PINN for the Burner Ambipolar Potential

The burner's 1D axial potential and density profiles are solved by a PINN that carries quasineutrality and ambipolarity as constraints, with extrapolation honesty built in.

A one-dimensional PINN

The burner equilibrium is axial: fields, densities, and the ambipolar potential Phi(z) vary along the open field line. A PINN represents Phi(z) and species densities as networks of the axial coordinate, trained so the parallel force balance holds and quasineutrality plus ambipolarity are satisfied. It is lower-dimensional than the breeder's 2D solve but far more extrapolative.

Burner PINN residuals along z:

  R1: d p_par/dz + (p_par - p_perp) dlnB/dz - n q dPhi/dz  = 0
  R2: sum_s q_s n_s(Phi)                                  = 0   (quasineutral)
  R3: Gamma_i(Phi) - Gamma_e(Phi)                         = 0   (ambipolar)

  Networks: Phi_theta(z), n_s,theta(z)
  Boundary: plug/throat fields (26.49 T / 17 T), end-cell states

Structural constraints

Electron density is written in Boltzmann form so quasineutrality is structurally near-satisfied, and the mirror-ratio dependence enters through B(z). The confining potential depth Phi_c is the key output; because Pastukhov confinement depends exponentially on Phi_c/T_i, the PINN is trained to resolve Phi accurately where that sensitivity is highest.

# 1D ambipolar PINN step (schematic)
def step(net_phi, net_n, z):
    Phi = net_phi(z); n = boltzmann_and_ions(net_n, Phi, B(z))
    r1 = parallel_force_balance(Phi, n, B(z))
    r2 = quasineutrality(n)
    r3 = ambipolarity(Phi, n)
    return w1*mse(r1) + w2*mse(r2) + w3*mse(r3)

Honesty is part of the model

This PINN produces a self-consistent burner equilibrium in simulation, but the four gates travel with every output: the plug coil is overstressed ~3-3.9x at the design bore, the regime is 166-830x beyond any device, the He-3 demand is ~400x domestic supply, and simulated availability of 0.86-0.995 is 30-100x short of hyperscale Tier III's 0.99982. The PINN's confidence band is dominated by the regime extrapolation, and that band is reported to every consumer.

• Solves Phi(z), n_s(z), pressures along the open field line.
• Exponential Phi_c/T_i sensitivity drives accuracy requirements.
• Every result carries the four burner gates as reported caveats.

The burner PINN is a design study for a machine that does not exist; it is used to explore and bound the concept, never to claim a validated operating point.