Recent progress in the design of the K-DEMO divertor

•A water-cooled tungsten monoblock divertor concept has been considered in the K-DEMO.•The detached divertor study has been carried out by the impurity seeding for N, Ne, and Ar to reduce the peak heat flux and particle flux.•The optimum designs were derived by the response surfaces optimization method for CuCrZr and RAFM steel, the major candidates for the heat sink in the K-DEMO.•The alternative divertor concepts were studied for the super X-divertor and snowflake divertor.