HBF SCIENTIFIC LAB · 7.5.2

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Laboratory 06 · Electrostatic energy recovery

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Models electrostatic recovery from an MeV alpha spectrum two independent ways: a discrete multistage energy ledger that closes source, recovered and residual energy exactly, and the published Rax–Kolmes–Fisch adiabatic E×B limit solved by bisection against its analytic endpoints.

multistage electrostatic ledgerRax adiabatic limitChild–Langmuir screenupper-bound recovery
Model scope: the stage ledger credits Erec=qΔφ to the highest strictly admissible stage for each simulated alpha and checks Esource=Erecovered+Eresidual exactly. Particle rate and current follow Ṅ=Pα/Ēα and I=2eṄ. The structural spectrum is calculated in the reaction centre-of-mass frame, so device-frame boost, joint energy–angle transport and stage-local space-charge physics lie outside this ledger and are reported as separate screens.

Conversion and plant ledger

Source spectrum and collector residual

Adiabatic E×B theoretical limit

54.7356° represents energy equipartition: one parallel and two perpendicular degrees of freedom.

Implements Rax, Kolmes & Fisch (2025) Eqs. 62, 65 and 68. It assumes an optimally large geometry and does not include the real birth distribution, collisions, neutral absorption, surfaces, or material stress.

What must be demonstrated next

GateMinimum evidenceCurrent state
keV benchmarkReproduce TMX 48±2% net and 100 keV beam 65±7%, including suppressor and pressure effects.Published external benchmarks; not reproduced by hardware here.
MeV helium/alpha beamCalibrated 0.1–5 MeV beam, spectrum/angles, MV electrodes, net load power and uncertainty.Missing.
Space charge and surfacesSelf-consistent Poisson/particle solution, secondary electrons, charge exchange, sputtering, heat flux and lifetime.Only screening scales here.
Integrated plasmaMeasured extraction fraction from p–¹¹B plasma and simultaneous collector operation.No published demonstration found.
Plant balanceFusion source, plasma sustainment, magnets, vacuum, conditioning, heat recovery and auxiliaries measured over a complete cycle.Scenario inputs only.