A Dimensionless Integral Framework for Fusion Beta Optimization in Magnetically Confined Plasmas​

This work proposes a novel performance metricfor magnetically confined plasmas inspired bythe power coefficient integral used in windturbine theory. By drawing a structural analogyto the Betz power efficiency model, we define adimensionless integral, Cβ, that evaluates howspatial variations in local plasma beta, βloc,contribute to overall confinement efficiency. Theformulation incorporates two profile functions,a(Λ) and a'(Λ), analogous to axial and angularinduction factors in wind energy systems, whichare reinterpreted here in terms of radial transportand flow dynamics in plasma. Initial simulationsusing synthetic yet physically motivated radialprofiles explore how Cβ varies with magneticfield strength, plasma temperature, and systemscale length (λ). These simulations reveal trendsin efficiency saturation and confinementsensitivity, illustrating the usefulness of themodel even in early-stage conceptual form. Theintegral is normalized to ensure device-independent comparisons, and 3D parametersweeps offer insight into performance limits andoptimization potential. This framework providesa new lens for evaluating plasma performanceand offers a stepping stone toward morerigorous, transport-derived models. Future workwill integrate experimental or first-principlestransport data to fully ground the integral inplasma physics theory and apply it to predictivemodeling for fusion reactor design.​