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

This work proposes a novel performance metric for magnetically confined plasmas inspired by the power coefficient integral used in wind turbine theory. By drawing a structural analogy to the Betz power efficiency model, we define a dimensionless integral, Cβ , that evaluates how spatial variations in local plasma beta, β_loc , contribute to overall confinement efficiency. The formulation incorporates two profile functions, a(Λ) and a'(Λ) , analogous to axial and angular induction factors in wind energy systems, which are reinterpreted here in terms of radial transport and flow dynamics in plasma. Initial simulations using synthetic yet physically motivated radial profiles explore how Cβ varies with magnetic field strength, plasma temperature, and system scale length (λ) . These simulations reveal trends in efficiency saturation and confinement sensitivity, illustrating the usefulness of the model even in an early-stage conceptual form.