We investigate theoretically and experimentally the possibility of energy deposition enhancement when a relativistic electron beam interacts with a high density plasma. The beam‐plasma instability is studied taking into account the angular spread of the beam, the electron‐ion collisions, and the density gradients. The beam (500 kV, 250 kA, 50 ns) interacts with a thin CH2foil. Contrary to previous experiments, the plasma expansion from the foil target is found to be symmetric. The maximum temperature estimated by x‐ray diodes is 13 eV. The measured parameters (temperature, density, gradients), together with the theoretical study, show that the beam‐plasma instability is ineffective in the expanding target.