Spacecraft Surface Charging & ESD Simulator

Plasma Environment

Electron temperature kT_e 8.0 keV

Plasma density n_e 1.0 cm⁻³

Surface coating

Surface Potentials

SAFE

Sunlit surface

0 V

Shadowed surface

0 V

Differential ΔV

0 V

Arc discharges

How it works

Every exposed spacecraft surface floats to whatever potential V makes its net current zero. Three currents compete for each surface patch:

Thermal electron flux:  J_e = e·n_e·√(kT_e / 2πm_e) · exp(eV/kT_e), V≤0
Thermal ion flux:       J_i = e·n_i·√(kT_i / 2πm_i)            (≈ constant, m_i ≫ m_e)
Photoemission (sunlit): J_ph = J_ph0 · exp(-eV/kT_ph), V>0 ; else J_ph0

C · dV/dt = J_i + J_ph − J_e     (surface capacitance C)

Electrons are ~40–1800× lighter than ions, so their thermal flux dominates and every unlit surface drifts negative — this is exactly what happens to the shadowed side of a real GEO satellite during a substorm injection of hot (1–20 keV) plasma. Sunlit surfaces are rescued by photoemission: UV knocks electrons out, and that outward current keeps them near a small positive potential, self-limited because photoelectrons with kT_ph ≈ 1–2 eV fall back once V rises.

kT_e / n_e — hotter, denser plasma (a substorm) pushes shadowed surfaces to a deeper negative equilibrium.
Dielectric coating — can't bleed charge sideways to the grounded bus, so it reaches a more extreme potential than a conductive surface before anything neutralizes it.
Differential ΔV = V_sun − V_shade — the real driver of arcing. A single uniformly-charged spacecraft floating at −5 kV relative to open space is harmless; a −1 kV gap between two adjacent surfaces punches through the intervening insulator.
When |ΔV| crosses the ~1 kV arc threshold, a discharge fires: it locally re-equalizes the two potentials and can inject a damaging current transient into nearby electronics — the leading cause of GEO satellite anomalies attributed to space weather.

This model integrates the charging ODE in real time with a scaled capacitance so the multi-second GEO charging transient is visible within a few seconds on screen — the physics (current balance, exponential retardation, photoemission self-limiting) is the same used in NASA's NASCAP spacecraft-charging codes, just sped up for demonstration.

⚡ ESD ARC

Sunlit surface Shadowed surface Ambient electrons

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