Content-Length: 338876 | pFad | https://link.springer.com/doi/10.1007/s11207-019-1421-y

86400 On the Power-Law Distribution of Pitch-Angle Scattering Times in Solar Wind Turbulence | Solar Physics Skip to main content
Log in

On the Power-Law Distribution of Pitch-Angle Scattering Times in Solar Wind Turbulence

  • Published:
Solar Physics Aims and scope Submit manuscript

A Correction to this article was published on 12 June 2019

This article has been updated

Abstract

The propagation of energetic particles in the solar wind depends in a sensitive way on the pitch-angle scattering of particles in the presence of magnetic turbulence. The well-known quasi-linear theory gives an expression for the pitch-angle scattering rate under the assumption of small turbulence levels, but both in the solar wind and in other astrophysical environments the turbulent magnetic field fluctuations can be large. Therefore, a reliable assessment of the pitch-angle scattering requires an investigation that goes beyond the quasi-linear theory. To this end, we employ a recently developed model of synthetic magnetic turbulence, which allows reproduction of a very long spectrum, while varying the turbulence level and the turbulence intermittency. Test particles representing protons with energies in the range \(70~\mbox{keV}\,\mbox{--}\,1~\mbox{MeV}\) are injected in the turbulence spectrum plus a background magnetic field, and the pitch-angle scattering rate is determined by following the individual particles. Using turbulence and intermittency levels comparable to those observed in the solar wind, we find a broad power-law distribution of pitch-angle scattering times, which encompasses the quasi-linear value but extends to values both much larger and much smaller. We find that the distribution of pitch-angle scattering times also depends on the intermittency level. This finding shows that a description of parallel transport based on a single value of the pitch-angle scattering time is not sufficient. These numerical results are compared with observations of the distribution of magnetic variances at the particle resonant scale, measured in the solar wind by the Ulysses spacecraft.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Figure 1
Figure 2
Figure 3
Figure 4

Similar content being viewed by others

Change history

  • 12 June 2019

    Correction to: Solar Phys (2019) 294:34 https://doi.org/10.1007/s11207-019-1421-y

    This article was published with an omission in the Acknowledgement text. Please find in this document the correct Acknowledgement text that should be regarded as the final version by the reader.

    Acknowledgement The work by S. Perri has been supported by the Agenzia Spaziale Italiana under the contract ASI-INAF 2015-039-R.O “Missione M4 di ESA: Partecipazione Italiana alla fase di assessment della missione THOR”. The work by F. Pucci has been supported by Fonds Wetenshappelijk Onderzoek—Vlaanderen (FWO) through the postdoctoral fellowship 12X0319N.

References

  • Amato, E.: 2014, The origen of galactic cosmic rays. Int. J. Mod. Phys. D 23, 1430013. DOI .

    Article  ADS  MathSciNet  Google Scholar 

  • Beresnyak, A.: 2013, Asymmetric diffusion of magnetic field lines. Astrophys. J. Lett. 767, L39. DOI .

    Article  ADS  Google Scholar 

  • Bieber, J.W., Smith, C.W., Matthaeus, W.H.: 1988, Cosmic-ray pitch-angle scattering in isotropic turbulence. Astrophys. J. 334, 470. DOI .

    Article  ADS  Google Scholar 

  • Boris, J.P., Shanny, R.A.: 1972, Proceedings: Fourth Conference on Numerical Simulation of Plasmas, November 2, 3, 1970, Naval Research Laboratory.

    Google Scholar 

  • Carbone, V.: 1994, Scaling exponents of the velocity structure functions in the interplanetary medium. Ann. Geophys. 12, 585. DOI .

    Article  ADS  Google Scholar 

  • Crooker, N.U., Gosling, J.T., Bothmer, V., Forsyth, R.J., Gazis, P.R., Hewish, A., Horbury, T.S., Intriligator, D.S., Jokipii, J.R., Kóta, J., Lazarus, A.J., Lee, M.A., Lucek, E., Marsch, E., Posner, A., Richardson, I.G., Roelof, E.C., Schmidt, J.M., Siscoe, G.L., Tsurutani, B.T., Wimmer-Schweingruber, R.F.: 1999, CIR morphology, turbulence, discontinuities, and energetic particles. Space Sci. Rev. 89, 179. DOI .

    Article  ADS  Google Scholar 

  • Dasso, S., Milano, L.J., Matthaeus, W.H., Smith, C.W.: 2005, Anisotropy in fast and slow solar wind fluctuations. Astrophys. J. Lett. 635, L181. DOI .

    Article  ADS  Google Scholar 

  • Giacalone, J.: 2012, Energetic charged particles associated with strong interplanetary shocks. Astrophys. J. 761, 28. DOI .

    Article  ADS  Google Scholar 

  • Giacalone, J., Jokipii, J.R.: 1999, The transport of cosmic rays across a turbulent magnetic field. Astrophys. J. 520, 204. DOI .

    Article  ADS  Google Scholar 

  • Horbury, T.S., Forman, M., Oughton, S.: 2008, Anisotropic scaling of magnetohydrodynamic turbulence. Phys. Rev. Lett. 101(17), 175005. DOI .

    Article  ADS  Google Scholar 

  • Horbury, T.S., Balogh, A., Forsyth, R.J., Smith, E.J.: 1996, The rate of turbulent evolution over the Sun’s poles. Astron. Astrophys. 316, 333.

    ADS  Google Scholar 

  • Horbury, T.S., Balogh, A., Forsyth, R.J., Smith, E.J.: 1997, ULYSSES observations of intermittent heliospheric turbulence. Adv. Space Res. 19, 847. DOI .

    Article  ADS  Google Scholar 

  • Kennel, C.F., Petschek, H.E.: 1966, Limit on stably trapped particle fluxes. J. Geophys. Res. 71, 1. DOI .

    Article  ADS  Google Scholar 

  • Kirk, J.G., Duffy, P., Gallant, Y.A.: 1996, Stochastic particle acceleration at shocks in the presence of braided magnetic fields. Astron. Astrophys. 314, 1010.

    ADS  Google Scholar 

  • Klafter, J., Blumen, A., Shlesinger, M.F.: 1987, Stochastic pathway to anomalous diffusion. Phys. Rev. A 35, 3081. DOI .

    Article  ADS  MathSciNet  Google Scholar 

  • Laitinen, T., Kopp, A., Effenberger, F., Dalla, S., Marsh, M.S.: 2016, Solar energetic particle access to distant longitudes through turbulent field-line meandering. Astron. Astrophys. 591, A18. DOI .

    Article  ADS  Google Scholar 

  • Lazarian, A., Yan, H.: 2014, Superdiffusion of cosmic rays: Implications for cosmic ray acceleration. Astrophys. J. 784, 38.

    Article  ADS  Google Scholar 

  • Malara, F., Di Mare, F., Nigro, G., Sorriso-Valvo, L.: 2016, Fast algorithm for a three-dimensional synthetic model of intermittent turbulence. Phys. Rev. E 94(5), 053109. DOI .

    Article  ADS  Google Scholar 

  • Palmer, I.D.: 1982, Transport coefficients of low-energy cosmic rays in interplanetary space. Rev. Geophys. Space Phys. 20, 335. DOI .

    Article  ADS  Google Scholar 

  • Perri, S.: 2018, Superdiffusion of relativistic electrons at supernova remnant shocks. Plasma Phys. Control. Fusion 60(1), 014005. DOI .

    Article  ADS  Google Scholar 

  • Perri, S., Zimbardo, G.: 2007, Evidence of superdiffusive transport of electrons accelerated at interplanetary shocks. Astrophys. J. Lett. 671, L177. DOI .

    Article  ADS  Google Scholar 

  • Perri, S., Zimbardo, G.: 2008, Superdiffusive transport of electrons accelerated at corotating interaction regions. J. Geophys. Res. 113, A03107. DOI .

    Article  ADS  Google Scholar 

  • Perri, S., Zimbardo, G.: 2009, Ion superdiffusion at the solar wind termination shock. Astrophys. J. Lett. 693, L118. DOI .

    Article  ADS  Google Scholar 

  • Perri, S., Zimbardo, G.: 2012a, Magnetic variances and pitch-angle scattering times upstream of interplanetary shocks. Astrophys. J. 754, 8. DOI .

    Article  ADS  Google Scholar 

  • Perri, S., Zimbardo, G.: 2012b, Superdiffusive shock acceleration. Astrophys. J. 750, 87. DOI .

    Article  ADS  Google Scholar 

  • Perri, S., Zimbardo, G.: 2015, Short acceleration times from superdiffusive shock acceleration in the heliosphere. Astrophys. J. 815, 75. DOI .

    Article  ADS  Google Scholar 

  • Perri, S., Amato, E., Zimbardo, G.: 2016, Transport of relativistic electrons at shocks in shell-type supernova remnants: diffusive and superdiffusive regimes. Astron. Astrophys. 596, A34. DOI .

    Article  ADS  Google Scholar 

  • Perri, S., Zimbardo, G., Effenberger, F., Fichtner, H.: 2015, Parameter estimation of superdiffusive motion of energetic particles upstream of heliospheric shocks. Astron. Astrophys. 578, A2. DOI .

    Article  ADS  Google Scholar 

  • Pucci, F., Malara, F., Perri, S., Zimbardo, G., Sorriso-Valvo, L., Valentini, F.: 2016, Energetic particle transport in the presence of magnetic turbulence: influence of spectral extension and intermittency. Mon. Not. Roy. Astron. Soc. 459, 3395. DOI .

    Article  ADS  Google Scholar 

  • Reames, D.V.: 1999, Particle acceleration at the Sun and in the heliosphere. Space Sci. Rev. 90, 413. DOI .

    Article  ADS  Google Scholar 

  • Saul, L., Möbius, E., Isenberg, P., Bochsler, P.: 2007, On pitch-angle scattering rates of interstellar pickup ions as determined by in situ measurement of velocity distributions. Astrophys. J. 655, 672. DOI .

    Article  ADS  Google Scholar 

  • Sorriso-Valvo, L., Carbone, F., Perri, S., Greco, A., Marino, R., Bruno, R.: 2018, On the statistical properties of turbulent energy transfer rate in the inner heliosphere. Solar Phys. 293, 10. DOI .

    Article  ADS  Google Scholar 

  • Sugiyama, T., Shiota, D.: 2011, Sign for super-diffusive transport of energetic ions associated with a coronal-mass-ejection-driven interplanetary shock. Astrophys. J. Lett. 731, L34. DOI .

    Article  ADS  Google Scholar 

  • Wang, Y., Qin, G., Zhang, M., Dalla, S.: 2014, A numerical simulation of solar energetic particle dropouts during impulsive events. Astrophys. J. 789, 157. DOI .

    Article  ADS  Google Scholar 

  • Xu, S., Yan, H.: 2013, Cosmic-ray parallel and perpendicular transport in turbulent magnetic fields. Astrophys. J. 779, 140. DOI .

    Article  ADS  Google Scholar 

  • Yordanova, E., Balogh, A., Noullez, A., von Steiger, R.: 2009, Turbulence and intermittency in the heliospheric magnetic field in fast and slow solar wind. J. Geophys. Res. 114, A08101. DOI .

    Article  ADS  Google Scholar 

  • Zimbardo, G., Perri, S.: 2013, From Lévy walks to superdiffusive shock acceleration. Astrophys. J. 778, 35. DOI .

    Article  ADS  Google Scholar 

  • Zimbardo, G., Perri, S.: 2017, Superdiffusive shock acceleration at galaxy cluster shocks. Nat. Astron. 1, 0163. DOI .

    Article  ADS  Google Scholar 

  • Zimbardo, G., Perri, S.: 2018, Understanding the radio spectral indices of galaxy cluster relics by superdiffusive shock acceleration. Mon. Not. Roy. Astron. Soc. 478, 4922. DOI .

    Article  ADS  Google Scholar 

Download references

Acknowledgement

The work by S. Perri has been supported by the Agenzia Spaziale Italiana under the contract ASI-INAF 2015-039-R.O “Missione M4 di ESA: Partecipazione Italiana alla fase di assessment della missione THOR”.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Silvia Perri.

Ethics declarations

Disclosure of Potential Conflicts of Interest

The authors declare that they have no conflicts of interest.

Additional information

Publisher’s Note

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

This article belongs to the Topical Collection:

Solar Wind at the Dawn of the Parker Solar Probe and Solar Orbiter Era

Guest Editors: Giovanni Lapenta and Andrei Zhukov

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Perri, S., Pucci, F., Malara, F. et al. On the Power-Law Distribution of Pitch-Angle Scattering Times in Solar Wind Turbulence. Sol Phys 294, 34 (2019). https://doi.org/10.1007/s11207-019-1421-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11207-019-1421-y

Keywords

Navigation









ApplySandwichStrip

pFad - (p)hone/(F)rame/(a)nonymizer/(d)eclutterfier!      Saves Data!


--- a PPN by Garber Painting Akron. With Image Size Reduction included!

Fetched URL: https://link.springer.com/doi/10.1007/s11207-019-1421-y

Alternative Proxies:

Alternative Proxy

pFad Proxy

pFad v3 Proxy

pFad v4 Proxy