Griffiths Rotating Electromagnetic Nozzle Analytical Framework for Geometry-Stabilised Plasma Acceleration and Universal Plume Augmentation

GREMN v17 — Griffiths Rotating Electromagnetic Nozzle Analytical Framework for Geometry-Stabilised Plasma Acceleration and Universal Plume Augmentation This record contains the complete analytical manuscript, supplementary material, and plain language summary. Submitted for peer review February 2026. What This Version Provides Version17 represents a fundamental repositioning from prior versions. The paper has been rebuilt as a rigorous archival analytical contribution derived entirely from first principles from the resistive MHD governing equations and Maxwell’s equations — no empirical fitting parameters, no assumed results. Core analytical contributions: 1. Rotating Field Solution The field B(r,θ,t) = B₀(r)[cos(mθ−ωt)ê_r + sin(mθ−ωt)ê_θ] produced by contra-rotating permanent magnets is derived via the modified Bessel equation from the resistive MHD induction equation. Electromagnetic skin depth δ = √(2/ωμ₀σ) = 0.8–10 cm is comparable to nozzle radius a = 5–12 cm, confirming full volumetric field penetration. 2. Induced Current Density J_θ(r) = σ(ωB₀/k)[1 − exp(−(a−r)/δ)] derived analytically from Faraday’s law and Ohm’s law, with the exponential factor accounting for finite skin-depth penetration. 3. Electromagnetic Thrust Integral F_EM = 2π∫∫ J_θ B_r r dr dz derived by explicit integration of the Lorentz force density, yielding F_EM = 2πσB₀²ωa²L C_geom = 15–25 N at the 1 MW design point. 4. Linearised Stability Analysis Full MHD dispersion relation derived from first principles. Critical stability parameter Ω_s/γ_KH = (dv_θ/dr)/(v_A k) = 3.5–15 at design conditions — complete suppression of Kelvin-Helmholtz, Rayleigh-Taylor, and drift-wave instabilities confirmed. 5. Thermal Nozzle Efficiency Derived from adiabatic invariant conservation with ambipolar electron pressure gradient correction. Mirror efficiency η_mirror = 0.75–0.85 for R_mirror = 20–60. 6. Formal Uncertainty Propagation ±36% (1σ) uncertainty on F/P propagated from three independent sources in quadrature: plasma conductivity σ (±30%), geometric factor C_geom (±15%), mirror efficiency η_mirror (±10%). Performance Summary Total thrust (1 MW standalone): 60–85 N Specific impulse: 2,500–4,000 s Thrust-to-power ratio: 60–85 mN/kW EM thrust contribution: 15–25 N Thermal thrust contribution: 45–60 N KH stability margin Ω_s/γ_KH: 3.5–15 Skin depth: 0.8–10 cm Rotation frequency: 100–300 Hz Analytical uncertainty (F/P): ±36% (1σ) TRL: 3–4 Performance positioning: GREMN occupies the gap between Hall thrusters (F/P = 50–70 mN/kW, I_sp < 3,000 s) and VASIMR (F/P = 5–8 mN/kW, I_sp > 4,000 s) — a performance combination unoccupied by any existing electric propulsion system. Universal Augmentation Capability GREMN operates as a retrofittable downstream collar compatible with any propulsion source producing a directed plasma or partially ionised exhaust. Coupling physics are derived from first principles for each host class: Hall thruster: 18–28% augmentation — Plume collimation + breathing-mode suppression (40–70% amplitude reduction) Gridded ion engine: 8–15% augmentation — Space-charge relief above Child-Langmuir current density limit MPD thruster: 12–22% augmentation — Electrode erosion reduction; peak/avg current density ratio 3–6× reduced to 1.2–1.8× Chemical rocket: 0.05–0.2% augmentation — I_sp gain via RF pre-ionisation annulus Nuclear thermal: 0.5–2% augmentation — Extended mission endurance Literature and Novelty 65 references spanning helicon plasma physics (Boswell, Chen, Charles), magnetic nozzle theory (Ahedo, Merino, Longmier/VX-200), MHD stability (Chandrasekhar, Freidberg, Kruskal–Schwarzschild), shear stabilisation (Terry, Biglari–Diamond–Terry, Burrell H-mode), and all five host propulsion classes. Four explicit novelty claims distinguished from VASIMR, HDLT, RMF, and LFA prior art: • Rotating permanent magnets separate field rotation from RF plasma heating, permitting independent optimisation of each • Shear flow co-designed as both stability mechanism and thrust source — builds on Biglari–Diamond–Terry but adds J×B thrust as co-equal output • First analytical framework for retrofittable augmentation coupling to multiple host propulsion classes from first principles • Breathing-mode suppression identified and quantified as primary Hall thruster augmentation benefit Validation Pathway Phase 1 — Laboratory breadboard (Months 1–12, est. USD 1–2M) F/P ≥ 50 mN/kW at 50 kW; RF coupling efficiency ≥ 70%; breathing-mode suppression ≥ 40% on 5 kW Hall thruster. Phase 2 — Integrated ground demonstration (Months 13–18, est. USD 3–5M) F ≥ 60 N at 1 MW; I_sp ≥ 2,500 s; F/P ≥ 60 mN/kW; ≥ 200 hours cumulative operation. Phase 3 — Flight demonstration (Months 19–24, est. USD 8–12M) ≥ 80% of analytical predictions confirmed; ≥ 90 days continuous operation; in-space augmentation validation. Changes from v5.1 • Power class revised: 5–12 kW → 1 MW standalone design point • Full MHD derivations from Maxwell’s equations added throughout • Rotating field solution derived via Bessel equation (new) • Electromagnetic thrust by explicit Lorentz force integration (new) • Linearised dispersion relation and stability analysis from first principles (new) • Formal uncertainty propagation ±36% replacing stated ranges (new) • Augmentation coupling physics derived for all five host propulsion classes (new) • 65-reference literature review with explicit prior art arguments (expanded from ~15) • Nomenclature section (65 symbols) added • Plain language summary added for public engagement • Restructured as single consolidated manuscript Document Status and Related Records Status: Submitted for peer review, February 2026 Related Zenodo records: • Griffiths, W. (2026). GNMT: Griffiths Nuclear Microwave-Thermal Propulsion Architecture v7.0. Zenodo. • Griffiths, W. (2026). DIGSP: Deterministic Intelligent Governing System for Propulsion. Zenodo. Citation Griffiths, W. (2026). Griffiths Rotating Electromagnetic Nozzle (GREMN) v6.0: Analytical Framework for Geometry-Stabilised Plasma Acceleration and Universal Plume Augmentation. Zenodo. https://doi.org/[DOI] Contact: waynegriffiths9@gmail.com | ORCID: 0009-0009-4905-7909