SUPERCONDUCTOR DISKS AND CYLINDERS IN AN AXIAL MAGNETIC-FIELD - II - NONLINEAR AND LINEAR AC SUSCEPTIBILITIES

The ac susceptibility chi = chi' - i chi '' of superconductor cylinder s of finite length in a magnetic field applied along the cylinder axis is calculated using the method developed in the preceding paper, part I. This method does not require any approximation of the infinitely e xtended magnetic field outside the cylinder or disk but directly compu tes the current density J inside the superconductor. The material is c haracterized by a general current-voltage law E(J), e.g., E(J) = E-c[J /J (c)(B)](n(B)), where E is the electric field, B = mu(0)H the magnet ic induction, E-c a prefactor, J(c) the critical current density, and n greater than or equal to 1 the creep exponent. For n > 1, the nonlin ear ac susceptibility is calculated from the hysteresis loops of the m agnetic moment of the cylinder, which is obtained by time integration of the equation for J(r,t). For n much greater than 1 these results go over into the Bean critical state model. For n=1, and for any linear complex resistivity rho(ac)(omega)=E/J, the Linear ac susceptibility i s calculated from an eigenvalue problem which depends on the aspect ra tio bla of the cylinder or disk. In the limits b/a much less than 1 an d b/a much greater than 1, the known results for thin disks in a perpe ndicular held and long cylinders in a parallel field are reproduced. F or thin disks in a perpendicular field, at large frequencies chi(omega ) crosses over to the behavior of slabs in parallel geometry since the magnetic field Lines are expelled and have to dow around the disk. Th e results presented may be used to obtain the nonlinear or linear resi stivity from contact-free magnetic measurements on superconductors of realistic shape.