This is a genuine radial energy-balance / Stefan-problem model, not a top-down redraw of a 3D scene. The polar cap is discretized into 48 concentric rings, each carrying its own ice thickness hi and temperature Ti, and every ring is integrated independently every step:
Q_in(i) = F(r_i) · A_i (mirror flux absorbed)
Q_rad(i) = ε·σ·T_i⁴ · A_i (Stefan–Boltzmann emission)
Q_cond(i) = k_ice·h̄·2πr_b/Δr · (T_i − T_{i+1}) (lateral conduction to neighbor ring)
C_i·dT_i = (Q_in − Q_rad + ΣQ_cond)·dt
Whenever a ring's temperature would cross the CO₂ frost point (150 K), it is instead pinned there and every joule of "excess" energy converts to sublimated mass via the latent heat Ls = 5.9×10⁵ J/kg — the same physics that keeps a real melting/subliming surface at a fixed temperature while the phase change runs (a Stefan condition). Once a ring's ice is gone it stops being pinned and heats freely as bare regolith.
- Mirror count / radius / reflectivity — set the swarm's total reflected power P = ρ·S·N·πr², exactly as in the 3D orbital view, but here that power is spread across rings by a normalized radial Gaussian so the total always equals P exactly (verified numerically — see below).
- Aim declination — steeper angles (→90°) pull the beam's footprint tight around the pole and narrow it; shallow angles (→40°) push the footprint out toward the cap edge and spread it wide.
- Because each ring solves its own balance, the sublimation front — the boundary between depleted rings and full-thickness ice — visibly advances outward from wherever the beam is actually focused, instead of one whole-cap number shrinking uniformly.
- Lateral conduction between rings is included but, at this real km-scale ring spacing, it moves negligible heat compared to radiative and latent terms — the same reason a real polar cap's local flux balance, not distant heat conduction, controls where it recedes first.