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Notes: Propagation of a nonrelativistic electron beam in a plasma in a strong magnetic field has been studied using electrostatic one-dimensional particle simulation models. Electron beams of finite pulse length and of continuous injection are followed in time to study the effects of beam–plasma interaction on the beam propagation. For the case of pulsed beam propagation, it is found that the beam distribution rapidly spreads in velocity space generating a plateaulike distribution with a high energy tail extending beyond the initial beam velocity. This rapid diffusion takes place within a several amplification length of the beam–plasma instability given by (ωpω2b) −1/3V0, where ωp, ωb, and V0 are the target plasma, beam–plasma frequencies, and the beam drift speed. This plateaulike distribution, however, becomes unstable as the high energy tail electrons free-stream, generating a secondary beam. A similar process is observed to take place for the case of continuous beam injection when the beam density is small compared with the total density nb/nt〈1. In particular, the electron velocity distribution is found monotonically decreasing in energy, having a high energy tail whose energy reaches twice the initial beam energy. Such an electron distribution is also seen in laboratory experiments and in computer simulations performed for a uniform, periodic system. When the beam density is increased so that the beam current exceeds the thermal return current, enbV0(approximately-greater-than)enevt, where ne and vt are the density and thermal speed of the ambient electrons, beam propagation becomes much slower due to the electric field generated by the excess charges associated with the beam electrons.Beam electrons are reflected from the ambient plasma as if they are bouncing off a rigid wall. When the beam velocity is increased while holding the beam density constant, simulations show that the beam current can exceed significantly the return current generated by the thermal electrons enevt. It is shown that the electric field generated by the beam–plasma instability accelerates the ambient electrons opposite to the beam propagation, thereby enhancing the return current.