Particle-in-cell (PIC) simulations are focusing on the individual trajectories of a very large number of particles in self-consistent and external electric and magnetic fields; they are widely used in the study of plasma jets, for example. The main disadvantage of PIC simulations is the large simulation runtime,which often requires a parallel implementation of the algorithm. The current paper focuses on a PIC1d3v simulation algorithm and describes the successful implementation of a parallel version of it on a multi-core architecture, using OpenMP, with very promising experimental and theoretical results.