Critical edge ion heat flux for L-H transition: parameter dependence and projections to high field tokamaks

L-H transition experiments on Alcator C-Mod with toroidal field B_T of 4.0—7.8T strengthen the basis for projecting power requirements for future fusion devices, including burning plasmas such as ITER and SPARC. The favored ITPA scaling law for H-mode power threshold P_th captures the approximate dependence of P_th on B_T and density n, though uncertainty remains. C-Mod transport and power balance analysis confirms and extends a prior result from ASDEX Upgrade (AUG): a critical surface-integrated ion heat flux per particle Q_i/n is needed to enable the L-H transition. Analysis indicates that Q_i at the L-H transition increases linearly with both n and B_T, trends not necessarily reflected in experimental P_th due to the changing balance of edge electron and ion heat fluxes, which depends in turn on the auxiliary heating scheme and electron-ion equilibration. Data drawn from both C-Mod and AUG yield an expression for the edge ion heat flux at the L-H transition, Q_i/S∼n^1.07B_T ^0.76, where S is the plasma surface area. The result is consistent with a critical shear in edge E×B being necessary for H-mode access.