  In this paper we prove a classification theorem for the zero sets of real
analytic Beltrami fields. Namely, we show that the zero set of a real analytic
Beltrami field on a real analytic, connected $3$-manifold without boundary is
either empty after removing its isolated points or can be written as a
countable, locally finite union of differentiably embedded, connected
$1$-dimensional submanifolds with (possibly empty) boundary and tame knots.
Further we consider the question of how complicated these tame knots can
possibly be. To this end we prove that on the standard (open) solid toroidal
annulus in $\mathbb{R}^3$, there exist for any pair $(p,q)$ of positive,
coprime integers countable infinitely many distinct real analytic metrics such
that for each such metric there exists a real analytic Beltrami field,
corresponding to the eigenvalue $+1$ of the curl operator, whose zero set is
precisely given by a standard $(p,q)$-torus knot. The metrics and the
corresponding Beltrami fields are constructed explicitly and can be written
down in Cartesian coordinates by means of elementary functions alone.
