Ambipolar Potential Solver

Computing the electrostatic barriers that plug the burner's magnetic mirror, the control problem at the heart of tandem-mirror confinement.

Electrostatics as confinement

A tandem mirror confines its central-cell ions not only with magnetic fields but with electrostatic potential barriers raised at the high-density end plugs. Computing that ambipolar potential self-consistently is the burner's defining plasma-physics workload on L0, because it determines whether the central cell is confined at all.

The self-consistent problem

The potential and the plasma density are mutually dependent: density sets the potential through quasi-neutrality and the plug physics, and the potential sets which ions are confined, which sets the density. The solver iterates this coupling along the machine axis, from central cell through the throat at 17 T to the plug at 26.49 T, until it converges on a consistent profile.

# Ambipolar/quasi-neutral closure along axis (schematic):
# sum_species q_s n_s(phi, B) = 0     # quasi-neutrality -> phi(z)
# n_s from confined + passing populations in mirror field B(z)
# barrier: phi_plug - phi_center confines central-cell ions
# solved self-consistently for phi(z), n(z)

Why end-plug density is the lever

The barrier height depends on plug density, so end-plug density is the primary control lever of the burner, the counterpart to the breeder's shape and current. The solver maps how barrier height and central-cell confinement respond to plug density and heating, defining the operating window the control system must hold and the sensitivity around it.

• Axial potential profile and barrier height
• Plug-density to barrier-height sensitivity
• Central-cell confinement time versus barrier
• Coupling to end-loss distribution for the DEC train

The solver's output trains the burner twin's ambipolar-potential and end-plug surrogates, so the real-time twin can estimate barrier health and confinement from diagnostics without re-solving the self-consistent problem each step. This is the burner's version of paying for expensive physics once, offline, to enable fast control.

The escaping end-loss ions that the barrier deliberately does not confine are the input to direct energy conversion. The potential solver therefore couples directly to the DEC train design, tying the burner's confinement physics to its energy-harvesting physics within one L0 workload family.