Radiation of a variable charge flying into medium

Xingzhen Fan; Andrey V. Tyukhtin

Home/Archive/arXiv

arXiv · 2305.04314

Radiation of a variable charge flying into medium

Xingzhen Fan·Andrey V. Tyukhtin

View original source ↗Read source document ↗Export metadata ↓

Abstract

We study an electromagnetic radiation of a small bunch having a variable charge value and crossing a flat interface between two media. Both media are homogeneous, stationary, and isotropic. They may have frequency dispersion but no spatial dispersion. Cherenkov radiation can be generated in the second medium only. It is assumed that the bunch charge value decreases exponentially starting from some time moment after the charge enters the second medium. This means that we take into account the scatter of the particle path lengths, connected with a statistical nature of energy losses of particles. It is taken into account that the filamentous trace consisting of immobile charges is formed in the second medium. We obtain the general solution of the problem. The asymptotic study for the wave zone is carried out. We obtain expressions for the spherical wave as well as for the cylindrical wave generated in the second medium if the charge velocity is sufficiently high. The main properties of radiation are described. If the process of the bunch decay starts from the boundary between media, then the angular distribution of the radiation energy has the single maximum in each from two regions. In the second medium, the radiation, as a rule, is greater than in the vacuum area, and this difference increases with increasing the charge velocity. If the charge velocity is higher than the speed of light in the second medium, then, along with appearance of Cherenkov radiation, the properties of spherical wave change radically. In particular, the main maximum of the angular distribution of the radiation energy increases sharply. If the distance from the charge entry point to the region of the bunch decay is sufficiently large, then the complex interference pattern with many extrema take place.

Explore related subjects

physics.class-ph physics.acc-ph physics.optics

Keep this discovery

BibTeX RIS

Xingzhen Fan, Andrey V. Tyukhtin. 2023-05-07. Radiation of a variable charge flying into medium. https://arxiv.org/abs/2305.04314

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Projection Angles of Projectiles in Sports: Qualitative Assessment of the Effects of Aerodynamic Forces or Run-Up

We examine two major factors that influence the optimum projection angle: aerodynamic forces and the effect of run-up. With respect to aerodynamics, we consider not only the drag but also the lift generated by spin during flight. By linearizing the equations of motion that include these forces, we derive perturbation solutions with respect to drag and lift coefficients and clarify their qualitative effects. The results show that both drag and lift reduce the optimum projection angle, with the latter exerting a stronger influence. To investigate the effect of run-up, we use an extended projection model in which the initial speed depends on the initial angle. Analysis of this model reveals that a stronger run-up increases the relative projection angle but decreases the launch angle observed from the ground. These findings provide a mechanical explanation for the release angle in shot put and the takeoff angle in long jump. The present study establishes a simple theoretical framework for clarifying the respective roles of aerodynamic and run-up effects in determining the optimum projection angles in sports.

physics.class-ph↗

arXiv2026

Dunkl-Based Modeling of Vibrational Modes in Lightweight Elastic Beams

Optimizing slender elastic structures for renewable energy applications requires non-classical continuum formulations capable of accounting for spatial micro-interactions without sacrificing analytical tractability. Here, we extend beam vibration mechanics by replacing standard spatial derivatives with the Dunkl differential operator. This modification introduces a reflection-coupled mathematical structure that accounts for spatial parity effects across the beam domain. We formulate the governing dynamic equations into a generalized eigenvalue problem and derive exact analytical expressions for modal characteristics under standard boundary conditions. The classical limit confirms exact convergence to classical Euler-Bernoulli formulations. Parametric analyses reveal that the Dunkl parameter acts as a reflection-induced modulation parameter, significantly shifting natural frequencies and altering the modal characteristics of higher modes. These results provide an analytical baseline for dynamic optimization in lightweight structural components.

physics.class-ph↗

arXiv2026

A purely mechanical system realizing a Coulomb-like interaction

We solve in closed form a one-dimensional relativistic system: two masses interacting only through elastic collisions with a massless mediator bouncing between them. Momenta, times, and positions are hyperbolic functions of the collision index. The mediator energy, interpreted as the pair's effective potential, obeys an exact discrete Coulomb law, $V\propto 1/r$, with a Lorentz-invariant action as coupling. A massive Newtonian mediator instead transmits a $1/r^{3}$ force; one adiabatic invariant traces both laws to the mediator's dispersion relation. Continued to negative mediator energy, the closed forms turn trigonometric, binding a one-dimensional mechanical analog of the Coulomb atom.

physics.class-ph↗