Spectral Disruption Prediction: Real-Time Plasma Stability via the MHD Generator

We propose a spectral framework for real-time disruption prediction in tokamak fusion reactors. The magnetohydrodynamic (MHD) stability of a plasma equilibrium is characterized by the eigenvalue spectrum of the linearized MHD force operator \(\mathcal{L}\). We show that: (1) the spectral gap \(|\lambda_1|\) serves as a continuous stability margin, replacing binary disruption classifiers; (2) the eigenvector \(v_1\) localizes the incipient instability, identifying WHERE to inject mitigating gas; (3) the killed generator formula \(\mathbb{E}[\tau_{\text{disrupt}}] = -\mathbf{1}^\top M_{\text{killed}}^{-1} A(0)\) gives the expected time to disruption from a single matrix inverse; (4) runaway electron dynamics during disruptions follow a Fokker--Planck equation solvable by the same spectral machinery. We demonstrate the runaway electron component numerically: the Dreicer-field physics is reproduced, the critical momentum and runaway fraction match analytical theory, and the expected runaway time is computed in 0.001 seconds. The full disruption prediction system requires collaboration with MHD stability experts; this paper provides the spectral computation infrastructure and identifies the integration path. For ITER, where a single unmitigated disruption costs weeks of repair and tens of millions of euros, even 5 ms of additional warning time has extraordinary value.