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Optimization of Current Leads for HTS Elements Immersed in Liquid Nitrogen

The dimension of metallic current leads is optimized for minimizing the cooling load, taking into account the Ohmic heat generation of conductor part immersed in liquid nitrogen. Since HTS elements in liquid nitrogen are located well below the liquid level for thermal and electrical safety, considerable length of leads is in contact with liquid at constant temperature. In theory, the conductor size needs to be optimized for the upper part above the liquid surface, but a large cross-sectional area is favored for the lower part immersed in liquid in order to reduce the cooling load. On the other hand, this current-lead design aims at a simple metallic conductor with uniform cross-section for the entire length. It is rigorously shown that there exists a unique optimum for the total length-to-area ratio to minimize the overall cooling load, if the length fraction of liquid part is given. A new and useful design formula is derived upon the Wiedemann-Franz law for the temperature-dependent properties of conductor.