  We investigate properties of a solar wind-like plasma including a secondary
alpha particle population exhibiting a parallel temperature anisotropy with
respect to the background magnetic field, using linear and quasi-linear
predictions and by means of one-dimensional hybrid simulations. We show that
anisotropic alpha particles can drive a parallel fire hose instability
analogous to that generated by protons, but that, remarkably, the instability
can be triggered also when the parallel plasma beta of alpha particles is below
unity. The wave activity generated by the alpha anisotropy affects the
evolution of the more abundant protons, leading to their anisotropic heating.
When both ion species have sufficient parallel anisotropies both of them can
drive the instability, and we observe generation of two distinct peaks in the
spectra of the fluctuations, with longer wavelengths associated to alphas and
shorter ones to protons. If a non-zero relative drift is present, the unstable
modes propagate preferentially in the direction of the drift associated with
the unstable species. The generated waves scatter particles and reduce their
temperature anisotropy to marginally stable state, and, moreover, they
significantly reduce the relative drift between the two ion populations. The
coexistence of modes excited by both species leads to saturation of the plasma
in distinct regions of the beta/anisotropy parameter space for protons and
alpha particles, in good agreement with in situ solar wind observations. Our
results confirm that fire hose instabilities are likely at work in the solar
wind and limit the anisotropy of different ion species in the plasma.
