  We demonstrate that superconductors with broken inversion symmetry support a
family of stable, spatially localized configurations of the self-knotted
magnetic field. These solutions, that we term ``toroflux,'' are the
superconducting counterparts of the Chandrasekhar-Kendall states (spheromaks)
that appear in highly conducting, force-free astrophysical and nuclear-fusion
plasmas. The superconducting torofluxes are solutions of superconducting
models, in the presence of a parity-breaking Lifshitz invariant associated with
the $O$ point-group symmetry. These solutions are characterized by a
non-vanishing helicity of the magnetic field, and also by a toroidal dipole
moment of the magnetic field. We demonstrate that a magnetic dipole or a
ferromagnetic inclusion in the bulk of a noncentrosymmetric superconductor
sources finite-energy toroflux solutions.
