Estimate of the magnetic field strength in heavy-ion collisions

TL;DR

This work estimates the magnetic field generated in noncentral heavy-ion collisions using the UrQMD transport model across SPS to LHC energies, focusing on the central fireball region and employing Li4nard-Wiechert potentials to compute $eB_y$. It finds field magnitudes of $eB_y \sim 0.1 m_\pi^2$ at SPS, $eB_y \sim m_\pi^2$ at RHIC, and a lower-bound extrapolation of $eB_y \sim 15 m_\pi^2$ at LHC, with a fairly uniform field in the central region and a dependence on impact parameter. The results are corroborated by a simple semianalytical model of two Lorentz-contracted spheres, which agrees within a few percent and provides quick estimates, including the LHC lower bound. Overall, the study supports the potential observability of CME-related effects and indicates central-region energy densities compatible with deconfinement and chiral restoration, reinforcing the physical relevance of strong magnetic fields in heavy-ion collisions.

Abstract

Magnetic fields created in the noncentral heavy-ion collision are studied within a microscopic transport model, namely the Ultrarelativistic Quantum Molecular Dynamics model (UrQMD). Simulations were carried out for different impact parameters within the SPS energy range ($E_{lab} = 10 - 158 A$ GeV) and for highest energies accessible for RHIC. We show that the magnetic field emerging in heavy-ion collisions has the magnitude of the order of $eB_y \sim 10^{-1} m_π^2$ for the SPS energy range and $eB_y \sim m_π^2$ for the RHIC energies. The estimated value of the magnetic field strength for the LHC energy amounts to $eB_y \sim 15 m_π^2$.

Figures (6)

• Figure 1: The transverse plane of a noncentral heavy-ion collision. The impact parameter of the collision is $b$. The magnetic field is to be calculated at the origin $O$ and along the $y$-axis.
• Figure 2: The time evolution of the magnetic field strength $eB_y$ at the central point $O$ (see Fig.\ref{['tr']}) in Au-Au collisions with impact parameter $b=4$ fm in the UrQMD model, in one event ("1 ev.") and averaged over 100 events ("100 ev."). The symbols are plotted every $\Delta t=0.2$ fm/c for $E_{lab} = 60A$ GeV and $\Delta t=0.01$ fm/c for $\sqrt{s_{NN}}=200$ GeV.
• Figure 3: The time evolution of the magnetic field strength $eB_y$ at the central point $O$ (see Fig.\ref{['tr']}) in Au--Au collisions with impact parameter, $b=4$ fm, in the UrQMD model, for different bombarding energies. The symbols are plotted every $\Delta t=0.2$ fm/c for $E_{lab} = 60A$ GeV and $\Delta t=0.01$ fm/c for $\sqrt{s_{NN}}=200$ GeV. The magnetic field obtained by modelling the gold ions as two Lorenz contracted non-interacting uniformly charged spheres with radius $R=7$ fm are shown by dashed lines.
• Figure 4: The dependence of the magnetic field on the coordinate $y$. The calculation was carried out for Au--Au collisions with impact parameter $b=4$ fm in the UrQMD model. The magnetic field is taken at fixed time corresponding to its maximum value at $y=0$.
• Figure 5: The time evolution of the energy density in the central region (see text for details) for SPS and RHIC energies.