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In situ observations of the solar wind show a limited level of particletemperature anisotropy with respect to the interplanetary magnetic fielddirection. Kinetic electromagnetic instabilities are efficient to prevent theexcessive growth of the anisotropy of particle velocity distribution functions.Among them, the firehose instabilities are often considered to prevent theincrease of the parallel temperature and hence to shape the velocitydistribution functions of electrons and protons in the solar wind. We present anon-linear modeling of the parallel firehose instability, retaining a kineticdescription for both the electrons and protons. One-dimensional (1D) fullykinetic Particle-In-Cell simulations using the Energy Conserving semi-implicitmethod (ECsim) are performed to clarify the role of the electron temperatureanisotropy in the development of the parallel proton firehose instability. Wefound that in the presence of an electron temperature anisotropy, such that thetemperature parallel to the background magnetic field is higher than thetemperature in the perpendicular direction, the onset of the parallel protonfirehose instability occurs earlier and its growth rate is faster. The enhancedwave fluctuations contribute to the particle scattering reducing thetemperature anisotropy to a stable, nearly isotropic state. The simulationresults compare well with linear theory. A test case of 1D simulations atoblique angles with respect to the magnetic field is also considered, as afirst step to study the cumulative effect of protons and electrons on the fullspectrum of instabilities.

Particle-In-Cell simulations of the parallel proton firehose instability influenced by the electron temperature anisotropy in solar wind conditions