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A study on the dielectric characteristics of various cryogenic materials should be conducted to design an electrically reliable high-voltage superconducting apparatus. Especially, the dielectric characteristics of gaseous and solid insulation materials are important for designing current lead parts, and those of gaseous and solid insulation materials are indispensable for designing superconducting coil parts. A subcooled liquid nitrogen (LN2) cooling system is the most promising, with respect to insulation, thermal stability, and current capacity, in the development of a high-voltage superconducting apparatus. In this paper, dielectric experiments on gaseous nitrogen ( GN2), LN2, and glass fiber reinforced plastic are conducted under ac and lightning impulse voltage for various pressures. Sphere-to-plane electrode systems are used to examine the dielectric characteristics of insulation materials according to field utilization factor (ξ). The experimental results are analyzed by a finite element method. The empirical formulae for calculating the electrical breakdown voltages of various cryogenic insulation materials at sparkover are presented.