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

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 w0 (where w0 is the tape width), the simulated value of P saturates close to the loss power ∼ (2/π)P flat (where P 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 w0/R → 0. For R w0, 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 w0/R → 2π, and P decreases further from the value for a loosely twisted tape, reaching ∼ (2/π) 2 P flat .

Round-Core-Radius-Dependent Electromagnetic Coupling of Multifilament Helical Superconducting Tapes in a Swept Magnetic Field

“…For an effective tape width w, by taking the thin-filament limit of w/R → 0, we obtain the following analytical formula for the loss power per unit length [12], which coincides with that for a twisted tape [14]:…”

“…Unless specified otherwise, the dimensions are as follows: the total tape width is w 0 = 2 mm, the width of an SC filament is w 1 = 0.485 mm, the slot width is s 1 = 20 µm, the thickness of the SC tape is d 0 = 2 µm, and the radius of the hollow cylinder is R = 3 mm. The helical SC tape is assumed to be so thin (d 0 w 0 ) that it can be approximated as an infinitesimally thick surface described by the coordinates [12]…”

“…In previous work, by adopting the thin-sheet approximation that takes account of only the perpendicular field component, we derived the steady-state Faraday-Maxwell equation for a constantly swept applied magnetic field B a = βt x with rate β = dB a /dt [12], [14]. We base the present numerical simulation on the following two-dimensional Faraday-Maxwell equation on the tape surface (ξ, ζ) extended to multi-filament helical SC tapes:…”

“…The power dissipated on the tape surface per unit length is given by [11], [12] P total = P sc + P couple ,…”