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Register a new userAnalysis of Magnetization Loss on a Twisted Superconducting Strip in a Constantly Ramped Magnetic Field
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Magnetization loss on a twisted superconducting (SC) tape in a ramped magnetic field is theoretically investigated through the use of a power law for the electric field--current density characteristics and a sheet current approximation. First, the Maxwell equation in a helicoidal coordinate system is derived to model a twisted SC tape, taking account of the response to the perpendicular field component in the steady state. We show that a loosely twisted tape can be viewed as the sum of a portion of tilted flat tapes of infinite length by examining the perpendicular field distribution on a twisted tape. The analytic formulae for both magnetization and loss power in the tilted flat tape approximation are verified based on the analytic solution of the reduced Maxwell equation in the loosely twisted tape limit of $L_{rm p}rightarrow infty$ with the twist pitch length $L_{rm p}$. These analytic formulae show that both magnetization and loss power decrease by a factor of $B(1+1/2n,1/2)/pi$ (where $B$ is the beta function) for an arbitrary power of SC nonlinear resistivity $n$, compared with those in a flat tape of infinite length. Finally, the effect of the field-angle dependence of the critical current density $J_{rm c}$ on the loss power is investigated, and we demonstrate that it is possible to obtain an approximate estimate of the loss power value via $J_{rm c}$ in an applied magnetic field perpendicular to the tape surface (i.e., parallel to the $c$ axis).
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We investigate theoretically the dependence of magnetization loss of a helically wound superconducting tape on the round core radius $R$ and the helical conductor pitch in a ramped magnetic field. Using the thin-sheet approximation, we identify the two-dimensional equation that describes Faradays law of induction on a helical tape surface in the steady state. Based on the obtained basic equation, we simulate numerically the current streamlines and the power loss $P$ per unit tape length on a helical tape. For $R gtrsim w_0$ (where $w_0$ is the tape width), the simulated value of $P$ saturates close to the loss power $sim(2/pi)P_{rm flat}$ (where $P_{rm flat}$ is the loss power of a flat tape) for a loosely twisted tape. This is verified quantitatively by evaluating power loss analytically in the thin-filament limit of $w_0/Rrightarrow 0$. For $R lesssim w_0$, upon thinning the round core, the helically wound tape behaves more like a cylindrical superconductor as verified by the formula in the cylinder limit of $w_0/Rrightarrow 2pi$, and $P$ decreases further from the value for a loosely twisted tape, reaching $sim (2/pi)^2 P_{rm flat}$.
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