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We calculate exact one-dimensional collisionless plasma equilibria for acontinuum of flux tube models, for which the total magnetic field is made up ofthe `force-free' Gold-Hoyle magnetic flux tube embedded in a uniform andanti-parallel background magnetic field. For a sufficiently weak backgroundmagnetic field, the axial component of the total magnetic field reverses atsome finite radius. The presence of the background magnetic field means thatthe total system is not exactly force-free, but by reducing its magnitude thedeparture from force-free can be made as small as desired. The distributionfunction for each species is a function of the three constants of motion;namely the Hamiltonian and the canonical momenta in the axial and azimuthaldirections. Poisson's Equation and Amp\`{e}re's Law are solved exactly, and thesolution allows either electrically neutral or non-neutral configurations,depending on the values of the bulk ion and electron flows. These equilibriahave possible applications in various solar, space and astrophysical contexts,as well as in the laboratory.

Neutral and non-neutral collisionless plasma equilibria for twisted flux tubes: The Gold-Hoyle model in a background field