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Laser Physics Letters

Quasi-classical dynamics of a charged particle under conditions of ionization losses in a weak magnetic field

Sergey Vladimirovich Sazonov

Published Feb 21, 2024• 1 citation
Publisher

Abstract

Abstract The quasi-classical dynamics of a charged particle in a weak magnetic field in the presence of dissipative losses caused by ionization of the medium is studied. The approximate approach proposed here is a generalization of the Caldirola—Kanai method for quantizing the translational motion of particles in dissipative media. It is shown that a weak curvature of a classical trajectory by the magnetic field is accompanied by an isotropic increase of uncertainty of the particle coordinates to the some maximum value at the moment the localized probability density wave packet stops. The limitation of the increase of coordinate uncertainty is due to irreversible ionization losses.

DOI
10.1088/1612-202x/ad2925

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Abstract A version of the quasi-classical approach is proposed, which makes it possible to describe the straight-line motion of a micro-particle in a bulk dissipative medium. From the side of the medium, the particle is acted upon by the force of viscous friction and the drag force, which are proportional to the velocity and the square of the velocity, respectively. In addition, an external conservative force is applied to the particle. The Green’s function of the particle and the quasi-classical coherent state in the form of a three-dimensional localized wave packet are found. It is shown that the translational motion of the wave packet is accompanied by a monotonic increase in the uncertainties of the particle coordinates up to certain maximum asymptotic values. Due to the drag force, these asymptotic uncertainties contain information about the corresponding initial uncertainties in the coordinates of the micro-particle, about its initial velocity, as well as about the external conservative force.
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An approximate self-consistent approach is proposed that allows describing the quasi-classical translational dynamics of a non-relativistic particle in a dissipative medium with arbitrary dependence of the corresponding dissipative forces on velocity. It is shown that dissipation suppresses the quantum properties of the particle. This leads to the necessity of interpreting propagation in a dissipative medium as a continuous process of measuring the particle state. As examples, non-stationary coherent states of the particle are considered at three stages of its deceleration in the medium due to ionization losses. These stages correspond to high-energy losses, losses in the vicinity of the Bragg peak, and low-energy losses at the final stage of propagation.