Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

High-frequency heating of the solar wind triggered by low-frequency turbulence

Abstract

The fast solar wind’s high speeds and non-thermal features require that considerable heating occurs well above the Sun’s surface. Two leading theories seem incompatible: low-frequency ‘Alfvénic’ turbulence, which transports energy outwards and is observed ubiquitously by spacecraft but seems insufficient to explain the observed dominance of ion over electron heating; and high-frequency ion-cyclotron waves, which explain the non-thermal heating of ions but lack an obvious source. Here we argue that the recently proposed ‘helicity barrier’ effect, which limits electron heating by inhibiting the turbulent cascade of energy to the smallest scales, can unify these two paradigms. Our six-dimensional simulations show how the helicity barrier causes the large-scale energy to grow through time, generating small parallel scales and high-frequency ion-cyclotron-wave heating from low-frequency turbulence, while simultaneously explaining various other long-standing observational puzzles. The predicted causal link between plasma expansion and the ion-to-electron heating ratio suggests that the helicity barrier could contribute to key observed differences between fast and slow wind streams.

This is a preview of subscription content, access via your institution

Access options

Rent or buy this article

Prices vary by article type

from$1.95

to$39.95

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: The time evolution confirms the formation of the helicity barrier.
Fig. 2: Fluctuation spectra exhibit a steep transition region around kρi = 1.
Fig. 3: Evidence for ICW fluctuations in the saturated state.
Fig. 4: The evolution of the ion distribution function fi(w, w) shows how ICWs heat ions.

Similar content being viewed by others

Data availability

The 6D simulations presented in this article generated approximately 30 TB of data. Interested parties are invited to contact the corresponding author to make arrangements for the transfer of those data.

Code availability

All analysis scripts presented in this work are available on request from the corresponding author. The PEGASUS++ code will be made publicly available in the near future in conjunction with a detailed publication about its numerical methods. Readers can contact the corresponding author to get updates.

References

  1. Cranmer, S. R. & Winebarger, A. R. The properties of the solar corona and its connection to the solar wind. Ann. Rev. Astron. Astrophys. 57, 157–187 (2019).

    Article  ADS  Google Scholar 

  2. Marsch, E. Kinetic physics of the solar corona and solar wind. Living Rev. Solar Phys. 3, 1 (2006).

    Article  ADS  Google Scholar 

  3. Parker, E. N. Dynamical theory of the solar wind. Space Sci. Rev. 4, 666–708 (1965).

    Article  ADS  Google Scholar 

  4. Hansteen, V. H. & Leer, E. Coronal heating, densities, and temperatures and solar wind acceleration. J. Geophys. Res. 100, 21577–21594 (1995).

    Article  ADS  Google Scholar 

  5. Kohl, J. L. et al. First results from the SOHO Ultraviolet Coronagraph Spectrometer. Sol. Phys. 175, 613–644 (1997).

    Article  ADS  Google Scholar 

  6. Cranmer, S. R., Field, G. B. & Kohl, J. L. Spectroscopic constraints on models of ion cyclotron resonance heating in the polar solar corona and high-speed solar wind. Astrophys. J. 518, 937–947 (1999).

    Article  ADS  Google Scholar 

  7. Bale, S. D. et al. Highly structured slow solar wind emerging from an equatorial coronal hole. Nature 576, 237–242 (2019).

    Article  ADS  Google Scholar 

  8. De Pontieu, B. et al. Chromospheric Alfvénic waves strong enough to power the solar wind. Science 318, 1574–1577 (2007).

    Article  ADS  Google Scholar 

  9. Tomczyk, S. et al. Alfvén waves in the solar corona. Science 317, 1192–1196 (2007).

    Article  ADS  Google Scholar 

  10. Velli, M., Grappin, R. & Mangeney, A. Turbulent cascade of incompressible unidirectional Alfvén waves in the interplanetary medium. Phys. Rev. Lett. 63, 1807–1810 (1989).

    Article  ADS  Google Scholar 

  11. van Ballegooijen, A. A., Asgari-Targhi, M., Cranmer, S. R. & DeLuca, E. E. Heating of the solar chromosphere and corona by Alfvén wave turbulence. Astrophys. J. 736, 3 (2011).

    Article  ADS  Google Scholar 

  12. Shoda, M., Suzuki, T. K., Asgari-Targhi, M. & Yokoyama, T. Three-dimensional simulation of the fast solar wind driven by compressible magnetohydrodynamic turbulence. Astrophys. J. Lett. 880, L2 (2019).

    Article  ADS  Google Scholar 

  13. Quataert, E. & Gruzinov, A. Turbulence and particle heating in advection-dominated accretion flows. Astrophys. J. 520, 248–255 (1999).

    Article  ADS  Google Scholar 

  14. Schekochihin, A. A., Kawazura, Y. & Barnes, M. A. Constraints on ion versus electron heating by plasma turbulence at low beta. J. Plasma Phys. 85, 905850303 (2019).

    Article  Google Scholar 

  15. Schekochihin, A. A. et al. Astrophysical gyrokinetics: kinetic and fluid turbulent cascades in magnetized weakly collisional plasmas. Astrophys. J. Suppl. Ser. 182, 310 (2009).

    Article  ADS  Google Scholar 

  16. Chandran, B. D. G. et al. Perpendicular ion heating by low-frequency Alfvén-wave turbulence in the solar wind. Astrophys. J. 720, 503–515 (2010).

    Article  ADS  Google Scholar 

  17. Chandran, B. D. G., Dennis, T. J., Quataert, E. & Bale, S. D. Incorporating kinetic physics into a two-fluid solar-wind model with temperature anisotropy and low-frequency Alfvén-wave turbulence. Astrophys. J. 743, 197 (2011).

    Article  ADS  Google Scholar 

  18. Vech, D., Klein, K. G. & Kasper, J. C. Nature of stochastic ion heating in the solar wind: testing the dependence on plasma beta and turbulence amplitude. Astrophys. J. Lett. 850, L11 (2017).

    Article  ADS  Google Scholar 

  19. Arzamasskiy, L., Kunz, M. W., Chandran, B. D. G. & Quataert, E. Hybrid-kinetic simulations of ion heating in Alfvénic turbulence. Astrophys. J. 879, 53 (2019).

    Article  ADS  Google Scholar 

  20. Cerri, S. S., Arzamasskiy, L. & Kunz, M. W. On stochastic heating and its phase-space signatures in low-beta kinetic turbulence. Astrophys. J. 916, 120 (2021).

    Article  ADS  Google Scholar 

  21. Teaca, B., Weidl, M. S., Jenko, F. & Schlickeiser, R. Acceleration of particles in imbalanced magnetohydrodynamic turbulence. Phys. Rev. E 90, 021101 (2014).

    Article  ADS  Google Scholar 

  22. Isenberg, P. A. & Vasquez, B. J. Perpendicular ion heating by cyclotron resonant dissipation of turbulently generated kinetic Alfvén waves in the solar wind. Astrophys. J. 887, 63 (2019).

    Article  ADS  Google Scholar 

  23. Hollweg, J. V. & Isenberg, P. A. Generation of the fast solar wind: a review with emphasis on the resonant cyclotron interaction. J. Geophys. Res. Space Phys. 107, SSH 12-1–SSH 12-37 (2002).

  24. Kennel, C. F. & Engelmann, F. Velocity space diffusion from weak plasma turbulence in a magnetic field. Phys. Fluids 9, 2377–2388 (1966).

    Article  ADS  Google Scholar 

  25. Isenberg, P. A. & Vasquez, B. J. A kinetic model of solar wind generation by oblique ion-cyclotron waves. Astrophys. J. 731, 88 (2011).

    Article  ADS  Google Scholar 

  26. Kasper, J. C., Maruca, B. A., Stevens, M. L. & Zaslavsky, A. Sensitive test for ion-cyclotron resonant heating in the solar wind. Phys. Rev. Lett. 110, 091102 (2013).

    Article  ADS  Google Scholar 

  27. Zhao, G. Q. et al. Dependence of ion temperatures on alpha-proton differential flow vector and heating mechanisms in the solar wind. Astrophys. J. Lett. 889, L14 (2020).

    Article  ADS  Google Scholar 

  28. Hollweg, J. V. Compressibility of ion cyclotron and whistler waves: can radio measurements detect high-frequency waves of solar origin in the corona? J. Geophys. Res. 105, 7573–7582 (2000).

    Article  ADS  Google Scholar 

  29. Shebalin, J. V., Matthaeus, W. H. & Montgomery, D. Anisotropy in MHD turbulence due to a mean magnetic field. J. Plasma Phys. 29, 525–547 (1983).

    Article  ADS  Google Scholar 

  30. Woodham, L. D. et al. Parallel-propagating fluctuations at proton-kinetic scales in the solar wind are dominated by kinetic instabilities. Astrophys. J. Lett. 884, L53 (2019).

    Article  ADS  Google Scholar 

  31. Voitenko, Y. & Goossens, M. Excitation of high-frequency Alfvén waves by plasma outflows from coronal reconnection events. Sol. Phys. 206, 285–313 (2002).

    Article  ADS  Google Scholar 

  32. Meyrand, R., Squire, J., Schekochihin, A. A. & Dorland, W. On the violation of the zeroth law of turbulence in space plasmas. J. Plasma Phys. 87, 535870301 (2021).

    Article  Google Scholar 

  33. Cho, J. Magnetic helicity conservation and inverse energy cascade in electron magnetohydrodynamic wave packets. Phys. Rev. Lett. 106, 191104 (2011).

    Article  ADS  Google Scholar 

  34. Kunz, M. W., Stone, J. M. & Bai, X.-N. Pegasus: a new hybrid-kinetic particle-in-cell code for astrophysical plasma dynamics. J. Comp. Phys. 259, 154–174 (2014).

    Article  MathSciNet  MATH  ADS  Google Scholar 

  35. Chen, C. H. K. Recent progress in astrophysical plasma turbulence from solar wind observations. J. Plasma Phys. 82, 535820602 (2016).

    Article  Google Scholar 

  36. Davidson, P. A. Turbulence: An Introduction for Scientists and Engineers (Oxford Univ. Press, 2004).

  37. Schekochihin, A. A. MHD turbulence: a biased review. Preprint at https://arxiv.org/abs/2010.00699 (2021).

  38. McManus, M. D. et al. Cross helicity reversals in magnetic switchbacks. Astrophys. J. Suppl. Ser. 246, 67 (2020).

    Article  ADS  Google Scholar 

  39. Leamon, R. J. et al. Observational constraints on the dynamics of the interplanetary magnetic field dissipation range. J. Geophys. Res. 103, 4775–4788 (1998).

    Article  ADS  Google Scholar 

  40. Bowen, T. A. et al. Constraining ion-scale heating and spectral energy transfer in observations of plasma turbulence. Phys. Rev. Lett. 125, 025102 (2020).

    Article  ADS  Google Scholar 

  41. Chen, C. H. K., Boldyrev, S., Xia, Q. & Perez, J. C. Nature of subproton scale turbulence in the solar wind. Phys. Rev. Lett. 110, 225002 (2013).

    Article  ADS  Google Scholar 

  42. Duan, D. et al. Anisotropy of solar wind turbulence in the inner heliosphere at kinetic scales: PSP observations. Astrophys. J. Lett. 915, L8 (2021).

    Article  ADS  Google Scholar 

  43. Huang, S. Y. et al. The ion transition range of solar wind turbulence in the inner heliosphere: Parker Solar Probe observations. Astrophys. J. Lett. 909, L7 (2021).

    Article  ADS  Google Scholar 

  44. Howes, G. G. & Quataert, E. On the interpretation of magnetic helicity signatures in the dissipation range of solar wind turbulence. Astrophys. J. Lett. 709, L49–L52 (2010).

    Article  ADS  Google Scholar 

  45. Huang, S. Y. et al. Kinetic scale slow solar wind turbulence in the inner heliosphere: coexistence of kinetic Alfvén Waves and Alfvén ion cyclotron waves. Astrophys. J. Lett. 897, L3 (2020).

    Article  ADS  Google Scholar 

  46. Zhao, G. Q. et al. Magnetic helicity signature and its role in regulating magnetic energy spectra and proton temperatures in the solar wind. Astrophys. J. 906, 123 (2021).

    Article  ADS  Google Scholar 

  47. Chandran, B. D. G. et al. Resonant interactions between protons and oblique Alfvén/ion-cyclotron waves in the solar corona and solar flares. Astrophys. J. 722, 710–720 (2010).

    Article  ADS  Google Scholar 

  48. Vasquez, B. J., Isenberg, P. A. & Markovskii, S. A. Proton perpendicular heating in turbulence simulations: determination of the velocity diffusion coefficient. Astrophys. J. 893, 71 (2020).

    Article  ADS  Google Scholar 

  49. Marsch, E. et al. Solar wind protons: three-dimensional velocity distributions and derived plasma parameters measured between 0.3 and 1 AU. J. Geophys. Res. 87, 52–72 (1982).

    Article  ADS  Google Scholar 

  50. Verniero, J. L. et al. Parker Solar Probe observations of proton beams simultaneous with ion-scale waves. Astrophys. J. Suppl. Ser. 248, 5 (2020).

    Article  ADS  Google Scholar 

  51. Li, X. et al. A kinetic Alfvén wave and the proton distribution function in the fast solar wind. Astrophys. J. Lett. 719, L190–L193 (2010).

    Article  ADS  Google Scholar 

  52. Wang, Y. M. & Sheeley, N. R. Solar wind speed and coronal flux-tube expansion. Astrophys. J. 355, 726 (1990).

    Article  ADS  Google Scholar 

  53. Cranmer, S. R. in Solar Wind 11/SOHO 16: Connecting Sun and Heliosphere Special Publication 592 (eds Fleck, B. et al.) 159 (ESA, 2005).

  54. Chandran, B. D. G. An approximate analytic solution to the coupled problems of coronal heating and solar-wind acceleration. J. Plasma Phys. 87, 905870304 (2021).

    Article  Google Scholar 

  55. Byers, J. A., Cohen, B. I., Condit, W. C. & Hanson, J. D. Hybrid simulations of quasineutral phenomena in magnetized plasma. J. Comp. Phys. 27, 363–396 (1978).

    Article  MathSciNet  ADS  Google Scholar 

  56. Goldreich, P. & Sridhar, S. Toward a theory of interstellar turbulence. Strong Alfvénic turbulence. Astrophys. J. 438, 763–775 (1995).

    Article  ADS  Google Scholar 

  57. Kasper, J. C. et al. Alfvénic velocity spikes and rotational flows in the near-Sun solar wind. Nature 576, 228–231 (2019).

    Article  ADS  Google Scholar 

  58. Stone, J. M. et al. Athena: a new code for astrophysical MHD. Astrophys. J. Suppl. Ser. 178, 137–177 (2008).

    Article  ADS  Google Scholar 

  59. Lynn, J. W., Parrish, I. J., Quataert, E. & Chandran, B. D. G. Resonance broadening and heating of charged particles in magnetohydrodynamic turbulence. Astrophys. J. 758, 78 (2012).

    Article  ADS  Google Scholar 

  60. Cho, J. & Lazarian, A. Simulations of electron magnetohydrodynamic turbulence. Astrophys. J. 701, 236–252 (2009).

    Article  ADS  Google Scholar 

  61. Meyrand, R., Kanekar, A., Dorland, W. & Schekochihin, A. A. Fluidization of collisionless plasma turbulence. Proc. Natl. Acad. Sci. USA 116, 1185–1194 (2019).

    Article  MathSciNet  MATH  ADS  Google Scholar 

  62. Matthaeus, W. H. & Goldstein, M. L. Measurement of the rugged invariants of magnetohydrodynamic turbulence in the solar wind. J. Geophys. Res. 87, 6011–6028 (1982).

    Article  ADS  Google Scholar 

  63. Isenberg, P. A. & Lee, M. A. A dispersive analysis of bispherical pickup ion distributions. J. Geophys. Res. 101, 11055–11066 (1996).

    Article  ADS  Google Scholar 

  64. Pongkitiwanichakul, P., Chandran, B. D. G., Isenberg, P. A. & Vasquez, B. J. Resonant interactions between protons and oblique Alfvén/ion-cyclotron waves. In Twelfth International Solar Wind Conference AIP Conference Series Vol. 1216 (eds Maksimovic, M. et al.) 72–75 (AIP, 2010).

  65. Gary, S. P. & Borovsky, J. E. Alfvén-cyclotron fluctuations: linear Vlasov theory. J. Geophys. Res. Space Phys. 109, A06105 (2004).

    Article  ADS  Google Scholar 

  66. Hellinger, P., Trávníček, P., Kasper, J. C. & Lazarus, A. J. Solar wind proton temperature anisotropy: linear theory and WIND/SWE observations. Geophys. Res. Lett. 33, L09101 (2006).

    Article  ADS  Google Scholar 

  67. Klein, K. G. & Chandran, B. D. G. Evolution of the proton velocity distribution due to stochastic heating in the near-Sun solar wind. Astrophys. J. 820, 47 (2016).

    Article  ADS  Google Scholar 

  68. Martinović, M. M. et al. The enhancement of proton stochastic heating in the near-Sun solar wind. Astrophys. J. Suppl. Ser. 246, 30 (2020).

    Article  ADS  Google Scholar 

  69. He, J. et al. Sunward propagating Alfvén waves in association with sunward drifting proton beams in the solar wind. Astrophys. J. 805, 176 (2015).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

We thank B. Dorland, B. Chandran and A. Mallet for illuminating discussions. J.S. and R.M acknowledge support from the Royal Society Te Apārangi, New Zealand, through Marsden Fund grant number UOO1727 and Rutherford Discovery Fellowship RDF-U001804. M.W.K. and E.Q. were supported by the Department of Energy through the NSF/DOE Partnership in Basic Plasma Science and Engineering, award numbers DE-SC0019046 and DE-SC0019047, with additional support for E.Q. from a Simons Investigator Award from the Simons Foundation. L.A. acknowledges the support of the Institute for Advanced Study, and the work of A.A.S. was supported in part by UK EPSRC grant number EP/R034737/1. This research was part of the Frontera computing project at the Texas Advanced Computing Center, which is made possible by National Science Foundation award number OAC-1818253. Further computational support was provided by the New Zealand eScience Infrastructure (NeSI) high-performance computing facilities, funded jointly by NeSI’s collaborator institutions and the NZ MBIE, and through the PICSciE-OIT TIGRESS High Performance Computing Center and Visualization Laboratory at Princeton University. The funders had no role in study design, data collection and analysis, decision to publish or preparation of the manuscript.

Author information

Authors and Affiliations

Authors

Contributions

J.S. and R.M. conceived the study. L.A., M.W.K. and J.S. developed the numerical methods and model, with J.S. and L.A. performing the simulations. Data analysis and visualization was carried out by J.S. and L.A., with all authors contributing to general understanding and interpretation of the results. The manuscript was written primarily by J.S. with M.W.K, A.A.S. and E.Q. leading revisions and editing.

Corresponding author

Correspondence to Jonathan Squire.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature Astronomy thanks Munehito Shoda, Christopher Chen and Philip Isenberg for their contribution to the peer review of this work.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data

Extended Data Fig. 1 Electric field noise and numerical cooling.

Contributions to the energy budget per unit volume of the imbalanced simulation from the energy injection (ε/V; dashed red line), increase in thermal energy \({Q}_{i}={\partial }_{t}\langle {m}_{i}{v}_{{{{{{\rm{th}}}}}}}^{2}/2\rangle\) (blue line), growth rate of mechanical energy \({\partial }_{t}\langle n{m}_{i}{u}_{i}^{2}/2+{B}^{2}/8\pi \rangle\) (green line), and resistive dissipation εη/V (V is the volume and 〈 … 〉 denotes a box average). The black line shows the total energy budget \({{{{{\rm{Total}}}}}}=\varepsilon /V-{\varepsilon }_{\eta }/V-{\partial }_{t}\langle {m}_{i}{v}_{{{{{{\rm{th}}}}}}}^{2}/2\rangle -{\partial }_{t}\langle n{m}_{i}{u}_{i}^{2}/2+{B}^{2}/8\pi \rangle\), which is constant and negative, indicating numerical cooling that is effectively independent of the turbulence or the heating of ions.

Extended Data Fig. 2 The effect of particle noise on turbulence spectra.

Perpendicular (k) spectra of the magnetic field (\({{{{{{\mathcal{E}}}}}}}_{{{{{{\boldsymbol{B}}}}}}}\)), electric field \({{{{{{\mathcal{E}}}}}}}_{{{{{{\boldsymbol{E}}}}}}}\), and KAW-normalized density \({{{{{{\mathcal{E}}}}}}}_{{n}_{{{{{{\rm{KAW}}}}}}}}={\beta }_{i}(1+2{\beta }_{i}){{{{{{\mathcal{E}}}}}}}_{n}\) in the saturated state (solid lines) and at very early times (averaged over t≤0.2τA). The latter is from before the turbulence has developed and is thus a proxy for the noise floor in a given quantity. At the smallest scales, kρi 3, spectra are only modestly above the noise floor and therefore uncertain.

Extended Data Fig. 3 Measurement of the parallel spectrum.

Two-dimensional perpendicular magnetic-field spectrum \({{{{{{\mathcal{E}}}}}}}_{{B}_{\perp }}({k}_{\perp },{k}_{\parallel })={{{{{{\mathcal{E}}}}}}}_{{B}_{x}}({k}_{\perp },{k}_{\parallel })+{{{{{{\mathcal{E}}}}}}}_{{B}_{y}}({k}_{\perp },{k}_{\parallel })\) from the balanced simulation. The method recovers the large- and small-scale scalings of k with k measured using structure functions (see fig. 2 of ref. 19), as well as the predicted 2D spectrum in the kρi < 1 range (see appendix B of ref. 37).

Extended Data Fig. 4 Assessment of the influence of stochastic heating.

We show perpendicular spectra of the electric potential Φ, computed from the curl free part of E. Colored lines show various times from the imbalanced simulation. The black line shows the equivalent balanced simulation, which is averaged over the early period of the simulation (between t = 3.5τA and t = 4.5τA) when stochastic-ion heating absorbs the majority of the turbulent energy flux19 Despite the larger turbulence amplitude in the imbalanced simulation, the electric-potential fluctuations around kρi ~ 1 – those important for stochastic heating – are smaller.

Extended Data Fig. 5 Development of the ion beam.

We compare the rate of change parallel thermal energy (solid lines; see text) with the work done on particles by the parallel electric field ewEfi〉 (dotted lines). The thick dark-blue lines show the saturated state and the orange-pink lines show t = 7τA. The similarity of the magnitude and general shape of the two measures of heating suggests that Landau damping is responsible for the formation of the ion beam.

Supplementary information

Supplementary Video 1

A fly-through slice of the perpendicular electric field in the saturated state. A sampling of the magnetic-field-line structure is shown by the blue lines.

Supplementary Video 2

Time evolution of the perpendicular electric field magnitude.

Supplementary Video 3

Time evolution of the y component of the magnetic field.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Squire, J., Meyrand, R., Kunz, M.W. et al. High-frequency heating of the solar wind triggered by low-frequency turbulence. Nat Astron 6, 715–723 (2022). https://doi.org/10.1038/s41550-022-01624-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41550-022-01624-z

This article is cited by

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing