NUMERICAL STUDYING ENERGY PARAMETERS OF MULTIELECTRON ATOM IN A MAGNETIC FIELD: HELIUM

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.

Nanoparticle Based Water Treatment Model in Squeezing Channel under Magnetic Field

The process of water treatment by nanoparticles is one of the most considerable subjects in the cross-field of hydrodynamics, chemistry and mathematics. This paper is dedicated to the case of the flows that appear when squeezing and stretching a spongy with a mix of water with nanoparticles and contaminants. It is assumed that fluid is homogeneous at the starting moment, the parameters of the nanoparticles and contaminants are known, and there is a constant non-homogeneous magnetic field applied to the system. The flow starts moving when the walls of the channel shift to each other. Exact and numerical solutions of the system of ordinary differential equations are used to receive the results. The article gives an answer to the question about stability of the flow and proposes the technique to evaluate the essential characteristics of the system to achieve the treatment process efficiency. The main result is that the considered system shows excellent treatment properties during some part of squeezing stage. This effect does not appear without magnetic field.

Model of electromagnetic interactions with spin-1/2 neutral particles

We address the bound-state dynamics of relativistic spin-1/2 neutral particles (in this paper, Dirac neutrinos) with anomalous magnetic dipole moment in the presence of an electromagnetic (EM) field described by a generalized Dirac–Pauli equation. This equation of motion is derived including appropriate couplings between Lorentz scalar and pseudoscalar fields with the EM field in the Lagrangian of the system. Specifically, we exactly solve the bound-state problem of neutrinos in the presence of a homogeneous magnetic field in cylindrical coordinates. We comment on the relevance of this approach to study Dirac neutrino self-interactions.

Inhomogeneous Winding for Loosely Coupled Transformers to Reduce Magnetic Loss

Wireless power transfer has been proved promising in various applications. The homogeneous winding method in loosely coupled transformers incurs unnecessary intense magnetic field distribution in the center and causes extra magnetic loss. An inhomogeneous winding method is proposed in this paper, and a relatively homogeneous magnetic field distribution inside the core is achieved. This paper investigated the magnetic loss of homogeneous winding and inhomogeneous winding for wireless power transfer. A theoretical model was built to evaluate magnetic loss under inhomogeneous winding. The coupling coefficient and magnetic loss were investigated individually and comparisons were made between different width ratio combinations. Theoretical analysis was validated in experiments.

Modular symmetry and zeros in magnetic compactifications

We discuss the modular symmetry and zeros of zero-mode wave functions on two-dimensional torus T2 and toroidal orbifolds T2/ℤN (N = 2, 3, 4, 6) with a background homogeneous magnetic field. As is well-known, magnetic flux contributes to the index in the Atiyah-Singer index theorem. The zeros in magnetic compactifications therefore play an important role, as investigated in a series of recent papers. Focusing on the zeros and their positions, we study what type of boundary conditions must be satisfied by the zero modes after the modular transformation. The consideration in this paper justifies that the boundary conditions are common before and after the modular transformation.

From signal-based to comprehensive magnetic resonance imaging

We present and evaluate a new insight into magnetic resonance imaging (MRI). It is based on the algebraic description of the magnetization during the transient response—including intrinsic magnetic resonance parameters such as longitudinal and transverse relaxation times (T1, T2) and proton density (PD) and experimental conditions such as radiofrequency field (B1) and constant/homogeneous magnetic field (B0) from associated scanners. We exploit the correspondence among three different elements: the signal evolution as a result of a repetitive sequence of blocks of radiofrequency excitation pulses and encoding gradients, the continuous Bloch equations and the mathematical description of a sequence as a linear system. This approach simultaneously provides, in a single measurement, all quantitative parameters of interest as well as associated system imperfections. Finally, we demonstrate the in-vivo applicability of the new concept on a clinical MRI scanner.

MOVEMENT OF CHARGED PARTICLES IN MAGNETIC AND NONUNIFORM STOCHASTIC ELECTRIC FIELDS

The equation of motion of charged plasma particles in a homogeneous magnetic field and in an inhomogeneous stochastic electric field with a characteristic oscillation frequency much lower than the electron cyclotron frequency and much higher than the ion cyclotron frequency is solved. The diffusion motion, as well as the drift of ions and guiding center of electrons, due to the inhomogeneity of the stochastic electric field, is considered. The obtained values of the diffusion coefficient and drift velocity are used in the Fokker-Planck equation to determine the stationary distribution of the plasma density due to the effect of an inhomogeneous stochastic field.

Nonlinear triggering process of whistler-mode rising-tone emissions in a homogeneous magnetic field

We perform an electromagnetic particle simulation of triggered emissions in a uniform magnetic field for understanding of nonlinear wave-particle interaction in the vicinity of the magnetic equator. A finite length of a whistler-mode triggering wave packet with a constant frequency is injected by oscillating an external current at the equator. We find that the first subpacket of rising-tone triggered emissions is generated after termination of the injection of the triggering wave in the homogeneous magnetic field. By analyzing resonant currents and resonant electron dynamics in the simulation, we find that the formation of an electron hole in a velocity phase space forms resonant currents, and the currents cause wave amplification and frequency increase. As the very initial stage of the generation process, phase-bunching occurs at the wavefront of the triggering wave. The phase-bunching is caused by the rotation of electrons in the velocity phase space because of the gradient of the distribution function in the parallel velocity. The phase-bunched untrapped electrons are scattered to the loss cone giving energy to the electromagnetic waves, while the electrons in the low density region are trapped by the wave potential, forming an electron hole. The time scale of the initial formation process of the electron hole is related to the duration time of the triggering wave necessary for generation of triggered emissions. The duration time is determined by the interaction time. For the generation of triggered emissions, the interaction time is more than 1/4 of the nonlinear trapping period in the present simulation.