Collisionless electron beam–plasma instabilities are expected to play an important role in fast ignition. Such beams are produced by the short high power ignition laser interacting with long scale length plasmas. Here we present results from a one-dimensional Vlasov–Poisson code used to investigate different electron beam temperatures and background plasma conditions. The simulations demonstrate that the beam–plasma instabilities drive large amplitude electrostatic waves that undergo the parametric decay instability driving backwards propagating electrostatic waves and much lower frequency ion acoustic waves. Saturation of the beam–plasma instability creates a plateau in the electron distribution function consistent with quasi-linear theory. We observe the creation of high energy tails in the electron and ion distribution functions, formed by the trapping of particles in the waves formed during the collapse of the beam. The high energy tails of the ion distribution are found to account for up to one-half of the energy gained by the ion population from the beam collapse. Furthermore, at the highest electron beam temperatures we observe the formation of long-lived coherent phase–space structures. These phase–space structures are a direct consequence of the cascade nature of the parametric instability driving up lower wavenumber modes that have higher phase velocities that can in turn accelerate electrons to energies in excess of the initial beam energy. A quasi-linear treatment also shows similar effects but the simulations are clearly beyond a simple quasi-linear treatment and demonstrate the transfer of energy from an incident beam to the ion population via collisionless effects. The implications of these mechanisms for the fast ignition scheme will be discussed.