MODELING OF OSCILLATORY AND ROTARY TRAJECTORIES OF ELECTRONS IN GRADIENT MAGNETIC FIELD MAGNETRON GUN

The motion of electrons in cylindrical magnetic field with variable strength along the axis is considered. The formation of a beam with energy of 55 keV in the longitudinal direction during its transport in solenoidal magnetic field with large gradient has been studied. The bifurcation regimes of the dynamics of particles during their move-ment along the transport axis both forward to the target and back to the cathode region are considered. The operat-ing modes of the gun are obtained, in which the particle experiences the "bottleneck" effect and returns to the cath-ode region. It is shown that for given electron energy and fixed magnetic field, the parameter that determines the reflection of the particle is the polar angle of entry with respect to the axis of the cylindrical magnetic field. The re-sults of numerical simulation on the motion of the electron flow are presented.

ON EFFECTIVE ACCELERATION OF CHARGED PARTICLES IN VACUUM

The results of studying the dynamics of particles in the fields of large-amplitude transverse electromagnetic waves are presented. The main attention is paid to the description of the found conditions, under which the effective transfer of wave energy to charged particles in vacuum is possible.

SIMULATION OF THE COMPENSATION OF A HIGH-CURRENT ION BEAM BY AN ELECTRON BEAM IN A CUSP MAGNETIC SYSTEM

The results of 2.5D-simulation of the dynamics of particles of a high-current ion beam moving in a magnetic field of acute-angled geometry (cusp), compensated in charge and current by an electron beam injected along the radius onto the axis from the periphery, uniformly in azimuth, are presented. The influence of own space charge fields and polarization fields on the dynamics of ions is clarified. It is shown that at high densities of the electron and ion beams, the electron beam injected into the cusp together with the ion beam, moving along the magnetic field lines, drags the ion beam away from the axis to the periphery into the region of zero magnetic field. At the exit from the cusp, the electron beam injected along the radius onto the axis drifts along the axis in a uniform magnetic field, while the ion beam performs oscillatory motion by radius in the crossed the electric field of the electron beam space charge and the longitudinal magnetic field.

A quantum route to the classical Lagrangian formalism

Using the recently developed groupoidal description of Schwinger’s picture of Quantum Mechanics, a new approach to Dirac’s fundamental question on the role of the Lagrangian in Quantum Mechanics is provided. It is shown that a function [Formula: see text] on the groupoid of configurations (or kinematical groupoid) of a quantum system determines a state on the von Neumann algebra of the histories of the system. This function, which we call q-Lagrangian, can be described in terms of a new function [Formula: see text] on the Lie algebroid of the theory. When the kinematical groupoid is the pair groupoid of a smooth manifold M, the quadratic expansion of [Formula: see text] will reproduce the standard Lagrangians on TM used to describe the classical dynamics of particles.