  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 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-$\beta_{\parallel c}$ regimes, where
$\beta_{\parallel c}$ 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.
