Gridded Ion Thruster

Gridded Ion Thruster (propulsion/electric/gridded-ion-thruster)

Use when the task is gridded ion thruster design and performance analysis for electrostatic propulsion: converting electrical power into thrust by extracting ions from a discharge plasma and accelerating them electrostatically through the net voltage between the screen and accelerator grids of a two-grid (or three-grid) ion optics assembly. This leaf sizes the thruster from the net beam voltage, the ion optics geometry and the space-charge perveance limit, and trades the result against a hall thruster at equal power. It implements the standard Kaufman thruster performance model in pure Python, stdlib only, with xenon as the reference propellant. It pairs with propulsion/electric/hall-thruster, its crossed-field sibling, and with propulsion/rocket/rocket-sizing for the mission loop.

Domain quick reference

• Electrostatic acceleration: a singly charged ion extracted from the plasma and accelerated through the net beam voltage V_net reaches the axial velocity v_i = sqrt(2eV_net/m_i), with m_i the ion mass. Unlike a hall thruster there is no crossed magnetic field; the ions are accelerated by the electric field between the grids only.
• Ion exhaust velocity: v_i = sqrt(2eV_net/m_i). For xenon (m_i = 2.180e-25 kg, 131.293 u) a 1100 V net voltage gives about 40209 m/s.
• Specific impulse: I_sp = v_i / g0 with g0 = 9.80665 m/s^2. Gridded thrusters run at high net voltage and reach about 3000 to 4500 s at 1000 to 1500 V, well above hall thrusters.
• Child-Langmuir space-charge limit: the planar current density J_CL = (4eps0/9) * sqrt(2e/m_i) * V_net^(3/2) / d^2, with eps0 the vacuum permittivity and d the effective acceleration gap (screen to accelerator grid spacing). The grids cannot extract more than this density at a given voltage and gap.
• Beam current with perveance margin: I_b = eta_perv * J_CL * A_extract
  • eta_grid, where eta_perv is the perveance margin (typical 0.4 to 0.8, the optics run below the space-charge limit) and eta_grid the grid transparency (fraction of the extraction plane open to beamlets, about 0.6 to 0.7).
• Thrust from the beam current: T = I_b * sqrt(2m_iV_net/e) * eta_d, valid for singly charged axial ions; eta_d is the divergence efficiency, cos of the mean beam half-angle, about 0.98 to 0.995.
• Thrust-to-power: T/P = 2 * eta_T / (g0 * I_sp), the sizing bridge between power, efficiency and impulse. Total efficiency eta_T of 0.6 to 0.7 covers beam, discharge and power processing losses.
• Power chain: beam power P_b = I_b * V_net; total input power P_total = P_b / eta_power with eta_power the thruster plus PPU efficiency.
• Rocket equation: m_prop = m_dry * (exp(delta_v / (g0 * I_sp)) - 1) for a mission with final dry mass m_dry.
• Gridded vs hall at equal power: the gridded thruster gives the higher specific impulse (4100 s vs 1600 s typical) and about one fifth of the propellant mass flow, but a lower thrust-to-power ratio and a lower thrust density, because beam extraction is space-charge limited by the Child-Langmuir perveance of the ion optics; the hall thruster has no such grid limit in its crossed-field discharge.
• Units are SI throughout: N, m/s, s, W, V, A, m, kg.
• ECSS E-ST-35-03 frames the space propulsion context; the relations above are standard engineering methodology, summary-only.

Workflow

1. Fix the operating point: net beam voltage V_net, effective screen-to-accelerator gap d, extraction area A_extract, grid transparency eta_grid and perveance margin eta_perv, with xenon as the default propellant (xenon_ion_mass).
2. Get the ion exhaust velocity with exhaust_velocity and the specific impulse with isp_from_net_voltage; confirm I_sp sits in the 3000 to 4500 s range for a 1000 to 1500 V net voltage.
3. Check the ion optics against the space-charge limit: child_langmuir_density gives the maximum extractable current density at the gap; beam_current_from_perveance gives the beam current the optics deliver at the chosen perveance margin. Verify the margin is below one, so the grid design stays under the limit.
4. Compute thrust from the beam current with thrust_from_beam_current, applying the divergence efficiency (about 0.985) when the beam half-angle is known.
5. Build the power chain: beam_power, then total_power with the thruster plus PPU efficiency eta_power; cross-check the sizing with thrust_from_power at the total efficiency eta_T.
6. For a mission, size the propellant with propellant_mass_for_delta_v and report m_prop and the initial mass.
7. For a technology trade at equal power, run gridded_vs_hall_compare and weigh the gridded specific impulse and propellant saving against the hall thrust-to-power advantage.
8. Confirm the deterministic checks with the contract test scripts/test_gridded_ion_thruster.py.

Worked example

A gridded ion thruster on xenon: V_net = 1100 V, d = 0.8 mm, A_extract = 0.028 m^2, eta_grid = 0.68, eta_perv = 0.6, eta_d = 0.985, eta_T = 0.65.

• Ion mass: m_i = 131.293 * 1.66054e-27 = 2.1802e-25 kg.
• Exhaust velocity: v_i = sqrt(2 * 1.602e-19 * 1100 / 2.1802e-25) = 40209 m/s.
• Specific impulse: I_sp = 40209 / 9.80665 = 4100 s, inside the 3000 to 4500 s band for 1100 V net.
• Child-Langmuir limit: J_CL = (4 * 8.854e-12 / 9) * sqrt(2*e/m_i) * 1100^1.5 / (8e-4)^2 = 272.0 A/m^2.
• Beam current: I_b = 0.6 * 272.0 * 0.028 * 0.68 = 3.107 A, well under the 7.62 A the un-margined optics could pass (J_CL * A_extract * eta_grid at margin 1).
• Thrust from the beam: T = 3.107 * sqrt(2 * 2.1802e-25 * 1100 / e) * 0.985 = 0.16744 N.
• Beam power: P_b = 3.107 * 1100 = 3417.5 W. With eta_power = 0.66 for the discharge plus PPU chain, P_total = 3417.5 / 0.66 = 5178 W.
• Sizing cross-check: T = 2 * 0.65 * 5178 / (9.80665 * 4100) = 0.16741 N, within 0.02% of the beam-side thrust, so the 0.65 total efficiency and the power chain are consistent.
• Thrust-to-power: T/P_total = 0.16744 / 5178 = 32.3 mN/kW, inside the 25 to 45 mN/kW gridded band.
• Mission: delta-v 2000 m/s on a 1000 kg dry spacecraft gives m_prop = 1000 * (exp(2000 / (9.80665 * 4100)) - 1) = 51.0 kg, initial mass 1051.0 kg; the identity (m_dry + m_prop) / m_dry = exp(delta_v / (g0 * I_sp)) holds exactly.
• Technology trade at 5000 W against a hall thruster (I_sp 1600 s, eta_T 0.5): gridded thrust 0.1617 N against hall 0.3187 N, so the hall gives 63.7 mN/kW against 32.3 mN/kW for the gridded, but the gridded I_sp is 2.56 times higher and its propellant mass flow about 0.198 times the hall value.

Verification

• Confirm exhaust_velocity(1100, m_xe) returns 40208.8 m/s and isp_from_net_voltage returns 4100.2 s, within the 3000 to 4500 s band at 1100 V.
• Confirm child_langmuir_density(1100, 0.8e-3, m_xe) returns 271.96 A/m^2 and beam_current_from_perveance(1100, 0.8e-3, 0.028, 0.68, 0.6, m_xe) returns 3.107 A.
• Confirm thrust_from_beam_current on that beam returns 0.16744 N and that the power-bridge value from thrust_from_power(P_total, 0.65, 4100.2) agrees within 1%.
• Confirm the thrust-to-power ratio on total input power (32.3 mN/kW) sits in the 25 to 45 mN/kW gridded band, and that the 167 mN thrust at 5.2 kW input matches the 100 to 250 mN band of the 2.3 to 5 kW thruster class.
• Confirm propellant_mass_for_delta_v(2000, 1000, 4100.2) returns 51.0 kg and that (1000 + m_prop) / 1000 equals exp(2000 / (g0 * isp)).
• Confirm gridded_vs_hall_compare(5000, 4100, 1600, 0.65, 0.5) gives a hall thrust above the gridded thrust, an I_sp ratio of 2.56 and a mass flow ratio of 0.198.
• Confirm every non-positive voltage, gap, area, current, power and mass, and every efficiency or perveance margin outside (0, 1] raises ValueError.
• Run the contract test offline: python3 scripts/test_gridded_ion_thruster.py (30 tests, deterministic).

Related leaves

• propulsion/electric/hall-thruster: the crossed-field sibling; lower specific impulse and higher thrust-to-power, for the comparison and the technology trade.
• propulsion/rocket/rocket-sizing: the mass and delta-v loop around the thruster sizing.
• propulsion/rocket/propellant-selection: propellant families and impulse properties for the chemical side of the trade.
• propulsion/rocket/nozzle-design: exit flow and thrust terms for chemical thrusters, the alternative to electric propulsion.

Pitfalls

• Sizing the optics at the space-charge limit: the grids cannot pass more than the Child-Langmuir density at a given voltage and gap, and real optics run at a perveance margin below one (0.6 in the worked example, delivering 3.107 A against the 7.62 A un-margined pass) - quoting the limit current as the beam current overstates the thruster.
• Forgetting the grid transparency: only the fraction of the extraction plane open to beamlets (eta_grid about 0.6 to 0.7) contributes to the beam current; using the full extraction area ignores the grid shadowing.
• Mixing the two thrust routes: thrust_from_beam_current needs the divergence efficiency and the beam-side numbers, while thrust_from_power needs the total efficiency over the input power - the worked example checks them to within 1%, so a larger gap means an input inconsistency, not a physical effect.
• Comparing to a hall thruster on thrust alone: at 5000 W the gridded thruster gives 0.1617 N against 0.3187 N hall, but its I_sp is 2.56 times higher and its propellant flow about a fifth - the technology trade must weigh impulse and propellant against thrust-to-power.
• Using the wrong propellant mass: the model is calibrated on xenon (m_i = 2.180e-25 kg); exhaust velocity, perveance and the mission mass all depend on the ion mass, so another propellant needs its own mass constant.
• Reading I_sp off the beam voltage without the space-charge caveat: the 4100 s at 1100 V is only reachable while the optics stay under the perveance limit - raising V_net raises the extractable density but also the voltage standoff demand on the grid design.

Behavior contract (gate 3)

Run the deterministic contract test (stdlib unittest, offline):

python3 scripts/test_gridded_ion_thruster.py

The test covers the 1100 V worked-example contract (exhaust velocity, specific impulse inside the sanity band, Child-Langmuir density, beam current from perveance margin and grid transparency, beam-side thrust, beam and total power, the sizing bridge agreement within 1%, thrust-to- power in the gridded band, rocket-equation propellant mass), voltage and gap scaling laws of the space-charge limit, thrust and power chain scaling, the gridded vs hall comparison at equal power, and ValueError rejection of non-positive voltage, gap, area, current, power, mass and out-of-range efficiency or perveance margin.

Compliance

• Standards referenced, not reproduced: ECSS E-ST-35-03 is a free ESA download (ecss.nl/standards); the gridded ion thruster relations above are standard engineering methodology, summary-only per standards-map.yaml.
• compliance: STANDARDS-REF, gated: false.