Analytic solution of a generalized critical state model of type II superconductors

For a type II superconductor obeying a generalized critical state model characterized by J_c of type J_c(H) = J₀H₀ⁿ (|H| + H₀)ⁿ, we present an analytical solution of magnetic field profiles inside a cylindrical sample subject to an arbitrary cyclic magnetic field applied parallel to the cylindrical axis. Consistency with published analytic solutions for the special cases n=0 viz. Bean's model [1] and n = 1, viz. the Kim-Anderson model [2,3], is verified.