Abstract: An electrode structure for a combustion vessel including a first electrode and a first dielectric barrier. The first electrode is made of a conductive material, has a rod-like shape, and protrudes from an inner surface of the combustion vessel. The first dielectric barrier is made of a dielectric material. The first electrode has, on its surface, a first exposed surface exposed in the combustion space and a first coated surface coated with the first dielectric barrier. A predischarge progresses while the first coated surface serves as a start point or an end point of the progress. A main discharge progresses while the first exposed surface serves as a start point or an end point of the progress. The main discharge includes a creeping discharge that creeps along a surface of the first dielectric barrier, and goes through a spatial region where the predischarge occurs.