An arc discharge apparatus includes a body unit including a housing and a transmissive member fixed to the housing, the housing having a coolant inlet and a coolant outlet, and an electrode unit on the housing, the electrode unit including an anode and a cathode facing each other, wherein the anode includes a main body portion connected to the housing, an anode tip coupled to the main body portion, and a cooling line in the anode and in contact with an inner wall of the anode tip, the cooling line being connected to the coolant inlet and to the coolant outlet.