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The case of ac transport at in-phase alternating applied magnetic fields for a superconducting rectangular strip with finite thickness has been investigated. The applied magnetic field is considered perpendicular to the current flow. We present numerical calculations assuming the critical state model of the current distribution and ac loss for various values of aspect ratio, transport current and applied field amplitude. A rich phenomenology is obtained due to the metastable nature of the critical state. We perform a detailed comparison with the analytical limits and we discuss their applicability for the actual geometry of superconducting conductors. We also define a loss factor which allow a more detailed analysis of the ac behavior than the ac loss. Finally, we compare the calculations with experiments, showing a significant qualitative and quantitative agreement without any fitting parameter.
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A simple analytical expression is presented for hysteretic ac loss $Q$ of a superconducting strip simultaneously exposed to an ac transport current $I_0cosomega t$ and a phase-different ac magnetic field $H_0cos(omega t+theta_0)$. On the basis of Beans critical state model, we calculate $Q$ for small current amplitude $I_0ll I_c$, for small magnetic field amplitude $H_0ll I_c/2pi a$, and for arbitrary phase difference $theta_0$, where $I_c$ is the critical current and $2a$ is the width of the strip. The resulting expression for $Q=Q(I_0,H_0,theta_0)$ is a simple biquadratic function of both $I_0$ and $H_0$, and $Q$ becomes maximum (minimum) when $theta_0=0$ or $pi$ ($theta_0=pi/2$).
Analytic expressions for alternating current (ac) loss in radially arranged superconducting strips are presented. We adopt the weight-function approach to obtain the field distributions in the critical state model, and we have developed an analytic method to calculate hysteretic ac loss in superconducting strips for small-current amplitude. We present the dependence of the ac loss in radial strips upon the configuration of the strips and upon the number of strips. The results show that behavior of the ac loss of radial strips carrying bidirectional currents differs significantly from that carrying unidirectional currents.
Current distribution for a thin superconducting strip shielded by two ideally conducting plains has been calculated. It is shown that at microwave requencies the current density has maximum over the center of the strip in contrast to the dc current pattern, which exhibits crowding over the edges.
The hysteretic ac loss of a current-carrying conductor in which multiple superconducting strips are polygonally arranged around a cylindrical former is theoretically investigated as a model of superconducting cables. Using the critical state model, we analytically derive the ac loss $Q_n$ of a total of $n$ strips. The normalized loss $Q_n/Q_1$ is determined by the number of strips $n$ and the ratio of the strip width $2w$ to the diameter $2R$ of the cylindrical former. When $n>> 1$ and $w/R<< 1$, the behavior of $Q_n$ is similar to that of an infinite array of coplanar strips.
We study long Josephson junctions with the critical current density alternating along the junction. New equilibrium states, which we call the field synchronized or FS states, are shown to exist if the applied field is from narrow intervals centered around equidistant series of resonant fields, $H_m$. The values of $H_m$ are much higher than the flux penetration field, $H_s$. The flux per period of the alternating critical current density, $phi_i$, is fixed for each of the FS states. In the $m$-th FS state the value of $phi_i$ is equal to an integer amount of flux quanta, $phi_i =mphi_0$. Two types of single Josephson vortices carrying fluxes $phi_0$ or/and $phi_0/2$ can exist in the FS states. Specific stepwise resonances in the current-voltage characteristics are caused by periodic motion of these vortices between the edges of the junction.
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