Mpd Thruster

Magnetoplasmadynamic Thruster (propulsion/electric/mpd-thruster)

Use when the task is the steady operating point of a self-field magnetoplasmadynamic (MPD) electromagnetic thruster for electric propulsion: the discharge current drives its own azimuthal magnetic field, and the JxB body force on the coaxial arc is the sole acceleration mechanism. This leaf computes the electromagnetic thrust from the current-squared thrust law, the exhaust velocity and specific impulse from the propellant mass flow, the jet kinetic power and the thrust-to-power ratio on the jet-power basis, and reports the reference-only class-band verdict. Pure Python, stdlib only. It pairs with propulsion/rocket/rocket-sizing for the delta-v mission loop and with its electrostatic pack siblings, which own the other electric acceleration mechanisms; this leaf has no voltage input at all and carries the propellant as a mass-flow label only.

Domain quick reference

• Self-field electromagnetic thrust: T = (mu0/(4 pi)) * J^2 * ln(r_a/r_c), with J the total discharge current (A) and r_a/r_c the anode-to-cathode radius ratio of the coaxial electrode pair (r_a > r_c). The current-squared law of the steady self-field arc (Jahn, "Physics of Electric Propulsion", McGraw-Hill 1968, reported in the Sutton Rocket Propulsion Elements electric-propulsion chapter); mu0/(4 pi) is the 1e-7 N/A^2 coefficient. Electrode falls, ionization and thermal-pressure contributions are neglected: the ideal electromagnetic thrust.
• Effective exhaust velocity (definition, not a nozzle expansion): v_e = T/m_dot with m_dot the total propellant mass flow.
• Specific impulse: Isp = v_e/g0, g0 = 9.80665 m/s^2.
• Jet kinetic power: P_j = T^2/(2 m_dot); the exact identity P_j = 0.5 * m_dot * v_e^2 follows from v_e = T/m_dot.
• Thrust-to-power (jet-power basis): T/P_j = 2 * m_dot / T in N/W, reported in mN/kW by scaling by 1e6.
• Reference-only class bands (published ranges for the steady self-field MPD class, reported never enforced): Isp 1000-4000 s, thrust-to-power 10-40 mN/kW.
• Units are SI throughout: A, N, kg/s, m/s, s, W.
• 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 current J (A), anode-to-cathode radius ratio r_a/r_c (> 1) and propellant mass flow m_dot (kg/s, argon carried as a mass-flow label only).
2. Run the self-field electromagnetic thrust traverse with self_field_thrust(current_j, radius_ratio): the electromagnetic thrust from the discharge-current-squared law. Zero current is allowed and returns 0.0 exactly.
3. Run the exhaust-velocity and specific-impulse traverse: exhaust_velocity(thrust, mass_flow) gives v_e = T/m_dot, then specific_impulse(v_e) gives Isp = v_e/g0.
4. Run the jet-power and thrust-to-power traverse: jet_power(thrust, mass_flow) gives P_j = T^2/(2 m_dot), then thrust_to_power(thrust, p_j) gives the N/W ratio; scale by 1e6 for mN/kW.
5. Run the band-verdict traverse: mpd_band_verdict(isp, thrust_to_power_mn_per_kw) reports the position of the point against the reference-only class bands; out-of-band never raises.
6. Collapse the point with mpd_operating_point(current_j, radius_ratio, mass_flow), the single-point summary dict with thrust, exhaust velocity, specific impulse, jet power, thrust-to-power (N/W and mN/kW) and the nested band verdict.
7. Confirm the deterministic checks with the contract test scripts/test_mpd_thruster.py.

Worked example

Steady self-field MPD point at the published anchor: J = 10 kA (10000 A), r_a/r_c = 10, m_dot = 0.1 g/s = 1.0e-4 kg/s argon.

• Thrust: T = 1e-7 * (1e4)^2 * ln(10) = 23.02585092994046 N, within 1 percent of the 23.0 N receipt target. The coefficient identity holds: T/J^2 = 2.302585093e-7 N/A^2.
• Exhaust velocity: v_e = T/m_dot = 230258.5092994046 m/s.
• Specific impulse: Isp = v_e/g0 = 23479.833510873195 s.
• Jet power: P_j = T^2/(2 m_dot) = 2650949.0552391997 W (about 2.65 MW); the identity P_j = 0.5 * m_dot * v_e^2 holds.
• Thrust-to-power: T/P_j = 8.685889638065036e-06 N/W = 8.685889638065037 mN/kW; the identity T/P_j = 2 * m_dot / T holds.
• Band verdict: isp_position 'above' the reported 1000-4000 s class band, thrust_to_power_position 'below' the reported 10-40 mN/kW band, enforced False. The anchor fixes m_dot at 0.1 g/s, so the ideal current-squared law implies an exhaust velocity far above the class-typical range; the verdict reports this position and never enforces it.
• Query-2 companion point at J = 5 kA (same ratio and mass flow): T = 5.756462732485115 N, exactly one quarter of the 10 kA thrust by the J^2 law; v_e = 57564.62732485115 m/s; Isp = 5869.958377718299 s; P_j = 165684.31595244998 W; T/P_j = 3.4743558552260144e-05 N/W = 34.74355855226015 mN/kW (inside the reported 10-40 mN/kW band); verdict isp_position 'above', thrust_to_power_position 'inside', enforced False. At fixed mass flow, doubling J quadruples the thrust but quarters the jet-power-basis thrust-to-power, the discharge-current-scaling signature of the law.

Verification

• Confirm self_field_thrust(10000, 10) returns 23.02585092994046 N and equals 23.0 N within 1 percent.
• Confirm exhaust_velocity(23.02585092994046, 1e-4) is 230258.5092994 m/s and specific_impulse of that value is 23479.833510873195 s.
• Confirm jet_power(23.02585092994046, 1e-4) is 2650949.0552391997 W and equals 0.5 * m_dot * v_e^2; confirm thrust_to_power gives 8.685889638065037 mN/kW and equals 2 * m_dot / T.
• Confirm the scaling identities: T at 20 kA is 4 * T at 10 kA, T at 5 kA is T(10 kA)/4, T at ratio 100 is 2 * T at ratio 10 and T at ratio 1000 is 3 * T at ratio 10 (all within 1e-12 relative).
• Confirm self_field_thrust(0, 10) is exactly 0.0 and zero-current thrust is 0 at any valid ratio.
• Confirm the band verdict reports isp 'above' and thrust-to-power 'below' at the anchor, 'inside' at (2000 s, 20 mN/kW), and never raises on out-of-band points.
• Confirm every non-finite input, negative discharge current, radius ratio at or below 1, non-positive mass flow, negative thrust or exhaust velocity and non-positive jet power raises ValueError.
• Run the contract test offline: python3 scripts/test_mpd_thruster.py (32 tests, deterministic).

Related leaves

• propulsion/electric/hall-thruster, propulsion/electric/gridded-ion-thruster and propulsion/electric/electrothermal-thruster: the other electric pack slots, each owning a distinct acceleration mechanism; this leaf owns the electromagnetic self-field slot.
• propulsion/rocket/rocket-sizing: the delta-v and propellant mass loop around a single thruster operating point.
• propulsion/rocket/nozzle-design: the chemical-thruster nozzle branch, the alternative thrust path this leaf never uses.

Pitfalls

• Reading the ideal law as total thrust: T = (mu0/(4 pi)) J^2 ln(r_a/r_c) is the ideal electromagnetic thrust; electrode falls, ionization and thermal-pressure contributions are neglected, a recorded idealization of the anchor.
• Expecting a voltage input: the model has no voltage, no applied magnetic field and no electrode-fall or arc-resistance term; the discharge current and geometry alone set the operating point.
• Enforcing the class bands: the 1000-4000 s impulse and 10-40 mN/kW thrust-to-power ranges are published class bands that mpd_band_verdict reports but never enforces; a point outside the band is not an error and never raises.
• Mixing the acceleration mechanisms with the pack siblings: hall, gridded and electrothermal thrusters use their own electric acceleration or heating mechanisms, while this leaf accelerates the coaxial arc electromagnetically through its self-field; do not apply the sibling machinery here.
• Feeding a radius ratio at or below 1: a coaxial electrode pair needs r_a > r_c, so radius_ratio <= 1 raises ValueError; the ln(r_a/r_c) geometry factor is undefined at or below unity.
• Forgetting the jet-power basis: the thrust-to-power here is T/P_j = 2 * m_dot / T on the jet kinetic power, reported in mN/kW by the 1e6 scale, not on an input electrical power that the model does not have.

Behavior contract (gate 3)

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

python3 scripts/test_mpd_thruster.py

The test covers the 10 kA worked-example contract (thrust 23.02585092994046 N within 1 percent of 23.0 N, exhaust velocity 230258.5 m/s, specific impulse 23479.83 s, jet power 2.651 MW, thrust-to-power 8.686 mN/kW), the current-squared scaling of thrust with discharge current, the log-geometry scaling with radius ratio, the coefficient identity T/J^2 = 1e-7 ln(10), the definition and jet-power identities, the zero-current boundary, the band-verdict semantics including out-of-band points that never raise, ValueError rejection of non-physical inputs across the module, and determinism of repeated runs. The suite passes under both /usr/bin/python3 (3.9.6) and the pyenv 3.13.12 interpreter.

Compliance

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