The arc discharge apparatus comprises a plurality of carbon electrodes connected to respective phases of a power supply for heating a silica powder and causing it to fuse by generating arc discharge between the carbon electrodes. All of the carbon electrodes have a density in a range from 1.30 g/cm3 to 1.80 g/cm3, and variability in density among the carbon electrodes is 0.2 g/cm3 or less. The carbon particles that constitute the carbon electrodes preferably have a particle diameter of 0.3 mm or less.