Calculation and measurement of coupling loss in a no-insulation ReBCO racetrack coil exposed to AC magnetic field
S. Otten, Jeroen ter Harmsel, M. Dhallé, Herman H.J. ten Kate
Abstract
Abstract No-insulation coils are self-protecting and can therefore generally be operated at higher current densities. However, the electrical turn-to-turn connections may cause additional AC loss when charging the coil or when it is exposed to a time-dependent magnetic field. In this work, we study the case of a no-insulation Re BCO tape racetrack coil exposed to a uniform AC field applied parallel to the tape surface. We show that an anisotropic continuum model allows to formulate analytical approximations for coupling loss in the low- and high-frequency limits. For intermediate frequencies, the continuum model needs to be evaluated numerically. The model was validated with representative measurements of AC loss in the coils, measured calorimetrically as well as magnetically using pick-up coils. The validation experiment confirms the predicted frequency dependence of the coupling loss, which is <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>P</mml:mi> <mml:mo>∝</mml:mo> <mml:msup> <mml:mi>f</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:math> at low frequencies and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>P</mml:mi> <mml:mo>∝</mml:mo> <mml:msqrt> <mml:mi>f</mml:mi> </mml:msqrt> </mml:math> at high frequencies, due to the skin effect. The transition between low- and high-frequency regimes occurs around a characteristic frequency <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mi>f</mml:mi> <mml:mrow> <mml:mi mathvariant="normal">c</mml:mi> </mml:mrow> </mml:msub> </mml:math> that is directly related to the characteristic time constant <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>τ</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mn>2</mml:mn> <mml:mi>π</mml:mi> <mml:msub> <mml:mi>f</mml:mi> <mml:mrow> <mml:mi mathvariant="normal">c</mml:mi> </mml:mrow> </mml:msub> </mml:math> associated with the current decay in (dis)charge experiments.