# Magnetic field in nuclear collisions at ultra high energies

## TL;DR

This study models the magnetic fields generated in ultra high energy proton-proton and nucleus-nucleus collisions, showing rapid decay over time and dependence on atomic number, with implications for phenomena like W boson condensation.

## Contribution

It provides detailed estimations of magnetic field strengths in ultra high energy collisions using different charge distribution models, highlighting the impact of nuclear size and collision energy.

## Key findings

- Magnetic field reaches tens of GeV$^{2}$ immediately after collision.
- Field strength decreases rapidly with time.
- Field amplitude increases with atomic number.

## Abstract

The magnetic field created in proton-proton and nucleus-nucleus collisions at ultra high energies are studied with models of point-like charges and hard sphere for distribution of the constituents for vacuum conditions. The various beam ions are considered from light to heavy nuclei at energies corresponded to the nominal energies of proton beam within the projects of further accelerator facilities high-energy Large Hadron Collider (HE-LHC) and Future Circular Collider (FCC). The magnetic field strength immediately after collisions reaches the value tens of GeV$^{2}$ while the approach with point-like charges some overestimate the amplitude of the field in comparison with more realistic hard sphere model. The absolute value of magnetic field rapidly decrease with time and increases with growth of atomic number. The amplitude for $eB$ is estimated at level $100$ GeV$^{2}$ in order to magnitude for quark-quark collisions at energies corresponded to the nominal energies of proton beams. These estimations are close to the range for onset of $W$ boson condensation.