Analytical model of the critical current of a bent NbSn strand

曲げ変形を受けたNbSnの臨界電流値の解析モデル

小泉 徳潔; 村上 陽之; 辺見 努; 中嶋 秀夫

Koizumi, Norikiyo; Murakami, Haruyuki; Hemmi, Tsutomu; Nakajima, Hideo

核融合炉で使用されるケーブル・イン・コンジット(CIC)導体では、巨大な電磁力を受けて、内部の素線が曲げ変形して、臨界電流性能が劣化するという現象が観測されている。本劣化を定量的に評価するためには、素線の曲げ変形と臨界電流性能の劣化を簡易的に評価する解析モデルの構築が必要である。そこで、著者らは、NbSn線を曲げた場合の臨界電流値の劣化を、素線構成材料NbSn,銅,ブロンズ,バリア材(Ta, Nb)の弾性変形に加えて、新たに、銅及びブロンズの塑性変形、フィラメント断線の影響を考慮して計算する解析モデルを開発した。本解析モデルを用いた計算結果と一様に曲げ歪を加えたNbSn線の臨界電流値の測定結果を比較し、解析結果がよく一致することを確認した。これにより、モデルの妥当性を検証した。加えて、曲げ変形で銅,ブロンズが塑性変形、あるいは一部のフィラメントが断線した後に、曲げ戻すと素線が引張歪を受けて、臨界電流値が曲げ前のそれよりも高くなりうることを解析的に示し、他の研究者が示した試験結果を定量的に説明することもできた。

Critical current performance of a large NbSn cable-in-conduit conductor (CICC) was degraded by periodic bending of strands due to a large transverse electromagnetic force. The degradation of each strand due to this bending should be evaluated in calculations of the critical current of a CICC, but a suitable model has not been developed yet. Therefore, the authors have developed a new analytical model which takes into account plastic deformation of copper and bronze and filament breakage. Calculated results were compared with test results for uniformly bent NbSn bronze-route strands. Calculated results assuming a high-transverse resistance model (HTRM) show good agreement with the test results, a finding which confirms the validity of the model. Because of a much shorter calculation time than for numerical simulation, the developed model seems much more practical for use in calculating the critical current performance of a NbSn CICC. In addition, simulation results show that since the neutral axis of a bent strand shifts to the compressive side due to plastic deformation of the copper and bronze, and/or filament breakage, the strand is elongated by bending. This elongation may enhance the strand's critical current performance. Moreover, calculated results indicate that dependence of the critical current on the bending strain is affected by the bending history if the strand is excessively bent, especially when filaments are broken. In a real magnet, since a strand in a CICC is normally subject to the maximum electromagnetic force prior to an evaluation of its performance at a lower electromagnetic force, the effect of over-bending should be taken into account in calculations of its critical current performance, especially when filament breakage occurs.