Vortex structure in charged condensate

We study magnetic fields in the charged condensate that we have previously argued should be present in helium-core white dwarf stars. We show that below a certain critical value the magnetic field is entirely expelled from the condensate, while for larger values it penetrates the condensate within flux-tubes that are similar to Abrikosov vortex lines; yet higher fields lead to the disruption of the condensate. We find the solution for the vortex lines in both relativistic and nonrelativistic theories that exhibit the charged condensation. We calculate the energy density of the vortex solution and the values of the critical magnetic fields. The minimum magnetic field required for vortices to penetrate the helium white dwarf cores ranges from roughly 10 ⁷ to 10 ⁹ Gauss. Fields of this strength have been observed in white dwarfs. We also calculate the London magnetic field due to the rotation of a dwarf star and show that its value is rather small.