Longitudinal critical current in type II superconductors. I. Helical vortex instability in the bulk

The vortex lattice in type II superconductors is unstable against the growth of helical perturbations if the current along the vortices exceeds a critical value. The longitudinal critical current, the pitch, and the spatially varying amplitude of the elliptically polarized helices are calculated from the London theory at the onset of instability in planar current distributions far from the surface. For weak pinning (_L² c ₆₆) the wavelength and width of the mode extend over the entire specimen, and the critical current is 2H(c ₆₆/c ₁₁)^1/4. For moderate pinning (c _{66 L}² c ₁₁) the wavelength and width are close to Campbell's pinning length (c ₁₁/_L)^1/2, and the critical current times its mean density is 2H ²(_L/c ₁₁)^1/2. For strong pinning (_L² c ₁₁) helical instability occurs at pin-free vortex sections, the helix wavelength is 2.2d, and the critical current density is 0.47Hd/² (H, d, c ₁₁ and c ₆₆), and _L are the magnetic field, spacing, elastic moduli, and pinning parameter of the vortex lattice, and is the magnetic penetration depth).