On the effect of the maximal proper acceleration in the inertia

TL;DR

This paper explores how a hypothetical maximal proper acceleration could slightly increase particle kinetic energy in accelerators, leading to a small but measurable reduction in luminosity, especially at high bunch populations.

Contribution

It introduces the concept that maximal proper acceleration affects particle energy and luminosity in accelerators, providing quantitative estimates of these effects.

Findings

Luminosity reduction of order 10^{-3} to 10^{-5} for LHC bunches.

Luminosity loss can reach up to 10^{-3} in laser plasma accelerators.

Effect increases with the square of the bunch population.

Abstract

The effect of a hypothetical maximal proper acceleration on the mass of a charged particles is investigated in the context of particle accelerators. In particular, it is shown that maximal proper acceleration implies an increase in the kinetic energy of the particle being accelerated with respect to the relativistic energy. Such an increase in kinetic energy leads to a reduction of the luminosity of the bunches with respect to the expected luminosity in the relativistic models of the bunches. This relative loss in luminosity is of the order $10^{-3}$ to $10^{-5}$ for the LHC bunches and can be of order up to $10^{-3}$ for certain laser plasma accelerator facilities. Although the effect is small, it increases with the square of the bunch population.