Efficient Numerical Modeling of the Magnetization Loss on a Helically Wound Superconducting Tape in a Ramped Magnetic Field

TL;DR

This paper presents a theoretical and numerical study of magnetization loss in helically wound superconducting tapes, revealing how core radius and pitch affect power loss and providing analytical limits for different geometries.

Contribution

It introduces a thin-sheet approximation model for magnetization loss in helical tapes and derives analytical expressions for loss behavior in different geometric regimes.

Findings

Loss power saturates near (2/π) times flat tape loss for large core radius.

Loss decreases further as core radius shrinks, approaching (2/π)^2 times flat tape loss.

Theoretical results are validated by numerical simulations and analytical calculations.

Abstract

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 Faraday's 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 $w_0/R\rightarrow 0$. 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 $w_0/R\rightarrow 2\pi$, and $P$ decreases further from the value for a loosely twisted tape, reaching $\sim (2/\pi)^2 P_{\rm flat}$.