Theory of Electrical Currents from Bunching of Electrons with Boltzmann Equation

Inspired at the theory of free electron laser, this paper uses the Boltzmann equation to derive electric currents from a bunching of electrons passing along a cylindrical geometry. Some concepts derived from classical mechanics to justify steps along the construction of theory have been used. These concepts enter because the term in Boltzmann equation that gives account of a mechanical force. It is demonstrated that the bunching obeys the principles of classical electrodynamics. Therefore, it is verified Ohm law by which a kind of electric resistance is derived. Finally, the full electric charge turns out to be proportional to permittivity inside cylinder as well as to module of current density vector.