A design of a superconducting accelerator for a pulsed positron beam of ~1 MeV for positron annihilation lifetime spectroscopy is proposed. The total system can be extremely small with an application of superconducting technology. Both a miniaturization and easy maintenance of the accelerator can be achieved by usage of a small liquidless refrigerator for cooling of a superconducting RF cavity. Moreover, the operation duty cycle of the superconducting cavity is ~100% which is much larger than that of a normal conducting one. The required RF power to drive the system is ~10 W, therefore a large-size klystron is not necessary. The designed system including a slow positron source is small (~2 m 3 ) enough to be used in a general laboratory.1 Introduction Positron annihilation lifetime spectroscopy (PALS) is the unique method to investigate microscopic characteristic of materials [1]. For PALS, two methods are commonly used to supply positrons in specimens. One is usage of fast beta + rays emitted from radioisotopes (RIs). The RI sealed with thin films is sandwiched by two pieces of specimens during the PALS measurment. The other method is usage of a pulsed slow positron beam. In this case, a specimen has to be mounted in the vacuum. Applying of PALS to materials under extreme conditions (i.e., high temperature, high pressure, and high stress) is difficult with these two methods. The sealed RI might be destroyed under such extreme conditions in the former case and we have to solve a troublesome task that the extreme conditions have to be kept in the vacuum in the later case.PALS for materials under extreme conditions in atmosphere become possible with a high energy positron beam (~1 MeV), because higher energy positrons can pass through the vacuum window of a beamline. Actually, high-energy positron beams generated by electrostatic accelerators have been applied for PALS in materials at high temperatures [2,3]. A normal conducting accelerator has also been developed for PALS [4]. However, all the systems including their controllers so far developed are too huge to be used in a general laboratory.We propose a small accelerator system for high energy (~1 MeV) PALS, in which a superconducting accelerator is used. The overall system can be made extremely small (~2 m 3 ). Both a miniaturization and easy maintenance of the accelerator can be achieved when the superconducting cavity is cooled with a small liquidless refrigerator. To our knowledge, this is the first time a superconducting accelerators is cooled only by a liquidless refrigerator. In this paper, we discuss a design of a superconducting accelerator which is specially optimized for PALS.