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Recently, affinity magnetic beads have been widely used in immunomagnetic cell sorting (IMCS) technology. Today, we can easily sort and analyze DNA and antibodies (immunoglobulin) using various types of affinity magnetic beads available in the market. The diameters of these affinity magnetic beads used in immunomagnetic cell sorting are limited to above approximately 1 mum because of the low magnetic fields induced by permanent magnets. Now, nano-sized affinity magnetic beads are strongly desired to achieve high resolutions. We have been studying and attempting to develop a high-gradient magnetic separation (HGMS) system that employs a superconducting magnet to induce a considerably higher magnetic field than that induced by a permanent magnet in order to trap smaller nano-sized affinity magnetic beads by a filter made of fine stainless steel wool. In this study, we constructed a prototype of a desktop-type HGMS system using a cryocooler-cooled LTS magnet and conducted preliminary experiments on trapping the nano-sized magnetic particles. Furthermore, we investigated the magnetic field distribution and magnetic force around a magnetic wire in the filter by means of a numerical simulation.