Nuclear Fusion Tokamak with Self Sustaining Resonance

Nuclear Fusion Tokamak with Self-Sustaining Resonance

Richard J. Reyes - Original Release: April 14, 2026
Latest: April 14, 2026

Overview

This work presents a control-theoretic architecture for tokamak operation that achieves sustained burn conditions through closed-loop regulation of confinement, power balance, and stability constraints, using only standard diagnostics and actuators.

The framework introduces a coherence-controlled transport model in which plasma confinement is parameterized by a scalar observable $I(t)\in [0,1]$, derived from turbulence suppression and shear locking measurements. This enables real-time modulation of the energy confinement time τE(I)\tau_E(I)τE(I), transforming plasma stability into a controllable quantity.

A staged allocator enforces simultaneous satisfaction of three constraints:

• thermal balance,
• divertor loading,
• magnetic safety profile,

producing a self-consistent operating point that is maintained as a stable attractor under feedback control.

The system is implemented as an operator-ready control loop, with explicit handling of noise, actuator limits, and real-time diagnostics.

Core Result

The system defines a closed-loop evolution governed by:

W→I→τE(I)→M(t)W \rightarrow I \rightarrow \tau_E(I) \rightarrow M(t)W→I→τE(I)→M(t)

where:

• $W$: plasma thermal energy
• $I$: coherence proxy
• τE(I)\tau_E(I)τE(I): confinement time
• $M(t)$: thermal margin

with

M(t)=(1−ζ~)Pα+ηiPEM−WτE(I)M(t) = (1 - \tilde{\zeta}) P_\alpha + \eta_i P_{EM} - \frac{W}{\tau_E(I)}M(t)=(1−ζ~)Pα+ηiPEM−τE(I)W

A sustained burn regime is achieved when:

ζ~Pα≥Prack+PEM,M(t)≥0\tilde{\zeta} P_\alpha \ge P_{rack} + P_{EM}, \quad M(t) \ge 0ζ~Pα≥Prack+PEM,M(t)≥0

Under these conditions, the system enters a latched state in which the plasma remains within a bounded, stable region of state space over extended durations.

This establishes a control-stabilized burn regime, in which confinement, power balance, and safety constraints are simultaneously satisfied through feedback.

Key Mathematical Structure

The construction follows the chain:

plasma state measurement
↓
coherence proxy $I(t)$
↓
transport mapping τE(I)\tau_E(I)τE(I)
↓
energy balance dynamics
↓
constraint enforcement (thermal, divertor, safety)
↓
staged control allocation
↓
feedback stabilization
↓
invariant burn region Ωburn\Omega_{burn}Ωburn
↓
sustained operation.

The burn region is defined as:

Ωburn={Mth≥0,  Mdiv≥0,  qmin≥qthr}\Omega_{burn} = \{ M_{th} \ge 0,\; M_{div} \ge 0,\; q_{min} \ge q_{thr} \}Ωburn={Mth≥0,Mdiv≥0,qmin≥qthr}

and is shown to be forward invariant under bounded perturbations, establishing stability of the operating regime.

A composite Lyapunov functional

Lexp=L0+ξTPξL_{exp} = L_0 + \xi^T P \xiLexp=L0+ξTPξ

combines slow burn dynamics with fast 3D instability suppression, yielding:

L˙exp≤−c0L0−cξ∥ξ∥2+dest∥η∥2\dot{L}_{exp} \le -c_0 L_0 - c_\xi \|\xi\|^2 + d_{est}\|\eta\|^2L˙exp≤−c0L0−cξ∥ξ∥2+dest∥η∥2

which guarantees convergence to the burn manifold up to bounded noise.

Dimensional and Control Constraints

The system operates within a bounded parameter regime defined by:

• confinement scaling: τE(I)=τ0[1+(τgain−1)Ip]\tau_E(I) = \tau_0[1 + (\tau_{gain}-1)I^p]τE(I)=τ0[1+(τgain−1)Ip]
• actuator limits: PEM,Uloop,χcd,σedgeP_{EM}, U_{loop}, \chi_{cd}, \sigma_{edge}PEM,Uloop,χcd,σedge
• dimensionless plasma constraints: βN,q95,H98y2,ρ∗\beta_N, q_{95}, H_{98y2}, \rho_*βN,q95,H98y2,ρ∗

A dual-loop architecture is enforced:

• slow supervisory loop (burn regulation),
• fast stability loop (3D MHD suppression).

The control law includes explicit robustness margins:

Mmin≥ΓTresp,Δth,ΔrackM_{min} \ge \Gamma T_{resp}, \quad \Delta_{th}, \Delta_{rack}Mmin≥ΓTresp,Δth,Δrack

ensuring stability under measurement noise, delays, and actuator uncertainty.

Scope and Interpretation

This work establishes a control-stable tokamak operating regime based on a diagnostic-driven transport model.

It does not claim:

• a first-principles derivation of plasma transport,
• a proof of ignition independent of external power,
• complete resolution of turbulence or MHD physics.

The latch condition is defined as virtual (accounting-based) unless energy harvesting hardware is present.

Open problems include:

• deriving τE(I)\tau_E(I)τE(I) from turbulence physics,
• full spectral stability analysis of MHD modes,
• integration with first-principles transport solvers,
• experimental validation on SPARC-class devices.

Relation to Prior Work

This manuscript builds on tokamak transport theory, control barrier function methods, and Wave Confinement Theory (WCT).

The contribution extends prior work by:

• formalizing plasma confinement as a control-invariant region,
• introducing a coherence-based transport parameterization,
• constructing a staged allocator for multi-constraint regulation,
• integrating estimation, control, and stability into a unified architecture.

Within WCT, the burn state is interpreted as a macroscopic curvature-locked eigenmode, selected by feedback constraints.

Significance

If validated experimentally, this framework provides:

• a deployable control architecture for sustained tokamak operation,
• a method for real-time confinement regulation,
• a pathway to stable long-duration burn regimes without new hardware.

More broadly, it suggests that fusion stability can be achieved through structured feedback and constraint enforcement, rather than requiring full predictive control of plasma microphysics.

Keywords

tokamak control; fusion energy; plasma confinement; energy balance; coherence proxy; transport modeling; control barrier functions; Lyapunov stability; MHD stabilization; SPARC tokamak; real-time plasma control; wave confinement theory.

Author & Contact

Author: Richard J. Reyes
ORCID iD: 0009-0005-5975-8718
Email: reyes.ricky30@gmail.com