Investigation of the chaotic dynamics of an electron beam with a virtual cathode in an external magnetic field

Abstract

-The effect of the strength of the focusing magnetic field on chaotic dynamic processes occurring in an electron beam with a virtual cathode, as well as on the processes whereby the structures form in the beam and interact with each other, is studied by means of two-dimensional numerical simulations based on solving a self-consistent set of Vlasov-Maxwell equations. It is shown that, as the focusing magnetic field is decreased, the dynamics of an electron beam with a virtual cathode becomes more complicated due to the formation and interaction of spatiotemporal longitudinal and transverse structures in the interaction region of a vircator. The optimum efficiency of the interaction of an electron beam with the electromagnetic field of the vircator is achieved at a comparatively weak external magnetic field and is determined by the fundamentally two-dimensional nature of the motion of the beam electrons near the virtual cathode.

Microwave radiation power of relativistic electron beam with virtual cathode in the external magnetic field

“…It has been also demonstrated that for the strong magnetic fields the output power is saturated on the low power level. The same results have been also obtained in theoretical and experimental works [22][23][24]. However, the physical mechanisms of such power behavior are still uninvestigated in the most cases.…”

“…8 and based on 2.5D model developed in our previous work. 24 The equations of charged particles motion (2) are used for the electron beam simulation and solved numerically by means of B oris algorithm. 27 The electromagnetic fields in the drift chamber of REB are obtained by means of the numerical solution of Maxwell's equations (1) in cylindrical geometry on the shifted spatiotemporal meshes.…”

“…26,29 The space charge and current densities on the meshes are calculated with the help of the bilinear weighing procedure (PIC-method). 26 To model the electromagnetic power output, we use the approach 24 based on the filling the section of electrodynamical system (L < z < 1:2L) with the conducting medium with the conductance r. Fig. 1 shows the dependencies of the normalized output power of the electromagnetic radiation of REB with VC on the external magnetic field induction obtained with the help of the numerical simulation for two values of the initial electron energy, W e .…”

“…The tendency of the output power value to decrease with the external magnetic field growth leading particularly to the appearance of the third maximum M 3 is determined by the effect of the beam transverse dynamics suppression in the increasing magnetic field resulting in the lowering of the interaction efficiency of the VC in the electron beam with electromagnetic fields (see Ref. 24).…”

“…It is the consequence of the lowering of the interaction efficiency of the VC in the electron beam with the electromagnetic fields conditioned by the beam transverse dynamics suppression in the increasing magnetic field that was discovered in work. 24 Actually, the strong external magnetic field causes the reflected from VC electrons to move back to the entrance electrode on the trajectories similar to the trajectories of electrons moving from the injection plane to the VC. So, the total energy that the electron beam gives to the electromagnetic fields in such motion and, hence, the output power is low.…”