The formation and evolution of coherent structures in an electron plasma is investigated in the Malmberg‐Penning trap ELTRAP in different regimes of operation, using a CCD diagnostic system. In the trapped plasma configuration the experimental results are in agreement with the two dimensional Euler fluid behavior of the (bounce averaged) electron columns, as found in the literature. In the beam regime, where a low energy electron plasma continuously flows from the emitting thermionic cathode to a collector, a rapid development of coherent structures is found when a part of the beam is reflected back to the source, due to space charge effects. The convective evolution of the structures along the beam is studied by varying the strength of the confined magnetic field. The observed nonlinear processes are interpreted using a tridimensional particle‐in‐cell code which solves the fluid, drift‐Poisson system.