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Force-free magnetic fields, i.e. fields that are either parallel or antiparallel to the electric current, occur in the solar chromosphere and also have been used in certain magnetic confinement schemes in controlled thermonuclear fusion research. In this paper, we derive a general expression for force-free fields that decay resistively and are spatially periodic. The general expression that is found consists of a sum of spatial Fourier modes with the property that all wave vectors have the samedoi:10.1090/qam/693873 fatcat:hxrtcn3chrgu5khxs4atvwsqqm