Both one‐ and two‐dimensional particle simulation models have been used to study the nonlinear behavior of the electrostatic hydrogen cyclotron instabilities driven by the electron current along the magnetic field. It is found that the instability saturates as a result of electron velocity space diffusion along the magnetic field. The cyclotron waves remain highly coherent in the nonlinear stage. When the electron drift speed is comparable to the thermal speed, substantial ion heating as well as particle cross‐field diffusion comparable to Bohm diffusion has been observed. Comparisons of the simulation results with the theoretical predictions and the observations in both laboratory and space plasmas are discussed.