No abstract

There are presented the results of  calculating the energies of the helium atom energy in a homogeneous magnetic field on the basis of the new numerical quantum-mechanical approach.  The approach is based on the numerical difference solution of the Schrödinger equation, the model potential method and the operator perturbation theory formalism. The obtained results on energy of the helium atom in dependence upon the magnetic field strength  are  compared with available  theoretical results, obtained on the basis of alternative numerical Hartree-Fock and diagonalization methods.

We have performed an advanced modelling nonlinear dynamics elements for relativistic backward-wave tube (RBWT) with accounting for dissipation and space charge field effects etc. The temporal dependences of the normalized field amplitude (power) in a wide range of variation of the controlling parameters (electric length of an interaction space N, bifurcation parameter L and relativistic factor γ 0) are computed. The dynamic and topological invariants of the RBWT dynamics in auto-modulation and chaotic regimes such as correlation dimensions values, embedding, Kaplan-York dimensions, Lyapunov's exponents, Kolmogorov entropy etc are calculated. It has been discovered the "beak" effect on the plane of parameters: bifurcation Piers-like parameter L-relativistic factor γ 0 .