Pillar 4 · End-to-End Verification Compiled Vacuum Demonstrator Biot–Savart Fréchet Bounds

Anatomy of a Tolerance-Aware Vacuum-Fixture Certificate

Step through the 5-stage pipeline showing how PlasmaLean turns 3D coil curves $\gamma_i : S^1 \to \mathbb{R}^3$ and rigorous Biot–Savart Fréchet derivative bounds into a machine-checked certificate of magnetic confinement quality under $\pm\varepsilon$ manufacturing tolerances. Below the walkthrough, experiment with the interactive Certificate Margin Calculator.

⬇ Download CERTIFICATE_WALKTHROUGH.md

Stage 1

Verification Takeaway:

Interactive Vacuum-Fixture Tolerance Margin Sandbox

Adjust the coil-to-plasma clearance $d_{\min}$, manufacturing tolerance $\varepsilon$, and nominal field strength $B_{\text{nom}}$ to see how the Lipschitz Fréchet bound certifies the worst-case normal magnetic field error $\eta_{\text{cert}}$.

Engineering & Geometric Parameters

Coil-to-Plasma Clearance $d_{\min}$ (m): 0.15 m

Manufacturing Tolerance $\varepsilon$ (mm): 1.2 mm

Nominal Field Magnitude $B_{\text{nom}}$ (T): 1.00 T

Target Max Normal Error $\eta_{\max}$: 1.50 %

Lean 4 Certificate Inequality Evaluation

Biot–Savart Lipschitz Constant $L_{\text{BS}}$

Max Field Perturbation $\Delta B = L_{\text{BS}}\varepsilon$

Certified Min Field $B_{\min}$

Certified Normal Error Bound $\eta_{\text{cert}}$