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We study the possibility of constructing steady magnetic fields satisfyingthe force balance equation of ideal magnetohydrodynamics with tangentialboundary conditions in asymmetric confinement vessels, i.e. bounded regionsthat are not invariant under continuous Euclidean isometries (translations,rotations, or their combination). This problem is often encountered in thedesign of next-generation fusion reactors. We show that such configurations arepossible if one relaxes the standard assumption that the vessel boundarycorresponds to a pressure isosurface. We exhibit a smooth solution thatpossesses an Euclidean symmetry and yet solves the boundary value problem in anasymmetric ellipsoidal domain while sustaining a non-vanishing pressuregradient. This result provides a definitive answer to the problem of existenceof regular ideal magnetofluidostatic equilibria in asymmetric bounded domains.The question remains open whether regular asymmetric solutions of the boundaryvalue problem exist.

Symmetric Ideal Magnetofluidostatic Equilibria with Non-Vanishing Pressure Gradients in Asymmetric Confinement Vessels