Forcefree

Forcefree is a term used in plasma physics to describe a magnetic field configuration in which the Lorentz force is zero. In a force-free plasma, the current density J is parallel to the magnetic field B, so J × B = 0. Using Ampere’s law, ∇ × B = μ0 J, this implies ∇ × B = α B, where α is a scalar function of position. If α is constant throughout the region, the field is a linear force-free field; if α varies in space, the field is a nonlinear force-free field.

Force-free fields are considered in contexts where magnetic forces dominate over plasma pressure and gravity, i.e., low-beta plasmas. They are especially important in solar physics, where the solar corona is modeled as a force-free atmosphere and coronal magnetic fields are inferred by force-free extrapolation from measurements of the photospheric magnetic field (vector magnetograms).

Applications include modeling of solar active regions, astrophysical jets, and certain laboratory plasma configurations where the force-free assumption approximates the equilibrium. In fusion research, nearly force-free current sheets and relaxed states can occur, though complete force-free equilibria must still be compatible with pressure and gravitational terms.

Limitations include departures from the force-free condition in real plasmas, measurement errors in boundary data, and the mathematical ill-posedness of some extrapolation problems. Force-free models are therefore approximations that improve with better boundary data and more sophisticated nonlinear extrapolation methods.

See also: force-free field, linear force-free field, nonlinear force-free field, magnetic helicity, NLFFF extrapolation.

---