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A non-relativistic, charged-particle beam is placed into a crossed magneticfield. For such a system, the nonlinear electrostatic oscillations generationin the different degrees of the beam freedom may be triggered by theenergy/momentum exchange between the beam's particles and these externalfields. The influence of oscillation dynamics of these fields and beam havebeen studied based on the cold-fluid hydrodynamic description. As a result, thenecessary conditions under resonant amplification of the beam's naturaloscillations are identified. Present results demonstrate that the beam densityincreases when the amplitude of radial and axial velocities increase. Thisprocess decreases the radius of the beam over the course of time. The technicalapplication of the process applies in real accelerators such as a gyrotrons,FELs, and cyclotrons, where transverse size is limited by the size of thevacuum chamber. Thus redistribution of energy between the external field andthe kinetic energy of the beam can effectively accelerate the beam by using anexternal magnetic field. These fields with both axial and radial directions usefurther this beam as an effective light source by identifying the resonancefrequency to improve stability, focus particles, and wave propagation.

Amplification of coupled nonlinear oscillations of charged particle beam in crossed magnetic fields