Magnetic field in nuclear collisions at ultra high energies

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.