Mark Davidson
A class of analytic solutions for force-free electromagnetic fields
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ABSTRACT. A method for producing a large class of force-free electromagnetic field solutions in curved spacetime is presented. Analytic examples in flat spacetime are given. All the solutions start with a null electromagnetic free-field solution with special properties. Then, a transformation of the null free-field solution produces a solution to the force-free problem. Examples based on the Hopf-Ra ada electromagnetic knot are presented. All of the solutions considered have the property that both invariants of the Faraday tensor are zero. This requires that in a local Lorentz frame the electric and magnetic fields are perpendicular and equal in magnitude. Thus these degenerate null fields are quite idealized cases, and they may only be relevant to real physical systems in certain limits. We provide a software program which can be used to check the validity of at least one of the solutions found.