An experimental illustration of the transition between two basic transport regimes for wave-particle interaction is reported. A striking feature is that chaos, although present in both regimes, does not need to be invoked to explain the observed behavior. This experimental realization for a theoretical paradigm opens the possibility to check the validity of basic models, as is normally required in physics. Indeed, among seemingly simple problems exhibiting complex behavior is the classical interaction of an electron with electrostatic waves. Launching a low-intensity electron beam in a Traveling Wave Tube (TWT) recently allowed observing the real-world consequences of the richness of the electron trajectory. Here we show that self-consistent effects are nevertheless acting on a modulated test electron beam through the collective excitation of beam modes. The transition between two different particle transport regimes (stochastic diffusion in a set of waves and slow chaos associated to a pulsating separatrix) is directly measured by increasing the amplitude of the excitation.