Field Distribution of a Cylinder-Shaped Type-II Superconductor with Limited Axial Length

Abstract

The self-field effects $\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}} {B'}$ of bulk magnetization current are considered when the applied field $\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}} {B} _a$ is parallel to the rotation axis of a cylinder-shaped type-II superconductor with limited axial length L and radius R, and by using finite-element analysis in a self-consistent way, the field-dependent magnetization current density function $J_m (|B|)[\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}} {B} (\rho ,z) = \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}} {B} _a + \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}} {B'} (\rho ,z)]$, the current density, and the field distributions are derived from magnetic moment hysteresis loop m(B _a) for the superconductor with full field penetration. When B _a≫B _p, the average field inside the cylinder $\left\langle B \right\rangle = \mu _0 [H_a + f_c (L/2R)M]$ in the Bean model approximation, and the function f _c(L/2R) is quantitively given for arbitrary parameter L/2R, where B _a=μ₀ H _a and M=m/(πR ² L). In addition, the influences of the self-field on the measured m(B _a) loop are discussed.