Catalyzed Deuterium Operation in Pulsed Field-Reversed Configuration Systems: Helium-3 Recycle, Secondary Burn, and Requirements for Net Energy Gain

<title>Abstract</title> <p>Helium-3 recycle provides the largest modeled reduction in the confinement requirement for pulsed field-reversed-configuration D-D operation, but the reduction is conditional on separator retention, charged-product deposition, radiative transfer, and energy recovery. Four accounting tiers distinguish terminal operation, incidental in-situ burn, helium-3 recycle, and full catalysis. Single-pass secondary burn remains exposure-limited and contributes less than 2.4 × 10⁻³ to the energy multiplier at demonstrated parameters; recycling helium-3 instead increases the charged credit per primary reaction and reduces the ideal confinement floor by a factor of 4.8 after pressure dilution. The 20 T selected external-field target is paired with a 19 T program operating floor. The floor is a selected design specification obtained by rounding the 18.80 T crossing of a stipulated nτ_E = 10²⁰ m⁻³ s reference for pure D under one empirical scaling. Its low-xₛ relation is evaluated at xₛ = 0.4 within the published xₛ domain but extrapolated from sub-keV data to 100 keV. It is not a Tier-2 minimum: the same Tier-2 reference crosses at 19.87 T, so the selected target only just clears it. Confinement at temperature and full-cycle separator, deposition, radiation, and recovery performance remain open gates.</p>