methods enable more realistic 3D MHD simulations than previous models regarding the coronal heating problem above an AR -- simply because of the ability to use a large amount of CPUs efficiently in parallel.

Figures

Figures reproduced from arXiv: 1908.08557 by the authors.

Figure 1
Figure 1. Hinode line-of-sight magnetogram (grayscale, saturated at ±300 G) with overlaid velocity vectors (blue) obtained with a local correlation tracking. The observation was made near disc center and is from 2007 November 14 [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Distribution of co-aligned uncalibrated SOT/NFI and calibrated SOT/SP data. The red line rep￾resents a least-absolute-deviation (LAD) fit with its uncertainty interval marked by dotted lines. Figure taken from Bourdin (2014a); see [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Granulation driver velocity field (grayscale, saturated black is 8 km/s) with overplotted velocity vectors (red). One grayscale square represents one simulation pixel with a side length of 230 km [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (9 more)
Figure 4
Figure 4. Figure 4: Histograms of LCT (blue) and granulation driver (red) velocities. 2.4. Magnetic-field extrapolation We use the vector potential A for our computation and the magnetic field B is then only a derived quantity that is always divergence free and is unique for any given gau…
Figure 5
Figure 5. Figure 5: In-plane magnetic field lines (red) in a vertical cut through a strong flux concentration in the lower part of the model. The gray scale indicates the logarithmic density. The blue dashed line is the actual physical boundary of the simulation domain at z = 0 Mm. slight…
Figure 6
Figure 6. Figure 6: Logarithmic temperature (color code) in the lower atmosphere for a vertical cut through a strong flux concentration together with the in-plane magnetic field lines (white) at the same location as in figure 5. The red-dashed line indicates the location of the photospher…
Figure 7
Figure 7. Figure 7: Data remapping strategy for the parallel FFTs in the module ‘fourier fftpack’. this can only be done in a sequential way and requires significantly more communication cycles for a large number of processors. The same holds true for the remapping back to the original su…
Figure 8
Figure 8. Figure 8: Reduction of required data space for monolithic files in an extreme case, where the needed outer ghosts are colored in green and the physical domain is blue. The redundant inner ghost cells (see numbers) being saved with the distributed ‘io dist’ IO module in the Penci…
Figure 9
Figure 9. Figure 9: Collective IO strategy of the module ‘collect xy’, where data is collected in subdomain layers along (x, y) and is written to multiple files by the collecting (here rightmost) processors in each (x, y)-plane. The vertical separation of the layers depicts the z-directio…
Figure 10
Figure 10. Figure 10: Example content of a ‘var.h5’ file, here from the corona sample. The conversion factor from code units to physical units is 10−8 for the density. This sample stores the logarithmic density lnrho as three-dimensional data array, together with the logarithmic temperatur…
Figure 11
Figure 11. Figure 11: Content of the file ‘grid.h5’ from the corona sample, where we use a non-equidistant grid in the z-direction. The unit length is 107 in SI units and we use double precision for floating-point numbers. The array dz 1 contains the inverse grid spacing along the z-direct…
Figure 12
Figure 12. Figure 12: Comparison of the hard scaling before (triangles) and after (circles) the implementation of a massive-parallel FFT in the Pencil Code versus the theoretical scaling limit (dashed red line). The IO strategy is crucial for large-scale models in nowadays science where la…

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Works this paper leans on

38 extracted references · 17 canonical work pages

  1. [1]

    and Gudiksen, B., On the nature of coronal loops above the quiet sun network

    Bingert, S., Zacharias, P., Peter, H. and Gudiksen, B., On the nature of coronal loops above the quiet sun network. urlcolor=magenta Adv. in Space Res. http://adsabs.harvard.edu/abs/2010AdSpR..45..310B , 2010, 45, 310--313, DOI: urlcolor=blue 10.1016/j.asr.2009.08.020 https://doi.org/10.1016/j.asr.2009.08.020

    work page doi:10.1016/j.asr.2009.08.020 2010

  2. [2]

    urlcolor=magenta Contr

    Bourdin , P.A., Denoising observational data . urlcolor=magenta Contr. Astron. Obs. Skalnate Pleso http://adsabs.harvard.edu/abs/2011CoSka..41..149B , 2011, 41, 149--155

    work page 2011

  3. [3]

    Bourdin, P.A., Observationally driven 3D MHD model of the solar corona above a magnetically active region , 2014 a (uni-edition GmbH., Berlin), ISBN: 978-3-944072-03-6, DOI: urlcolor=blue 11858/00-1735-0000-0022-5F1B-D https://doi.org/11858/00-1735-0000-0022-5F1B-D

    work page 2014

  4. [4]

    urlcolor=magenta Cent

    Bourdin, P.A., Standard 1D solar atmosphere as initial condition for MHD simulations and switch-on effects . urlcolor=magenta Cent. Eur. Astrophys. Bull. http://adsabs.harvard.edu/abs/2014CEAB...38....1B , 2014 b , 38, 1--10

    work page 2014

  5. [5]

    urlcolor=magenta ApJL http://adsabs.harvard.edu/abs/2017ApJ...850L..29B , 2017, 850, L29 (5pp), DOI: urlcolor=blue 10.3847/2041-8213/aa9988 https://doi.org/10.3847/2041-8213/aa9988

    Bourdin, P.A., Plasma Beta Stratification in the Solar Atmosphere: A Possible Explanation for the Penumbra Formation. urlcolor=magenta ApJL http://adsabs.harvard.edu/abs/2017ApJ...850L..29B , 2017, 850, L29 (5pp), DOI: urlcolor=blue 10.3847/2041-8213/aa9988 https://doi.org/10.3847/2041-8213/aa9988

    doi:10.3847/2041-8213/aa9988 2017

  6. [6]

    and Peter, H., Observationally driven 3D MHD model of the solar corona above an active region

    Bourdin, P.A., Bingert, S. and Peter, H., Observationally driven 3D MHD model of the solar corona above an active region . urlcolor=magenta A&A http://adsabs.harvard.edu/abs/2013A&A...555A.123B , 2013, 555, A123, DOI: urlcolor=blue 10.1051/0004-6361/201321185 https://doi.org/10.1051/0004-6361/201321185

    doi:10.1051/0004-6361/201321185 2013

  7. [7]

    and Peter, H., Coronal loops above an Active Region: Observation versus model

    Bourdin, P.A., Bingert, S. and Peter, H., Coronal loops above an Active Region: Observation versus model . urlcolor=magenta PASJ http://adsabs.harvard.edu/abs/2014PASJ...66S...7B , 2014, 66, 1--8, DOI: urlcolor=blue 10.1093/pasj/psu123 https://doi.org/10.1093/pasj/psu123

    work page doi:10.1093/pasj/psu123 2014

  8. [8]

    and Peter, H., Coronal energy input and dissipation in a solar Active Region 3D MHD model

    Bourdin, P.A., Bingert, S. and Peter, H., Coronal energy input and dissipation in a solar Active Region 3D MHD model . urlcolor=magenta A&A http://adsabs.harvard.edu/abs/2015A&A...580A..72B , 2015, 580, A72, DOI: urlcolor=blue 10.1051/0004-6361/201525839 https://doi.org/10.1051/0004-6361/201525839

    work page doi:10.1051/0004-6361/201525839 2015

Show all 38 references
  1. [9]

    and Peter, H., Scaling laws of coronal loops compared to a 3D MHD model of an active region

    Bourdin, P.A., Bingert, S. and Peter, H., Scaling laws of coronal loops compared to a 3D MHD model of an active region . urlcolor=magenta A&A http://adsabs.harvard.edu/abs/2016A&A...589A..86B , 2016, 589, A86, DOI: urlcolor=blue 10.1051/0004-6361/201525840 https://doi.org/10.1...

    2016 doi

  2. [10]

    and Brandenburg , A., Magnetic Helicity Reversal in the Corona at Small Plasma Beta

    Bourdin , P.A., Singh , N. and Brandenburg , A., Magnetic Helicity Reversal in the Corona at Small Plasma Beta . urlcolor=magenta ApJ http://adsabs.harvard.edu/abs/2018ApJ...869....2B , 2018, 869, 2, DOI: urlcolor=blue 10.3847/1538-4357/aae97a https://doi.org/10.3847/1538-4357/aae97a

    2018 doi

  3. [11]

    and Cheung , M.C.M., A model for the formation of the active region corona driven by magnetic flux emergence

    Chen , F., Peter , H., Bingert , S. and Cheung , M.C.M., A model for the formation of the active region corona driven by magnetic flux emergence . urlcolor=magenta A&A http://adsabs.harvard.edu/abs/2014A&A...564A..12C , 2014, 564, A12, DOI: urlcolor=blue 10.1051/0004-6361/2013...

    2014 doi

  4. [12]

    and Antiochos , S.K., Effect of coronal elemental abundances on the radiative loss function

    Cook , J.W., Cheng , C.C., Jacobs , V.L. and Antiochos , S.K., Effect of coronal elemental abundances on the radiative loss function . urlcolor=magenta ApJ http://adsabs.harvard.edu/abs/1989ApJ...338.1176C , 1989, 338, 1176--1183, DOI: urlcolor=blue 10.1086/167268 https://doi....

    1989 doi

  5. [13]

    and Nordlund, ., Bulk heating and slender magnetic loops in the solar corona

    Gudiksen, B. and Nordlund, ., Bulk heating and slender magnetic loops in the solar corona . urlcolor=magenta ApJL http://adsabs.harvard.edu/abs/2002ApJ...572L.113G , 2002, 572, L113--116, DOI: urlcolor=blue 10.1086/341600 https://doi.org/10.1086/341600

    2002 doi

  6. [14]

    and Nordlund, ., An ab initio approach to the solar coronal heating problem

    Gudiksen, B. and Nordlund, ., An ab initio approach to the solar coronal heating problem . urlcolor=magenta ApJ http://adsabs.harvard.edu/abs/2005ApJ...618.1020G , 2005, 618, 1020--1030, DOI: urlcolor=blue 10.1086/426063 https://doi.org/10.1086/426063

    2005 doi

  7. [15]

    and Carlsson, M., On Redshifts and Blueshifts in the Transition Region and Corona

    Hansteen, V.H., Hara, H., Pontieu, B.D. and Carlsson, M., On Redshifts and Blueshifts in the Transition Region and Corona . urlcolor=magenta ApJ http://adsabs.harvard.edu/abs/2010ApJ...718.1070H , 2010, 718, 1070--1078, DOI: urlcolor=blue 10.1088/0004-637X/718/2/1070 https://d...

    2010 doi

  8. [16]

    urlcolor=magenta Sol

    Klimchuk , J.A., On Solving the Coronal Heating Problem . urlcolor=magenta Sol. Phys. http://adsabs.harvard.edu/abs/2006SoPh..234...41K , 2006, 234, 41--77, DOI: urlcolor=blue 10.1007/s11207-006-0055-z https://doi.org/10.1007/s11207-006-0055-z

    2006 doi

  9. [17]

    and Golub , L., The Hinode (Solar-B) Mission: An Overview

    Kosugi , T., Matsuzaki , K., Sakao , T., Shimizu , T., Sone , Y., Tachikawa , S., Hashimoto , T., Minesugi , K., Ohnishi , A., Yamada , T., Tsuneta , S., Hara , H., Ichimoto , K., Suematsu , Y., Shimojo , M., Watanabe , T., Shimada , S., Davis , J.M., Hill , L.D., Owens , J.K....

    2007

  10. [18]

    and Tsuneta , S., The Hinode Spectro-Polarimeter

    Lites , B.W., Akin , D.L., Card , G., Cruz , T., Duncan , D.W., Edwards , C.G., Elmore , D.F., Hoffmann , C., Katsukawa , Y., Katz , N., Kubo , M., Ichimoto , K., Shimizu , T., Shine , R.A., Streander , K.V., Suematsu , A., Tarbell , T.D., Title , A.M. and Tsuneta , S., The Hi...

    2013 doi

  11. [19]

    and Moreno-Insertis, F., On the Origin of the Type II Spicules: Dynamic Three-dimensional MHD Simulations

    Mart \' nez-Sykora, J., Hansteen, V. and Moreno-Insertis, F., On the Origin of the Type II Spicules: Dynamic Three-dimensional MHD Simulations . urlcolor=magenta ApJ http://adsabs.harvard.edu/abs/2011ApJ...736....9M , 2011, 736, 9, DOI: urlcolor=blue 10.1088/0004-637X/736/1/9 ...

    2011 doi

  12. [20]

    urlcolor=magenta ApJ http://adsabs.harvard.edu/abs/1972ApJ...174..499P , 1972, 174, 499--510, DOI: urlcolor=blue 10.1086/151512 https://doi.org/10.1086/151512

    Parker, E.N., Topological Dissipation and the Small-Scale Fields in Turbulent Gases . urlcolor=magenta ApJ http://adsabs.harvard.edu/abs/1972ApJ...174..499P , 1972, 174, 499--510, DOI: urlcolor=blue 10.1086/151512 https://doi.org/10.1086/151512

    1972 doi

  13. [21]

    urlcolor=magenta ApJ http://adsabs.harvard.edu/abs/1988ApJ...330..474P , 1988, 330, 474--479, DOI: urlcolor=blue 10.1086/166485 https://doi.org/10.1086/166485

    Parker, E.N., Nanoflares and the solar X-ray corona . urlcolor=magenta ApJ http://adsabs.harvard.edu/abs/1988ApJ...330..474P , 1988, 330, 474--479, DOI: urlcolor=blue 10.1086/166485 https://doi.org/10.1086/166485

    1988 doi

  14. [22]

    and Bingert, S., Constant cross section of loops in the solar corona

    Peter, H. and Bingert, S., Constant cross section of loops in the solar corona . urlcolor=magenta A&A http://adsabs.harvard.edu/abs/2012A&A...548A...1P , 2012, 548, A1, DOI: urlcolor=blue 10.1051/0004-6361/201219473 https://doi.org/10.1051/0004-6361/201219473

    2012 doi

  15. [23]

    and Korreck , K.E., Structure of solar coronal loops: from miniature to large-scale

    Peter , H., Bingert , S., Klimchuk , J.A., de Forest , C., Cirtain , J.W., Golub , L., Winebarger , A.R., Kobayashi , K. and Korreck , K.E., Structure of solar coronal loops: from miniature to large-scale . urlcolor=magenta A&A http://adsabs.harvard.edu/abs/2013A&A...556A.104P...

    2013 doi

  16. [24]

    and Cameron , R.H., Limitations of force-free magnetic field extrapolations: Revisiting basic assumptions

    Peter , H., Warnecke , J., Chitta , L.P. and Cameron , R.H., Limitations of force-free magnetic field extrapolations: Revisiting basic assumptions . urlcolor=magenta A&A http://adsabs.harvard.edu/abs/2015A&A...584A..68P , 2015, 584, A68, DOI: urlcolor=blue 10.1051/0004-6361/20...

    2015 doi

  17. [25]

    and Dahlburg , R.B., Coronal Heating, Weak MHD Turbulence, and Scaling Laws

    Rappazzo , A.F., Velli , M., Einaudi , G. and Dahlburg , R.B., Coronal Heating, Weak MHD Turbulence, and Scaling Laws . urlcolor=magenta ApJL http://adsabs.harvard.edu/abs/2007ApJ...657L..47R , 2007, 657, L47--L51, DOI: urlcolor=blue 10.1086/512975 https://doi.org/10.1086/512975

    2007 doi

  18. [26]

    and Dahlburg , R.B., Nonlinear Dynamics of the Parker Scenario for Coronal Heating

    Rappazzo , A.F., Velli , M., Einaudi , G. and Dahlburg , R.B., Nonlinear Dynamics of the Parker Scenario for Coronal Heating . urlcolor=magenta ApJ http://adsabs.harvard.edu/abs/2008ApJ...677.1348R , 2008, 677, 1348--1366, DOI: urlcolor=blue 10.1086/528786 https://doi.org/10.1...

    2008 doi

  19. [27]

    urlcolor=magenta ApJ http://adsabs.harvard.edu/abs/2012ApJ...750...62R , 2012, 750, 62, DOI: urlcolor=blue 10.1088/0004-637X/750/1/62 https://doi.org/10.1088/0004-637X/750/1/62

    Rempel , M., Numerical Sunspot Models: Robustness of Photospheric Velocity and Magnetic Field Structure . urlcolor=magenta ApJ http://adsabs.harvard.edu/abs/2012ApJ...750...62R , 2012, 750, 62, DOI: urlcolor=blue 10.1088/0004-637X/750/1/62 https://doi.org/10.1088/0004-637X/750/1/62

    2012 doi

  20. [28]

    urlcolor=magenta ApJ http://esoads.eso.org/abs/2017ApJ...834...10R , 2017, 834, 10, DOI: urlcolor=blue 10.3847/1538-4357/834/1/10 https://doi.org/10.3847/1538-4357/834/1/10

    Rempel , M., Extension of the MURaM Radiative MHD Code for Coronal Simulations . urlcolor=magenta ApJ http://esoads.eso.org/abs/2017ApJ...834...10R , 2017, 834, 10, DOI: urlcolor=blue 10.3847/1538-4357/834/1/10 https://doi.org/10.3847/1538-4357/834/1/10

    2017 doi

  21. [29]

    and Sanchez Almeida , J., Empirical model of an average solar granule ; in Cool Stars, Stellar Systems, and the Sun , edited by R

    Ruiz Cobo , B., del Toro Iniesta , J.C., Rodriguez Hidalgo , I., Collados , M. and Sanchez Almeida , J., Empirical model of an average solar granule ; in Cool Stars, Stellar Systems, and the Sun , edited by R. Pallavicini and A.K. Dupree , Vol. 109 of Astronomical Society of t...

    1996

  22. [30]

    and Title, A.M., On the patterns of the solar granulation and supergranulation

    Schrijver, C.J., Hagenaar, H.J. and Title, A.M., On the patterns of the solar granulation and supergranulation . urlcolor=magenta ApJ http://adsabs.harvard.edu/abs/1997ApJ...475..328S , 1997, 475, 328--337, DOI: urlcolor=blue 10.1086/303528 https://doi.org/10.1086/303528

    1997 doi

  23. [31]

    urlcolor=magenta ApJ http://adsabs.harvard.edu/abs/1957ApJ...126..202S , 1957, 126, 202, DOI: urlcolor=blue 10.1086/146386 https://doi.org/10.1086/146386

    Spiegel , E.A., The Smoothing of Temperature Fluctuations by Radiative Transfer . urlcolor=magenta ApJ http://adsabs.harvard.edu/abs/1957ApJ...126..202S , 1957, 126, 202, DOI: urlcolor=blue 10.1086/146386 https://doi.org/10.1086/146386

    1957 doi

  24. [32]

    and H \"a rm, R., Transport phenomena in a completely ionized gas

    Spitzer, L. and H \"a rm, R., Transport phenomena in a completely ionized gas . urlcolor=magenta Phys. Rev. http://adsabs.harvard.edu/abs/1953PhRv...89..977S , 1953, 89, 977--981, DOI: urlcolor=blue 10.1103/PhysRev.89.977 https://doi.org/10.1103/PhysRev.89.977

    1953 doi

  25. [33]

    and Owens , J.K., The Solar Optical Telescope for the Hinode Mission: An Overview

    Tsuneta , S., Ichimoto , K., Katsukawa , Y., Nagata , S., Otsubo , M., Shimizu , T., Suematsu , Y., Nakagiri , M., Noguchi , M., Tarbell , T., Title , A., Shine , R., Rosenberg , W., Hoffmann , C., Jurcevich , B., Kushner , G., Levay , M., Lites , B., Elmore , D., Matsushita ,...

    2008

  26. [34]

    and Berger , M.A., On the Relationship Between Photospheric Footpoint Motions and Coronal Heating in Solar Active Regions

    van Ballegooijen , A.A., Asgari-Targhi , M. and Berger , M.A., On the Relationship Between Photospheric Footpoint Motions and Coronal Heating in Solar Active Regions . urlcolor=magenta ApJ http://adsabs.harvard.edu/abs/2014ApJ...787...87V , 2014, 787, 87, DOI: urlcolor=blue 10...

    2014 doi

  27. [35]

    and DeLuca , E.E., Heating of the Solar Chromosphere and Corona by Alfv \'e n Wave Turbulence

    van Ballegooijen , A.A., Asgari-Targhi , M., Cranmer , S.R. and DeLuca , E.E., Heating of the Solar Chromosphere and Corona by Alfv \'e n Wave Turbulence . urlcolor=magenta ApJ http://adsabs.harvard.edu/abs/2011ApJ...736....3V , 2011, 736, 3, DOI: urlcolor=blue 10.1088/0004-63...

    2011 doi

  28. [36]

    and Erd \'e lyi , R., Magnetic tornadoes as energy channels into the solar corona

    Wedemeyer-B \"o hm , S., Scullion , E., Steiner , O., Rouppe van der Voort , L., de La Cruz Rodriguez , J., Fedun , V. and Erd \'e lyi , R., Magnetic tornadoes as energy channels into the solar corona . urlcolor=magenta Nature http://adsabs.harvard.edu/abs/2012Natur.486..505W ...

    2012 doi

  29. [37]

    , " * write output.state after.block = add.period write newline

    ENTRY address adsurl author booktitle chapter chaptertitle doi englishtitle edition editor eid howpublished institution isbn journal key month note number organization pages publisher location school series seriesnumber title type volume year label extra.label sort.label short...

  30. [38]

    write newline

    " write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 gl...

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.