  In the solar wind an equipartition of kinetic energy densities can be easily
established between thermal and suprathermal electrons and the instability
conditions are markedly altered by the interplay of these two populations. The
new thresholds derived here for the periodic branch of firehose instability
shape the limits of temperature anisotropy reported by the observations for
both electron populations. This instability constraint is particularly
important for the suprathermal electrons which, by comparison to thermal
populations, are even less controlled by the particle-particle collisions. An
extended quasilinear approach of this instability confirms predictions from
linear theory and unveil the mutual effects of thermal and suprathermal
electrons in the relaxation of their temperature anisotropies and the
saturation of growing fluctuations.
