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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