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Sub-sonic compressible magnetohydrodynamic turbulence I. Alfv\'enic and fast-magnetosonic injection, amplitude dependence, and compressibility effects

T0 review · 4 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Sub-sonic MHD turbulence is not universal: its cosmic-ray-relevant spectrum, anisotropy, and curvature statistics depend on injection type, amplitude, and plasma beta, and the $K^{-2.5}$ law used in transport models holds only at large ampl

desk verdict Solid parameter sweep, but the headline exponents are not yet converged numbers. read the letter →

arxiv 2608.01386 v1 pith:PWEDELZD submitted 2026-08-02 physics.plasm-ph astro-ph.GAastro-ph.HE

Eleonora Puzzoni , Silvio Sergio Cerri , Dimitri Laveder , Thierry Passot , Pierre-Louis Sulem This is my paper
classification physics.plasm-phastro-ph.GAastro-ph.HE
keywords magnetohydrodynamicturbulencecosmic-raytransportplasmabetafastmagnetosonicwavesAlfvénicmagnetic-fieldcurvaturemagneticmirrorsdecayingsimulations
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

This paper asks whether the sub-sonic magnetohydrodynamic turbulence that cosmic rays must cross in the Galaxy has a universal character, or whether it is stamped by how it was stirred and by the plasma it lives in. Using $1024^3$ freely decaying ideal-MHD simulations, it shows the latter: the spectral shape and anisotropy, the fraction of energy carried by fast-magnetosonic fluctuations, and the statistics of magnetic-field-line curvature and mirroring points all depend on the type of injected waves (Alfvénic, fast-magnetosonic, or mixed), on the fluctuation amplitude $\delta B/B_0$, and on the plasma compressibility $\beta$. The headline result is a negative one for a widely used assumption: the curvature power law $\mathrm{PDF}(K_\parallel)\propto K_\parallel^{-2.5}$ that cosmic-ray scattering models rely on is realized only for large-amplitude turbulence ($\delta B/B_0>1$) in a low-compressibility ($\beta\gg1$) plasma. If this is right, cosmic-ray transport models that assume one universal turbulence spectrum or one curvature statistics are missing a regime dependence that matters, and their confinement predictions must be re-evaluated region by region.

What carries the argument

The load-bearing objects are two curvature observables defined along the local magnetic-field direction: the parallel field-line curvature $K_\parallel=|(\hat b\cdot\nabla)\hat b|$, which measures how sharply field lines bend, and the mirroring curvature $K_M=|\hat b\cdot\nabla\ln B|$, which measures the parallel scale of magnetic-mirror sites; curvature- and mirror-scattering models of cosmic-ray confinement feed on their high-value power-law tails. The evidence is produced by $1024^3$ freely decaying ideal-MHD simulations (PLUTO code, WENO-Z reconstruction, HLLD Riemann solver) seeded at wavenumbers $|k|/k_0\le4$ with arc-polarized Alfvén waves and/or linear fast-magnetosonic waves over $\

What would settle it

Rerun the same injection sets — Alfvénic and fast-magnetosonic, low and high amplitude, at $\beta=1$ and $\beta=200$ — at $2048^3$ resolution, or as several independent phase realizations at $1024^3$, and re-measure the inertial-range spectral indices and the high-$K_\parallel$ and high-$K_M$ PDF slopes. If the $k_\perp^{-5/3}$, $k_z^{-2}$, and $K^{-2.5}$ exponents move by more than the fit uncertainty, or if the curvature tails change shape with resolution, the claimed regime dependence is not verified.

Watch

Extended reading notes

Core claim

The paper's central claim is that fully developed sub-sonic compressible MHD turbulence is not one universality class: the properties relevant to cosmic-ray transport keep a memory of the large-scale injection. The density-fluctuation level ends up the same whether seeding is Alfvénic or fast-magnetosonic, because fast modes are rapidly eroded by shocks and the decay then matches the Alfvénic case. But the fast-mode energy share stays relevant (30–50%) only for purely fast injection, and the spectra differ strongly with injection type and amplitude: anisotropic $k_\perp^{-5/3}$, $k_z^{-2}$ for low-amplitude Alfvénic or mixed injection; isotropic, shock-dominated $k^{-2}$ for fast injection;

Load-bearing premise

The power-law indices and the curvature and mirror PDF tails rest on a single decaying $1024^3$ realization per parameter set, with injection at $|k|/k_0\le4$ and spectral fits over roughly $k/k_0=5$ to 30 (even shorter for parallel spectra), and no resolution-convergence check; if that range is not converged or the single realization is atypical, the reported exponents could shift.

Editorial extensions

If this is right

  • Curvature-scattering models of cosmic-ray confinement that assume $\mathrm{PDF}(K_\parallel)\propto K_\parallel^{-2.5}$ are on safe ground only for large-amplitude ($\delta B/B_0>1$), high-$\beta$ turbulence; elsewhere the curvature tails are much steeper, so curvature scattering is weaker than those models predict.
  • Quasi-linear-theory treatments that assume a Goldreich–Sridhar $k_\perp^{-5/3}$/$k_\parallel^{-2}$ spectrum for Alfvénic turbulence or an Iroshnikov–Kraichnan $k^{-3/2}$ spectrum for fast-mode turbulence need to identify which regime the target environment is in, since neither scaling holds across injection type and amplitude.
  • For regions whose large-scale driving is purely fast-magnetosonic, fully developed turbulence keeps a 30–50% fast-mode share and a shock-populated, nearly isotropic $k^{-2}$ spectrum — a scattering environment qualitatively different from Alfvénic-driven turbulence.
  • The density-fluctuation level in the developed turbulence is fixed by the sonic Mach number regardless of injection type, so density contrast alone cannot distinguish the driving mechanism, while curvature and mirror statistics can.

Reading between the lines

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

  • (editorial extension) The strong dependence on large-scale conditions implies cosmic-ray transport models for specific regions (Galactic disk, halo, clusters) should be driven by measured or simulated large-scale forcing of that region rather than a universal spectrum — the direction the paper stakes out for Paper II.
  • (editorial extension) The paper's parallel spectra steepen beyond $k_\parallel^{-2}$ at $\beta\gg1$; if that persists at higher resolution, gyro-resonant scattering along the guide field is suppressed exactly where the curvature $K^{-2.5}$ law holds, pointing to mirroring rather than curvature or resonance as the leading confinement mechanism in high-$\beta$ regions.
  • (editorial extension) A testable prediction: environments with $\delta B/B_0\lesssim1$ and strong density fluctuations should show field-line curvature PDF exponents near $-7$ rather than $-2.5$; solar-wind measurements or larger-box simulations could check this.
  • (editorial extension) The specific exponents here come from one realization and a short inertial range; re-measuring them with larger boxes or ensembles is the cheapest way to see whether the quantitative scalings survive, while the qualitative regime dependence is the solid part.
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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

4 major / 4 minor

Summary. This paper presents 1024^3 ideal-MHD simulations of freely decaying, sub-sonic compressible turbulence, varying the nature of the initial fluctuations (Alfvénic, fast-magnetosonic, and mixed), the initial amplitude ($\delta B/B_0\simeq0.25$–$5$), and the plasma compressibility ($\beta=1,2,200$). The authors analyze how the developed turbulent state depends on these parameters, focusing on quantities relevant to cosmic-ray transport: density-fluctuation levels, spectral anisotropy and power-law indices, the relative energy in Alfvén/slow/fast modes, and the statistics of field-line curvature $K_\parallel$ and mirroring curvature $K_M$. The main claims are that the level of density fluctuations is set mainly by the sonic Mach number and not by the injection type; that fast-mode energy remains significant only when the injection is purely fast; that low-amplitude Alfvénic/mixed injection produces strong anisotropy ($k_\perp^{-5/3}$, $k_z^{-2}$), whereas low-amplitude fast injection gives a quasi-isotropic $k^{-2}$ shock-dominated spectrum; and that the often-used $\mathrm{PDF}(K_\parallel)\propto K_\parallel^{-2.5}$ scaling appears only for large-amplitude, high-$\beta$ turbulence.

Significance. If the quantitative results hold, the paper provides a useful parameter-space survey for a topic—compressible MHD turbulence in the sub-sonic regime and its implications for cosmic-ray scattering—where several published models assume specific scalings (Goldreich-Sridhar anisotropy, $K_\parallel^{-2.5}$ curvature statistics, Iroshnikov-Kraichnan fast-mode spectra). The authors are careful to distinguish linear-mode, Helmholtz, and frequency-wavevector decompositions and explicitly flag where linear-mode decomposition is unreliable. The study also compares against external predictions (Yang et al. 2019; Cho & Lazarian 2003; Makwana & Yan 2020) rather than fitting its own theory to its own data, which is a strength. The qualitative conclusion that these turbulence properties are sensitive to injection type, amplitude, and $\beta$ is valuable and likely robust. However, the quantitative exponents—which are the paper's main deliverable for Paper II—are supported only by single-decaying-run measurements with short inertial ranges and no convergence tests, so the numerical significance is currently uncertain.

major comments (4)
  1. [§3.3 and §4.1, Figs. 7–10] The quantitative payload—the spectral indices $k_\perp^{-5/3}$, $k_z^{-2}$, $k^{-3/2}$, $k^{-2}$, and especially the claim that $\mathrm{PDF}(K_\parallel)\propto K_\parallel^{-2.5}$ emerges only for $\delta B/B_0>1$ at $\beta\gg1$—rests on a single decaying $1024^3$ realization per parameter set, with one draw of random phases. No second realization, no 512^3 or 2048^3 run, and no fit-range/error analysis are provided. The inertial range is short (roughly $k/k_0=5$–$30$, and shorter for parallel spectra), and the fits are not documented. Given that the claimed exponents differ by small amounts (e.g., $-5/3$ vs. $-3/2$, or $-2.5$ vs. $-3.5$), a different phase realization could plausibly change the fitted indices by more than the separation between the claims. The authors should either provide convergence/ensemble checks or explicitly downgrade these exponents to qualitative indications.
  2. [§3.1 and Table 1] The normalization time $t^*$ is not defined uniformly. For Alfvénic injection with $\delta B/B_0\le1$, it is the peak of $J_{\rm rms}$; for large-amplitude runs and for small-amplitude fast-magnetosonic runs, it is instead the onset of steady fluctuation spectra. All subsequent time averages ($1\lesssim t/t^*\lesssim1.25$) and time evolutions are presented using this definition. Since the early-time behavior is dominated by different physical processes in the two classes of runs, the comparison of decay rates and of spectra across the table may be biased by this choice. At minimum, the sensitivity of the quoted exponents to the averaging window should be checked, and the definition should be stated consistently in the figure captions.
  3. [§4.1, Fig. 9] The claim of a $k_z^{-2}$ parallel spectrum for low-amplitude Alfvénic/mixed injection at $\beta=1$ is based on a very short range, $k_z/k_0\lesssim15$, with the text itself noting that the spectrum is noticeably steeper at smaller scales. Similarly, the $k_z^{-3}$ claim at $\beta=200$ is fitted over an even shorter range. Because the parallel spectrum is the quantity most directly relevant to quasi-linear cosmic-ray scattering, this is a load-bearing point. The authors should provide the fit interval, the fitted slope with uncertainty, and ideally a demonstration that the result is stable under changing the fit range or the averaging window.
  4. [§3.1, Figs. 2–3 and Appendix C] Quantitative statements about the energy fraction in fast/slow/Alfvén modes at $\delta B/B_0>1$ (e.g., 'near equipartition between the three MHD modes' for large-amplitude fast injection) rely on a linear-mode decomposition that the authors themselves state is not fully reliable at large amplitudes. The caveats in §3.1 and Appendix C are welcome, but the paper still presents these numbers as results. Either the mode-decomposed energy fractions should be restricted to the $\delta B/B_0\lesssim1$ cases, or an independent check (e.g., comparison with nonlinear measures or with Helmholtz decomposition) should be provided to show that the qualitative conclusions do not depend on the linear assumption.
minor comments (4)
  1. [Throughout] There are several typographical errors that should be corrected: 'yelding' (Introduction), 'magnetosnic' (Introduction), 'turbulent turbulent state' (§3.1), 'yeld' (Appendix C), and 'at timest' (Appendix D).
  2. [§3.3, Figs. 7–8] The method used to fit the power-law indices in the PDF tails is not described: no fit range, no uncertainty, no criterion for what counts as the power-law portion. This is important for reproducibility, especially because the $K_\parallel^{-2.5}$ claim is one of the paper's central results.
  3. [Appendix B] In the description of Figure B.1, the sentence 'where $K^*$ is the value $K^*$ at which each PDF peaks' is redundant and likely contains a typo; also the figure itself would benefit from the same fit-range information as Figures 7–8.
  4. [§4.2, Fig. 11] The text describes several scalings ($k_\parallel\propto k_\perp^{2/3}$, $k_\parallel\propto k_\perp^{1/2}$, constant anisotropy) in different wavenumber bands, but the figure lacks guide lines for these slopes. Adding reference lines would make the claims easier to verify.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: simulation outputs are measured and compared with external predictions; no central claim reduces to an input fit or to a self-citation chain.

full rationale

The derivation chain is self-contained against external benchmarks. Initial conditions are constructed from standard linear fast-mode relations and arc-polarized Alfvén solutions (Del Zanna 2001; Cho & Lazarian 2003), not from the quantities later reported. The spectral exponents (k_perp^{-5/3}, k_z^{-2}, k^{-2}, k^{-3/2}) and the PDF(K_parallel) tail indices are fitted to the simulated fields and then compared with independent published predictions (Goldreich & Sridhar 1995; Iroshnikov 1963; Kraichnan 1965; Yang et al. 2019; Makwana & Yan 2020), rather than being 'predicted' from parameters fitted to the same data. The emergence of the -2.5 curvature scaling is presented as a measured regime dependence relative to an external prediction, not as a consequence of the simulation setup. No uniqueness theorem or ansatz is imported from the authors' own prior work to force the chosen interpretation. The only self-citation visible in the text, Bouchet et al. 2026, appears in Section 3.3 as a 'see also' supporting the secondary remark that polarization of deltaB is irrelevant in low-curvature regions; this is not load-bearing for the central claims. The paper itself flags its limitations (decaying runs, M_s<=1 regime, linear-mode decomposition not to be over-interpreted, unresolved questions about parallel-cascade steepening), which are robustness concerns rather than circular reasoning. A separate reviewer concern is that the quantitative indexes rest on single 1024^3 realizations with short inertial ranges and no resolution/convergence check; that is a sample-size/statistical-typicality risk, not an equivalence between inputs and outputs.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The paper introduces no new physical entities. It defines a new diagnostic observable, the mirroring curvature K_M, but that is a derived statistic, not a postulate. The main free parameters are the design choices (beta and amplitude) and the fitted spectral indices, which are measured from the simulations.

free parameters (3)
  • Initial fluctuation amplitude deltaB/B0 = 0.33, 1, 5 (and 0.25, 0.14)
    Chosen by hand to span sub- and super-Alfvénic regimes. The conclusions are conditioned on these specific amplitude values.
  • Plasma beta = 1, 2, 200
    Chosen by hand to explore high and low compressibility while keeping the flow sub-sonic. Central to the compressibility claims.
  • Spectral and PDF power-law indices = -5/3, -2, -3/2, -3.6, -4.5, -6.9, -8.0 (various figures)
    Fitted to simulation spectra and PDFs over a limited inertial range without reported uncertainties. They underpin the central claims about spectral shape and curvature statistics.
assumptions (5)
  • domain assumption Ideal MHD equations with an isothermal equation of state adequately model sub-sonic turbulence in the regimes considered, neglecting collisionless effects at high beta.
    Section 2 states the model; the authors acknowledge that kinetic effects (e.g., Arzamasskiy et al. 2023) are neglected and that the study is limited to Ms <= 1.
  • domain assumption A single realization at 1024^3 with random phases is statistically representative of the turbulence in each parameter set.
    No ensemble averaging is performed; all conclusions rest on individual runs listed in Table 1.
  • domain assumption The inertial range at 1024^3 with injection at |k|/k0 <= 4 is long enough to identify power-law scalings.
    Spectral fits in Figures 9 to 11 use a short range and no resolution convergence study is provided.
  • ad hoc to paper Linear MHD mode decomposition remains meaningful even where applied at deltaB/B0 > 1.
    The paper uses mode decomposition at large amplitude (Section 3.1) while itself stating it should not be over-interpreted (Appendix C). Conclusions about mode fractions in large-amplitude runs rest on this caveated assumption.
  • standard math Fourier and Helmholtz decompositions and power-spectrum estimation are standard and error-free.
    Used throughout Sections 3 and 4 without derivation.

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Cite this review

Pith. "Pith review of Sub-sonic compressible magnetohydrodynamic turbulence I. Alfv\'enic and fast-magnetosonic injection, amplitude dependence, and compressibility effects." pith.science (2026). https://pith.science/paper/PWEDELZD

@misc{pith2026260801386,
  author       = {Pith},
  title        = {Pith review of: Sub-sonic compressible magnetohydrodynamic turbulence I. Alfv\'enic and fast-magnetosonic injection, amplitude dependence, and compressibility effects},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PWEDELZD}},
  note         = {Machine review of arXiv:2608.01386}
}
abstract

We investigate how sub-sonic compressible magnetohydrodynamic (MHD) turbulence properties that are relevant for cosmic-ray (CR) transport in the Galaxy are affected by the nature and amplitude of initial fluctuations, and by the plasma compressibility $\beta$. We perform 3D simulations of decaying compressible ideal-MHD turbulence at $1024^3$ resolution with the PLUTO code. The level of density fluctuations in fully developed turbulence is insensitive to whether this state is reached starting from Alfv\'enic or fast-magnetosonic perturbations. Fast-magnetosonic injection is characterized by an early phase of rapid shock dissipation, followed by a turbulence-dominated decay with a rate comparable to that of the Alfv\'enic case. The contribution of fast-magnetosonic fluctuations in fully developed turbulence remains relevant only when the initial injection consists exclusively of fast modes. Large-amplitude turbulence ($\delta B/B_0>1$) is characterized by a nearly isotropic Kolmogorov or Iroshnikov-Kraichnan spectrum for Alfv\'enic or fast-magnetosonic injection, respectively. At low amplitudes ($\delta B/B_0\ll1$), both initial Alfv\'enic and mixed-wave perturbations lead to strongly anisotropic turbulence with spectra $\propto k_\perp^{-5/3}$ and $\propto k_z^{-2}$ (becoming steeper at $\beta\gg1$), whereas fast-magnetosonic perturbations produce a turbulent state populated by shocks with a nearly isotropic $k^{-2}$ spectrum. Magnetic-field curvature and mirror structures are strongly sensitive to fluctuation amplitude and plasma $\beta$. The predicted -2.5 power-law scaling emerges only in the large-amplitude regime at high $\beta$. This work highlights that features of sub-sonic compressible MHD turbulence that may affect CR transport are sensitive to large-scale conditions and to the plasma $\beta$. Their effect on CR diffusion and field-line random walk is the object of Paper II.

Figures

Figures reproduced from arXiv: 2608.01386 by the authors.

Figure 1
Figure 1. Top to bottom: Time evolution of the root-mean-square current, magnetic field fluctuations, Alfvénic Mach number (inset: sonic Mach number), and density fluctuations. Left: small-amplitude injection of Alfvénic (red at β = 1 and orange at β = 200), fast-magnetosonic (black; β = 1), and mixed waves (brown; β = 1). Right: large-amplitude injection of Alfvénic (magenta at β = 2, olive green and dark cyan for different … view at source ↗
Figure 2
Figure 2. Top panel: Time evolution of the compressible (dot￾ted line), and solenoidal (dashed line) velocity fluctuations, for Alfvénic (in red at β = 1 and in orange at β = 200), fast (in black), and mixed (in brown) injection. Bottom panel: Time evo￾lution of the energy fraction in the Alfvén (solid line), slow (dot￾ted line), and fast (dashed line) modes for the same simulations. highly compressive as for fast-magnetosoni… view at source ↗
Figure 4
Figure 4. 3D plots of magnetic-fluctuation amplitude [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figures from the paper (7 more)
Figure 5
Figure 5. Figure 5: Normalized current-density magnitude |J|/Jrms in fully developed turbulence for Alfvénic injection with δB˜ ≃ 0.3 at β = 1 (left column) and δB˜ ≃ 2.3 at β = 200 (right column). Top panels: (x, y) plane at z = 0. Bottom panels: (y, z) plane at x = 0. isotropic and homo…
Figure 7
Figure 7. Figure 7: PDF of the magnetic-field curvature K∥ versus K∥/K∗ (K∗ is the value of K∥ that maximizes the PDF), averaged over times 1 ≲ t/t ∗ ≲ 1.25. Left panel: small-amplitude turbulence (δB/B0 ≪ 1). Right panel: large-amplitude turbulence (δB/B0 ≳ 1). Power￾law fits and indices…
Figure 8
Figure 8. Figure 8: PDF of the field-aligned gradient of magnetic-field strength [PITH_FULL_IMAGE:figures/full_fig_p008_8.png]
Figure 9
Figure 9. Figure 9: Magnetic-field spectra as a function of k⊥ (left) and kz (right), averaged over times 1 ≲ t/t ∗ ≲ 1.25, for low-amplitude turbulence (δB/B0 ≪ 1). Power laws are provided for reference. The gray shaded area indicates the dissipative range. The insets show the time evolu…
Figure 10
Figure 10. Figure 10: Same as Figure 9, but for large-amplitude turbulence ( [PITH_FULL_IMAGE:figures/full_fig_p009_10.png]
Figure 11
Figure 11. Figure 11: Anisotropy of magnetic-field fluctuations [PITH_FULL_IMAGE:figures/full_fig_p010_11.png]
Figure 12
Figure 12. Figure 12: Scale-dependent anisotropy k∥/k⊥ of magnetic-field fluctuations decomposed into Alfvén (solid), slow (dotted), and fast (dashed) modes for different simulations at t ≈ t ∗ . differences between the various type of fluctuations. For low￾amplitude Alfvénic injection at …

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Works this paper leans on

112 extracted references · 31 canonical work pages

  1. [1]

    , keywords =

    The streaming instability: a review. , keywords =

  2. [2]

    Physical Review X , keywords =

    Kinetic Turbulence in Collisionless High- Plasmas. Physical Review X , keywords =. doi:10.1103/PhysRevX.13.021014 , archivePrefix =. 2207.05189 , primaryClass =

    arXiv

  3. [3]

    , keywords =

    In Situ Measurement of Curvature of Magnetic Field in Turbulent Space Plasmas: A Statistical Study. , keywords =. doi:10.3847/2041-8213/ab846e , archivePrefix =. 1912.09046 , primaryClass =

    arXiv

  4. [4]

    , keywords =

    Large-amplitude hydromagnetic waves. , keywords =. doi:10.1029/JA079i016p02302 , adsurl =

    work page doi:10.1029/ja079i016p02302

  5. [5]

    Nature Astronomy , keywords =

    The spectrum of magnetized turbulence in the interstellar medium. Nature Astronomy , keywords =. doi:10.1038/s41550-025-02551-5 , archivePrefix =. 2504.07136 , primaryClass =

    arXiv

  6. [6]

    Local relaxation and scale-dependent alignment in compressible, magnetized turbulence

    Scale-dependent alignment in compressible magnetohydrodynamic turbulence. arXiv e-prints , keywords =. doi:10.48550/arXiv.2504.15538 , archivePrefix =. 2504.15538 , primaryClass =

    work page Pith review arXiv doi:10.48550/arxiv.2504.15538

  7. [7]

    , keywords =

    Numerical Study of Cosmic Ray Diffusion in Magnetohydrodynamic Turbulence. , keywords =. doi:10.1088/0004-637X/728/1/60 , archivePrefix =. 1002.2646 , primaryClass =

    arXiv

  8. [8]

    , keywords =

    Spectra of Strong Magnetohydrodynamic Turbulence from High-resolution Simulations. , keywords =. doi:10.1088/2041-8205/784/2/L20 , archivePrefix =. 1401.4177 , primaryClass =

    arXiv

Show all 112 references
  1. [9]

    Living Reviews in Computational Astrophysics , keywords =

    MHD turbulence. Living Reviews in Computational Astrophysics , keywords =. doi:10.1007/s41115-019-0005-8 , archivePrefix =. 1910.03585 , primaryClass =

    1910 arXiv

  2. [10]

    Astrophysics of cosmic rays

  3. [11]

    , keywords =

    Development of anisotropy in incompressible magnetohydrodynamic turbulence. , keywords =. doi:10.1103/PhysRevE.78.066301 , archivePrefix =. 0808.3061 , primaryClass =

    arXiv

  4. [12]

    , keywords =

    Spectral Breaks as a Signature of Cosmic Ray Induced Turbulence in the Galaxy. , keywords =. doi:10.1103/PhysRevLett.109.061101 , archivePrefix =. 1207.3706 , primaryClass =

    arXiv

  5. [13]

    , keywords =

    The origin of galactic cosmic rays. , keywords =. doi:10.1007/s00159-013-0070-7 , archivePrefix =. 1311.7346 , primaryClass =

    arXiv

  6. [14]

    , keywords =

    Spectrum of Magnetohydrodynamic Turbulence. , keywords =. doi:10.1103/PhysRevLett.96.115002 , archivePrefix =. astro-ph/0511290 , primaryClass =

    arXiv

  7. [15]

    arXiv e-prints , keywords =

    Polarized 3D Synthetic Turbulence I: Magnetic Field Line Random Walk. arXiv e-prints , keywords =. doi:10.48550/arXiv.2605.22729 , archivePrefix =. 2605.22729 , primaryClass =

    doi arXiv

  8. [16]

    Reviews of Plasma Physics , year = 1965, month = jan, volume =

    Transport Processes in a Plasma. Reviews of Plasma Physics , year = 1965, month = jan, volume =

    1965

  9. [17]

    , keywords =

    Astrophysical Hydromagnetic Turbulence. , keywords =. doi:10.1007/s11214-013-0009-3 , archivePrefix =. 1307.5496 , primaryClass =

    arXiv

  10. [18]

    Living Reviews in Solar Physics , keywords =

    The Solar Wind as a Turbulence Laboratory. Living Reviews in Solar Physics , keywords =. doi:10.12942/lrsp-2013-2 , adsurl =

    2013 doi

  11. [19]

    , keywords =

    Plasma Wave-particle Acceleration as the Origin of the Galactic Gamma-Ray Bubbles. , keywords =. doi:10.3847/1538-4357/ae1224 , adsurl =

    doi

  12. [20]

    , keywords =

    Turbulent Regimes in Collisions of 3D Alfv \'e n-wave Packets. , keywords =. doi:10.3847/1538-4357/ac93fe , archivePrefix =. 2207.04301 , primaryClass =

    arXiv

  13. [21]

    , keywords =

    Scattering of Energetic Particles by Anisotropic Magnetohydrodynamic Turbulence with a Goldreich-Sridhar Power Spectrum. , keywords =. doi:10.1103/PhysRevLett.85.4656 , archivePrefix =. astro-ph/0008498 , primaryClass =

    arXiv

  14. [22]

    , keywords =

    Extending the Big Power Law in the Sky with Turbulence Spectra from Wisconsin H Mapper Data. , keywords =. doi:10.1088/0004-637X/710/1/853 , archivePrefix =. 0905.4413 , primaryClass =

    arXiv

  15. [23]

    , keywords =

    The Anisotropy of Magnetohydrodynamic Alfv \'e nic Turbulence. , keywords =. doi:10.1086/309213 , archivePrefix =. astro-ph/0003403 , primaryClass =

    arXiv

  16. [24]

    , keywords =

    New Regime of Magnetohydrodynamic Turbulence: Cascade below the Viscous Cutoff. , keywords =. doi:10.1086/339453 , archivePrefix =. astro-ph/0112195 , primaryClass =

    arXiv

  17. [25]

    , keywords =

    Compressible Sub-Alfv \'e nic MHD Turbulence in Low- Plasmas. , keywords =. doi:10.1103/PhysRevLett.88.245001 , archivePrefix =. astro-ph/0205282 , primaryClass =

    arXiv

  18. [26]

    , keywords =

    Compressible magnetohydrodynamic turbulence: mode coupling, scaling relations, anisotropy, viscosity-damped regime and astrophysical implications. , keywords =. doi:10.1046/j.1365-8711.2003.06941.x , archivePrefix =. astro-ph/0301062 , primaryClass =

    2003

  19. [27]

    , keywords =

    Galactic Cosmic Rays in the Local Interstellar Medium: Voyager 1 Observations and Model Results. , keywords =. doi:10.3847/0004-637X/831/1/18 , adsurl =

    doi

  20. [28]

    , keywords =

    Parametric decay of oblique arc-polarized Alfv \'e n waves. , keywords =. doi:10.1029/2001GL012911 , adsurl =

    doi

  21. [29]

    Science Advances , keywords =

    Reconnection-driven energy cascade in magnetohydrodynamic turbulence. Science Advances , keywords =. doi:10.1126/sciadv.abn7627 , archivePrefix =. 2210.10736 , primaryClass =

    arXiv

  22. [30]

    , keywords =

    Interstellar Turbulence I: Observations and Processes. , keywords =. doi:10.1146/annurev.astro.41.011802.094859 , archivePrefix =. astro-ph/0404451 , primaryClass =

    arXiv

  23. [31]

    Physical Review , year = 1950, month = jul, volume =

    The Hydromagnetic Equations. Physical Review , year = 1950, month = jul, volume =. doi:10.1103/PhysRev.79.183 , adsurl =

    1950 doi

  24. [32]

    , keywords =

    Cosmic Ray Propagation in Galactic Turbulence. , keywords =. doi:10.1088/0004-637X/782/1/36 , archivePrefix =. 1310.5732 , primaryClass =

    arXiv

  25. [33]

    Plasma Physics and Controlled Fusion , keywords =

    Plasma turbulence in the interstellar medium. Plasma Physics and Controlled Fusion , keywords =. doi:10.1088/1361-6587/ab49eb , archivePrefix =. 1912.08237 , primaryClass =

    1912 arXiv

  26. [34]

    , keywords =

    Plasmoid Instability in the Multiphase Interstellar Medium. , keywords =. doi:10.3847/2041-8213/accf1f , archivePrefix =. 2211.06434 , primaryClass =

    arXiv

  27. [35]

    , keywords =

    Hydromagnetic waves in high beta plasmas. , keywords =. doi:10.1086/157391 , adsurl =

    doi

  28. [36]

    , keywords =

    The theory of cosmic ray scattering on pre-existing MHD modes meets data. , keywords =. doi:10.1093/mnras/stab355 , archivePrefix =. 2011.09197 , primaryClass =

    2011 arXiv

  29. [37]

    International Journal of Modern Physics D , keywords =

    The origin of Galactic cosmic rays: Challenges to the standard paradigm. International Journal of Modern Physics D , keywords =. doi:10.1142/S0218271819300222 , archivePrefix =. 1903.11584 , primaryClass =

    1903 arXiv

  30. [38]

    , keywords =

    PAMELA and AMS-02 e ^ + and e ^ - spectra are reproduced by three-dimensional cosmic-ray modeling. , keywords =. doi:10.1103/PhysRevD.89.083007 , archivePrefix =. 1311.5575 , primaryClass =

    arXiv

  31. [39]

    Journal of Plasma Physics , keywords =

    A weak turbulence theory for incompressible magnetohydrodynamics. Journal of Plasma Physics , keywords =. doi:10.1017/S0022377899008284 , archivePrefix =. astro-ph/0008148 , primaryClass =

    arXiv

  32. [40]

    Journal of Plasma Physics , keywords =

    Fast magneto-acoustic wave turbulence and the Iroshnikov-Kraichnan spectrum. Journal of Plasma Physics , keywords =. doi:10.1017/S0022377823000259 , archivePrefix =. 2303.00643 , primaryClass =

    arXiv

  33. [41]

    , keywords =

    On the Existence of Fast Modes in Compressible Magnetohydrodynamic Turbulence. , keywords =. doi:10.3847/1538-4357/ac4d9d , archivePrefix =. 2201.07965 , primaryClass =

    arXiv

  34. [42]

    Journal of Computational Physics , keywords =

    An unsplit Godunov method for ideal MHD via constrained transport. Journal of Computational Physics , keywords =. doi:10.1016/j.jcp.2004.11.016 , archivePrefix =. astro-ph/0501557 , primaryClass =

    2004 arXiv

  35. [43]

    , keywords =

    The Transport of Cosmic Rays across a Turbulent Magnetic Field. , keywords =. doi:10.1086/307452 , adsurl =

    doi

  36. [44]

    The Origin of Cosmic Rays

  37. [45]

    Toward a Theory of Interstellar Turbulence. II. Strong Alfvenic Turbulence. , keywords =. doi:10.1086/175121 , adsurl =

    doi

  38. [46]

    , keywords =

    On the Growth and Saturation of the Gyroresonant Streaming Instabilities. , keywords =. doi:10.3847/1538-4357/ab328a , archivePrefix =. 1811.01951 , primaryClass =

    arXiv

  39. [47]

    , keywords =

    Standard self-confinement and extrinsic turbulence models for cosmic ray transport are fundamentally incompatible with observations. , keywords =. doi:10.1093/mnras/stac2909 , archivePrefix =. 2112.02153 , primaryClass =

    arXiv

  40. [48]

    , keywords =

    Energy Cascade and Damping in Fast-mode Compressible Turbulence. , keywords =. doi:10.3847/2041-8213/ae0c97 , archivePrefix =. 2508.03443 , primaryClass =

  41. [49]

    , year = 1963, month = jan, volume =

    Turbulence of a Conducting Fluid in a Strong Magnetic Field. , year = 1963, month = jan, volume =

    1963

  42. [50]

    Soviet Physics Doklady , year = 1973, month = aug, volume =

    Acoustic Turbulence. Soviet Physics Doklady , year = 1973, month = aug, volume =

    1973

  43. [51]

    , keywords =

    Reconciling cosmic ray transport theory with phenomenological models motivated by Milky-Way data. , keywords =. doi:10.1093/mnras/stac1240 , archivePrefix =. 2109.10977 , primaryClass =

    arXiv

  44. [52]

    , keywords =

    Cosmic ray transport in large-amplitude turbulence with small-scale field reversals. , keywords =. doi:10.1093/mnras/stad2609 , archivePrefix =. 2304.12335 , primaryClass =

    arXiv

  45. [53]

    , keywords =

    Self-similar Cosmic-Ray Transport in High-resolution Magnetohydrodynamic Turbulence. , keywords =. doi:10.3847/2041-8213/ae1ca3 , archivePrefix =. 2507.10651 , primaryClass =

    arXiv

  46. [54]

    , keywords =

    Three-Dimensional Acoustic Turbulence: Weak Versus Strong. , keywords =. doi:10.1103/PhysRevLett.133.207201 , archivePrefix =. 2407.08352 , primaryClass =

    arXiv

  47. [55]

    Akademiia Nauk SSSR Doklady , year = 1941, month = jan, volume =

    The Local Structure of Turbulence in Incompressible Viscous Fluid for Very Large Reynolds' Numbers. Akademiia Nauk SSSR Doklady , year = 1941, month = jan, volume =

    1941

  48. [56]

    Akademiia Nauk SSSR Doklady , year = 1941, month = apr, volume =

    Dissipation of Energy in Locally Isotropic Turbulence. Akademiia Nauk SSSR Doklady , year = 1941, month = apr, volume =

    1941

  49. [57]

    Physics of Fluids , year = 1965, month = jul, volume =

    Inertial-Range Spectrum of Hydromagnetic Turbulence. Physics of Fluids , year = 1965, month = jul, volume =. doi:10.1063/1.1761412 , adsurl =

    1965 doi

  50. [58]

    Physics of Fluids , year = 1967, month = jul, volume =

    Inertial Ranges in Two-Dimensional Turbulence. Physics of Fluids , year = 1967, month = jul, volume =. doi:10.1063/1.1762301 , adsurl =

    1967 doi

  51. [59]

    , year = 1969, month = may, volume =

    The Effect of Wave-Particle Interactions on the Propagation of Cosmic Rays. , year = 1969, month = may, volume =. doi:10.1086/149981 , adsurl =

    1969 doi

  52. [60]

    , keywords =

    Diffusion of Cosmic Rays in MHD Turbulence with Magnetic Mirrors. , keywords =. doi:10.3847/1538-4357/ac2de9 , archivePrefix =. 2106.08362 , primaryClass =

    arXiv

  53. [61]

    Journal of Plasma Physics , keywords =

    Particle transport through localized interactions with sharp magnetic field bends in MHD turbulence. Journal of Plasma Physics , keywords =. doi:10.1017/S0022377823000946 , archivePrefix =. 2304.03023 , primaryClass =

    arXiv

  54. [62]

    , keywords =

    Compressible Magnetohydrodynamic Turbulence in Interstellar Plasmas. , keywords =. doi:10.1086/323470 , archivePrefix =. astro-ph/0106425 , primaryClass =

    arXiv

  55. [63]

    Journal of Computational Physics , keywords =

    On the divergence-free condition in Godunov-type schemes for ideal magnetohydrodynamics: the upwind constrained transport method. Journal of Computational Physics , keywords =. doi:10.1016/j.jcp.2003.09.016 , archivePrefix =. astro-ph/0310183 , primaryClass =

    2003 arXiv

  56. [64]

    , volume =

    Role of Magnetic Reconnection in Magnetohydrodynamic Turbulence , author =. , volume =. 2017 , month =. doi:10.1103/PhysRevLett.118.245101 , url =

    2017 doi

  57. [65]

    arXiv e-prints , keywords =

    Anisotropic Cosmic Ray Transport in strong MHD Turbulence due to Magnetic Mirroring and Resonant Curvature Scattering. arXiv e-prints , keywords =. doi:10.48550/arXiv.2509.15320 , archivePrefix =. 2509.15320 , primaryClass =

    doi

  58. [66]

    Journal of Plasma Physics , keywords =

    Self-organization in collisionless, high- turbulence. Journal of Plasma Physics , keywords =. doi:10.1017/S0022377824001296 , archivePrefix =. 2405.02418 , primaryClass =

    arXiv

  59. [67]

    Physical Review X , keywords =

    Properties of Magnetohydrodynamic Modes in Compressively Driven Plasma Turbulence. Physical Review X , keywords =. doi:10.1103/PhysRevX.10.031021 , archivePrefix =. 1907.01853 , primaryClass =

    1907 arXiv

  60. [68]

    , year = 2017, month = jul, volume = 468, pages =

    Disruption of sheet-like structures in Alfv \'e nic turbulence by magnetic reconnection. , year = 2017, month = jul, volume = 468, pages =. doi:10.1093/mnras/stx670 , adsurl =

    2017 doi

  61. [69]

    , keywords =

    Simulations of Incompressible Magnetohydrodynamic Turbulence. , keywords =. doi:10.1086/321413 , archivePrefix =. astro-ph/0012491 , primaryClass =

    arXiv

  62. [70]

    , keywords =

    Dynamic Alignment in Driven Magnetohydrodynamic Turbulence. , keywords =. doi:10.1103/PhysRevLett.97.255002 , archivePrefix =. astro-ph/0602382 , primaryClass =

    arXiv

  63. [71]

    The Journal of Open Source Software , keywords =

    PyPLUTO: a data analysis Python package for the PLUTO code. The Journal of Open Source Software , keywords =. doi:10.21105/joss.08448 , archivePrefix =. 2501.09748 , primaryClass =

  64. [72]

    , keywords =

    PLUTO: A Numerical Code for Computational Astrophysics. , keywords =. doi:10.1086/513316 , archivePrefix =. astro-ph/0701854 , primaryClass =

    arXiv

  65. [73]

    Journal of Computational Physics , keywords =

    High-order conservative finite difference GLM-MHD schemes for cell-centered MHD. Journal of Computational Physics , keywords =. doi:10.1016/j.jcp.2010.04.013 , archivePrefix =. 1001.2832 , primaryClass =

    2010 arXiv

  66. [74]

    , keywords =

    The PLUTO Code for Adaptive Mesh Computations in Astrophysical Fluid Dynamics. , keywords =. doi:10.1088/0067-0049/198/1/7 , archivePrefix =. 1110.0740 , primaryClass =

    arXiv

  67. [75]

    Journal of Computational Physics , keywords =

    Systematic construction of upwind constrained transport schemes for MHD. Journal of Computational Physics , keywords =. doi:10.1016/j.jcp.2020.109748 , archivePrefix =. 2004.10542 , primaryClass =

    2020

  68. [76]

    Journal of Computational Physics , year = 2005, month = sep, volume =

    A multi-state HLL approximate Riemann solver for ideal magnetohydrodynamics. Journal of Computational Physics , year = 2005, month = sep, volume =. doi:10.1016/j.jcp.2005.02.017 , adsurl =

    2005 doi

  69. [77]

    Physics of Plasmas , year = 1997, month = mar, volume =

    Scaling of anisotropic spectra due to the weak interaction of shear-Alfv \'e n wave packets. Physics of Plasmas , year = 1997, month = mar, volume =. doi:10.1063/1.872158 , adsurl =

    1997 doi

  70. [78]

    , keywords =

    Strong turbulence and magnetic coherent structures in the interstellar medium. , keywords =. doi:10.1051/0004-6361/202450710 , archivePrefix =. 2409.16699 , primaryClass =

    arXiv

  71. [79]

    Physics of Plasmas , keywords =

    Scaling of spectral anisotropy with magnetic field strength in decaying magnetohydrodynamic turbulence. Physics of Plasmas , keywords =. doi:10.1063/1.873159 , adsurl =

    doi

  72. [80]

    , keywords =

    Critical Balance and the Physics of Magnetohydrodynamic Turbulence. , keywords =. doi:10.3847/1538-4357/ab8f2a , archivePrefix =. 2006.04677 , primaryClass =

    2006 arXiv

  73. [81]

    Galaxies , keywords =

    Cosmic Ray Processes in Galactic Ecosystems. Galaxies , keywords =. doi:10.3390/galaxies11040086 , archivePrefix =. 2306.09924 , primaryClass =

    arXiv

  74. [82]

    , keywords =

    Relativistic Particle Transport and Acceleration in Structured Plasma Turbulence. , keywords =. doi:10.3847/1538-4357/ac5332 , archivePrefix =. 2112.09555 , primaryClass =

    arXiv

  75. [83]

    , keywords =

    Test Particle Energization of Heavy Ions in Magnetohydrodynamic Turbulence. , keywords =. doi:10.3847/1538-4357/ac5abe , archivePrefix =. 2112.09603 , primaryClass =

    arXiv

  76. [84]

    Journal of Physics Conference Series , year = 2006, series =

    Cosmic ray transport in the Galaxy. Journal of Physics Conference Series , year = 2006, series =. doi:10.1088/1742-6596/47/1/014 , adsurl =

    2006 doi

  77. [85]

    , keywords =

    Turbulence and Particle Heating in Advection-dominated Accretion Flows. , keywords =. doi:10.1086/307423 , archivePrefix =. astro-ph/9803112 , primaryClass =

    arXiv

  78. [86]

    Nature Astronomy , keywords =

    Efficient micromirror confinement of sub-teraelectronvolt cosmic rays in galaxy clusters. Nature Astronomy , keywords =. doi:10.1038/s41550-024-02442-1 , archivePrefix =. 2311.01497 , primaryClass =

    arXiv

  79. [87]

    , keywords =

    Global Simulations of Galactic Winds Including Cosmic-ray Streaming. , keywords =. doi:10.3847/1538-4357/834/2/208 , archivePrefix =. 1602.04856 , primaryClass =

    arXiv

  80. [88]

    , keywords =

    Cosmic ray feedback in galaxies and galaxy clusters. , keywords =. doi:10.1007/s00159-023-00149-2 , archivePrefix =. 2306.03141 , primaryClass =

    arXiv

  81. [89]

    , keywords =

    Turbulent diffusion of streaming cosmic rays in compressible, partially ionized plasma. , keywords =. doi:10.1093/mnras/stac3207 , archivePrefix =. 2205.08174 , primaryClass =

    arXiv

  82. [90]

    , keywords =

    Simulations of the Small-Scale Turbulent Dynamo. , keywords =. doi:10.1086/422547 , archivePrefix =. astro-ph/0312046 , primaryClass =

    arXiv

  83. [91]

    Physics of Plasmas , keywords =

    Turbulence, magnetic fields, and plasma physics in clusters of galaxies. Physics of Plasmas , keywords =. doi:10.1063/1.2179053 , archivePrefix =. astro-ph/0601246 , primaryClass =

    arXiv

  84. [92]

    Journal of Plasma Physics , keywords =

    MHD turbulence: a biased review. Journal of Plasma Physics , keywords =. doi:10.1017/S0022377822000721 , archivePrefix =. 2010.00699 , primaryClass =

    2010 arXiv

  85. [93]

    , keywords =

    Analytical description of nonlinear cosmic ray scattering: isotropic and quasilinear regimes of pitch-angle diffusion. , keywords =. doi:10.1051/0004-6361/200912755 , adsurl =

    doi

  86. [94]

    , keywords =

    Cosmic-Ray Lifetime in the Galaxy - Experimental Results and Models. , keywords =. doi:10.1007/BF00212240 , adsurl =

    doi

  87. [95]

    , keywords =

    Global diffusion of cosmic rays in random magnetic fields. , keywords =. doi:10.1093/mnras/stw217 , archivePrefix =. 1509.03766 , primaryClass =

    arXiv

  88. [96]

    , keywords =

    Cascading of Fast-Mode Balanced and Imbalanced Turbulence. , keywords =. doi:10.1086/513864 , archivePrefix =. astro-ph/0608307 , primaryClass =

    arXiv

  89. [97]

    , keywords =

    Cosmic-ray hydrodynamics: Alfv \'e n-wave regulated transport of cosmic rays. , keywords =. doi:10.1093/mnras/stz263 , archivePrefix =. 1805.11092 , primaryClass =

    arXiv

  90. [98]

    arXiv e-prints , keywords =

    Fast Magnetosonic Turbulence in Two-Dimensional Relativistic Plasmas. arXiv e-prints , keywords =. doi:10.48550/arXiv.2604.04276 , archivePrefix =. 2604.04276 , primaryClass =

    doi arXiv

  91. [99]

    Physics of Plasmas , keywords =

    Formation and evolution of coherent structures in 3D strongly turbulent magnetized plasmas. Physics of Plasmas , keywords =. doi:10.1063/5.0141512 , archivePrefix =. 2303.15351 , primaryClass =

    arXiv

  92. [100]

    , keywords =

    Cosmic-Ray Parallel and Perpendicular Transport in Turbulent Magnetic Fields. , keywords =. doi:10.1088/0004-637X/779/2/140 , archivePrefix =. 1307.1346 , primaryClass =

    arXiv

  93. [101]

    , keywords =

    Cosmic-Ray Scattering and Streaming in Compressible Magnetohydrodynamic Turbulence. , keywords =. doi:10.1086/423733 , archivePrefix =. astro-ph/0408172 , primaryClass =

    arXiv

  94. [102]

    , keywords =

    Cosmic-Ray Propagation: Nonlinear Diffusion Parallel and Perpendicular to Mean Magnetic Field. , keywords =. doi:10.1086/524771 , archivePrefix =. 0710.2617 , primaryClass =

    arXiv

  95. [103]

    Physics of Plasmas , keywords =

    Role of magnetic field curvature in magnetohydrodynamic turbulence. Physics of Plasmas , keywords =. doi:10.1063/1.5099360 , archivePrefix =. 1904.08284 , primaryClass =

    1904 arXiv

  96. [104]

    , keywords =

    Curvature of Magnetic Field Lines in Compressible Magnetized Turbulence: Statistics, Magnetization Predictions, Gradient Curvature, Modes, and Self-gravitating Media. , keywords =. doi:10.3847/1538-4357/ab9360 , archivePrefix =. 2002.01926 , primaryClass =

    2002 arXiv

  97. [105]

    Soviet Physics Doklady , year = 1970, month = nov, volume =

    Spectrum of Acoustic Turbulence. Soviet Physics Doklady , year = 1970, month = nov, volume =

    1970

  98. [106]

    , keywords =

    Numerical Testing of Mirror Diffusion of Cosmic Rays. , keywords =. doi:10.3847/2041-8213/ad0fe5 , archivePrefix =. 2311.18001 , primaryClass =

    arXiv

  99. [107]

    , keywords =

    Multispacecraft Analysis of the Properties of Magnetohydrodynamic Fluctuations in Sub-Alfv \'e nic Solar Wind Turbulence at 1 au. , keywords =. doi:10.3847/1538-4357/ac822e , archivePrefix =. 2204.05410 , primaryClass =

    arXiv

  100. [108]

    Physics of Plasmas , year = 2017, month = may, volume =

    The basis for cosmic ray feedback: Written on the wind. Physics of Plasmas , year = 2017, month = may, volume =. doi:10.1063/1.4984017 , adsurl =

    2017 doi

  101. [109]

    N.,& Stewart, J

    Cox, A. N.,& Stewart, J. N. 1969,

    1969

  102. [110]

    Tscharnuter W. M. 1987,

    1987

  103. [111]

    1992, in ASP Conf

    Terlevich, R. 1992, in ASP Conf. Ser. 31,

    1992

  104. [112]

    F., Tytler, D

    Zheng, W., Davidsen, A. F., Tytler, D. & Kriss, G. A

Pith tools

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