Non-symmetric force-free magnetic fields with closed field lines and nested flux surfaces

We construct a smooth one-parameter family of force-free magnetic fields, curl B = αB with α not identically zero, on embedded solid tori in ℝ³. The family bifurcates from the explicit non-symmetric vacuum field constructed by Omar E. López in Exact nonsymmetric vacuum magnetic field with nested toroidal flux surfaces and nonzero rotational transform (arXiv:2610.29921). For every sufficiently small positive parameter the field is nowhere zero, every field line is closed, the factor α is constant along each line, and the domain is foliated by nested invariant tori around a regular magnetic axis; the field has no continuous Euclidean symmetry. The proof writes the field in coordinates adapted to its closed lines, which reduces the force-free condition to two scalar equations for an embedding, and solves them with the Nash–Moser implicit function theorem in Hamilton's form. The approximate right inverse comes from tame estimates for a family of closure-projected Dirichlet problems. Rigorous interval arithmetic certifies a coercivity constant and the nonvanishing of the first-order current, and an exact rational determinant excludes Killing symmetries. The result is perturbative, gives smooth (not explicit) fields, and concerns closed field lines only.