Science nugget: Resolving proton and alpha beams for improved understanding of plasma kinetics: SWA-PAS observations - Solar Orbiter

Resolving proton and alpha beams for improved understanding of plasma kinetics: SWA-PAS observations

(Solar Orbiter Nugget #40 by Roberto Bruno¹, Rossana De Marco¹, Raffaella D’Amicis¹, Denise Perrone², Maria Federica Marcucci¹, Daniele Telloni³, Raffaele Marino⁴, Luca Sorriso-Valvo^5,12, Vito Fortunato⁶, Gennaro Mele⁷, Francesco Monti⁸, Andrei Fedorov⁹, Philippe Louarn⁹, Chris J. Owen¹⁰, and Stefano Livi¹¹)

Introduction

A crucial step in unraveling the mechanisms behind wave-particle interactions, which drive the heating and acceleration of solar wind particles, lies in the detailed analysis of the non-Maxwellian characteristics of the particle velocity distribution function (VDF). Features such as temperature anisotropies and particle beams offer critical insights into these processes. In particular, the ability to separate the beam from the core within the VDF, especially for the two dominant solar wind components, is essential. This separation enhances our understanding of how energy is transferred and provides a clearer picture of the underlying physics that governs solar wind dynamics and thermodynamics. For example, by separating the two populations for the protons, we can distinguish between the behaviors of the bulk solar wind plasma (core) and the faster, more energetic population (beam) that might arise from different physical processes. The beam is a secondary proton population, often moving faster than the core. It is typically more anisotropic and is believed to originate from processes such as wave-particle interactions, proton-proton collisions, or magnetic reconnection in the solar corona.

The presence of a proton beam can drive various plasma instabilities that impact the evolution of the solar wind. These instabilities, such as the Alfvén-cyclotron instability and the mirror-mode instability, can generate waves and turbulence, affecting the heating, acceleration, and scattering of particles. If the core and beam are not separated, we might overlook these instabilities and their impact on the plasma's behavior.

A similar conclusion applies to alpha particles, though specific studies that separately analyze the core and beam kinetics of alpha particles are currently lacking. To the best of our knowledge, our recently published study [1] is the first to provide a full 3D kinetic characterization of both populations in phase space, representing a significant advancement in solar wind kinetic research.

Separating different ion populations

We used an innovative numerical approach, applying a machine learning clustering technique to distinguish between the different populations within the VDF, surpassing the limitations of the traditional bi-Maxwellian fitting method [2]. This approach simplifies the identification of distinct particle populations and allows for the generation of robust statistics on the kinetic properties of both core and beam populations for protons and alpha particles. In Figure 1a, we present, for the first time in the literature, the RTN velocity space for the proton core (red), proton beam (black), alpha core (blue), and alpha beam (green) populations, as identified by our code [2]. We calculated moments for approximately 60,000 particle VDFs at 4-s cadence within a high-velocity stream observed at 0.58 AU by the Proton and Alpha Sensor (PAS) onboard Solar Orbiter. PAS is one of the three sensors in the Solar Wind Analyser (SWA) plasma suite [3]. As expected, the four populations are aligned with the average magnetic field vector. Proton core, alpha core, alpha beam, and proton beam velocity fluctuations are all distributed over the surfaces of a sort of hemispheres characterized by different radii [4]. Interestingly enough, the concavity of these hemispheres for proton and alpha beams is opposite to that of the proton core and, less clearly, to that of the alpha core. This distinct feature in velocity space is closely associated with Alfvénic fluctuations. In the following sections, we will focus specifically on the Alfvénic characteristics of the velocity fluctuations observed in the core and beam populations of protons and alpha particles. For a more detailed analysis of the kinetic properties of both the core and beam, we refer the reader to our recently published work [1].

Figure 1a: RTN velocity space for the proton core (red), proton beam (black), alpha core (blue), and alpha beam (green), with projections onto orthogonal planes (gray dots). The cyan arrow marks the average magnetic field direction, while the star shows the center of mass velocity (fluid speed) projection. Colored dots represent the average speed of each population. The time interval covers 12 hours, with a PAS sampling time of 4 seconds. Figure 1b: Schematic of phase space in the RTN system showing velocity fluctuations of the proton core (p1, red), alpha core (α1, blue), proton beam (p2, black), and alpha beam (α2, green) due to Alfvén waves. The black star represents the fluid velocity from all populations. The cyan arrow marks the average magnetic field direction and the WF, marked by the intersection of dashed lines, is located 1 Alfvén speed from the bulk velocity V_bulk . The various Δ V^WF represent the velocity drift of each population from WF.

Estimating the correct Alfvén velocity fluctuation for each population

The mechanism at the basis of these fluctuations is sketched in Figure 1b. There is a particular frame in phase space that represents the center of the oscillations of protons and alphas [5, 6, 7]. This frame is the wave frame (WF). In this frame, no electric field is associated with the fluctuations, and each particle’s velocity will change only in direction maintaining a constant speed. Consequently, each particle will be forced to move on the surface of a constant radius in phase space, being the concavity of the resultant hemisphere due to the value of the particle’s drift velocity with respect to the WF.

The WF in Figure 1b is represented by the crossing point of the two dashed lines, which limit the amplitude of the fluctuations of each population around this pivotal point. This point is one Alfvén speed from the bulk velocity, i.e. the velocity of the center of mass, represented by the black star symbol. Then, the correct amplitude for each of the Alfvén velocity components V^*_{A_{i = R, T, N}} should be determined by the following relation:

V^*_{A_{i = R, T, N}} = V_{A_{i = R, T, N}} ΔV^WF / |V_A|

where V_{A_{i = R, T, N}} and |V_A| represent the generic component and the speed value of the Alfvén velocity obtained from its canonical form [8], respectively. The parameter ΔV^WF is the drift velocity of the specific ion population from the WF.

Figure 2. Column a), top panel: values of the normal component of the proton core velocity fluctuations V_{N_p1} values of the normal component of Alfvén velocity fluctuations V_{A_N}. Column a), bottom panel: same values on the vertical axis vs corrected values of the normal component of Alfvén velocity fluctuations V^*_{A_Np₁}(see text). Column b), same format as for column a but relative to the proton beam velocity fluctuations.

The bottom row of Figure 2 illustrates the effect of the correction applied to the amplitude of the normal component of the Alfvén velocity fluctuations (eq. 1) for the proton core (column a) and proton beam (column b) shown in the top row. This correction improves energy equipartition and enhances the V-V_A correlation coefficient, particularly for the proton core population. The scatter plots for the proton core and beam display opposite correlation signs, as these two populations are located on opposite sides relative to the WF.

Figure 3. Column a), top panel: values of the normal component of the alpha core velocity fluctuations V_{N_α1} values of the normal component of Alfvén velocity fluctuations V_{A_N}. Column a), bottom panel: same values on the vertical axis vs corrected values of the normal component of Alfvén velocity fluctuations V^*_{A_N}α1 (see text). Column b), same format as for column a) but relative to the alpha beam velocity fluctuations.

Figure 3, in the same format as Figure 2, shows the effect of the correction applied to the amplitude of the normal component of the Alfvén velocity fluctuations (eq. 1) for the alpha core (column a) and alpha beam (column b). In this case, the improvements in both energies equipartition and the V-VA correlation are even greater than those observed for protons. As in Figure 2, the scatter plots for these two populations exhibit opposite correlation signs, with the α core aligned with the proton core and the alpha beam aligned with the proton beam relative to the WF.

Conclusion

The analysis, extensively presented in [1], carefully examines the distinct kinetic features of the core and beam for both protons and alpha particles and offers a more accurate approach to understanding the physical processes that govern particle distribution in the solar wind. Separating the core and beam in the proton and alpha velocity distribution function is crucial for: i) identifying different origins and behaviors in the different particle populations; ii) understanding plasma instabilities that affect solar wind heating and acceleration; iii) analyzing temperature anisotropies and energy transfer processes; iv) accurately modeling the transport and evolution of solar wind particles, giving insights into the mechanisms that govern solar wind evolution during the expansion.

In conclusion, this separation plays a pivotal role in constructing a far more complete and accurate understanding of the solar wind's dynamics. This is absolutely essential for advancing both theoretical studies and precise modeling efforts.

Acknowledgments

This work is supported by the grant “Machine Learning on Solar Wind Velocity Distribution Functions” financed by the National Institute for Astrophysics under the call “Fundamental Research 2023.” Solar Orbiter is a space mission of international collaboration between ESA and NASA, operated by ESA. Solar Orbiter SWA data are derived from scientific sensors that 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 Spatiales (CNES, France), the Centre national d'études spatiales (CNRS, France), the Czech contribution to the ESA PRODEX programme and NASA.

Solar Orbiter SWA work at INAF/IAPS is currently funded under ASI grant 2018-30-HH.1-2022. The authors acknowledge T. Horbury and the MAG Team for Solar Orbiter magnetic field data.

Affiliations

1 INAF-Istituto di Astrofisica e Planetologia Spaziali, Roma, Italy;

2 ASI - Italian Space Agency, Rome, Italy

3 INAF - Osservatorio Astrofisico di Torino, Torino, Italy

4 Université Lyon, CNRS, École Centrale de Lyon, Écully, France

5 CNR, Istituto per la Scienza e la Tecnologia dei Plasmi, Bari, Italy

6 Planetek Italia S.R.L., Bari, Italy

7 LEONARDO spa, Grottaglie, Taranto, Italy

8 TSD-Space, Napoli, Italy

9 Institut de Recherche en Astrophysique et Planétologie, CNRS, Université de Toulouse, CNES, Toulouse, France

10 Mullard Space Science Laboratory, UCL, Holmbury St. Mary, Dorking, Surrey, UK

11 Southwest Research Institute, San Antonio, TX, USA