Negative mass instability and cyclotron radiation of a flux of relativistic electrons-oscillators

A system of nonlinear self-consistent equations, describing the development of one-dimensional field fluctuations of a space charge of a plane thin (with a thickness of the Larmor diameter) relativistic electron flux moving in a homogeneous magnetic field in a free space is determined. The proper field of a perturbed flux along with a Coulomb one also contains eddy components. At low flux concentration the corrections for the cyclotron frequency harmonics of its free oscillations. The instability increment, caused by the negative mass effect, decreases with the growth of the translational electron velocity. At relativistic particle velocities the eddy fields play a great role. Taking into account the effects related to these fields, in particular, radiation, carrying energy away from the flux, the increment dependence on the particle energy and cyclotron harmonics number is qualitatively changed