Prof. Dr.-Ing.
Stefanos Fasoulas


Prof. Dr.-Ing. Sabine Klinkner

Prof. Dr. rer. nat. Alfred Krabbe

Prof. Fasoulas

Sheyla Fröhler-Valdez

Prof. Klinkner

Annegret Möller

Prof. Krabbe

Barbara Klett


Dr. Thomas Wegmann


Institut für Raumfahrtsysteme
Pfaffenwaldring 29
70569 Stuttgart

Tel. +49 711 685-69604
Fax +49 711 685-63596
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Magnetoplasmadynamische Triebwerke


Theoretical Basis of Operation

Thrust production: The design and acceleration principle of the AF-MPD thruster is demonstrated in the figure below. The thruster consists of a central cathode and a coaxial anode ring placed at end of a nozzle-like (isolated) hardware extension. The configuration is surrounded by a magnetic coil or permanent magnet in such a way that the produced ('applied') field forms another (magnetic) kind of nozzle opening downstream.

The acceleration and energy production process is derived from generalized Ohm's law (for high degree of ionization) and the corresponding energy equation



Consequently, the following mechanisms are active.

  • The Hall acceleration mechanism: as the discharge current crosses the applied magnetic field, azimuthal currents are induced which yield axial and radial Lorentz (j x B) forces where the axial component directly accelerates the plasma while the radial component builds up a pressure hill. The magnitude of azimuthal currents (in relationship to the discharge current) depends on the so called Hall parameter wt, where w is the cyclotron frequency of electrons being a linear function of the magnetic induction B, and t is the collision time of electrons with heavy particles.
  • Rotational kinetic energy is created in the plasma, resulting from the applied meridional current crossing the applied magnetic field.
  • In addition, energy is added by Joule heating, which is converted into axial jet kinetic energy through the fringing magnetic field.
  • The self field is normally negligible in the AF-MPD compared to the applied field.

All types of non-directed (rotational and thermal) energies can theoretically be converted into 'useful' axial velocities in the mechanical and the magnetic nozzle. The latter again operates through azimuthal currents that compensate, in the ideal case, centrifugal forces and overpressure.

The aerodynamic thrust due to the expansion of the plasma in a physical nozzle has also to be considered, its size depending on the geometry of the nozzle, the mass flow and energy input.

As a consequence, for AF-MPD acceleration to be effective, we need, before all, a strong magnetic field (B) of adequate shape, optimal degree of ionization (to have good coupling of mass to electromagnetic effects), and moderate particle density in the discharge region. Considering the acceleration mechanisms, a light weight propellant appears preferable for Isp gain.

As a general tendency, thrust and discharge voltage are rising with the strength of the magnetic field and the discharge current. An important phenomenon which characterizes AF-MPD propulsion is the fact that a substantial part of the acceleration processes takes place outside of the hardware device. The discharge current, who is also depending on B bulges out far downstream as B increases. The left figure shows measured current distributions at different magnetic field strengths. The same dependency applies at a decrease of density. That leads to the important influence of ambient pressure as demonstated in the right figure where specific thrust (F/I) is shown to increase as the tank pressure (and therefore the gas density) is reduced. At still lower pressure, saturation may occur. The environmental influence on the overall process (participation of ambient gas in the acceleration process) is given, leading to an uncertainty of thrust and particularly Isp determination. Even with condensable propellants, this effect is not reliably avoided due to the wide extension of the plume and the normally moderate dimensions of the vacuum facility. A real verification of the operation principle needs therefore an experiment in space (MATEX).

Typical self field discharge current distribution at different magnetic field strength (X9, DLR, 100 mg/s Ar, p = 2 Pa)
Thrust per current as function of the tank pressure (X 13, DLR)


Hardware development status

Currently IRS is testing the SX3 thruster, a 100 kW water-cooled AF-MPD. SX1, a 10 kW thruster is currently under construction. To present the constructing principle ZT1 , a thruster of the lower to medium power class (6 - 12 kW), is presented and shown as schematic in the figure below.

  1. Cathode liner (Cu)
  2. Insulator (Peek)
  3. Anode gas connector
  4. Back flange (SS)
  5. Anode liner (TZM)
  1. Hollow cathode (WT20)
  2. Anode (WL10)
  3. Cathode gas connector
  4. Fixing
  5. Insulation tube
  1. Insulation injection(BN)
  2. Cathode centering (BN)
  3. Neutral liner (TZM)

In this type of self field thruster the propellant (noble gas) is fed through the hollow cathode (1) and through a circular slit along the anode (7) which in this case consists of a radiation cooled cylindrical tungsten body thermally isolated against the surrounding coil. The use of the secondary 'anode' gas is to prevent serious destabilization through anode starving i. e. lack of current conducting matter at the anode surface as a consequence of the radial pressure distribution. The device reached a thrust of 70 mN at a mass flow of 6/1 mg/s of argon. The thruster is radition cooled and therefore no longterm test are feasible. Therefore the water cooled thruster SX1(~10 kW) and SX3(~100kW) had been built to study phenomenons, such as heat loads or the cathode erosion where the dependence of a permanent operation is the main interest.

ZT1 at 6 kW and 10mg/s during operation



Adam Boxberger
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