Regime-Based Electrodynamic Systems: Architecture, Energy Balance, and Scientific Foundation

Critical interpretation rule

The framework uses the Three-Level Energy Model. These three analytical levels are distinct and must never be collapsed into one:

Level 1 — Boundary accounting (complete device boundary) — all energy crossing the boundary is accounted; the aggregate term \(P_{\text{in,boundary}}\) is a macroscopic accounting quantity at the complete device boundary, not a continuous external feed; conservation laws fully apply.

Level 2 — Regime layer (internal operation) — energy already within the boundary undergoes event partition and feedback redistribution: regime formation, regime stability, and controlled extraction.

Level 3 — Gap physics (sealed discharger) — carrier dynamics governing nonlinear conductivity switching; carrier multiplication shapes the regime but does not multiply energy.

2.1 Active Core — Regime Formation (regime-forming path)

The active core is a nonlinear resonant structure based on an effective LC combination with a sealed discharger as the controlled nonlinear element. Operating at approximately 2.45 MHz, it uses a capacitive node (capacitors C2.1–C2.3) and a primary winding to sustain the electrodynamic regime. The effective resonant frequency is:

In nonlinear regimes, \(\omega_0\) may depend on amplitude, conductivity, and discharge parameters; the value above is understood as the equivalent resonant frequency for the chosen operating point.

The discharge provides dynamic nonlinear conductivity \(\sigma(E,t)\), enabling the system to reach and sustain a stable limit-cycle regime. This regime maintains high internal energy circulation with comparatively small maintenance power — a direct consequence of a high effective quality factor \(Q_{\text{eff}}\).

In this article, “circulation” denotes internal energy exchange and storage within the regime (fields/currents), not an additional external power inflow.

2.2 Extraction Path — Inductive Output and Feedback Routing

The extraction path operates on classical Faraday induction:

The time-varying magnetic flux generated by the active core's regime induces EMF in the extraction winding. This EMF is rectified, filtered, and converted to useful DC or AC output.

Lenz's law applies fully: extraction reduces the loaded quality factor:

Increased extraction leads to increased effective losses, which leads to increased maintenance power requirement.

2.3 The feedback loop

What happens step by step:

• Startup: A startup impulse (~0.015 Wh, ~15 sec, 9V battery) initiates the regime by establishing the initial capacitive node, after which the startup port is disconnected.
• Regime formation: The active core reaches a stable nonlinear regime (limit cycle) with high internal energy circulation.
• Extraction: The extraction path extracts power from the active core's regime via induction.
• Feedback: Part of the power induced in the extraction path is rectified and routed back through the BMS-controlled feedback path to the active core as maintenance power. This feedback remains an internal allocation within the device boundary.
• Regulation: The buffer + BMS smooths this feedback, compensating transients and load variations.
• Steady operation: feedback remains an internal power-routing mechanism within the device boundary. At regime level, the capacitive node is maintained by the stabilized internal feedback path. Complete-device accounting remains defined only by the total boundary balance: \(P_{\text{in,boundary}} = P_{\text{customer}} + P_{\text{losses}} + dE_{\text{stored}}/dt\).

2.4 The buffer and BMS role

The buffer layer is a transient-stabilization and control element, not an energy source. It performs transient smoothing, DC bus stabilization, short-term energy buffering, and BMS-controlled charge/discharge management.

In steady state, the buffer's net energy change averages to zero. Any energy withdrawn during transients is replenished from the DC bus. The Buffer/BMS layer manages internal energy routing in time, stabilizes the DC bus, and enforces control constraints. It does not generate energy.

4.1 Quality factor and maintenance power

The effective quality factor \(Q_{\text{eff}}\) determines the ratio of stored energy to energy lost per cycle:

For high \(Q_{\text{eff}}\): the regime retains most of its circulating energy each cycle. Only a small fraction needs to be replenished.

Depending on the operating point and coupling architecture, regimes may exist where \(\langle P_{\text{fb}} \rangle < \langle P_{\text{customer}} \rangle\); this does not alter the device-boundary balance, which remains \(\langle P_{\text{in,boundary}} \rangle = \langle P_{\text{customer}} \rangle + \langle P_{\text{losses}} \rangle + \langle dE_{\text{stored}}/dt \rangle\).

4.2 Sealed discharger as nonlinear Q-control

The sealed discharger in the active core is not an energy source — it is a controlled nonlinear element that shapes the regime. Townsend avalanche provides rapid conductivity switching:

The energy that drives carrier multiplication comes from the circuit's electric field.

The sealed discharger shapes the regime's conductivity and loss characteristics but supplies no net energy. It is a controlled switching element — necessary for regime operation, never an energy source. Its internal construction is sealed; the microscopic switching mechanism is treated as protected engineering know-how.

• The internal feedback path routes \(E_{\text{fb,event}}\) back to the active core as real internal power at the active core's functional boundary. This is already accounted for within \(P_{\text{in,boundary}}\) at the complete device boundary — it is not a second external source. Regime behavior and boundary accounting must not be conflated.
• The buffer + BMS regulates this internal power routing, smoothing transients and protecting the nonlinear regime from destabilization.
• High \(Q_{\text{eff}}\) allows the regime to sustain large internal energy circulation with small maintenance power — making the feedback architecture viable.
• “η > 100%” is always a boundary-definition or measurement-incompleteness error. When measured at the correct complete device boundary (for steady-state averaged power), the system obeys conservation laws without exception.
• Nonlinearity modifies dynamics, not conservation. The regime-based architecture provides engineering advantages (self-stabilization, load adaptation, progressive back-action) but does not create energy.