Electric fields control an electric combustion. Plasmas are created by a dielectrically impeded discharge. At least one part of the fuel is mixed with water vapor in the supply line and is subjected to a plasma discharge in a compact reactor that is in close contact with the burner in terms of reaction kinetics. In the associated device, a plasma reactor for creating a reactive plasma gas with at least one supply line for the fuel gas-water vapor mixture and an electric energy supply is integrated into the burner. The device provides suitable flow guidance of the fuel gas-air mixture, of the fuel gas-water vapor mixture, and of the reactive plasma gas.