# Magnetic field production at a first-order electroweak phase transition

## TL;DR

This study simulates the generation of magnetic seed fields during a first-order electroweak phase transition, revealing that about 10% of latent heat converts into magnetic energy, mainly during the Higgs oscillation phase.

## Contribution

It provides a numerical analysis of magnetic field production during a first-order electroweak phase transition using lattice simulations, highlighting the energy conversion and spectrum evolution.

## Key findings

- Approximately 10% of latent heat becomes magnetic energy.
- Magnetic field spectrum peaks shift to larger scales during transition.
- Magnetic fields are mainly generated during the Higgs oscillation stage.

## Abstract

We study the generation of magnetic field seeds during a first-order electroweak phase transition, by numerically evolving the classical equations of motion of the bosonic electroweak theory on the lattice. The onset of the transition is implemented by the random nucleation of bubbles with an arbitrarily oriented Higgs field in the broken phase. We find that about 10% of the latent heat is converted into magnetic energy, with most of the magnetic fields being generated in the last stage of the phase transition when the Higgs oscillates around the true vacuum. The energy spectrum of the magnetic field has a peak that shifts towards larger length scales as the phase transition unfolds. By the end of our runs the peak wavelength is of the order of the bubble percolation scale, or about a third of our lattice size.