Contributions of protons in electron firehose instability driven by solar wind core-halo electrons

Solar wind plasmas are replete with propagating modes and instabilities triggered by temperature anisotropies associated with different charged particle species. In situ measurements reveal the bounded magnitudes of these anisotropies at large heliocentric distances. This paper details the physical aspects related to the electron firehose instability as a major candidate to regulate the parallel electron temperature anisotropies assuming a dynamic interplay of solar wind protons and core/halo electrons under the dilute space plasma condition. The velocity moments based technique is adopted for quasi-linear kinetic theory by taking the bi-Maxwellian model for protons and distinct core-halo components of electrons whose temperatures may vary in time. On the basis of such a macroscopic quasi-linear procedure, a closed set of equations is formulated to depict the dynamical progression of the proton and core/halo electron temperatures along with wave energy density associated with the unstable mode. Unlike previous similar studies, the present analysis emphasizes the role of an initially unstable proton velocity distribution.