ac response of thin superconductors in the flux-creep regime

Abstract

We calculate both analytically and numerically the ac susceptibility χ(ω) and the nonlinear electromagnetic response of thin superconductor strips and disks of constant thickness in a perpendicular time-dependent magnetic field Ba(t)=B0cos ωt, taking account of the strong nonlinearity of the voltage-current characteristics below the irreversibility line. We consider integral equations of nonlinear nonlocal flux diffusion for a wide class of thermally activated creep models. It is shown that thin superconductors, despite being fully in the critical state, exhibit a universal Meissner-like electromagnetic response in the dissipative flux-creep regime. The expression for the linear ac susceptibility during flux creep appears to be similar to the susceptibility of Ohmic conductors, but with the relaxation time constant replaced by the time t elapsed after flux creep has started. This result is independent of any material parameter or temperature or dc field. For ωt≫:1, we obtain χ(ω)≈-1+pln (qiωt)/(iωt), where p and q are constants. Above a critical ac amplitude B0=Bl, the local response of the electric field becomes nonlinear, and there are two distinctive nonlinear regimes at B0>Bl, where Bl∼s(d/a)1/2Bp, Bp is a characteristic field of full flux penetration, s(T,B)=|dln j/dln t| is the dimensionless flux-creep rate and d and a are the sample thickness and width, respectively. For Bl<B0<Bh(ω) the response of the electric field is strongly nonlinear but nonhysteretic, since the ac field Ba(t) does not cause a periodic inversion of the critical state. As a result, the magnetic moment exhibits a Meissner-like nondissipative response, in stark contrast to the Bean model. For B0>Bh(ω) the ac field causes hysteresis dissipation due to a periodic remagnetization of the critical state that gives rise to the hysteretic magnetic response of the Bean model at B0≫:Bh. Here Bh(ω) weakly depends on ω and is of order (d/a)1/2Bp for a very wide frequency range, well below the irreversibility field, where s(T,B)≪1. Magnetization and ac losses at B0≫:Bh are calculated accounting for the nonlinearity of E(J) at J<Jc and a crossover between flux flow and flux creep at J≃Jc. All these regimes were confirmed by our computer simulations of nonlinear flux diffusion in strips and disks.

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