MHD Simulation Workloads

The magnetohydrodynamic solves that establish stability limits for both machines and generate training data for the twin's MHD module.

MHD as a stability oracle

Magnetohydrodynamics treats the plasma as a conducting fluid coupled to the magnetic field. L0 runs MHD workloads to answer the stability question for both machines: for the breeder, how close an equilibrium sits to disruptive limits; for the burner, whether the tandem-mirror configuration confines against interchange and other modes. These solves are the source of the twin's MHD module.

Ideal and resistive regimes

Kronos runs both ideal MHD, which asks whether a configuration is unstable in principle, and resistive MHD, which captures slower reconnection-driven modes that grow when finite resistivity lets field lines break. Ideal solves are cheaper eigenvalue problems; resistive solves are stiff, time-dependent, and communication-heavy, and they set the demand for low-latency interconnect.

• Ideal MHD stability spectra and growth rates
• Resistive tearing and reconnection dynamics
• Breeder disruption and vertical-stability margins
• Burner interchange and flute-mode stability in the mirror

The governing balance

The MHD momentum equation balances inertia, pressure gradient, and the Lorentz force, closed by Ohm's law and the induction equation. The equilibrium limit, where inertia vanishes, is the force balance the Grad-Shafranov solver enforces; the dynamic solves add time evolution to test whether small perturbations grow.

# Resistive MHD (schematic):
# rho (dv/dt + v.grad v) = -grad p + J x B
# dB/dt = curl(v x B) + eta/mu0 * laplacian(B)   # induction + resistive diffusion
# J = curl(B)/mu0   div(B)=0

These runs are tightly coupled and iterate to convergence, so they live on the reproducible bare-metal core rather than on elastic cloud. A breeder disruption study or burner stability scan that will inform control must be replayable, because its output becomes ground truth for a surrogate the twin runs in real time.

The value of MHD on L0 is that it converts an intractable real-time question into a tractable offline one. The twin cannot solve resistive MHD in 50 to 100 ms, but it can evaluate a stability-margin surrogate trained on these solves, so the expensive physics is paid for once here and consumed cheaply forever after.