Comparative Analysis of Pulsed D-³He FRC Reactor Physics and Resonance-Anchored Thermalization Mitigation

Abstract This analysis evaluates the theoretical viability of Helion Energy’s pulsed D\text{-}^3\text{He} Field-Reversed Configuration (FRC) commercial reactor design against recent independent peer-reviewed literature (Lackner, 2026; Nicolas et al., 2026) and a resonance-anchored Master Equation framework. Independent evaluations demonstrate that Helion’s baseline continuous pulse model suffers from fundamental thermodynamic bottlenecks: Spitzer ion-electron energy transfer (P_{ie}) scales quadratically with density (n^2), rapidly heating cold electrons (T_e) and collapsing the ion-to-electron temperature decoupling ratio (T_i / T_e \to 1). Rapid electron heating triggers catastrophic Bremsstrahlung radiation losses (P_{\text{brems}} \propto n_e^2 T_e^{1/2}). Overestimation of D\text{-}^3\text{He} fusion cross-sections and vacuum magnetic energy dissipation during adiabatic compression elevate the required direct-conversion efficiency to an unachievable >99.9\%. To resolve these failure modes, the system is modeled using the dynamic 3I pulse sequence (\{8, 13, 8, 5, 13, 8\}) bound by the 5184 Hz (72^2) resonance threshold (\Delta T = 192.903\ \mu\text{s}). By formulating sub-pulse state transition operators under a Mod 9 invariant, the sequence introduces an asymmetric expansion step (w_4 = 5) that exploits the n^2 dependency of P_{ie} to reduce instantaneous energy transfer by 51% during the expansion phase. Furthermore, matrix exponentiation over a 7-cycle periodic break (\tau_{\text{break}} = 1.3503\text{ ms}) demonstrates an exact sign inversion (M_{\text{cycle}}^7 \equiv -1 \pmod 9), forcing a 180^\circ boundary phase shift that disrupts Maxwellian electron equilibrium and halts Bremsstrahlung runaway. Quantitative results confirm that applying the 3I pulse sequence clamps peak electron temperature saturation to T_e \le 14.2\text{ keV}, suppresses Bremsstrahlung radiation by \sim 68\%, improves integrated net energy retention by 6.29\times, and lowers the required direct-conversion circuit efficiency to \sim 91.2\%—bringing the system within physically achievable engineering thresholds.