Power dependence of density limit due to plasma-wall interaction in a burning plasma

The density limit is one of the major obstacles to achieving the desired fusion performance in tokamaks. However, the underlying physics mechanism for its recently observed power dependence in experiments has not been well understood or predicted in theory. In this work, we derive for the first time the power-dependent scaling of the density limit from the plasma-wall self-organization (PWSO) theory [D.F. Escande 2022 NF]. These newly derived scalings successfully match the experimentally observed power dependence of density limits in multiple tokamak devices, such as, ASDEX-U and W7-AS, confirming the validity of the PWSO theory. Key influencing factors are identified as plasma-wall sputtering and particle confinement time. Additionally, the effects of non-sputtered impurities and fusion products are further evaluated. This PWSO-density limit model is then extended to the burning plasma regime and used to predict the conditions for entering burning plasma. Additionally, the impacts of non-sputtered impurities and fusion products are assessed. This refined PWSO-density limit model is then extended to the burning plasma regime to predict conditions necessary for achieving burning plasma scenarios.