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Miyaki-jima (巳焼島), also known as Miyaki Island is an imaginary island that formed 50 km east of Miyake-jima (三宅島) in 2001 by undersea volcanic activity. In the beginning, there is a military base, around 2050 volcano erupted, later it was changed into prison for criminal magicians. Using backdoor deals from Toudou Aoba, it essentially became Yotsuba private territory. Miyaki Island prison was secretly authorized by the military for Yotsuba to isolate dangerous magicians. 
The island made by lava is about seven square kilometers. At the time of World War III, the Defense Forces established a base on the island, but it was abandoned due to repeated eruptions in the 2050’s, and the facilities that are used to imprison criminal magicians have be placed at the western end of the island.
This was the place that had been chosen as a practice range for Miyuki's Niflheim because this island is the private property of the Yotsuba. In name the Defense Forces are responsible for the management of the magician prison but in actuality it is entrusted by the Yotsuba Family. This is not a known fact among the Ten Master Clans.
Even though this prison is under the jurisdiction of the Defense Forces, it is a remnant of the era where magicians are treated as weapons, there are also certain circumstances that have led to a large number of foreign operatives to be sent here. These foreign operatives are illegal agents that aren’t protected by the law and therefore pretty much don’t exist. If they are killed nobody can complain about it, due to this fact the prisoners are always looking for a way to escape.
The magicians sent to this island are strong men who must be isolated from civilians with the barrier of the ocean. To prevent them from escaping and to suppress those who resist the guards must also be fairly skilled. This is one of the reasons that the Defense Forces struck a deal with Yotsuba.