Magnetoplasmadynamische Triebwerke

Fremdfeld-MPD-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

where

and

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