Electrodynamic Dust Shield — Discrete Multi-Phase Electrode Field (2D)

Discrete Electrode Drive

Electrode voltage 2.0 kV

Drive frequency 3.0 Hz

Electrode pitch 12 mm

Drive phase count

Surface gravity Moon (1.62 m/s²)

Panel Readouts

Dust cleared

Particles remaining

500

Peak surface field

0 kV/m

Wave speed (f·λ)

0 mm/s

How this 2D model differs from the 3D sim

The 3D version plugs the drive voltage into a ready-made closed-form traveling wave, E ~ E₀ sin(kx − ωt)e^(−kz), and assumes it is exact everywhere. This 2D model never assumes that formula — it builds the field from scratch as the real electrostatic superposition of every individual electrode strip, each treated as a 2D line charge whose linear charge density tracks its own instantaneous drive voltage:

λᵢ(t) = 2πε₀·Vᵢ(t),   Vᵢ(t) = V₀ cos(ωt − 2πi/n)
Eₓ(x,y,t) = Σᵢ Vᵢ(t)·(x−xᵢ) / [(x−xᵢ)² + y²]
E_y(x,y,t) = Σᵢ Vᵢ(t)·y / [(x−xᵢ)² + y²]

Summing only the ~120 nearest electrodes (farther ones phase-cancel) reproduces a genuine traveling wave whose wavelength (verified numerically by Fourier analysis) is exactly λ = n_phases × pitch and whose phase velocity is exactly v = f·λ — the synchronous speed of a linear-induction-motor-style multi-phase drive — even though neither number was ever written into the code directly. At heights of a few pitch-lengths the discrete sum also decays at rate k = 2π/λ, converging onto the same idealized exponential the 3D sim assumes outright, but here the discreteness is visible up close: a coarse 3-phase drive shows a lumpy, harmonic-rich near-field ripple that a 6-phase drive smooths out, a real design trade-off electrodynamic-shield engineers actually weigh.

Electrode voltage — sets each electrode's instantaneous line-charge amplitude, hence the field strength grains feel.
Drive frequency — sets ω and, combined with the phase count and pitch, the wave's synchronous transport speed v = f·λ.
Electrode pitch — sets both the spatial wavelength and how tightly the near-field ripple is packed under the surface.
Phase count — a real EDS design choice: more phases (finer angular steps between neighboring electrodes) smooth the traveling wave and reduce harmonic ripple at the cost of more drive electronics.
Surface gravity — Moon (1.62 m/s²), Mars (3.71 m/s²) or Earth (9.81 m/s²), the force the field must beat to loft a grain.

Regolith grains here are still simple charged macro-particles (triboelectric charge, random sign) integrated under Newton's second law — but the force on each one, F = qE(x,y,t), now comes from the same discrete superposition the surface heat-strip visualizes, not from a hand-written sinusoid.

height axis exaggerated for visibility

Positively charged grain Negatively charged grain Electrode strip (colour = phase)