Kirichenko Y. Instabilities rotating streams of nonrelativistic electrons and cyclic high-current beams of relativistic electrons

In the thesis, the instabilities in a cylindrical layer of nonrelativistic or relativistic electrons in a coaxial resonator, or in the absence of an external wall of the coaxial resonator are theoretically investigated. The conditions are analyzed, at which the instabilities result in generation or amplification of axially and azi-muthally inhomogeneous waves. Electrons are moving in a radial electrostatic field or in crossed radial electrostatic and axial magnetic fields in circular or helical paths. It is shown that in the amplification mode of eigen oscillations of the resonator, the layer of electrons is unstable under conditions of Cher-enkov's or plasma resonances. The other mode of instabilities is also possible, when the waves of space charge in the layer of electrons are increased. The role of dissipative processes is analyzed. Under certain conditions it is the dissipative processes that give rise to instabilities. The nonlinear theory of electromag-netic field generation in orbitron is developed. The set of the equations including the equations of field excitation and equations of 2-dimensional motion is constructed and numerically solved. For the fixed pa-rameters of orbitron from the point of view of generated energy and electronic efficiency there is some optimal value of electron density in the interaction region. The method of retarded potentials was used to compute the disturbances of eigen - fields of a thin high-current beam of relativistic electrons. The ob-tained formulas can be employed for theoretical investigation of beam stability in an arbitrary cyclic ac-celerator, including a modified betatron and a stellatron. The conditions for parameters of a beam and a magnetic system of a stellatron were obtained, provided that low-frequency long-wave oscillations of beam in the stellatron are stable. The conditions have been analyzed, at which the interaction of trans-verse oscillations of the beam in the stellatron with heterogeneities of the two-turn stellarator field re-sults in the instability of these oscillations. A study has been made into the dynamics of collective accel-eration of ions by a virtual cathode of a high-current electron beam propagating between the zero- poten-tial planes. A set of integro-differential Vlasov-Poisson equations is solved numerically.