Critical fields of a superconducting cylinder

The self-consistent solutions of the nonlinear Ginzburg-Landau equations, which describe the behavior of a superconducting mesoscopic cylinder in an axial magnetic field H (provided there are no vortices inside the cylinder), are studied. Different, vortex-free states (M-, e-, d-, p-), which exist in a superconducting cylinder, are described. The critical fields (H 1, H 2, H p, H i, H r), at which the first or second order phase transitions between different states of the cylinder occur, are found as functions of the cylinder radius R and the GL-parameter $$\kappa $$ . The boundary $$\kappa _c (R)$$ , which divides the regions of the first and second order (s, n)-transitions in the icreasing field, is found. It is found that at R→∞ the critical value, is $$\kappa _c = 0.93$$ . The hysteresis phenomena, which appear when the cylinder passes from the normal to superconducting state in the decreasing field, are described. The connection between the self-consistent results and the linearized theory is discussed. It is shown that in the limiting case $$\kappa \to {1 \mathord{\left/ {\vphantom {1 {\sqrt 2 }}} \right. \kern-\nulldelimiterspace} {\sqrt 2 }}$$ and R ≫ λ (λ is the London penetration length) the self-consistent solution (which correponds to the socalled metastable p-state) coincides with the analitic solution found from the degenerate Bogomolnyi equations. The reason for the existence of two critical GL-parameters $$\kappa _0 = 0.707$$ and $$\kappa _0 = 0.93$$ in, bulk superconductors is discussed.