  New results on the groundstate energy of tight, magnetic knots are presented.
Magnetic knots are defined as tubular embeddings of the magnetic field in an
ideal, perfectly conducting, incompressible fluid. An orthogonal, curvilinear
coordinate system is introduced and the magnetic energy is determined by the
poloidal and toroidal components of the magnetic field. Standard minimization
of the magnetic energy is carried out under the usual assumptions of volume-
and flux-preserving flow, with the additional constraints that the tube
cross-section remains circular and that the knot length (ropelength) is
independent from internal field twist (framing). Under these constraints the
minimum energy is determined analytically by a new, exact expression, function
of ropelength and framing. Groundstate energy levels of tight knots are
determined from ropelength data obtained by the SONO tightening algorithm
developed by Pieranski (Pieranski, 1998) and collaborators. Results for torus
knots are compared with previous work done by Chui & Moffatt (1995), and the
groundstate energy spectrum of the first prime knots (up to 10 crossings) is
presented and analyzed in detail. These results demonstrate that ropelength and
framing determine the spectrum of magnetic knots in tight configuration.
