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Solar-Cycle Modulation and Photospheric Magnetic Control of Turbulence in the Young Solar Wind

T0 review · 5 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read Magnetic topology on the Sun sets turbulence in the young solar wind.

desk verdict A solid PSP-based demonstration of solar-cycle turbulence trends, whose source-control interpretation outruns the evidence. read the letter →

arxiv 2608.11438 v1 pith:O4437AA6 submitted 2026-08-11 astro-ph.SR physics.space-ph

Yanwen Wang , Rohit Chhiber , Arcadi V. Usmanov , Marc Swisdak , William H. Matthaeus This is my paper · ORCID
classification astro-ph.SRphysics.space-ph
keywords solarwindturbulenceParkerProbecyclecoronalholescrosshelicitymagneticconnectivityglobalMHDmodelvonKármánenergytransferrate
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 argues that the magnetic topology of the Sun's surface, not just processes inside the heliosphere, sets the turbulence level of the young solar wind. Using 25 Parker Solar Probe orbits from 2018 to 2025, it shows that fluctuation energy, the velocity–magnetic correlation known as cross helicity, and the turbulent energy-transfer rate all increase with sunspot number, and that the wind stays highly Alfvénic out to 0.5 AU at solar maximum while losing that character quickly at minimum. Tracing each measured wind parcel back to its solar footpoint with a global MHD model, the authors find that the most turbulent, most Alfvénic streams come from the interiors of unipolar coronal holes, while the least turbulent streams come from multipolar active-region environments. If true, this means solar-cycle changes in source-region structure directly control the heating and acceleration of the inner heliosphere.

What carries the argument

The load-bearing mechanism is the combination of in-situ turbulence diagnostics with magnetic connectivity tracing: each 2-hour PSP interval is assigned a photospheric footpoint by integrating the model magnetic field line sunward in the global MHD simulation, and turbulence is then compared across footpoint environments seen in EUV synoptic maps and photospheric magnetograms. The central organizing quantity is the detrended turbulence amplitude $R_{Z2} = Z^2/Z^2_{\rm fit}(r)$, together with the equivalent cross-helicity residual $\Delta\sigma_c$; these remove the strong radial decay of $Z^2$ and $\sigma_c$ so that intervals at different heliocentric distances can be compared. The energy-transfer estimate $\varepsilon_{VK} = f(\sigma_c) Z^3/\lambda$ ties the observed fluctuation energy to a heating rate, where $f(\sigma_c)$ accounts for the suppression of nonlinear interactions in highly Alfvénic flow. The topological distinction that carries the argument is unipolar (coronal-hole) versus multipolar (active-region) photospheric magnetic structure.

What would settle it

Repeat the connectivity analysis for a different solar-maximum Carrington rotation (or for all 25 orbits) and check whether the upper-20% $R_{Z2}$ intervals still map to unipolar coronal-hole interiors and the lower-20% to multipolar active-region environments; if a high-turbulence interval is found rooted in a multipolar region, or a low-turbulence interval in a coronal-hole interior, the source-topology control claim would fail. A complementary test: compare turbulence properties of two intervals at the same radius and wind speed but from opposite source topologies; under the paper's claim they should still differ in $Z^2$ and $\sigma_c$, whereas under pure local-evolution control they would be similar.

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Extended reading notes

Core claim

The paper's central claim is that the observed solar-cycle modulation of turbulence in the inner heliosphere is a direct consequence of solar source magnetic structure. In Parker Solar Probe data from orbits 1–25 (2018–2025), intervals at high sunspot number show enhanced turbulent energy density $Z^2$, sector-rectified cross helicity $\sigma_c$ (a measure of how correlated the velocity and magnetic fluctuations are, i.e., Alfvénicity), and the von Kármán energy transfer rate $\varepsilon_{VK} = f(\sigma_c) Z^3/\lambda$, while the radial profile of $\sigma_c$ stays highly imbalanced out to 0.5 AU during solar maximum but decays steeply during minimum. The authors connect each 2-hour PSP interval to a photospheric footpoint by tracing magnetic field lines in a global MHD model, and classify intervals by the detrended amplitude $R_{Z2} = Z^2/Z^2_{\rm fit}(r)$ and the cross-helicity residual $\Delta\sigma_c = \sigma_c - \sigma_{c,\rm fit}(r)$. The result is a sharp source-topology dependence: upper-20% turbulence intervals cluster inside unipolar coronal holes, lower-20% intervals cluster in multipolar active-region environments, and the footpoint magnetic-field strength itself does not order the subsets.

Load-bearing premise

The conclusion that photospheric source topology controls young-solar-wind turbulence rests on treating two Parker Solar Probe encounters — E6 near solar minimum and E22 near solar maximum — as representative of the source structure sampled across all 25 orbits, and on the global MHD model's field-line tracing identifying the true solar footpoints; the PFSS check shows individual footpoints can differ, so the association is statistical.

Editorial extensions

If this is right

  • Solar-cycle trends in turbulence previously measured at 1 AU are already present in the young solar wind between 0.15 and 0.5 AU, so the processes that set them act close to the Sun.
  • The photospheric magnetic topology, not the field strength at the footpoint, is the controlling factor: high-turbulence, highly Alfvénic wind comes from unipolar coronal holes, and low-turbulence wind from multipolar active regions.
  • During solar maximum the modeled turbulence-energy maximum shifts outward and closer to the Alfvén surface, so the region where turbulent heating is deposited moves outward in the cycle.
  • The equatorward extension of coronal holes at solar maximum raises the filling fraction of coronal-hole-sourced wind in the ecliptic, which can account for the observed enhancement of $Z^2$ and $\sigma_c$ without requiring a change in the turbulence physics itself.
  • Interfaces between streams from different source regions show enhanced radial speed and $R_{Z2}$, suggesting that shear-driven turbulence generation at such boundaries adds heating localized at stream interfaces.

Reading between the lines

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

  • If source topology is the controlling factor, then turbulence properties at a given heliocentric distance should be predictable from synoptic magnetograms alone; this is a testable forecast that could be checked against PSP or Solar Orbiter data without relying on the MHD model.
  • The statistical claim rests on two representative Carrington rotations (E6 and E22); a natural extension is to repeat the connectivity analysis for all 25 orbits, converting the two-encounter comparison into a robust cycle-wide distribution.
  • The association of low turbulence with multipolar active-region environments suggests that flux tubes rooted in closed-field or mixed-polarity regions are seeded with weaker and less Alfvénic fluctuations; this may connect to a deficit in cosmic-ray diffusion over such regions, though the paper does not make that link.
  • The finding that the energy-transfer rate increases with activity despite the Alfvénic suppression factor $f(\sigma_c)$ implies that the fluctuation-energy increase overcompensates, quantifying how much extra turbulent heating the inner heliosphere receives at solar maximum.
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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

5 major / 5 minor

Summary. The paper analyzes Parker Solar Probe data from its first 25 orbits (2018-2025) together with global MHD model connectivity tracing, SDO/AIA EUV synoptic maps, and photospheric magnetograms to claim that solar-cycle variations in the young solar wind's turbulence are controlled by the magnetic topology of the solar source regions. The authors find that, for heliocentric distances 0.15-0.5 AU, intervals with high sunspot number show enhanced fluctuation energy Z^2, enhanced sector-rectified cross helicity sigma_c, enhanced von Karman energy transfer rate epsilon_VK, and a less steep radial decay of sigma_c compared with low-SSN intervals. They then examine two representative PSP encounters (E6 near solar minimum and E22 near solar maximum) and, by tracing PSP-connected field lines to the photosphere, report that upper-quartile R_Z2 and Delta_sigma_c intervals tend to originate from unipolar coronal-hole interiors, while lower-quartile intervals tend to originate from multipolar active-region environments. The modeled Z^2 along the traced flux tubes peaks in the sub-Alfvenic corona, with a broader and more outward-displaced maximum during high solar activity.

Significance. If the source-control result holds, the paper would provide an important new constraint on the longstanding 'solar origin versus local evolution' debate: it would show that photospheric magnetic topology, not merely local dynamical evolution, sets the turbulence state of the inner heliosphere. The empirical SSN-binned analysis is a strength: it uses a large PSP dataset, the Appendix gives complete definitions of all diagnostics, and the authors report explicit robustness checks (median SSN binning and interval-level statistics). The connectivity analysis is also supplemented by a PFSS check, which is a useful independent diagnostic even though it is not quantified. The core empirical claim that solar-cycle trends seen at 1 AU are already established at 0.15-0.5 AU is well supported by the figures and robustness checks. The headline source-topology conclusion, however, currently rests on a qualitative and statistically unquantified analysis of two Carrington rotations, and it is this gap that prevents the paper from being fully persuasive.

major comments (5)
  1. [Coronal and Photospheric Influence on Young Solar-Wind Turbulence; Figs. 2, 3, 4, 6] The central source-control conclusion rests on exactly two Carrington rotations (E6/CR2235 and E22/CR2293) and on a visual classification of footpoints into 'unipolar coronal hole' versus 'multipolar active-region environment.' The abstract and Discussion generalize this to the whole solar cycle. For a load-bearing claim, the authors should either analyze additional PSP encounters spanning a range of SSN or, at minimum, provide a quantitative topology metric (e.g., flux imbalance, polarity-inversion-line distance, or magnetic-skeleton complexity) computed from the photospheric B_R maps, together with a formal two-sample test comparing the upper and lower R_Z2 and Delta_sigma_c subsets. The Appendix's statement that the PFSS/global-MHD association is 'interpreted statistically' promises a statistic that is never actually reported; this needs to be supplied.
  2. [Radial detrending and definition of turbulence and Alfvenicity subsets; Eqs. (8)-(11)] The R_Z2 and Delta_sigma_c classifications are defined by power-law and logarithmic radial fits whose parameters, uncertainties, and residuals are not reported. The E22 contrast R_Z2 =~0.3 versus =~3 could partly reflect a poor or activity-dependent fit rather than source physics. Please report A, alpha, c0, c1 and their uncertainties for both activity ranges, show residual distributions, and demonstrate that the high/low subset classification is stable to alternative detrending choices (e.g., median-binned radial trends or separate fits on independent radial sub-ranges).
  3. [Solar-Cycle Variations in the Young Solar Wind; Fig. 1] The high-SSN/low-SSN comparisons in Fig. 1 are not protected against ICME contamination. ICMEs are most frequent near solar maximum and can enhance Z^2, alter sigma_c, and reduce proton density independently of the source-topology mechanism emphasized later. The authors should either exclude intervals containing ICME signatures (using standard magnetic-field and plasma criteria) or show that the Figure 1 trends and the R_Z2 source associations are unchanged after such exclusion.
  4. [Coronal and Photospheric Influence on Young Solar-Wind Turbulence; Fig. 4] During E22 the high- and low-R_Z2 subsets are temporally sequential (CH interior -> AR complex -> CH edge) as the modeled connection moves monotonically across the source region. The clustering of footpoints in Figs. 2(b) and 3(b) may therefore be dominated by the long autocorrelation time of the solar wind rather than by an independent statistical association per 2-hr interval. Please report the effective number of independent samples (estimated from autocorrelation times) and perform a block-bootstrap or permutation test that preserves temporal ordering when testing whether high/low subsets are preferentially connected to distinct source types.
  5. [Coronal and Photospheric Influence on Young Solar-Wind Turbulence; Fig. 6 and adjacent text] The claim that 'the high and low turbulence-amplitude intervals are not simply ordered by the footpoint magnetic-field strength' is based on overlapping B_R distributions that are not displayed and on no test statistic. Since the abstract and Discussion attribute control to magnetic topology rather than field strength, this negative claim should be quantified (e.g., with median B_R, interquartile ranges, and a two-sample test per encounter) and should be accompanied by the quantitative topology metric requested above.
minor comments (5)
  1. [Radial detrending; Eq. (10)] Equation (10) restricts sigma_c,fit to [-1,1], but the text does not state how this restriction is implemented (clipping after the fit, or a constrained fit); please specify.
  2. [Fig. 1] The colorbar for the sunspot-number color scale is missing from the reproduced figure; please add it so the reader can interpret the bin colors.
  3. [Radial detrending; Eq. (8)] The 'geometric-mean radius r0' is defined in words but its actual value for each fit is not reported; please give r0 and the number of intervals entering each fit.
  4. [Abstract and Discussion] The term 'solar cycle' is used for a 7-year interval that covers only one ascending phase; consider a qualifier such as 'the rising phase of Cycle 25' to avoid overclaiming from a single partial cycle.
  5. [Modeled Evolution of Turbulent Fluctuations through the Corona; Fig. 5] The text states that observed and modeled Z^2 'occupy the same broad range' but no quantitative comparison (e.g., median ratio, RMS error, or correlation) is given; adding one would strengthen the claim of agreement.

Circularity Check

0 steps flagged · score 2.0 of 10

No circularity found: the solar-cycle trends are direct PSP/SILSO statistics and the source-topology association is an independent two-sample comparison, with self-citations only for model validation.

full rationale

No circular step is identified. The solar-cycle trends in Figure 1 are computed directly from PSP/SWEAP and FIELDS observations binned against SILSO daily sunspot numbers, using standard definitions in the Appendix for Z^2, sigma_c, sigma_D, lambda, and epsilon_VK. The source-control claim is not definitionally linked to these in-situ quantities: the R_Z2 and Delta_sigma_c subsets are formed from radial residuals of PSP data, while the footpoint classification comes from the global MHD solution with GONG/ADAPT magnetogram boundary conditions, SDO/AIA 193 Angstrom synoptic maps, and a PFSS cross-check. The paper states that the two MHD runs differ only in the boundary magnetogram and use identical coronal-base turbulence parameters, so the model does not inject the source dependence it is used to discover. Self-citations appear for the Usmanov et al. model, prior PSP-model comparisons, and the f(sigma_c) closure, but the central association is also checked externally by EUV dark-region coincidence and by the PFSS robustness test. The acknowledged PFSS footpoint differences ('we therefore interpret the association ... statistically, rather than as an exact footpoint identification') and the reliance on two Carrington rotations (E6 and E22) are limitations of precision and representativeness, not circular reductions. Because no fit parameter is renamed as a prediction and no equation reduces to its own input, the derivation chain is self-contained; the score of 2 reflects only the presence of non-load-bearing self-citations.

Assumptions & free parameters 8 free parameters · 6 assumptions · 0 invented entities

The central statistical claims rest on standard turbulence diagnostics whose formulas are given, on the validity of Taylor's hypothesis (restricted to r>=0.15 AU), and on the assumption that a single von Karman closure with a constant dimensionless coefficient describes the cross-helicity-dependent energy transfer. The source-region claim rests on the accuracy of the global MHD connectivity mapping and on the representativeness of two Carrington rotations. Free parameters include the radial detrending fits (A, alpha, c0, c1), the hand-chosen SSN thresholds and 20% quantile cut, the coronal-base turbulence parameters inherited from prior model development, and the unstated assumption that solar-maximum statistics are not contaminated by ICMEs, which were not excluded.

free parameters (8)
  • Z2 radial fit amplitude A = Not reported
    Z2_fit(r) = A (r/r0)^(-alpha), fitted separately to the low- and high-activity PSP samples; defines the detrended ratio R_Z2 and the high/low turbulence subsets (Appendix, 'Radial detrending').
  • Z2 radial fit exponent alpha = Not reported
    Same fit as above; the value changes the residual classification and therefore the source-region subsets.
  • sigma_c radial fit intercept c0 = Not reported
    sigma_c_fit(r) = c0 + c1 ln(r/r0); defines Delta_sigma_c and the high/low wave-like character subsets (Appendix).
  • sigma_c radial fit slope c1 = Not reported
    Same fit; governs how fast the expected sigma_c declines with radius.
  • SSN thresholds 75 and 80 = 75 (low), 80 (high)
    Hand-chosen cutoffs for the low- and high-activity radial trends in Fig. 1; robustness checks with median SSN are reported, but the cutoffs themselves are not derived.
  • High/low subset quantile = 20%
    The upper and lower 20% of R_Z2 and Delta_sigma_c define the source-region subsets in Figs. 2-4; changing the percentile changes the sampled footpoint populations.
  • Coronal-base turbulence parameters in the MHD model = Not reported; set in Ref. [11]
    Both simulation runs reuse the same boundary turbulence parameters and closures from the authors' prior model; the modeled Z2 evolution and its maximum location depend on these inherited values.
  • Dimensionless von Karman decay coefficient = Unassigned
    The paper drops the numeric coefficient in epsilon_VK and assumes it is constant with solar activity; if it varies, the solar-min/max comparison of energy transfer rates is affected (Appendix).
assumptions (6)
  • domain assumption Taylor's frozen-in-flow hypothesis is valid between 0.15 and 0.5 AU for converting temporal correlations to spatial scales.
    Used to compute lambda = V t_corr; the paper restricts the analysis to r >= 0.15 AU because of this hypothesis (Appendix).
  • domain assumption A single-scale von Karman phenomenology with lambda+ = lambda- = lambda and constant dimensionless coefficient describes the turbulence energy transfer.
    Underlies epsilon_VK = f(sigma_c) Z^3/lambda and the cross-helicity correction f(sigma_c) (Appendix).
  • domain assumption The global MHD model with GONG/ADAPT synoptic-map boundary conditions provides correct large-scale magnetic connectivity from the corona to 0.5 AU.
    Field-line tracing from PSP to the coronal base depends on the model solution; the PFSS comparison shows only broad agreement of individual footpoints (Appendix).
  • domain assumption Daily sunspot number is a valid index of the solar-activity state that set the solar wind sampled by PSP.
    SSN is the activity reference for all 25 orbits in Fig. 1 and for separating low/high-activity fits.
  • ad hoc to paper CR 2235 (E6) and CR 2293 (E22) are representative of solar-minimum and solar-maximum source configurations.
    The source-region conclusion is generalized from these two chosen encounters; no multi-rotation sampling is used.
  • domain assumption Solar-maximum turbulence statistics are not materially affected by ICMEs.
    No ICME identification or exclusion is described, although ICME frequency is high at solar maximum and ICMEs can elevate B and Z^2.

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Pith. "Pith review of Solar-Cycle Modulation and Photospheric Magnetic Control of Turbulence in the Young Solar Wind." pith.science (2026). https://pith.science/paper/O4437AA6

@misc{pith2026260811438,
  author       = {Pith},
  title        = {Pith review of: Solar-Cycle Modulation and Photospheric Magnetic Control of Turbulence in the Young Solar Wind},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/O4437AA6}},
  note         = {Machine review of arXiv:2608.11438}
}
read the original abstract

The solar wind is an outflow of solar plasma that expands from the corona to fill the heliosphere. Its turbulence provides a pathway for non-adiabatic heating and acceleration, and is therefore central to understanding the thermodynamic and magnetohydrodynamic (MHD) evolution of the young solar wind. However, the variation of its turbulence properties over the solar activity cycle and the connection of these properties to solar source regions remains incompletely understood. Here we analyze observations from 25 solar orbits of NASA's Parker Solar Probe (PSP) mission, in combination with a global MHD model, photospheric magnetograms, and extreme ultraviolet maps of the low corona, to investigate the solar-cycle dependence and the solar sources of turbulence in the very inner heliosphere. The observations reveal pronounced solar-activity variation in fluctuation amplitude, cross helicity, and related turbulence properties. By tracing PSP-connected magnetic flux tubes to their solar sources, we demonstrate that high turbulent-energy intervals are preferentially connected to coronal-hole sources with unipolar magnetic topology, whereas low turbulent-energy intervals are associated with multipolar topology and active-region environments. Our study combines in-situ measurements with numerical modeling and remote sensing observations to reveal how solar-cycle-dependent source structure determines turbulence variability and plasma heating in the young solar wind.

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Works this paper leans on

85 extracted references · 79 canonical work pages

  1. [1]

    H., Zank, G

    Matthaeus, W. H., Zank, G. P., Smith, C. W. & Oughton, S. Turbulence, Spatial Trans- port, and Heating of the Solar Wind.Physical Review Letters82, 3444–3447 (1999). 13

    1999

  2. [2]

    & Carbone, V

    Bruno, R. & Carbone, V. The Solar Wind as a Turbulence Laboratory.Living Reviews in Solar Physics10, 2 (2013)

    2013

  3. [3]

    Verscharen, D., Klein, K. G. & Maruca, B. A. The multi-scale nature of the solar wind. Living Reviews in Solar Physics16, 5 (2019)

    2019

  4. [4]

    & Sahraoui, F

    Goldstein, M., Wicks, R., Perri, S. & Sahraoui, F. Kinetic scale turbulence and dis- sipation in the solar wind: key observational results and future outlook.Philosophical Transactions of the Royal Society A: Math- ematical, Physical and Engineering Sciences 373(2015)

    2015

  5. [5]

    ApJS246, 48 (2020)

    Bandyopadhyay, R.et al.Enhanced Energy Transfer Rate in Solar Wind Turbulence Observed near the Sun from Parker Solar Probe. ApJS246, 48 (2020)

    2020

  6. [6]

    J., Smith, C

    Vasquez, B. J., Smith, C. W., Hamilton, K., MacBride, B. T. & Leamon, R. J. Evaluation of the turbulent energy cascade rates from the upper inertial range in the solar wind at 1 AU.Journal of Geophysical Research (Space Physics)112, A07101 (2007)

    work page 2007

  7. [7]

    Marino, R.et al.Heating the solar wind by a magnetohydrodynamic turbulent energy cas- cade.The Astrophysical Journal Letters677, L71–L74 (2008)

    work page 2008

  8. [8]

    T., Smith, C

    MacBride, B. T., Smith, C. W. & Forman, M. A. The Turbulent Cascade at 1 AU: Energy Transfer and the Third-Order Scaling for MHD. ApJ679, 1644–1660 (2008)

    work page 2008

Show all 85 references
  1. [9]

    V., Goldstein, M

    Usmanov, A. V., Goldstein, M. L., Besser, B. P. & Fritzer, J. M. A global MHD solar wind model with WKB Alfv´ en waves: Com- parison with Ulysses data. J. Geophys. Res. 105, 12675–12696 (2000)

    2000

  2. [10]

    J.et al.In situ observations of large-amplitude Alfv´ en waves heating and accelerating the solar wind.Science385, 962–966 (2024)

    Rivera, Y. J.et al.In situ observations of large-amplitude Alfv´ en waves heating and accelerating the solar wind.Science385, 962–966 (2024)

    2024

  3. [11]

    V., Chhiber, R., Matthaeus, W

    Usmanov, A. V., Chhiber, R., Matthaeus, W. H., Roy, S. & Goldstein, M. L. A Unified Three-dimensional Magnetohydrody- namic Model of the Solar Corona, Solar Wind, and Global Heliosphere with Turbu- lence Transport. ApJ993, 87 (2025)

    2025

  4. [12]

    E.et al.Theory of Cosmic Ray Transport in the Heliosphere

    Engelbrecht, N. E.et al.Theory of Cosmic Ray Transport in the Heliosphere. Space Sci. Rev.218, 33 (2022)

    2022

  5. [13]

    Solar wind sources and their variations over the solar cycle.Space Science Reviews124, 51–76 (2006)

    Schwenn, R. Solar wind sources and their variations over the solar cycle.Space Science Reviews124, 51–76 (2006)

    2006

  6. [14]

    J.et al.Solar wind obser- vations over Ulysses’ first full polar orbit

    McComas, D. J.et al.Solar wind obser- vations over Ulysses’ first full polar orbit. J. Geophys. Res.105, 10419–10434 (2000)

    2000

  7. [15]

    J.et al.The three-dimensional solar wind around solar maximum

    McComas, D. J.et al.The three-dimensional solar wind around solar maximum. Geo- phys. Res. Lett.30, 1517 (2003)

    2003

  8. [16]

    & Gosling, J

    Ebert, R., McComas, D., Elliott, H., Forsyth, R. & Gosling, J. Bulk properties of the slow and fast solar wind and interplanetary coronal mass ejections measured by ulysses: Three polar orbits of observations.Journal of Geophysical Research: Space Physics114 (2009)

    2009

  9. [17]

    Solar cycle variations of the solar wind.JPL Solar Wind Five(1983)

    Crooker, N. Solar cycle variations of the solar wind.JPL Solar Wind Five(1983)

    1983

  10. [18]

    P., Hu, Q

    Zhao, L.-L., Adhikari, L., Zank, G. P., Hu, Q. & Feng, X. S. Influence of the Solar Cycle on Turbulence Properties and Cosmic-Ray Diffusion. ApJ856, 94 (2018)

    2018

  11. [19]

    On the relative constancy of the solar wind mass flux at 1 au.The Astrophys- ical Journal Letters715, L121–L127 (2010)

    Wang, Y.-M. On the relative constancy of the solar wind mass flux at 1 au.The Astrophys- ical Journal Letters715, L121–L127 (2010)

    2010

  12. [20]

    & Meyer-Vernet, N

    Le Chat, G., Issautier, K. & Meyer-Vernet, N. The solar wind energy flux.Solar Physics 279, 197–205 (2012)

    2012

  13. [21]

    C., Hnat, B

    Chapman, S. C., Hnat, B. & Kiyani, K. Solar cycle dependence of scaling in solar wind fluc- tuations.Nonlinear Processes in Geophysics 15, 445–455 (2008)

    2008

  14. [22]

    Three-dimensional evolution of solar wind during solar cycles 22–24.The 14 Astrophysical Journal751, 128 (2012)

    Manoharan, P. Three-dimensional evolution of solar wind during solar cycles 22–24.The 14 Astrophysical Journal751, 128 (2012)

    2012

  15. [23]

    P., Adhikari, L., Zank, G

    Gautam, S. P., Adhikari, L., Zank, G. P., Sil- wal, A. & Zhao, L. Solar cycle dependence of the turbulence cascade rate at 1 au.The Astrophysical Journal968, 12 (2024)

    2024

  16. [24]

    E.et al.Parker solar probe: Four years of discoveries at solar cycle minimum

    Raouafi, N. E.et al.Parker solar probe: Four years of discoveries at solar cycle minimum. Space Science Reviews219, 8 (2023)

    2023

  17. [25]

    J.et al.The Solar Probe Plus Mis- sion: Humanity’s First Visit to Our Star

    Fox, N. J.et al.The Solar Probe Plus Mis- sion: Humanity’s First Visit to Our Star. Space Sci. Rev.204, 7–48 (2016)

    2016

  18. [26]

    Chen, C. H. K.et al.The Evolution and Role of Solar Wind Turbulence in the Inner Heliosphere. ApJS246, 53 (2020)

    2020

  19. [27]

    Viall, N. M. & Borovsky, J. E. Nine Out- standing Questions of Solar Wind Physics. Journal of Geophysical Research (Space Physics)125, e26005 (2020)

    2020

  20. [28]

    van der Holst, B.et al.Alfv´ en wave solar model (awsom): coronal heating.The Astro- physical Journal782, 81 (2014)

    2014

  21. [29]

    ApJ837, 75 (2017)

    Shiota, D.et al.Turbulent Transport in a Three-dimensional Solar Wind. ApJ837, 75 (2017)

    2017

  22. [30]

    I., van der Holst, B., Manch- ester, W

    Gombosi, T. I., van der Holst, B., Manch- ester, W. B. & Sokolov, I. V. Extended MHD modeling of the steady solar corona and the solar wind.Living Reviews in Solar Physics 15, 4 (2018)

    2018

  23. [31]

    V., Matthaeus, W

    Usmanov, A. V., Matthaeus, W. H., Gold- stein, M. L. & Chhiber, R. The Steady Global Corona and Solar Wind: A Three- dimensional MHD Simulation with Turbu- lence Transport and Heating. ApJ865, 25 (2018)

    2018

  24. [32]

    & Lef` evre, L

    Clette, F. & Lef` evre, L. SILSO Sunspot Number V2.0 [DataSet]. https://doi.org/10.24414/qnza-ac80 (2015). Published by WDC SILSO - Royal Observatory of Belgium (ROB)

    2015 doi

  25. [33]

    Taylor, G. I. The Spectrum of Turbulence. Proceedings of the Royal Society of London Series A164, 476–490 (1938)

    1938

  26. [34]

    V., Matthaeus, W

    Chhiber, R., Usmanov, A. V., Matthaeus, W. H., Parashar, T. N. & Goldstein, M. L. Contextual Predictions for Parker Solar Probe. II. Turbulence Properties and Taylor Hypothesis. ApJS242, 12 (2019)

    2019

  27. [35]

    N.et al.Measures of Scale- dependent Alfv´ enicity in the First PSP Solar Encounter

    Parashar, T. N.et al.Measures of Scale- dependent Alfv´ enicity in the First PSP Solar Encounter. ApJS246, 58 (2020)

    2020

  28. [36]

    B.Turbulent Flows(Cambridge University Press, 2000)

    Pope, S. B.Turbulent Flows(Cambridge University Press, 2000)

    2000

  29. [37]

    & Howarth, L

    de K´ arm´ an, T. & Howarth, L. On the Statistical Theory of Isotropic Turbulence. Proceedings of the Royal Society of London Series A164, 192–215 (1938)

    1938

  30. [38]

    C., Pontius, D

    Hossain, M., Gray, P. C., Pontius, D. H., Jr., Matthaeus, W. H. & Oughton, S. Phenomenology for the decay of energy- containing eddies in homogeneous MHD tur- bulence.Physics of Fluids7, 2886–2904 (1995)

    1995

  31. [39]

    H.et al.Transport of cross helicity and radial evolution of Alfv´ enicity in the solar wind

    Matthaeus, W. H.et al.Transport of cross helicity and radial evolution of Alfv´ enicity in the solar wind. Geophys. Res. Lett.31, L12803 (2004)

    2004

  32. [40]

    Chhiber, R., Wang, Y., Usmanov, A. V. & Matthaeus, W. H. Dynamical Age of Alfv´ enic Turbulence in the Solar Wind. ApJ1005, L10 (2026)

    2026

  33. [41]

    E., Wang, J

    Chhiber, R., Wang, Y., Cuesta, M. E., Wang, J. & Roy, S. A robust empirical relationship between speed and turbu- lence energy in the near-earth solar wind. Space Weather24, e2025SW004916 (2026). URL https://agupubs.onlinelibrary.wiley. com/doi/abs/10.1029/2025SW004916. E2025S...

    2026 doi

  34. [42]

    E., Denton, M

    Borovsky, J. E., Denton, M. H. & Smith, C. W. Some Properties of the Solar Wind Turbulence at 1 AU Statistically Exam- ined in the Different Types of Solar Wind 15 Plasma.Journal of Geophysical Research (Space Physics)124, 2406–2424 (2019)

    2019

  35. [43]

    A&A693, A243 (2025)

    D’Amicis, R.et al.On Alfv´ enic turbu- lence of solar wind streams observed by Solar Orbiter during March 2022 perihelion and their source regions. A&A693, A243 (2025)

    2025

  36. [44]

    Richardson, I. G. Solar wind stream inter- action regions throughout the heliosphere. Living Reviews in Solar Physics15, 1 (2018)

    2018

  37. [45]

    A., Goldstein, M

    Roberts, D. A., Goldstein, M. L., Matthaeus, W. H. & Ghosh, S. Velocity shear generation of solar wind turbulence. J. Geophys. Res. 97, 17 (1992)

    1992

  38. [46]

    E., Matthaeus, W

    DeForest, C. E., Matthaeus, W. H., Viall, N. M. & Cranmer, S. R. Fading Coronal Structure and the Onset of Turbulence in the Young Solar Wind. ApJ828, 66 (2016)

    2016

  39. [47]

    ApJ902, 94 (2020)

    Ruffolo, D.et al.Shear-driven Transition to Isotropically Turbulent Solar Wind Outside the Alfv´ en Critical Zone. ApJ902, 94 (2020)

    2020

  40. [48]

    & Buchlin, E

    Verdini, A., Velli, M. & Buchlin, E. Tur- bulence in the Sub-Alfv´ enic Solar Wind Driven by Reflection of Low-Frequency Alfv´ en Waves. ApJ700, L39–L42 (2009)

    2009

  41. [49]

    V., Matthaeus, W

    Chhiber, R., Usmanov, A. V., Matthaeus, W. H. & Goldstein, M. L. Contextual Predic- tions for the Parker Solar Probe. I. Critical Surfaces and Regions. ApJS241, 11 (2019)

    2019

  42. [50]

    J.et al.Defining the Middle Corona

    West, M. J.et al.Defining the Middle Corona. Sol. Phys.298, 78 (2023)

    2023

  43. [51]

    V., Matthaeus, W

    Chhiber, R., Usmanov, A. V., Matthaeus, W. H. & Goldstein, M. L. Large-scale Struc- ture and Turbulence Transport in the Inner Solar Wind: Comparison of Parker Solar Probe’s First Five Orbits with a Global 3D Reynolds-averaged MHD Model. ApJ923, 89 (2021)

    2021

  44. [52]

    Longcope, D. W. Topological Methods for the Analysis of Solar Magnetic Fields.Living Reviews in Solar Physics2, 7 (2005)

    2005

  45. [53]

    & Sheeley, N

    Wang, Y.-M. & Sheeley, N. R., Jr. Why Fast Solar Wind Originates from Slowly Expand- ing Coronal Flux Tubes. ApJ372, L45 (1991)

    1991

  46. [54]

    R., van Ballegooijen, A

    Cranmer, S. R., van Ballegooijen, A. A. & Edgar, R. J. Self-consistent Coronal Heating and Solar Wind Acceleration from Anisotropic Magnetohydrodynamic Turbu- lence. ApJS171, 520–551 (2007)

    2007

  47. [55]

    ApJ944, 82 (2023)

    Shi, C.et al.Proton and Electron Temper- atures in the Solar Wind and Their Correla- tions with the Solar Wind Speed. ApJ944, 82 (2023)

    2023

  48. [56]

    C.et al.Solar Wind Electrons Alphas and Protons (SWEAP) Investiga- tion: Design of the Solar Wind and Coronal Plasma Instrument Suite for Solar Probe Plus

    Kasper, J. C.et al.Solar Wind Electrons Alphas and Protons (SWEAP) Investiga- tion: Design of the Solar Wind and Coronal Plasma Instrument Suite for Solar Probe Plus. Space Sci. Rev.204, 131–186 (2016)

    2016

  49. [57]

    W.et al.The Solar Probe Cup on the Parker Solar Probe

    Case, A. W.et al.The Solar Probe Cup on the Parker Solar Probe. ApJS246, 43 (2020)

    2020

  50. [58]

    D.et al.The FIELDS Instrument Suite for Solar Probe Plus

    Bale, S. D.et al.The FIELDS Instrument Suite for Solar Probe Plus. Measuring the Coronal Plasma and Magnetic Field, Plasma Waves and Turbulence, and Radio Signatures of Solar Transients. Space Sci. Rev.204, 49–82 (2016)

    2016

  51. [59]

    & Harper, D

    Fr¨ anz, M. & Harper, D. Heliospheric coordi- nate systems. Planet. Space Sci.50, 217–233 (2002)

    2002

  52. [60]

    A., Goldstein, M

    Roberts, D. A., Goldstein, M. L., Klein, L. W. & Matthaeus, W. H. Origin and evolution of fluctuations in the solar wind - HELIOS observations and Helios-Voyager comparisons. J. Geophys. Res.92, 12023– 12035 (1987)

    1987

  53. [61]

    Matthaeus, W. H. & Goldstein, M. L. Mea- surement of the rugged invariants of magne- tohydrodynamic turbulence in the solar wind. J. Geophys. Res.87, 6011–6028 (1982)

    1982

  54. [62]

    E., Dasso, S., Matthaeus, W

    Ruiz, M. E., Dasso, S., Matthaeus, W. H. & Weygand, J. M. Characterization of the Tur- bulent Magnetic Integral Length in the Solar Wind: From 0.3 to 5 Astronomical Units. 16 Solar Physics289, 3917–3933 (2014)

    2014

  55. [63]

    Roy, S., Chhiber, R., Dasso, S., Ruiz, M. E. & Matthaeus, W. H. von Karman Correlation Similarity of the Turbulent Interplanetary Magnetic Field. ApJ919, L27 (2021)

    2021

  56. [64]

    J., Matthaeus, W

    Dasso, S., Milano, L. J., Matthaeus, W. H. & Smith, C. W. Anisotropy in Fast and Slow Solar Wind Fluctuations. ApJ635, L181– L184 (2005)

    2005

  57. [65]

    E.et al.Isotropization and Evo- lution of Energy-containing Eddies in Solar Wind Turbulence: Parker Solar Probe, Helios 1, ACE, WIND, and Voyager 1

    Cuesta, M. E.et al.Isotropization and Evo- lution of Energy-containing Eddies in Solar Wind Turbulence: Parker Solar Probe, Helios 1, ACE, WIND, and Voyager 1. ApJ932, L11 (2022)

    2022

  58. [66]

    Zhou, Y., Matthaeus, W. H. & Dmitruk, P. Colloquium: Magnetohydrodynamic tur- bulence and time scales in astrophysical and space plasmas.Reviews of Modern Physics 76, 1015–1035 (2004)

    2004

  59. [67]

    & Matthaeus, W

    Wan, M., Oughton, S., Servidio, S. & Matthaeus, W. H. von K´ arm´ an self- preservation hypothesis for magnetohydrody- namic turbulence and its consequences for universality.Journal of Fluid Mechanics697, 296–315 (2012)

    2012

  60. [68]

    Breech, B.et al.Turbulence transport throughout the heliosphere.Journal of Geophysical Research (Space Physics)113, A08105 (2008)

    2008

  61. [69]

    On the energy cascade rate of solar wind turbulence in high cross helicity flows.Journal of Geophysical Research: Space Physics116(2011)

    Podesta, J. On the energy cascade rate of solar wind turbulence in high cross helicity flows.Journal of Geophysical Research: Space Physics116(2011)

    2011

  62. [70]

    F., Berera, A., McComb, W

    Linkmann, M. F., Berera, A., McComb, W. D. & McKay, M. E. Nonuniversality and finite dissipation in decaying magnetohydro- dynamic turbulence.Physical review letters 114, 235001 (2015)

    2015

  63. [71]

    & Goldstraw, E

    Linkmann, M., Berera, A. & Goldstraw, E. E. Reynolds-number dependence of the dimen- sionless dissipation rate in homogeneous magnetohydrodynamic turbulence.Physical Review E95, 013102 (2017)

    2017

  64. [72]

    Li, C.et al.Non-universality and dissi- pative anomaly in compressible magnetohy- drodynamic turbulence.Journal of Fluid Mechanics992, A9 (2024)

    2024

  65. [73]

    P., Matthaeus, W

    Zank, G. P., Matthaeus, W. H. & Smith, C. W. Evolution of turbulent magnetic fluctuation power with heliospheric distance. J. Geophys. Res.101, 17093–17108 (1996)

    1996

  66. [74]

    ApJ782, 81 (2014)

    van der Holst, B.et al.Alfv´ en Wave Solar Model (AWSoM): Coronal Heating. ApJ782, 81 (2014)

    2014

  67. [75]

    P.et al.Theory and Transport of Nearly Incompressible Magnetohydrody- namic Turbulence

    Zank, G. P.et al.Theory and Transport of Nearly Incompressible Magnetohydrody- namic Turbulence. IV. Solar Coronal Turbu- lence. ApJ854, 32 (2018)

    2018

  68. [76]

    & Pouquet, A

    Politano, H. & Pouquet, A. von K´ arm´ an- Howarth equation for magnetohydrodynam- ics and its consequences on third-order lon- gitudinal structure and correlation functions. Phys. Rev. E57, R21–R24 (1998)

    1998

  69. [77]

    Matthaeus, W. H. & Velli, M. Who Needs Turbulence?. A Review of Turbulence Effects in the Heliosphere and on the Fundamental Process of Reconnection. Space Sci. Rev. 160, 145–168 (2011)

    2011

  70. [78]

    Usmanov, A. V. & Goldstein, M. L. A tilted- dipole MHD model of the solar corona and solar wind.Journal of Geophysical Research (Space Physics)108, 1354 (2003)

    2003

  71. [79]

    V., Goldstein, M

    Usmanov, A. V., Goldstein, M. L. & Matthaeus, W. H. Three-fluid, Three- dimensional Magnetohydrodynamic Solar Wind Model with Eddy Viscosity and Turbulent Resistivity. ApJ788, 43 (2014)

    2014

  72. [80]

    N.et al.Maksimovic, M., Issautier, K., Meyer-Vernet, N., Moncuquet, M

    Arge, C. N.et al.Maksimovic, M., Issautier, K., Meyer-Vernet, N., Moncuquet, M. & Pan- tellini, F. (eds)Air Force Data Assimila- tive Photospheric Flux Transport (ADAPT) Model. (eds Maksimovic, M., Issautier, K., Meyer-Vernet, N., Moncuquet, M. & Pan- tellini, F.)Twelfth Inter...

    2010

  73. [81]

    Lance, G. N. Numerical methods for high speed computers.(No Title)(1960)

    1960

  74. [82]

    R.et al.The Atmospheric Imag- ing Assembly (AIA) on the Solar Dynamics Observatory (SDO)

    Lemen, J. R.et al.The Atmospheric Imag- ing Assembly (AIA) on the Solar Dynamics Observatory (SDO). Sol. Phys.275, 17–40 (2012)

    2012

  75. [83]

    H., Wilcox, J

    Schatten, K. H., Wilcox, J. M. & Ness, N. F. A model of interplanetary and coronal mag- netic fields.Solar Physics6, 442–455 (1969)

    1969

  76. [84]

    Altschuler, M. D. & Newkirk Jr, G. Magnetic fields and the structure of the solar corona: I: Methods of calculating coronal fields.Solar Physics9, 131–149 (1969)

    1969

  77. [85]

    E., Wallace, S., Arge, C

    da Silva, D. E., Wallace, S., Arge, C. N. & Jones, S. Ensemble Forecasts of Solar Wind Connectivity to 1 R s Using ADAPT-WSA. Space Weather21, e2023SW003554 (2023). 18

    2023

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