Time-average and ergodic methods for the dynamics of electron plasmas

The paper deals with the dynamics of electrons confined by a twodimensional electrostatic field and by a constant magnetic field. The electrons undergo collisions with neutral atoms, with frequency much smaller with respect to the characteristic frequencies of the motion. In this situation, suitable time averages of the trajectories can be introduced in order to simplify the analysis of the problem. Two different approaches are described: 1) the time average of the trajectories and 2) the use of a suitable ergodic distribution. Results obtained with the two methods are presented and discussed