Modeling of axion and electromagnetic fields coupling in a particle-in-cell code

Axions have aroused widespread research interest because they can solve the strong CP problem and serve as a possible candidate for dark matter. Currently, people have explored a lot of axion detection experiments, including passively detecting the existing axions in the universe, and actively generating axions in the laboratory. Recently, axion-coupled laser-plasma interactions have been discussed as a novel method to detect axions. Petawatt (PW) lasers are considered as a powerful tool to study not only the vacuum polarization but also the axion coupling, due to their extreme fields. However, particle-in-cell (PIC) simulation is still missed in current studies, which limits the understanding of axion-coupled laser-plasma interactions. In this paper, we proposed the method to include the axion field and the coupling with electromagnetic (EM) fields in PIC codes. The axion wave equation and modified Maxwell's equations are numerically solved, while the EM field modulation from axions is considered as a first-order perturbation. Meanwhile, different axion field boundary conditions are considered to satisfy different simulation scenarios. The processes of conversions between axions and photons, and weak laser pulse propagation with axion effects are checked as benchmarks of the code. Such an extended PIC code may help researchers develop novel axion detection schemes based on laser-plasma interactions and provide a better understanding of axion-coupled astrophysical processes.