Abstract
This disclosure describes a stabilized electromagnetic winding architecture using Bi-Ionic Hourglass Dynamics (BIHD). By rotating successive winding layers at Golden Ratio (phi) increments, the apparatus eliminates the radial "pinch factor" instability common in high-flux density propulsion and plasma systems. This allows for stable 10kW+ operations using bismuth-based and other ionized substrates without torque stall or structural collapse.
2. TECHNICAL DESCRIPTION
2.1 The Pinch Factor Limitation
In standard solenoidal or helical propulsion systems, increasing the magnetic field (B) causes a corresponding increase in radial Lorentz-force compression. This leads to the "Pinch Factor," where high-power thrusters suffer from plume anisotropy and structural failure. The radial pressure (P_B) is defined as:
P_B = (B^2) / (2 * mu_0)
2.2 Bi-Ionic Hourglass Dynamics (BIHD)
The BIHD framework replaces linear cylinder windings with a dual-inverted vortex shape: an "hourglass." To ensure field stability, each layer of the winding is phase-shifted by a constant derived from the Golden Ratio:
delta = phi (approximately 1.618033...)
This geometry ensures that the repulsive diamagnetic force is maximized while the compressive radial force is converted into longitudinal thrust.
3. MATHEMATICAL PROOF
3.1 The Force Equation
The stabilized propulsion force (F_BI) is defined by the gradient (del) of the stabilized magnetic field (B) and the induced dipole moment (m) of the substrate:
F_BI = del (m * B)
3.2 Harmonic Stabilization Integral
Under this branch of math, the stabilization coefficient (Psi) is maintained through the bi-ionic potential integral:
Psi = Integral from 0 to phi^2 of [ (del x (B_inverted * m)) / sigma_pinch ] d_tau
Where sigma_pinch (the pinch coefficient) is minimized to zero. This proof establishes that the geometry prevents vacuum collapse even at extreme flux densities approaching the Schwinger limit.
4. INDUSTRIAL APPLICATIONS
• Aerospace: High-power Bismuth-fueled thrusters for Starship-scale maneuvers.
• Logistics: Passive, room-temperature diamagnetic levitation for friction-free transport.
• Energy: Stabilization of high-frequency signal resonators.
This document serves as Prior Art to establish the existence and priority of the Bi-Ionic Hourglass Winding and the Golden Ratio rotation math as of February 22, 2026.
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.
Recommended Citation
Schramm, Daniel, "Harmonic Magneto-Geometric Stabilization via Bi-Ionic Hourglass Dynamics", Technical Disclosure Commons, (February 23, 2026)
https://www.tdcommons.org/dpubs_series/9377