Toward the practical applications, on operation of conduction-cooled HTS SMES at temperatures well below 40[K] should be investigated, in order to take advantage of a greater critical current density of HTS and considerably reduce the size and weight of the system. In order to take advantage of a greater critical current density of high temperature superconducting (HTS) and considerably reduce the size and weight of the system, conduction-cooled HTS superconducting magnetic energy storage (SMES) at temperatures well below 40[K] should be investigated. This work focuses on the breakdown and flashover phenomenology of dielectrics exposed in air and/or vacuum for temperatures ranging from room temperature to cryogenic temperature. Firstly, we summarize the insulation factors of the magnet for the conduction cooled HTS SMES. And Secondly a surface flashover as well as volume breakdown in air and/or vacuum with two kind insulators has been investigated. Finally, we will discuss applications for the HTS SMES including aging studies on model coils exposed in vacuum at cryogenic temperature. The commercial application of many conduction-cooled HTS magnets, however, requires refrigeration at temperatures below 40[K], in order to take advantage of a greater critical current density of HTS and reduce considerably the size and weight of the system. The magnet is driven in vacuum condition. The need to reduce the size and weight of the system has led to the consideration of the vacuum as insulating media. We are studying on the insulation factors of the magnet for HTS SMES. And we experiment the spacer configure effect in the dielectric flashover characteristics. From the results, we confirm that our research established basic information in the insulation design of the magnet.