Regime-Based Electrodynamic Systems: Architecture and Energy Balance

Critical interpretation rule

Two levels of description must never be mixed:

1. System-Level (complete device boundary) — all energy flows accounted at the boundary; external electrical input defines total energy accounting; conservation laws fully apply.

2. Regime-Level (internal operation) — energy is structured and redistributed; used for regime formation, regime stability, controlled extraction.

2.1 Circuit A — Regime formation (Active Core)

Circuit A is a nonlinear resonant structure based on an effective LC combination with gas discharge as a controlled nonlinear element. 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 paper, “circulation” denotes internal energy exchange and storage within the regime (fields/currents), not an additional external power inflow.

2.2 Circuit B — Linear power extraction

Circuit B operates on classical Faraday induction:

The time-varying magnetic flux generated by Circuit A’s regime induces EMF in an 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: External power \(P_{\text{in,ext}}\) ignites the regime in Circuit A and charges the buffer.
• Regime formation: Circuit A reaches a stable nonlinear regime (limit cycle) with high internal energy circulation.
• Extraction: Circuit B extracts power from Circuit A’s regime via induction.
• Feedback: A portion of the device-internal DC-bus power is allocated back as maintenance power to Circuit A. This feedback remains an internal allocation within the Device Boundary.
• Regulation: The buffer + BMS smooths this feedback, compensating transients and load variations.
• Steady operation: The feedback is a power-routing mechanism, not an independent energy source. The external input at the Device Boundary supplies the net energy required by losses + delivered load power + storage change.

2.4 The buffer and BMS role

The buffer layer is not a hidden energy source. It performs transient smoothing, DC bus stabilization, startup energy storage, 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 time-averaged net energy is accounted for by \(P_{\text{in,ext}}\).

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 \(\langle P_{\text{fb}} \rangle < \langle P_{\text{load}} \rangle\); this does not alter the device-boundary balance, which remains \(\langle P_{\text{in,ext}} \rangle = \langle B_{\text{total}} \rangle + \langle P_{\text{load}} \rangle + \langle dE/dt \rangle\).

4.2 Gas discharge as nonlinear Q-control

The gas discharge in Circuit A is not an energy source — it is a controlled nonlinear element that shapes the regime.

Townsend avalanche provides rapid conductivity switching:

The energy for ionization comes from the circuit’s electric field, not from the medium.

The medium (air/gas) determines regime characteristics but does not supply net energy. It is a working medium — necessary for operation but not the energy source.

• The internal feedback path from Circuit B provides the maintenance power allocation for Circuit A. Sustained operation with nonzero \(P_{\text{load}}\) requires nonzero time-averaged \(P_{\text{in,ext}}\) at the Device Boundary.
• 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 device boundary, the system obeys conservation laws.
• Nonlinearity modifies dynamics, not conservation. The regime-based architecture provides engineering advantages (self-stabilization, load adaptation, progressive back-action) but does not create energy.