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# Magnetic field evolution in spatially inhomogeneous axion structures

Mar 2023

We study the time evolution of magnetic fields in various configurations ofaxions with spatially inhomogeneous wavefunctions. The generalization of theinduction equation for the magnetic field is derived for such systems. Basingon this equation, we study, first, the evolution of two Chern-Simons (CS) wavesinteracting with a linearly decreasing axion wavefunction. The nonzero gradientof axions results in the mixing between these CS waves. Then, we consider theproblem in a compact domain, when an initial CS wave is mirror symmetric. Inthis situation, the inhomogeneity of axions acts as the effective modificationof the $\alpha$-dynamo parameter. Thus, we conclude that the influence ofspatially inhomogeneous axion on the magnetic field evolution strongly dependson the geometry of the system.

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