A Universal Magnetic Helicity Integral
  A magnetic helicity integral is proposed which can be applied to domains which are not magnetically closed, i.e. have a non-vanishing normal component of the magnetic field on the boundary. In contrast to the relative helicity integral, which was previously suggested for magnetically open domains, it does not rely on a reference field and thus avoids all problems related to the choice of a particular reference field. Instead it uses a gauge condition on the vector potential, which corresponds to a particular topologically unique closure of the magnetic field in the external space. The integral has additional elegant properties and is easy to compute numerically in practice. For magnetically closed domains it reduces to the classical helicity integral. 
Gunnar Hornig