  The twist and writhe numbers and magnetic energy of an orthogonally perturbed
vortex filaments are obtained from the computation of the magnetic helicity of
geodesic and abnormal magnetohydrodynamical (MHD) vortex filament solutions.
Twist is computed from a formula recently derived by Berger and Prior [J. Phys.
A 39 (2006) 8321] and finally writhe is computed from the theorem that the
helicity is proportional to the sum of twist and writhe. The writhe number is
proportional to the total torsion and to integrals of the vector potential. The
magnetic energy is computed in terms of the integral of the torsion squared
which allows us to place a bound to energy in in the case of helical filaments
due to a theorem by Fukumoto [J. Phys. Soc. Japan,(1987)] in fluid vortex
filaments. It is also shown that filament torsion coincides with the magnetic
twist in the case under consideration, where a small orthogonal magnetic field
exist along the thin filament. A new Aharonov-Bohm (AB) phase term is obtained
in the writhe number expression which is not present in the Moffatt-Ricca (Proc
Roy Soc London A,1992) computation.
