The author investigates the mechanism whereby an electron beam interacts with a cold plasma in an open trap t o produce fast electrons, considering in particular the case where the electron plasma frequency, calculated from the cold plasma density, is considerably greater than the electron cyclotron frequency. It is assumed that the electron beam is the source of the electrons which are involved in the acceleration process. It is also assumed that the beam is the source of Langmuir oscillations with an anisotropic spectrum and that the electrons "ejected" from the beam, after interacting with the Langmuir oscillations, diffuse radially and at the same time accelerate. With these assumptions, it is possible to solve the kinetic equation with quasi-linear collision integral and to find the distribution function of the fast electrons at each point in the trap. It is also possible to calculate the "temperature" of the fast electrons and their total energy, and to determine how these quantities depend on the magnetic field strength and on the radius of the diaphragm limiting the diameter of the plasma. The results are in good agreement with experimental data.