Resonance behavior of a charged particle in presence of a time dependent magnetic field

Abstract

In this article, we have explored the resonance behavior of a particle in the presence of a time dependent magnetic field (TDMF). The particle is bound in a harmonic potential well. Based on the Hamiltonian description of the system in terms of action and angle variables, we have derived the resonance condition for the applied TDMF along z-direction which is valid for arbitrary frequencies along x and y directions of the two dimensional harmonic oscillator. We have also derived resonance condition for the applied magnetic field which is lying in a plane. Finally, we have explored resonance condition for the isotropic magnetic field. To check the validity of the theoretical calculation, we have solved equations of motion numerically for the parameter sets which satisfy the derived resonance condition. The numerical experiment fully agrees with the theoretically derived resonance conditions.

Exact Approach to Uniform Time-Varying Magnetic Field

“…Strictly related to the previous topic we also consider time-varying uniform magnetic fields that are widely used in theoretical and experimental works such as magnetic field susceptibility tests or biomedical studies [16][17][18]. The literature on this topic is quite vast, and we limit ourselves to a few exemplary applicative papers [19][20][21][22]. The typical approach is based on the quasistatic approximation where the magnetic field H( ) is given, in the SI system of units, by the flowing current density J( ), i.e., H( ) ≈ J( ).…”