Stress tensor of cosmic and laboratory type-II superconductors

It has recently been pointed out by P. B. Jones that for $B\ll H_{\mathrm{cl}}$ the anisotropic part of the stress tensor associated with the flux lines in a type-II superconductor could be considerably larger than $\frac{B^2}{4\pi }$, and that consequently the magnetic distortions of a neutron star could be appreciably larger than previously supposed. We calculate the stress tensor of a type-II superconductor using a thermodynamic approach, and find that the magnitude of the anisotropic term is just $\frac{\mathrm{BH}}{4\pi }$, which agrees in order of magnitude, but not in detail, with Jones's result. The stress tensor derived here is then compared with that found by Josephson. We find additional terms arising from the strain dependence of the magnetic free energy.