Regulation of temperature anisotropy for solar wind protons and alpha particles by collisions and instabilities

¹ Centre for Mathematical Plasma Astrophysics, Department of Mathematics, KU Leuven, Celestijnenlaan 200B, B-3001 Leuven, Belgium
² Institute for Physical Science and Technology, University of Maryland, College Park, MD 20742-2431, USA
³ Space Sciences Laboratory, University of California, Berkeley, CA 94720, USA
⁴ Institute for Theoretical Physics IV, Faculty for Physics and Astronomy, Ruhr University Bochum, D-44780 Bochum, Germany
⁵ Lunar & Planetary Laboratory, University of Arizona, Tucson, AZ 85721-0092, USA
⁶ Research Center in the intersection of Plasma Physics, Matter, and Complexity ( P 2 mc), Comisión Chilena de Energía Nuclear, Casilla 188-D, Santiago, Chile
⁷ Departamento de Ciencias Físicas, Facultad de Ciencias Exactas, Universidad Andres Bello, Sazié 2212, Santiago 8370136, Chile
⁸ Department of Physics and Materials Sciences, College of Arts and Sciences, Qatar University, 2713 Doha, Qatar
⁹ Korea Astronomy and Space Science Institute, Daejeon 34055, Korea
¹⁰ Department of Physics, GC University, Lahore, Katchery Road, Lahore 54000, Pakistan
¹¹ Institute of Physics, University of Maria Curie-Sklodowska, ul. Radziszewskiego 10, 20-031 Lublin, Poland

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Received: 2 September 2025
Accepted: 5 October 2025

Abstract

Context. Determining which mechanisms regulate proton and alpha particle temperature anisotropies in the solar wind is an outstanding problem in collisionless plasma systems. For decades, the occurrence distributions of the various charged particle species measured in the near-Earth solar wind have been known to be characterized by peculiar rhombic shapes in (β_∥, T_⊥/T_∥) phase space, where β_∥ is the ratio of parallel (with respect to the ambient magnetic field) plasma thermal pressure and the ambient magnetic field energy density and T_⊥, ∥ are temperatures in the perpendicular or parallel directions. Despite this fact, a convincing explanation for the physical mechanisms producing the low-β edges had not been forthcoming until recently.

Aims. Recent works have provided plausible explanations for the origin of these distributions by invoking the combined effects of collisions and instability excitation; however, the initial applications were limited to proton and electron plasmas. In the present paper, the same coupled mechanism is extended to include alpha particles (He⁺⁺), which dynamically couple to the protons.

Methods. We performed an ensemble simulation based upon the collisional relaxation equation that couples the protons and alpha particle dynamics in the low-beta regime. We also carried out another ensemble simulation based on the instability-induced quasi-linear relaxation equation for the high-beta regime.

Results. We find that the combined effects provide a satisfactory first-order explanation of the observed temperature distribution, resolving one of the long-standing problems in contemporary heliospheric physics.

Conclusions. The findings of the present study demonstrate that the collisional relaxation is adequate to describe the existence of an outer boundary associated with the proton and alpha particle occurrence distribution in the low-beta regime. For the high-beta regime, it is known that the instability-induced relaxation is important, and the present ensemble simulation confirms this notion.