L3 for the Burner: The Ambipolar Potential

The electrostatic potential that traps the burner's central-cell ions is what L3 must estimate and shape, a control target with no tokamak analogue.

Confinement you cannot see directly

In the tandem mirror, ions are confined by an axial electrostatic potential, not by closed magnetic flux surfaces. The confining potential dip between the end plugs and the central cell is the quantity that matters, but it is inferred, not measured directly, so L3 must estimate it from diagnostics and physics. This is the burner's counterpart to the breeder's equilibrium reconstruction.

Estimating and shaping the potential

The ambipolar-potential PINN enforces quasineutrality and ambipolar end-loss to solve phi(z) along the axis, conditioned on plug and central-cell diagnostics and on the DEC boundary potentials. State estimation fuses this physics with the available measurements to hold a best estimate of the potential profile, with uncertainty, in the twin. MPC then shapes the potential by acting on plug density and the DEC collectors.

# what the burner twin tracks, mirroring the breeder equilibrium
# breeder:  psi(R,Z)  reconstructed via Grad-Shafranov PINN
# burner:   phi(z)    reconstructed via ambipolar/quasineutral PINN
# both: physics residual + diagnostics -> state estimate + uncertainty

The potential couples to everything downstream: it sets central-cell confinement and hence the neutron and power output, and it depends on the DEC collector potentials at the ends. So the burner twin's coupled solve threads the ambipolar potential through the MHD/confinement, Neutronics, and Power Systems modules just as the breeder's threads the equilibrium.

Getting the potential wrong in either direction is costly, too shallow and the central cell leaks, too deep and plug demands and stability suffer, so L3 holds it with margin and lowers confidence (tightening the envelope) when observability of the potential degrades. The low-neutron D-3He burn (neutron fraction 5.44%) means the confinement is judged on the potential and confinement quality rather than dominated by neutronic loads as in the breeder.