In contrary to our recent work, there are important works which regard the electromagnetic field produced in heavy ion collisions as external, in the sense that they don't need to satisfy Maxwell equations coupled with the fluid. I share my picture in order to open a discussion:
The inhomogeneous Maxwell equations include the source. The primary source is coming from the spectators. However by creating the electromagnetic fields an induced source is also generated. As the time goes on the primary, or external, source becomes negligible but the induced source may or may not interact with the remnants of electromagnetic fields. As far as I know, It is still unclear that what happens in the interplay in early times, and how much of the produced fields survive to the thermalization time. When the fluid is formed depending on its properties it can act as a source for Maxwell equations or merely freeze the magnetic field within itself. If the fluid is highly conductive when one can legitimately neglect any source in the QGP phase and no interplay between electromagnetic and thermal energy will happen. In this scenario the external source is gone and the induced source is zero, since the local electric field is suppressed. On the other hand if the fluid is assumed to have a finite conductivity, and/or non-vanishing magnetization, then the survived fields from primary sources have induced a source with same order of themselves that should not be neglected.
https://arxiv.org/abs/0907.1396v1
https://arxiv.org/abs/1506.06620
https://arxiv.org/abs/1705.00536
Your want to some jobs with MHD. It is an great work., My major is MHD, But i found it is too difficult for me. So I have give it up.
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