PINNs for the Burner Ambipolar Potential

The tandem-mirror burner is confined by an electrostatic potential; Kronos solves that ambipolar potential with a physics-informed network.

Confinement by potential

The burner is a D-3He tandem-mirror generator. Unlike a tokamak, it confines the central-cell plasma with an axial electrostatic potential established by dense, hot end plugs at 26.49 T. Ions are held by the ambipolar potential difference between the plug and the central cell; get that potential wrong and confinement collapses. The twin must therefore solve the potential profile phi(z) along the machine axis in real time.

The quasineutral balance

The potential is set by requiring quasineutrality and ambipolar (equal ion and electron) end-loss along the field line. Kronos solves this with a PINN whose residual enforces the balance:

# ambipolar / quasineutral potential along the axis
#   sum_s Z_s n_s(phi(z), z) = 0        (quasineutrality)
#   Gamma_i(phi) = Gamma_e(phi)          (ambipolar end loss)
# densities follow Boltzmann-like response to phi and mirror trapping:
#   n_s(z) = n_s0 * exp(-Z_s e phi(z)/T_s) * (mirror-trapping factor)
# PINN residual = quasineutrality mismatch + ambipolarity mismatch

Solving this natively gives the plug potential and the confining potential dip in one forward pass. The plug-density controller (an MPC agent) uses the PINN to predict how a change in end-plug fueling or heating will move the ambipolar potential, and hence central-cell confinement, over the shadow horizon.

Coupling to DEC

The potential solve is not isolated: the direct-energy-conversion train sets the collector potentials at the machine ends, and those boundary potentials feed back into the ambipolar balance. Kronos co-conditions the potential PINN on the Power Systems module's DEC state so the confinement and the energy-extraction picture stay consistent. This is the burner analogue of the breeder's free-boundary coupling between coil currents and plasma shape.