Electromagnetic Radiation in a Semi-Compact Space

TL;DR

This paper studies electromagnetic radiation from a rotating point charge in a compact space, revealing mode discontinuities and effects of spatial squeezing, and confirms the classical Larmor formula in large volume limits.

Contribution

It introduces analysis of electromagnetic radiation in a compact space, highlighting mode discontinuities and the impact of spatial squeezing on radiation intensity.

Findings

Radiation exhibits discontinuities at specific frequencies due to mode appearance.

In small radius limit, non-zero Fourier modes are suppressed, but electric field squeezing enhances radiation.

Large volume limit reproduces the classical Larmor radiation formula.

Abstract

In this note, we investigate the electromagnetic radiation emitted from a revolving point charge in a compact space. If the point charge is circulating with an angular frequency $\omega_0$ on the $(x,y)$-plane at $z=0$ with boundary conditions, $x \sim x+2 \pi R$ and $y \sim y+2\pi R$, it emits radiation into the $z$-direction of $z$ in $ [-\infty, +\infty]$. We find that the radiation shows discontinuities as a function of $\omega_0 R$ at which a new propagating mode with a different Fourier component appears. For a small radius limit $\omega_0 R \ll 1$, all the Fourier modes except the zero mode on $(x,y)$-plane are killed, but an effect of squeezing the electric field totally enhances the radiation. In the large volume limit $\omega_0 R \rightarrow \infty$, the energy flux of the radiation reduces to the expected Larmor formula.