Exact nonsymmetric vacuum magnetic field with nested toroidal flux surfaces and nonzero rotational transform
We show that an exact vacuum magnetic field without continuous Euclidean symmetry can fill a bounded solid torus with nested toroidal flux surfaces and nonzero rotational transform. We construct such a field in closed form and show that it is nowhere vanishing. Every off-axis field line closes after one toroidal transit and one poloidal turn, with rotational transform $ι=-1$ on every flux surface. The solution provides an exact benchmark for three-dimensional equilibrium codes.
physics.plasm-ph↗