solar orbiter reveals non-field-aligned solar wind Proton beams and its role in wave growth activities

(Solar Orbiter nugget #16 by X. Zhu1, J. He1, D. Duan1, D. Verscharen2, C. J. Owen2, A. Fedorov3, P. Louarn3, T. Horbury4)

The coupling mechanism of the ubiquitous proton beams with fields is a cutting-edge scientific question in the solar wind wavelike turbulence. Using Solar Orbiter's high-quality measurements, it is found that the proton beam is not strictly parallel to the local magnetic field, exhibiting an intriguing feature of non-field-alignment. This non-field-aligned proton beam significantly influences the growth of wavelike turbulence at ion scales.


Solar Orbiter [1] carries the Solar Wind Analyzer/Proton Alpha Sensor (SWA/PAS) [2] - measuring the three-dimensional velocity distribution of solar wind ions with high angular and time resolutions, and the fluxgate magnetometer (MAG) [3] - measuring the magnetic field with high resolution. It provides us an opportunity to study particle dynamics and field-particle interactions in greater details, which are essential for understanding energy transfer processes in the solar wind.


Ion-scale waves, including Alfvén/ion-cyclotron waves and fast-magnetosonic/whistler waves, are prevalent in the inner heliosphere [4,5,6,7]. Their amplitudes are large enough to be identified by in-situ measurements out of the turbulent background. They contain sufficient energy and are able to influence solar wind evolution as a whole. The energy transfer associated with these waves is a significant energy conversion channel between fields and particles in the solar wind. However, the field-particle coherent coupling associated with these waves is still a mystery. How are these waves generated? What is the dynamic characteristic of the wave field and particles during the wave activity? To answer these questions, an advanced combination of observations and theoretical analysis is needed and has been conducted by Zhu et al. (2023), which is recently published on the ApJ.


Measurement of Non-Field-Aligned Proton Beams Associated with Wave Activities

On 02 August 2020, from 11:30 UT to 12:00 UT, Solar Orbiter meets an interval of ion-scale waves lasting about 30 minutes. During this period, the spacecraft is in the south to the Sun’s equatorial plane and immersed in the solar wind with an average speed of about 370 kilometers per second (Fig 1a).


Polarization and propagation analyses of the measured magnetic fields indicate that the enhanced wave-like fluctuations are circularly polarized, propagating along the local mean magnetic field direction (Fig 1b). SWA-PAS conducted regular measurements, capturing over 600 ion velocity distributions over half an hour. The ion velocity distributions exhibit a typical core-beam feature with a drift velocity roughly about the local Alfvén speed. Upon comparing the drift direction with the instantaneous magnetic field orientation, a remarkable observation emerges: the proton beams conspicuously deviate from the traditionally anticipated field-aligned drift (see Fig 1c). This kind of newly found observational feature is called “non-field-aligned beam” by the authors. Statistically, most drift velocities derived from the SWA/PAS measurements apparently deviate from the instant magnetic field direction (Fig 1d). The average deviation angle is about 176°.


Figure 1. (a) Position of Solar Orbiter and Earth in the Carrington coordinates. The yellow solid line denotes the back-tracing line along the interplanetary magnetic field from a magnetohydrodynamic model instantiation run by Predictive Science Inc. (b) Properties of polarization and propagation of the enhanced wave-like fluctuations as observed by Solar Orbiter on August 02 2023/11:30-12:00. (c) 2D slices of the proton velocity distributions measured by SWA/PAS at two times. Non-field-aligned beam feature is identifiable, with the black arrow and the blue line guiding the magnetic field and the drift directions, respectively. (d) (left) Distribution of the normalized drift velocity direction with the local magnetic field direction pointing towards the bottom pole and (right) the probability distribution function (PDF) of the angle between the magnetic field vector and the drift velocity vector ().



Non-Field-Aligned Proton Beam as An Intrinsic Perturbation of Eigenmode Wave:

Using the newly developed solver named as "Plasma Kinetic Unified Eigenmode Solutions" (PKUES for short), the authors probed the possible presence of unstable eigenmode solutions in the solar wind plasma and magnetic field conditions detected by the Solar Orbiter. By employing a dual bi-Maxwellian velocity distribution to approximate the core and beam distributions of solar wind protons, they pinpointed unstable eigenmode solutions linked to fast-magnetosonic/whistler waves counter-propagating to background magnetic field, illustrated in the left panel of Fig 2a. The wave instability is found to arise from the coherent coupling between proton beams and the field (see Fig 2a right panel).


Further analysis disclosed that both magnetic field and particle motions (proton core and beam distributions) exhibit perpendicular cyclotron eigen-perturbations with respect to the background magnetic field direction. Notably, these perpendicular cyclotron eigen-perturbations are out of phase (refer to Fig 2b). The study emphasizes that coupling between cyclotron eigen-perturbations of the beam and the electric field contribute to the unstable wave growth. Additionally, the non-in-phase nature of cyclotron eigen-perturbations between the field and particles causes the beam's drift direction to deviate from the magnetic field direction (see Fig 2c), aligning with observations by the Solar Orbiter.



This work highlights the need for in-depth analysis of solar wind turbulence at kinetic scales. To achieve this, high-quality measurements and comprehensive analyses of disturbances in fields and particles within the solar wind, similar to what Solar Orbiter offers, are crucial. Additionally, theoretical tools like PKUES are necessary for conducting a comprehensive theoretical analysis of the complete set of eigen-perturbations in eigenmode solutions. By combining observation and theory, we can maximize our understanding of these phenomena.


Figure 2. (a) (left) Dispersion relation and (right) growth rate of the unstable fast-magnetosonic/whistler branch. (b) The proton velocity distribution as seen from two orthogonal perspectives along and perpendicular to the background magnetic field. (c) Reconstructed time series of the fluctuating quantities for the solution with the maximum growth rate.


Accompanying movie for Figure 2










This work has been published in:

Xingyu Zhu, Jiansen He, Die Duan, Daniel Verscharen, Christopher J. Owen, Andrey Fedorov, Philippe Louarn and Timothy S. Horbury. (2023). Non-field-aligned Proton Beams and Their Roles in the Growth of Fast Magnetosonic/ Whistler Waves: Solar Orbiter Observations. The Astrophysical Journal, 953, 161.




1Peking University, No.5 Yiheyuan Road, Haidian District, Beijing, 100871, Peopleʼs Republic of China;

2Mullard Space Science Laboratory, University College London, Dorking RH5 6NT, UK

3Institut de Recherche en Astrophysique et Planétologie, 9, Avenue du Colonel ROCHE, BP 4346, F-31028 Toulouse Cedex 4, France

4Space and Atmospheric Physics, The Blackett Laboratory, Imperial College London, London SW72AZ, UK




[1] Müller, D., Cyr, O. S., Zouganelis, I., Gilbert, H. R., Marsden, R., Nieves-Chinchilla, T., ... & Williams, D. (2020). The solar orbiter mission-science overview. Astronomy & Astrophysics642, A1.

[2] Owen, C. J., Bruno, R., Livi, S., Louarn, P., Al Janabi, K., Allegrini, F., ... & Zouganelis, I. (2020). The solar orbiter solar wind analyser (SWA) suite. Astronomy & Astrophysics642, A16.

[3] Horbury, T. S., O’brien, H., Blazquez, I. C., Bendyk, M., Brown, P., Hudson, R., ... & Walsh, A. P. (2020). The solar orbiter magnetometer. Astronomy & Astrophysics642, A9.

[4] Jian, L. K., Russell, C. T., Luhmann, J. G., Strangeway, R. J., Leisner, J. S., & Galvin, A. B. (2009). Ion cyclotron waves in the solar wind observed by STEREO near 1 AU. The Astrophysical Journal701(2), L105.

[5] Boardsen, S. A., Jian, L. K., Raines, J. L., Gershman, D. J., Zurbuchen, T. H., Roberts, D. A., & Korth, H. (2015). MESSENGER survey of in situ low frequency wave storms between 0.3 and 0.7 AU. Journal of Geophysical Research: Space Physics120(12), 10-207.

[6] Bowen, T. A., Mallet, A., Huang, J., Klein, K. G., Malaspina, D. M., Stevens, M., ... & Whittlesey, P. (2020). Ion-scale electromagnetic waves in the inner heliosphere. The Astrophysical Journal Supplement Series246(2), 66.

[7] He, J., Zhu, X., Luo, Q., Hou, C., Verscharen, D., Duan, D., ... & Yao, Z. (2022). Observations of Rapidly Growing Whistler Waves in Front of Space Plasma Shock due to Resonance Interaction between Fluctuating Electron Velocity Distributions and Electromagnetic Fields. The Astrophysical Journal941(2), 147.


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