Optimization of conduction-cooled current leads with unsteady operating current

A generalized optimization method is presented for conduction-cooled or cryocooled current leads whose operating current may vary over a period of time. This study is part of our ongoing efforts to reduce the cooling load in HTS power applications, where the actual current level varies considerably over a day and over a year. The presented method is also applicable to superconducting magnets that are not always operational at full current. When the operating current is given as a function of time, the total or accumulated cooling load at the cold end is calculated by integrating the instantaneous load over the period. The optimal length-to-area ratio of conductor is determined to achieve a minimum in the total load. After an accurate procedure taking into full account the temperature-dependent properties of conductor is developed with numerical calculations, a simple and reasonably accurate method based on Wiedemann-Franz approximation is suggested for practical use.