Abstract
A review is given of some of the basic properties of force-free fields under circumstances when the conductivity of the medium is finite. Then the electric current density is related not only to the magnetic field, but also by Ohm's law to the electric field and plasma velocity, which must be considered in the solutions. It is pointed out that the natural constraint that the electric field and plasma velocity should be finite everywhere is not fulfilled in some previously used models. Models with a constant ratio α of the electric current density and magnetic field intensity have been used extensively in the past. They are of some importance since solutions with the plasma at rest are possible only if α is constant. However, it is shown that solutions of constant α cannot be matched to an external current-free region of finite conductivity since α can have no discontinuity in a medium where the conductivity varies continuously. Hence, for most applications models with a varying α and a moving plasma must be used. Some new, simple and consistent models, especially of cylindrical symmetry, are derived by prescribing the form of the magnetic field lines, or one electic field component, or one time-dependent electric current component.
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Boström, R. Models of force-free magnetic fields in resistive media. Astrophys Space Sci 22, 353–380 (1973). https://doi.org/10.1007/BF00647432
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DOI: https://doi.org/10.1007/BF00647432