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The inverse transfer of magnetic helicity is a fundamental process which mayexplain large scale magnetic structure formation and sustainement. Until veryrecently, direct numerical simulations (DNS) of the inverse transfer inmagnetohydrodynamics (MHD) turbulence have been done in incompressible MHD orat low Mach numbers only. We review first results obtained through DNS of theisothermal MHD equations at Mach numbers ranging from subsonic to about 10. Thespectral exponent of the magnetic helicity spectrum becomes flatter withincreasing compressibility. When considering the Alfv\'en velocity in place ofthe magnetic field however, results found in incompressible MHD, including adynamic balance between shear and twist, can be extended to supersonic MHD. Inthe global picture of an inverse transfer of magnetic helicity, three phenomenaare at work: a local direct transfer mediated by the large scale velocityfield, a local inverse transfer mediated by the intermediate scale velocityfield and a nonlocal inverse transfer mediated by the small scale velocityfield. The compressive part of the velocity field is geometrically favored inthe local direct transfer and contributes to the nonlocal inverse transfer, butplays no role in the local inverse transfer.

Emergence of magnetic structure in supersonic isothermal magnetohydrodynamic turbulence