Saturation mechanism of the fluctuation dynamo in supersonic turbulent plasmas

Magnetic fields in several astrophysical objects are amplified and maintained by a dynamo mechanism, which is the conversion of the turbulent kinetic energy to magnetic energy. A dynamo that amplifies magnetic fields at scales $<$ the driving scale of turbulence is known as the fluctuation dynamo. We study the properties of the fluctuation dynamo in supersonic turbulent plasmas, which is of relevance to the ISM, structure formation, and lab experiments of laser-plasma turbulence. Using simulations, we explore the properties of the exponentially growing and saturated state of the fluctuation dynamo for subsonic and supersonic turbulence. We confirm that the fluctuation dynamo efficiency decreases with compressibility. We show that the fluctuation dynamo generated magnetic fields are spatially intermittent and the level of intermittency decreases as the field saturates. We find a stronger back reaction of the magnetic field on the velocity for the subsonic case as compared to the supersonic case. Locally, we find that the level of alignment between vorticity and velocity, velocity and magnetic field, and current density and magnetic field in the saturated stage is enhanced in comparison to the exponentially growing phase for the subsonic case, but only the current density and magnetic field alignment is enhanced for the supersonic case. We show that both the magnetic field amplification (due to weaker stretching of field lines) and diffusion decreases when the field saturates, but the diffusion is enhanced relative to amplification. This occurs throughout the volume in the subsonic turbulence, but primarily in the strong-field regions for the supersonic case. This leads to the saturation of the fluctuation dynamo. Overall, both the amplification and diffusion of magnetic fields are affected and thus a drastic change in either of them is not required for the saturation. [Abstract abridged]