Grad-Shafranov Equilibrium Solver Farm

A parallel farm computing breeder magnetohydrostatic equilibria that anchor the negative-triangularity shape and seed the twin PINN.

Equilibrium is the starting point

Every breeder plasma calculation begins from an equilibrium: the magnetohydrostatic force balance that fixes the shape of the flux surfaces. For an axisymmetric tokamak this is the Grad-Shafranov equation, a nonlinear elliptic PDE for the poloidal flux. L0 runs a farm of these solves to map how equilibrium responds to plasma current, pressure, and coil configuration.

# Grad-Shafranov equation for poloidal flux psi(R,Z):
# R d/dR( (1/R) dpsi/dR ) + d2psi/dZ2
#   = -mu0 R^2 dp/dpsi - F dF/dpsi
# p(psi) : pressure profile   F(psi)=R B_toroidal
# solved for the breeder: R0 1.2 m, aspect ratio 2.5, Ip 9.66 MA

The negative-triangularity target

The breeder's design shape has negative triangularity, delta -0.30, chosen to access an ELM-free edge regime. The solver farm computes equilibria across current, pressure, and coil settings to find and hold this shape at the design point: R0 1.2 m, aspect ratio 2.5, plasma current 9.66 MA, and the fields consistent with 16.84 T peak, 8 T on-axis.

Why a farm, not a single solve

A single equilibrium is cheap; the design needs thousands. Shape scans, current and pressure sweeps, and coil-current studies each demand an independent solve, so the farm runs them in parallel, one equilibrium per core. This is where offline compute buys a dense map of the breeder's accessible equilibrium space.

• Shape scans around delta -0.30
• Plasma-current and pressure-profile sweeps
• Poloidal-field coil-current optimization
• Boundary and separatrix control studies

The farm's output is the training set for the twin's equilibrium PINN. Thousands of certified Grad-Shafranov solutions teach a network to reproduce equilibrium in a single fast forward pass, which is what lets the real-time twin track the negative-triangularity shape inside its 50 to 100 ms budget.

Because these equilibria anchor the entire breeder design, they run on the reproducible bare-metal core with pinned solvers and recorded seeds. An equilibrium that seeds a control surrogate must be exactly re-derivable, or the surrogate it trains cannot be trusted.