Electron acceleration by the $E_{0n}$ wave in a circular waveguide in the cyclotron resonance mode

A method for acceleration of electrons in a smooth cylindrical waveguide in the presence of the magnetic field of a solenoid is proposed. Electrons move in the waveguide along a helical trajectory that is shifted relative to the waveguide axis. Electrons are accelerated at the frequency of the cyclotron resonance along the waveguide axis by wave $E_{01}$ or $E_{02}$. It is shown that the acceleration results from synchronous rotation of particles in the transverse cross section of the waveguide and propagation of the wave along the waveguide axis. When the electric field reaches a maximum level and provides acceleration, electrons are located at the center of the waveguide. With a delay of one half of the period, the electric field provides deceleration and electrons are rotated by the magnetic field toward the wall of the waveguide to the region of lower deceleration. Acceleration is the total effect of the electron–field interaction over the period of electron rotation. Parameters of an accelerator are estimated for an energy of 10 MeV.