  The dissipation mechanism of the magnetic energy in turbulent collisionless
space and astrophysical plasmas is still not well understood. Its investigation
requires efficient kinetic simulations of the energy transfer in collisionless
plasma turbulence. In this respect, hybrid-kinetic simulations, in which ions
are treated as particles and electrons as an inertial fluid, have begun to
attract a significant interest recently. Hybrid-kinetic models describe both
ion- and electron scale processes by ignoring electron kinetic effects so that
they are computationally much less demanding compared to fully kinetic plasma
models. Hybrid-kinetic codes solve either the Vlasov equation for the ions
(Eulerian Vlasov-hybrid codes) or the equations of motion of the ions as
macro-particles (Lagrangian Particle-in-Cell (PIC)-hybrid codes). They consider
the inertia of the electron fluid using different approximations. We check the
validity of these approximations by employing our recently massively
parallelized three-dimensional PIC-hybrid code CHIEF which considers the
electron inertia without any of the common approximations. In particular we
report the results of simulations of two-dimensional collisionless plasma
turbulence. We conclude that the simulation results obtained using
hybrid-kinetic codes which use approximations to describe the electron inertia
need to be interpreted with caution. We also discuss the parallel scalability
of CHIEF, to the best of our knowledge, the first PIC-hybrid code which without
approximations describes the inertial electron fluid.
