The spread of the initial energy of electrons in a gyrotron due to the negative-mass instability developing in a magnetron-injector gun

The formation of an electron beam in a magnetron-injector gun of a gyrotron is investigated in the case when it is affected by the negative-mass instability due to the Coulomb repulsion and nonisochronous cyclotron rotation of particles. A technique is proposed for calculating the spread of the initial energy of electrons caused by the instability, which develops as the electron beam moves in the presence of a nonuniform magnetostatic field of the magnetron-injector gun. It is demonstrated that this instability can be one of the main factors providing the energy spread in electron guns of gyrotrons.