  Important efforts are currently made for understanding the so-called kinetic
instabilities, driven by the anisotropy of different species of plasma
particles present in the solar wind and terrestrial magnetosphere. These
instabilities are fast enough to efficiently convert the free energy of plasma
particles into enhanced (small-scale) fluctuations with multiple implications,
regulating the anisotropy of plasma particles. In this paper we use both linear
and quasilinear (QL) frameworks to describe complex unstable regimes, which
realistically combine different temperature anisotropies of electrons and ions
(protons). Thus parameterized are various instabilities, e.g., proton and
electron firehose, electromagnetic ion cyclotron, and whistler instability,
showing that their main linear properties are markedly altered by the interplay
of anisotropic electrons and protons. Linear theory may predict a strong
competition of two instabilities of different nature when their growth rates
are comparable. In the QL phase wave fluctuations grow and saturate at
different levels and temporal scales, by comparison to the individual
excitation of the proton or electron instabilities. In addition, cumulative
effects of the combined proton and electron induced fluctuations can markedly
stimulate the relaxations of their temperature anisotropies. Only whistler
fluctuations inhibit the efficiency of proton firehose fluctuations in the
relaxation of anisotropic protons. These results offer valuable premises for
further investigations in numerical simulations, to decode the full spectrum of
kinetic instabilities resulting from the interplay of anisotropic electrons and
protons in space plasmas.
