We investigate the scattering of strahl electrons by micro-instabilities as a mechanism for creating the electron halo in the solar wind. We develop a mathematical framework for the description of electron-driven microinstabilities and discuss the associated physical mechanisms. We find that an instability of the oblique fastmagnetosonic/whistler (FM/W) mode is the best candidate for a micro-instability that scatters strahl electrons into the halo. We derive approximate analytical expressions for its instability threshold and confirm their accuracy through comparison with numerical solutions to the hot-plasma dispersion relation. We find that the strahl-driven oblique FM/W instability creates copious FM/W waves under low-β c conditions when U 0s 3w c , where β c is the ratio of the core electrons' thermal pressure to the magnetic pressure, U 0s is the strahl speed, and w c is the thermal speed of the core. These waves have a propagation angle of about 60 • with respect to the background magnetic field and a frequency of about half the local electron gyro-frequency. We also derive an analytical expression for the strahl-driven oblique FM/W instability for β c values approaching unity. The comparison of our theory results with data from the Wind spacecraft confirms the relevance of the oblique FM/W instability for the solar wind. We show that the whistler heat-flux, ion-acoustic heat-flux, kinetic-Alfvénwave heat-flux, and electrostatic electron-beam instabilities cannot fulfill the requirements for self-induced scattering of strahl electrons into the halo. We make predictions for the electron strahl close to the Sun, which will be testable against measurements from Parker Solar Probe and Solar Orbiter.

We develop and apply a bespoke fitting routine to a large volume of solar wind electron distribution data measured by Parker Solar Probe over its first five orbits, covering radial distances from 0.13 to 0.5 au. We characterize the radial evolution of the electron core, halo, and strahl populations in the slow solar wind during these orbits. The fractional densities of these three electron populations provide evidence for the growth of the combined suprathermal halo and strahl populations from 0.13 to 0.17 au. Moreover, the growth in the halo population is not matched by a decrease in the strahl population at these distances, as has been reported for previous observations at distances greater than 0.3 au. We also find that the halo is negligible at small heliocentric distances. The fractional strahl density remains relatively constant at ∼1% below 0.2 au, suggesting that the rise in the relative halo density is not solely due to the transfer of strahl electrons into the halo.

We analyze the micro-kinetic stability of the electron strahl in the solar wind depending on heliocentric distance. The oblique fast-magnetosonic/whistler (FM/W) instability has emerged in the literature as a key candidate mechanism for the effective scattering of the electron strahl into the electron halo population. Using data from the Parker Solar Probe (PSP) and Helios, we compare the measured strahl properties with the analytical thresholds for the oblique FM/W instability in the low- and high-β ∥c regimes, where β ∥c is the ratio of the core parallel thermal pressure to the magnetic pressure. Our PSP and Helios data show that the electron strahl is on average stable against the oblique FM/W instability in the inner heliosphere. Our analysis suggests that the instability, if at all, can only be excited sporadically and on short timescales. We discuss the caveats of our analysis and potential alternative explanations for the observed scattering of the electron strahl in the solar wind. Furthermore, we recommend the numerical evaluation of the stability of individual distributions in the future to account for any uncertainties in the validity of the analytical expressions for the instability thresholds.

We propose a transport theory for the kinetic evolution of solar-wind electrons in the heliosphere. We derive a gyro-averaged kinetic transport equation that accounts for the spherical expansion of the solar wind and the geometry of the Parker spiral magnetic field. To solve our three-dimensional kinetic equation, we develop a mathematical approach that combines the Crank–Nicolson scheme in velocity space and a finite-difference Euler scheme in configuration space. We initialize our model with isotropic electron distribution functions and calculate the kinetic expansion at heliocentric distances from 5 to 20 solar radii. In our kinetic model, the electrons evolve mainly through the combination of ballistic particle streaming, the magnetic mirror force, and the electric field. By applying fits to our numerical results, we quantify the parameters of the electron strahl and the core part of the electron velocity distributions. The strahl fit parameters show that the density of the electron strahl is around 7% of the total electron density at a distance of 20 solar radii, the strahl bulk velocity and strahl temperature parallel to the background magnetic field stay approximately constant beyond a distance of 15 solar radii, and β ∥s (i.e., the ratio of the strahl parallel thermal pressure to the magnetic pressure) is approximately constant with heliocentric distance at a value of about 0.02. We compare our results with data measured by the Parker Solar Probe. Furthermore, we provide theoretical evidence that the electron strahl is not scattered by the oblique fast-magnetosonic/whistler instability in the near-Sun environment.

We present an observational analysis of the electron thermal energy budget using data from Parker Solar Probe. We use the macroscopic moments, obtained from our fits to the measured electron distribution function, to evaluate the thermal energy budget based on the second moment of the Boltzmann equation. We separate contributions to the overall budget from reversible and irreversible processes. We find that an irreversible thermal energy source must be present in the inner heliosphere over the heliocentric distance range from 0.15 to 0.47 au. The divergence of the heat flux is positive at heliocentric distances below 0.33 au, while beyond 0.33 au, there is a measurable degradation of the heat flux. Expansion effects dominate the thermal energy budget below 0.3 au. Under our steady-state assumption, the free streaming of the electrons is not sufficient to explain the observed thermal energy density budget. We conjecture that the most likely driver for the required heating process is turbulence. Our results are consistent with the known nonadiabatic polytropic index of the electrons, which we measure as 1.18 in the explored range of heliocentric distances.