Manifestation of the Aharonov–Bohm effect in hydrodynamic instability of an electron beam moving along a semiconductor nanotube

Abstract

We theoretically study a manifestation of the Aharonov–Bohm effect in hydrodynamic instability of a tubular nonrelativistic electron beam moving along a semiconductor nanotube with dielectric filling placed in a coaxial dc magnetic field. The calculations are performed with taking into account the retardation effect for electromagnetic fields. The dispersion equation for the coupled waves of the structure under study and the electron beam, as well as the expression for the increment of the hydrodynamic instability have been derived and numerically analyzed. The mechanism of nonlinear stabilization of the hybrid bulk-surface and surface electromagnetic waves is studied by the method of slowly varying in time amplitudes and phases. The physical cause of excitation of such waves is the Cherenkov resonance, and the nonlinear stabilization mechanism is based on the trapping of beam particles by the field of the excited wave. The numerical analysis shows that the time of saturation of the instability and the maximum field amplitudes depend on the number of magnetic flux quanta in the nanotube and changes with the period equal to one magnetic flux quantum. These dependences are the result of the Aharonov–Bohm effect.