Generalized Lawson-Cordey-Mills Accessibility of Fusion Ignition

A generalized ignition-accessibility framework is developed that unifies Lawson power balance, Cordey accessibility, the marginal ignition ridge, ignition entry points, and Mills thermal-runaway dynamics into a single self-consistent description of reactor-relevant burning plasmas. The 0D analysis recasts fusion ignition as a constrained dynamical pathway rather than a static threshold condition and demonstrates that radiation damping displaces the marginal ignition ridge, Cordey saddle, and ignition entry points toward higher densities and temperatures, thereby increasing the pressure required for ignition. In realistic 3D reactor geometry, this displacement translates into elevated plasma β requirements, establishing a direct connection between power balance, ignition accessibility, and macroscopic magnetohydrodynamic stability limits. A generalized thermal-runaway analysis reveals a previously unrecognized stabilizing feedback arising from transport, impurity and synchrotron damping, and the universally unfavorable power scaling of energy confinement, capable of reducing runaway growth and enabling steady-state burn. Enhanced confinement and spin-polarized fuels partially reopen the ignition window toward near-ideal DT performance.