The report is devoted to the results of the numerical study of the virtual cathode formation conditions in the relativistic electron beam under the influence of the self-magnetic and external axial magnetic fields. The azimuthal instability of the re
lativistic electron beam leading to the formation of the vortex electron structure in the system was found out. This instability is determined by the influence of the self-magnetic fields of the relativistic electron beam and it leads to the decrease of the critical value of the electron beam current (current when the non-stationary virtual cathode is formed in the drift space). The typical dependencies of the critical current on the external uniform magnetic field value were discovered. The effect of the beam thickness on the virtual cathode formation conditions was also analyzed.
We show that resonant electron transport in semiconductor superlattices with an applied electric and tilted magnetic field can, surprisingly, become more pronounced as the lattice and conduction electron temperature increases from 4.2 K to room tempe
rature and beyond. It has previously been demonstrated that at certain critical field parameters, the semiclassical trajectories of electrons in the lowest miniband of the superlattice change abruptly from fully localised to completely unbounded. The unbounded electron orbits propagate through intricate web patterns, known as stochastic webs, in phase space, which act as conduction channels for the electrons and produce a series of resonant peaks in the electron drift velocity versus electric field curves. Here, we show that increasing the lattice temperature strengthens these resonant peaks due to a subtle interplay between thermal population of the conduction channels and transport along them. This enhances both the electron drift velocity and the influence of the stochastic webs on the current-voltage characteristics, which we calculate by making self-consistent solutions of the coupled electron transport and Poisson equations throughout the superlattice. These solutions reveal that increasing the temperature also transforms the collective electron dynamics by changing both the threshold voltage required for the onset of self-sustained current oscillations, produced by propagating charge domains, and the oscillation frequency.
Two types of phase synchronization (accordingly, two scenarios of breaking phase synchronization) between coupled stochastic oscillators are shown to exist depending on the discrepancy between the control parameters of interacting oscillators, as in
the case of classical synchronization of periodic oscillators. If interacting stochastic oscillators are weakly detuned, the phase coherency of the attractors persists when phase synchronization breaks. Conversely, if the control parameters differ considerably, the chaotic attractor becomes phase-incoherent under the conditions of phase synchronization break.
