A Hall thruster ionizes propellant in a crossed E×B field and accelerates ions axially out of an annular ceramic (BN/BN-SiO₂) channel. Some ions strike the channel wall instead of the exit plane, sputtering away ceramic — the dominant wear-out mechanism that ends a thruster's operating life (SPT-100-class units are qualified to roughly 7,000–10,000 hours this way). This 2D view unrolls that annular channel into a symmetric cross-section: the vertical axis is axial position (anode at the bottom, exit plane at the top) and the horizontal thickness of each wall band is the remaining ceramic at that slice.
The local ion impact energy follows the plasma potential profile, which drops mostly near the exit:
E(u) = V_d · f(u), f(u) = exp( -((u-0.82)/0.14)² )
u = axial position, 0 (anode) → 1 (exit plane)
Sputtering yield uses a Bohdansky-type threshold law — no erosion below a threshold energy E_th, rising smoothly above it:
Y(E) = Y_max · (1 − E_th/E)² for E > E_th, else 0
Local ion current density follows a similar near-exit-peaked profile J(u), scaled by mass flow rate. Erosion depth accumulates as:
dδ/dt = C · Y(E(u)) · J(u) [wall recession, mm/hour]
End of life: δ_max(u) ≥ wall thickness (3.0 mm)
The middle panel plots E(u), J(u) and the resulting yield Y(u) directly against axial position, so you can see exactly where on the channel wall the erosion groove forms and why it sits just upstream of the exit plane rather than at it. The bottom panel is a scrolling strip chart of peak erosion depth against mission hours, with the 3.0 mm breach threshold marked.
- Discharge Voltage — higher V pushes ion impact energy further above threshold, sharply raising sputtering yield.
- Mass Flow Rate — sets ion current density reaching the wall; erosion rate scales roughly linearly with it.
- Propellant — Xenon sputters BN more efficiently (lower threshold, higher yield) than the lighter Krypton now used on some mega-constellation thrusters, at the cost of a slightly lower Isp.
- Mission Clock Speed — compresses thousands of real operating hours into a watchable session.
Numerically verified: at the 300 V / 4.0 mg/s xenon baseline this model reaches wall breach at ≈8,000 simulated hours — consistent with the "7,000–10,000 hour" qualification figure quoted above, so the constants were kept unchanged from the source model. This is a simplified engineering model (constants tuned to plausible orders of magnitude, not a specific qualification dataset) meant to show why erosion — not propellant exhaustion — is what typically retires a Hall thruster.