Deformations in the velocity distribution functions of protons and alpha particles observed by Solar Orbiter in the inner heliosphere

(Solar Orbiter Nugget #26 by D. Perrone1, A. Settino2, R. De Marco3, R. D’Amicis3, S. Perri4)



The solar wind is observed to be turbulent [1]. Turbulence in plasmas involves a complex cross-scale coupling of fields, thus how the energy contained in the large-scale fluctuations of electromagnetic and velocity fields cascades all the way down to the kinetic scales, and how such turbulence interacts with particles, remain unsolved problems in plasma physics. Answering this problem will have strong implications for space [1,4], astrophysical [5,6], and laboratory plasmas [7]. The heliosphere, characterized by nonlinear processes, such as the generation of shocks, waves, coherent structures, magnetic reconnection and particle acceleration, represents the best natural laboratory to study in-situ plasma turbulence. The nature of the turbulent magnetic fluctuations around proton scales has been studied in the interval of slow Alfvénic wind observed by Solar Orbiter in July 2020 at 0.64 AU [8], with a particular attention to the link between the emergence of coherent events and kinetic effects on the proton and alpha particle velocity distribution functions (VDFs).


Solar Orbiter measurements

Solar Orbiter was launched in February 2020 and, during its cruise phase, it has been embedded for the first time in a slow Alfvénic solar wind stream at a radial distance of about 0.64 AU [8]. This stream is characterized by three well-defined plasma regions, namely a main portion, an intermediate region, and a rarefaction region. 1h intervals in each of those regions, with a very high Alfvénicity, have been selected and studied separately, in order to enhance similarities and differences in their turbulence properties. Coherent structures naturally emerge over different time/spatial scales and their characteristics at ion scales have been investigated.

Figure 1 shows the distribution of the magnetic energy in time and timescales, by means of two techniques, the local intermittency measure (LIM) [9], and the partial variance of increments (PVI) [10]. Localized (in time) channels in the PVI and LIM signals broaden over time scales, suggesting a magnetic energy cascade from large towards small time scales. Thus, this non uniform distribution of energy indicates the emergence of coherent structures [12-17]. They can be strongly related to the presence of kinetic effects, such as particle energization, temperature anisotropy, and deviation from Maxwellian VDF [18-20]. Therefore, the bottom panels of Figure 1 show the increments of the deviation of the proton and alpha VDF from the thermodynamic equilibrium, enhancing a link between the presence of strong intermittent events and the distortion of both proton and alpha particle VDFs.

Figure 1. Logarithmic contour plots of the local intermittency measure (LIM) of the parallel, I∥ (a–c), and perpendicular, I⊥ (d-f), magnetic field fluctuations, where curved lines, at each side of the plots, indicate the cone of influence. Logarithmic contour plots of the magnetic PVI (g-i). Dimensionless proton (green) and alpha particle (violet) increment of non-Maxwellianity parameter, Δε (j-l) [11].


Vortex chain

An in-depth investigation has shown that coherent structures are mainly current sheets and vortex-like structures. The latter can be found either isolated or grouped in chains. An example of a vortex chain is shown in panel (a) of Figure 2, where the components of the magnetic field fluctuations are shown in the local magnetic field frame, with the direction of the local magnetic field along the z-direction.

Numerical simulations have also shown that turbulence leads to the generation of current sheets and vortices, which evolve in time interacting nonlinearly among each other [see, e.g., 21 and 22]. For example, if a simulated Solar Orbiter spacecraft was allowed to travel within a kinetic simulation, sampling magnetic field data along a linear trajectory in the numerical box, it would cross discontinuities and magnetic islands, with the latter appearing as a vortex chain (see panel b of Figure 2).

Figure 2. Panel (a): Example of a vortex chain crossed by Solar Orbiter and centered at 03:27:56.58 UT (black vertical dashed line) on July 17th. Components of the magnetic field fluctuations in the local magnetic field reference frame, where b0 is along the z-direction. The yellow box marks the width of the central vortex. Adapted from [11]. Panel (b): Contour plot of the out-of-plane current density from a multi-ion hybrid Vlasov Maxwell simulation, where the black dashed line represents the trajectory of a virtual Solar Orbiter spacecraft in the numerical box. Adapted from [21].


Deformation of the ion VDFs

Coherent structures are generally connected to strong distortions in the ion VDFs, such as the presence of a secondary field-aligned beam. A quantitative indication of the degree of distortion in the 3D ion VDFs observed by Solar Orbiter [23] is provided by the increased non-Maxwellianity parameter in correspondence of such intermittent regions and strong discontinuities (see Figure 1).

Figure 3 shows 2D contour plots of both proton and alpha particle VDFs close to the center of the main vortex structure (red vertical dashed line in Figure 2). The VDF of each ion population (protons and alpha particles) is displayed in their respective rest frame and significantly deviates from thermodynamic equilibrium. Indeed, the proton VDF shows a clear and stable field-aligned beam, while it is gyrotropic in the plane perpendicular to the magnetic field. Moreover, interestingly, the alpha particle VDF shows an oblique beam, a feature that needs further investigation. The same kinetic features are observed in correspondence of the other two vortex structures detected right before and after the main one.

Figure 3. 2D contour plots of the reduced velocity distribution functions of protons (top) and alpha particles (bottom) plotted in the rest frame coordinate system and at 03:27:55.78 UT on July 17th (red vertical dashed line in Figure 2) [11].


This study has been published in Denise Perrone, et al. 2023, Frontiers in Astronomy and Space Sciences, 10, 1250219



Solar Orbiter is a space mission of international collaboration between ESA and NASA, operated by ESA. Solar Orbiter Solar Wind Analyser (SWA) data are derived from scientific sensors which have been designed and created, and are operated under funding provided in numerous contracts from the UK Space Agency (UKSA), the UK Science and Technology Facilities Council (STFC), the Agenzia Spaziale Italiana (ASI), the Centre National d’Etudes SpaDales (CNES, France), the Centre National de la Recherche Scientifique (CNRS, France), the Czech contribution to the ESA PRODEX programme and NASA. DP, SP, and AS would like to acknowledge the International Space Science Institute (ISSI) for its support of the team “Unravelling solar wind microphysics in the inner heliosphere” dedicated in part to the analysis of Solar Orbiter data.



1 ASI—Italian Space Agency, Rome, Italy;

2 Space Research Institute, Austrian Academy of Sciences, Graz, Austria

3 National Institute for Astrophysics, Institute for Space Astrophysics and Planetology, Rome, Italy

4 Dipartimento di Fisica, Università Della Calabria, Rende, Italy



[1] Bruno, R., and Carbone, V. 2016, ‘Turbulence in the solar wind’ in Lecture notes in physics (Berlin, Germany: Springer)

[2] Marsch, E., Rosenbauer, H., Schwenn, R., Muehlhaeuser, K. H., and Neubauer, F. M. 1982, JGR, 87, 35

[3] Marsch, E., Schwenn, R., Rosenbauer, H., et al. 1982, JGR, 87, 52

[4] Verscharen, D., Klein, K. G., and Maruca, B. A. 2019, Living Rev. Sol. Phys., 16, 5

[5] Webb, G. M., Barghouty, A. F., Hu, Q., and le Roux, J. A. 2018, APJ, 855, 31

[6] Verscharen, D., Wicks, R. T., Alexandrova, O., et al. 2021, Exp. Astron., 54, 473 1007/s10686-021-09761-5

[7] White, T. G., Oliver, M. T., Mabey, P., et al. 2019, Nat. Commun., 10, 1758

[8] D’Amicis, R., Bruno, R., Panasenco, O., et al. 2021, A&A, 656, A21

[9] Farge, M. 1992, Annu. Rev. Fluid Mech., 24, 395

[10] Greco, A., Chuychai, P., Matthaeus, W. H., Servidio, S., and Dmitruk, P. 2008, GRL, 35, L19111

[11] Perrone, D., Settino, A., De Marco, R., D’Amicis, R., and Perri, D. 2023, Front. Astron. Space Sci., 10, 1250219

[12] Lion, S., Alexandrova, O., and Zaslavsky, A. 2016, APJ, 824, 47

[13] Greco, A., Perri, S., Servidio, S., Yordanova, E., and Veltri, P. 2016, APJL, 823, L39

[14] Perrone, D., Alexandrova, O., Mangeney, A., et al. 2016, APJ, 826, 196

[15] Perrone, D., Alexandrova, O., Roberts, O. W., et al. 2017, APJ, 849, 49

[16] Perrone, D., Bruno, R., D’Amicis, R., et al. 2020, APJ, 905, 142 4357/abc480

[17] Perrone, D., Perri, S., Bruno, R., et al. 2022, A&A, 668, A189

[18] Servidio, S., Valentini, F., Califano, F., and Veltri, P. 2012, PRL, 108, 045001 1103/PhysRevLett.108.045001

[19] Servidio, S., Chasapis, A., Matthaeus, W. H., et al. 2017, PRL, 119, 205101 1103/PhysRevLett.119.205101

[20] Sorriso-Valvo, L., Catapano, F., Retinò, A., et al. 2019, PRL, 122, 035102 https://doi.org10.1103/PhysRevLett.122.035102

[21] Perrone, D., Valentini, F., Servidio, S., Dalena, S., and Veltri, P. 2013, APJ, 762, 99

[22] Servidio, S., Valentini, F., Perrone, D., et al. 2015, JPP, 81, 325810107 1017/S0022377814000841

[23] De Marco, R., Bruno, R., Jagarlamudi, V. K., et al. 2023, A&A, 669, A108

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