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On the effect of the maximal proper acceleration in the inertia

Ricardo Gallego Torromé

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.

On the effect of the maximal proper acceleration in the inertia

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 to for the LHC bunches and can be of order up to for certain laser plasma accelerator facilities. Although the effect is small, it increases with the square of the bunch population.
Paper Structure (16 sections, 1 theorem, 56 equations)

This paper contains 16 sections, 1 theorem, 56 equations.

Table of Contents

  1. Introduction
  2. Spacetimes of maximal proper acceleration and its kinematics
  3. Spacetimes of maximal proper acceleration as high order jet geometries
  4. Notions of $4$-velocity in a geometry of maximal acceleration
  5. Redefinition of the energy and momentum observables
  6. The model of the classical point charged particle in spacetimes of maximal acceleration
  7. Model of the bunch of particles as a sole particle
  8. Phenomenological consequences of the redefinition of the energy in accelerator physics
  9. Effect of maximal acceleration in plasma wakefield acceleration and laser-electron acceleration
  10. Conclusion and discussion
  11. Jet bundles and generalized tensors
  12. Generalized higher order jet electromagnetism
  13. Notion of Spacetime of maximal proper acceleration
  14. The equation of motion for a point charged particle in higher order jet electrodynamics
  15. Preliminary kinematical considerations
  16. ...and 1 more sections

Key Result

Proposition B.1

There is a non-degenerate, symmetric form $g$ along a curve $\vartheta:I\to M_4$ defined by the expressions:

Theorems & Definitions (6)

  • Definition 2.1
  • Definition A.1
  • Definition A.2
  • Definition A.3
  • Proposition B.1
  • Definition B.2