The scaling laws for the magnetic compression of a toroidally rotating field reversed configuration (FRC) have been investigated in this work. The magnetohydrodynamics (MHD) simulations of the magnetic compression on rotating FRCs employing the NIMROD code (Sovinec et al 2004 J. Comput. Phys.195 355), are compared with the Spencer's one-dimensional (1D) theory (Spencer et al 1983 Phys. Fluids26 1564) for a wide range of initial flow speeds and profiles. The toroidal flow can influence the scalings directly through the alteration of the compressional work as also evidenced in the 1D adiabatic model, and indirectly by reshaping the initial equilibrium. However, in comparison to the static initial FRC equilibrium cases, the pressure and the radius scalings remain invariant for the magnetic compression ratio up to 6 in presence of the initial equilibrium flow, suggesting a broader applicable regime of the Spencer scaling law for FRC magnetic compression. The invariant scaling has been proven a natural consequence of the conservation of angular momentum of both fluid and magnetic field during the dynamic compression process.
This paper investigates the scaling laws for magnetic compression of a rotating field-reversed configuration (FRC) plasma. The study shows that the pressure and radius scaling laws remain invariant during the compression process, even in the presence of initial equilibrium flow, suggesting a broader applicable regime of the Spencer scaling law for FRC magnetic compression.