Thrust 0 mNIsp 0 sBeam 0 APower 0 kWv_e 0 km/sSpace charge 0 %loadingFPS 0

Drag to orbit, wheel or pinch to zoom. Gold spheres are xenon ions falling through the three perforated grids. The beam cone widens when the grid is over- or under-perveanced.

Gridded Ion Engine: Child–Langmuir Grid Optics, Isp and Orbit Raising

Tune the grid voltage, the gap and the gas, watch the space-charge limit choke the beam, then spend the xenon on five orbit missions.

Grids and propellant

Gas

Live readouts

Beam current vs beam voltage

Missions (Tsiolkovsky + spiral transfer)

Pick a mission to run it with the current engine settings.

Experiment: Isp against thrust at a fixed 2.3 kW

Independent numerical checks

Controls

Drag / one finger: orbit; wheel / pinch: zoom; Camera button cycles hero, grid close-up and top view.
Beam voltage sets the exhaust speed; the grid gap sets the maximum current the space charge allows; the set point is what the discharge chamber asks for.
The beam current is the smallest of: set point, Child–Langmuir limit, and the electric power available.
Missions use the current thrust and mass flow; they are computed instantly.

The science

Exhaust speed. An ion of mass m and charge e falling through a voltage V_b gains kinetic energy eV_b: v_e = √(2 e V_b / m). For xenon at 1100 V this is 40.2 km/s, about ten times a chemical rocket.

Space-charge limit. Between two grids a space-charge-limited ion current obeys Child–Langmuir: J = (4 ε₀/9) √(2e/m) V_t^3/2 / d_eff² with V_t the total voltage across the gap and d_eff = √((d + t)² + D²/4) an effective length for a round aperture (screen thickness t, aperture D). The current through all apertures is J times the open aperture area; the model uses 24 % aperture fraction of a 30 cm grid.

Thrust, flow, Isp. T = γ I_b √(2 m V_b/e), ṁ = I_b m / (e η_m) (η_m = 0.85 propellant utilisation), I_sp = T / (ṁ g₀). The beam half-angle α follows an illustrative curve with a minimum near 60 % of the perveance limit, and γ = (1 + cos α)/2 for a conical beam.

Power. P = I_b(V_b + ε_B) + I_accV_a with ε_B = 200 eV per beam ion for the discharge (a model value) and 1 % accelerator-grid current. Jet efficiency is T²/(2 ṁ P).

Orbit raising. Constant tangential thrust between circular coplanar orbits needs Δv = v_c1 − v_c2 (Edelbaum), v_c = √(μ/r); the mass is integrated with the rocket equation Δv = v_eff ln(m₀/m₁), v_eff = T/ṁ.

Simplifications. One-dimensional grid gap, singly charged ions, no grid erosion, no double ions, no eclipses or radiation belts, no inclination change; propellant utilisation and beam divergence are model values. This is an educational model, not a design tool, and it is not affiliated with any engine maker. Models built with Blender, scene by Three.js.