## Thrust Scaling in Applied-Field Magnetoplasmadynamic Thrusters

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Thrust Scaling in Applied-Field Magnetoplasmadynamic Thrusters

### Abstract

A theoretical and experimental investigation of the scaling of thrust of applied-field magnetoplasmadynamic thrusters (AF-MPDTs) with geometric and operational parameters is undertaken. The thrust of an AF-MPDT consists of applied-field, gasdynamic, and self-field components. Because the first of these components is dominant under nominal operating conditions, and therefore most relevant to optimizing the performance of this thruster for a given mission’s requirements, the applied-field thrust component is the focus of this work.

In the canonical applied-field thrust model, the thrust coefficient, which is the ratio of the measured thrust to the modeled thrust, is assumed to be constant. It is shown in this work that there exists a governing “confinement parameter,” which represents the ratio of the inward to outward radial forces acting on the plasma, and which depends on the total current, applied magnetic field, mass flow rate, acoustic velocity at the anode throat, the ratio of specific heats, and the thruster geometry. It is shown that this parameter defines two different modes of operation, and that the thrust coefficient is only constant on the boundary between these two modes, where the confinement parameter is equal to one. When the confinement parameter is greater than unity, the inward radial forces are larger than the outward radial forces, and the plasma is in a magnetic-confinement mode. In this mode, the plasma is pinched inward from the anode wall, reducing the volume on which the Lorentz force acts to generate thrust. It is demonstrated, using data from the literature, that increasing the pinching forces in this mode of operation reduces the thrust.

When the confinement parameter is less than unity, the outward radial forces exceed the inward radial forces, and the plasma is in the anode-confinement mode. In this mode, it is demonstrated that, for a given thruster, the thrust coefficient depends solely on the confinement parameter. Increasing the confinement parameter decreases the plasma density near the anode wall and increases the density near the thrust axis, which increases pressure on the tip of the cathode, and the rate of rotation of the plasma column. Both the increase in pressure, and the increase in azimuthal kinetic energy, result in increased applied-field thrust. The scaling of the thrust coefficient with the confinement parameter is demonstrated using measurements of total thrust for a number of thrusters in the literature. However, in order to demonstrate that this scaling is not affected by self-field or gasdynamic thrust components, a method for directly measuring the applied-field thrust component is devised and used to verify that the dependence is correct.