Hall Thruster

Hall Effect Thruster (propulsion/electric/hall-thruster)

Use when the task is Hall effect thruster design and performance analysis for electric propulsion: converting discharge power into thrust through an axial electric field in a crossed-field discharge, sizing the thruster from power, efficiency and specific impulse, and trading xenon against krypton as propellant. This leaf implements the standard HET performance model (Goebel and Katz style decomposition) in pure Python, stdlib only. It pairs with propulsion/rocket/rocket-sizing for the mission loop and propulsion/rocket/propellant-selection for the propellant families context.

Domain quick reference

• Thrust law: T = m_dot * v_e, where m_dot is the total propellant mass flow and v_e the effective exhaust velocity. The ideal exhaust velocity of a singly charged ion accelerated through the beam voltage V_b is sqrt(2eV_b/m_i); utilization factors multiply it down to the effective value.
• Exhaust velocity with utilization: v_e = sqrt(2eV_b/m_i) * eta_m * eta_d, with eta_m the mass utilization (ion mass flow over total mass flow, neutrals do not contribute) and eta_d the divergence efficiency cos^2(theta) for a mean beam half-angle theta.
• Thrust from the beam current: T = I_b * sqrt(2m_iV_b/e) * eta_d. The beam current carries the ion flow directly, so only the divergence loss appears.
• Specific impulse: I_sp = v_e / g0, g0 = 9.80665 m/s^2.
• Thrust-to-power: T/P = 2 * eta_T / (g0 * I_sp). This is the sizing bridge between power, efficiency and impulse.
• Total efficiency decomposition: eta_T = eta_m * eta_v * eta_c * eta_d, where eta_v is the voltage utilization V_b/V_d and eta_c the current utilization I_b/I_d (beam current over discharge current).
• Discharge power: P_d = V_d * I_d. The discharge current is the sum of the beam current and the electron backflow current, I_d = I_b + I_e, so eta_c = I_b/I_d is always below one.
• Anode vs total efficiency: eta_anode = T^2 / (2 * m_dot * P_d) uses only discharge power; eta_total = eta_anode * P_d / P_total includes magnet, cathode keeper and heater power.
• Propellant comparison: xenon (131.293 u, first ionization 12.13 eV) is the reference HET propellant; krypton (83.798 u, 14.00 eV) is lighter, so it gives a higher ideal exhaust velocity at the same voltage (about 25% higher at 270 V) but costs more ionization energy per ion and reaches lower mass utilization in practice.
• Rocket equation: m_prop = m_dry * (exp(delta_v / (g0 * I_sp)) - 1) for a mission with final mass m_dry; total initial mass is m_dry + m_prop.
• Units are SI throughout: N, kg/s, m/s, s, W, V, A, eV, u.
• 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: discharge power P_d, discharge voltage V_d, discharge current I_d (discharge_power), and the propellant.
2. Choose the efficiency decomposition eta_m, eta_v, eta_c, eta_d and confirm the implied total efficiency with hall_thruster_efficiency.
3. Get the exhaust velocity: beam voltage V_b = eta_v * V_d, then exhaust_velocity with the mass and divergence utilization, or isp_from_exhaust_velocity once I_sp is set.
4. Compute thrust from power, total efficiency and specific impulse with thrust_from_power, and the mass flow with mass_flow_from_thrust.
5. Cross-check the beam side: beam_current from the thrust and beam voltage, and beam_current_from_mass_flow from the ionized mass flow; the discharge current follows as I_b / eta_c.
6. Compare anode and total efficiency: anode_efficiency on the thrust, mass flow and discharge power, then total_efficiency_from_anode with the auxiliary power split.
7. For a mission, size the propellant with propellant_mass_for_delta_v and report m_prop and the initial mass.
8. For a propellant trade, run xenon_krypton_compare at the beam voltage and weigh the exhaust velocity gain of krypton against its ionization cost.
9. Confirm the deterministic checks with the contract test scripts/test_hall_thruster.py.

Worked example

A 5 kW class HET on xenon: P_d = 5000 W, eta_T = 0.5, I_sp = 1600 s, V_d = 300 V.

• Discharge current: I_d = P_d / V_d = 16.67 A (discharge_power cross-check: 300 * 16.667 = 5000.01 W).
• Thrust: T = 2 * 0.5 * 5000 / (9.80665 * 1600) = 0.31866 N, within 1% of 0.32 N.
• Mass flow: m_dot = T / (g0 * I_sp) = 2.031e-5 kg/s.
• Thrust-to-power: T/P = 6.373e-5 N/W.
• Efficiency decomposition: eta_T = 0.85 * 0.90 * 0.78 * 0.84 = 0.501, with eta_m = 0.85, eta_v = 0.90, eta_c = 0.78, eta_d = 0.84. The beam voltage is 0.90 * 300 = 270 V and the beam current about 0.78 * 16.67 = 13.0 A.
• Exhaust velocity check: v_e = g0 * I_sp = 15690.6 m/s; the ideal xenon velocity at 270 V is 19921 m/s, so 19921 * 0.85 * 0.84 = 14223 m/s effective for the beam-only case, with the voltage utilization bridging V_b to V_d in the full model.
• Anode vs total: eta_anode = T^2 / (2 * m_dot * P_d) = 0.500. With 300 W of magnet and cathode power (P_total = 5300 W), eta_total = 0.500 * 5000 / 5300 = 0.472.
• Mission: delta-v 2000 m/s on a 500 kg dry spacecraft gives m_prop = 500 * (exp(2000 / 15690.6) - 1) = 67.97 kg, initial mass 567.97 kg; the identity (m_dry + m_prop) / m_dry = exp(delta_v / (g0 * I_sp)) holds exactly.
• Propellant trade at V_b = 270 V: krypton ideal exhaust velocity 24935 m/s against xenon 19921 m/s, ratio 1.252, but krypton needs 14.00 eV per ion against 12.13 eV and its lower mass lowers the mass utilization at equal tank pressure, so xenon stays the default for high thrust-to-power.

Verification

• Confirm thrust_from_power(5000, 0.5, 1600) returns 0.31866 N and is within 1% of 0.32 N.
• Confirm propellant_mass_for_delta_v(2000, 500, 1600) returns 67.97 kg and that (500 + m_prop) / 500 equals exp(2000 / (g0 * 1600)).
• Confirm the efficiency product 0.85 * 0.90 * 0.78 * 0.84 equals the total efficiency used in the sizing.
• Confirm beam current round-trips: beam_current then thrust_from_beam_current recovers the thrust at fixed divergence efficiency.
• Confirm every non-positive power, voltage, current, mass, and every efficiency outside (0, 1] raises ValueError.
• Run the contract test offline: python3 scripts/test_hall_thruster.py (30 tests, deterministic).

Related leaves

• 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 on the ideal exhaust velocity: the real v_e is the ideal sqrt(2eV_b/m_i) multiplied down by the mass and divergence utilization (19921 m/s ideal against 14223 m/s effective in the worked example), so thrust sized on the ideal value overstates the thruster.
• Treating the discharge current as all beam: the discharge current is the beam current plus the electron backflow, I_d = I_b + I_e, so the current utilization eta_c = I_b/I_d is always below one and the beam-side cross-checks must use I_b = eta_c * I_d.
• Reporting the anode efficiency as the thruster efficiency: eta_anode (0.500 in the example) ignores the magnet, cathode keeper and heater power; eta_total falls to 0.472 once the 300 W auxiliary load is included in P_total.
• Trading krypton for xenon on exhaust velocity alone: krypton's ideal velocity is 1.252 times xenon's at 270 V, but it costs more ionization energy per ion (14.00 eV against 12.13 eV) and reaches lower mass utilization in practice, so xenon stays the default for high thrust-to-power.
• Mixing beam voltage and discharge voltage: the beam voltage is eta_v * V_d (270 V against the 300 V discharge in the example), and the ideal-velocity and beam-current relations all use V_b - feeding V_d in their place inflates the exhaust velocity.
• Reading a single efficiency factor as the total: eta_T is the product eta_m * eta_v * eta_c * eta_d (0.85 * 0.90 * 0.78 * 0.84 = 0.501), so quoting the mass utilization alone hides the other three losses.

Behavior contract (gate 3)

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

python3 scripts/test_hall_thruster.py

The test covers the 5 kW sizing contract (thrust within 1% of 0.32 N, rocket-equation propellant mass), thrust from power scaling, ideal and effective exhaust velocity with utilization factors, specific impulse, thrust-to-power, the efficiency decomposition and its bounds, anode vs total efficiency with the auxiliary power split, beam current round trip and beam current from mass flow, discharge power and current, the xenon vs krypton comparison, and ValueError rejection of non-positive power, voltage, current, mass and out-of-range efficiency.

Compliance

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