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We provide evidence that the sunward-propagating half of the solar wind electron halo distribution evolves without scattering in the inner heliosphere. We assume the particles conserve their total energy and magnetic moment, and perform a 'Liouville mapping' on electron pitch angle distributions measured by the Parker Solar Probe SPAN-E instrument. Namely, we show that the distributions are consistent with Liouville's theorem if an appropriate interplanetary potential is chosen. This potential, an outcome of our fitting method, is compared against the radial profiles of proton bulk flow energy. We find that the inferred potential is responsible for nearly 100 per cent of the proton acceleration in the solar wind at heliocentric distances 0.18-0.79 AU. These observations combine to form a coherent physical picture: the same interplanetary potential accounts for the acceleration of the solar wind protons as well as the evolution of the electron halo. In this picture the halo is formed from a sunward-propagating population that originates somewhere in the outer heliosphere by a yet-unknown mechanism. [ABSTRACT FROM AUTHOR]

Keywords: errata; addenda; plasmas; scattering; solar wind EN errata addenda plasmas scattering solar wind 2399 2400 2 06/21/23 20230801 NES 230801 1 INTRODUCTION A mathematical error appeared in Horaites et al. ([2]), which we will refer to as '[2]'. \end{eqnarray}$$ (5) Without the self-similarity condition (1), the equations (4), (5) above no longer uniquely specify the parameters SB T sb , SB s sb in terms of , , SB n sb , SB B sb [because SB s sb and SB T sb both appear in equation (5) and not equation (4)]. In light of the corrected equation (2) above, the parameter ' in equation (16), [2] should instead be defined as: $$\begin{eqnarray} \alpha ^\prime \equiv \kappa -\frac{\alpha B}{\alpha T}. [Extracted from the article]

We develop a kinetic theory for the electron strahl, a beam of energetic electrons which propagate from the sun along the Parker-spiral-shaped magnetic field lines. Assuming a Maxwellian electron distribution function in the near-sun region where the plasma is collisional, we derive the strahl distribution function at larger heliospheric distances. We consider the two most important mechanisms that broaden the strahl: Coulomb collisions and interactions with oblique ambient whistler turbulence (anomalous diffusion). We propose that the energy regimes where these mechanisms are important are separated by an approximate threshold, |${\cal E}_\mathrm{ c}$|⁠ ; for the electron kinetic energies |${\cal E}\,\lt\, {\cal E}_\mathrm{ c}$| the strahl width is mostly governed by Coulomb collisions, while for |${\cal E}\,\gt\, {\cal E}_\mathrm{ c}$| by interactions with the whistlers. The Coulomb broadening decreases as the electron energy increases; the whistler-dominated broadening, on the contrary, increases with energy and it can lead to efficient isotropization of energetic electrons and to the formation of the electron halo. The threshold energy |${\cal E}_\mathrm{ c}$| is relatively high in the regions closer to the sun, and it gradually decreases with the distance, implying that the anomalous diffusion becomes progressively more important at large heliospheric distances. At 1 au, we estimate the energy threshold to be about |${\cal E}_\mathrm{ c}\,\sim\, 200\, {\rm eV}$|⁠. [ABSTRACT FROM AUTHOR]

We propose a kinetic model describing the formation of the strahl and halo electron populations in the solar wind. We demonstrate that the suprathermal electrons propagating from the Sun along the Parker-spiral magnetic field lines are progressively focused into a narrow strahl at heliospheric distances r ≲ 1 au, while at r ≳ 1 au the width of the strahl saturates due to Coulomb collisions and becomes independent of the distance. Our theory of the strahl broadening does not contain free parameters and it agrees with Wind observations of the strahl width at 1 au to within  |$15\hbox{--}20{{\ \rm per\ cent}}$|⁠, for widths that are resolvable by the instrument. This indicates that Coulomb scattering, rather than anomalous turbulent diffusion, plays a dominant role in strahl formation in these observations. We further propose that the halo electron population at energies |$K \lesssim 200\, \, {\rm eV}$| may be composed of electrons that ran away from the Sun as an electron strahl, but later ended up on magnetic field lines leading them back to the Sun. The halo electrons are therefore not produced locally; rather, they are the fast electrons trapped by magnetic field lines on global heliospheric scales. Through the effects of magnetic defocusing and Coulomb pitch-angle scattering, a narrow source distribution at large heliocentric distances appears nearly isotropic at distances ∼1 au. At larger energies |$K \gtrsim 200\, \, {\rm eV}$|⁠, however, our theory indicates that the scattering provided by Coulomb collisions alone is not sufficient to isotropize a narrow sunward-propagating electron beam. [ABSTRACT FROM AUTHOR]

In this work, we analyse the kinetic stability of a solar wind electron distribution composed of core and strahl subpopulations. The core is modelled by a drifting Maxwellian distribution, while the strahl is modelled by an analytic function recently derived in (Horaites et al. 2018) from the collisional kinetic equation. We perform a numerical linear stability analysis using the LEOPARD solver (Astfalk & Jenko 2017), which allows for arbitrary gyrotropic distribution functions in a magnetized plasma. In contrast with previous reports, we do not find evidence for a whistler instability directly associated with the electron strahl. This may be related to the more realistic shape of the electron strahl distribution function adopted in our work, as compared to previous studies. We, however, find that for typical solar wind conditions, the core–strahl distribution is unstable to the kinetic Alfvén and magnetosonic modes. The maximum growth rates for these instabilities occur at wavenumbers kdi ≲ 1 (where di is the ion inertial length), at moderately oblique angles of propagation, thus providing a potential source of kinetic-scale turbulence. We therefore suggest that if the whistler modes are invoked to explain anomalous scattering of strahl particles, these modes may appear as a result of nonlinear mode coupling and turbulent cascade originating at scales kdi ≲ 1. [ABSTRACT FROM AUTHOR]

We develop a model for the strahl population in the solar wind - a narrow, low-density and high-energy electron beam centred on the magnetic field direction. Our model is based on the solution of the electron drift-kinetic equation at heliospheric distances where the plasma density, temperature and the magnetic field strength decline as power laws of the distance along a magnetic flux tube. Our solution for the strahl depends on a number of parameters that, in the absence of the analytic solution for the full electron velocity distribution function (eVDF), cannot be derived from the theory. We however demonstrate that these parameters can be efficiently found from matching our solution with observations of the eVDF made by the Wind satellite's SWE strahl detector. The model is successful at predicting the angular width (FWHM) of the strahl for the Wind data at 1 au, in particular by predicting how this width scales with particle energy and background density. We find that the strahl distribution is largely determined by the local temperature Knudsen number γ ~ |T dT/dx|/n, which parametrizes solar wind collisionality. We compute averaged strahl distributions for typical Knudsen numbers observed in the solar wind, and fit our model to these data. The model can be matched quite closely to the eVDFs at 1 au; however, it then overestimates the strahl amplitude at larger heliocentric distances. This indicates that our model may be improved through the inclusion of additional physics, possibly through the introduction of 'anomalous diffusion' of the strahl electrons. [ABSTRACT FROM AUTHOR]