The conversion of electromagnetic energy into magnetohydrodynamic energy occurs when the electric conductivity changes from negligible to finite values. This process is relevant during the epoch of reheating in the early universe at the end of inflation and before the emergence of the radiation-dominated era. We find that the conversion into kinetic and thermal energies is primarily the result of electric energy dissipation, while magnetic energy only plays a secondary role in this process. This means that since electric energy dominates over magnetic energy during inflation and reheating, significant amounts of electric energy can be converted into magnetohydrodynamic energy when conductivity emerges before the relevant length scales become stable.

The $\mathsf{\mu }$PPET [mu($\mathsf{\mu }$)on Probe with J-PET] project aims to investigate the “Muon Puzzle” seen in cosmic ray air showers. This puzzle arises from the observation of a significantly larger number of muons on Earth’s surface than that predicted by the current theoretical models. The investigated hypothesis is based on recently observed asymmetries in the parameters for the strong interaction cross-section and trajectory of an outgoing particle due to projectile–target polarization. The measurements require detailed information about muons at the ground level, including their track and charge distributions. To achieve this, the two PET scanners developed at the Jagiellonian University in Krakow (Poland), the J-PET detectors, will be employed, taking advantage of their well-known resolution and convenient location for detecting muons that reach long depths in the atmosphere. One station will be used as a muon tracker, while the second will reconstruct the core of the air shower. In parallel, the existing hadronic interaction models will be modified and fine-tuned based on the experimental results. In this work, we present the conceptualization and preliminary designs of $\mathsf{\mu }$PPET.