A mandrel has a main body having a substantially-cone-shape. The main body has, on its circumferential surface, a spiral-shaped groove at which the glass tube to be wound is held. The groove, in cross section, has a contact range in which the glass tube's circumferential surface is in contact. One end of the contact range corresponds to a circumference part of the glass tube in wound state which is closest to the axis of the main body of the mandrel, a part of the groove that extends from the circumference part towards the apex of the main body is parallel to the axis of the mandrel, and the pitch of the groove in the axial direction of the mandrel is formed smaller than the outer diameter of the glass tube. The glass tube wound on the mandrel is easily removed from the main body by lowering the mandrel. In the arc tube formed in such a way, any two glass tube portions, which are adjacent to each other in the axial direction of the arc tube, overlap with each other.