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Theoretically MPD thrusters can provide high thrust with extremely high specific impulse. What problems currently prevent this technology from being used in space exploration?

Is there any planned mission which will use MPD thrusters?

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MPD thruster shot

An MPD thruster in action

According to this Princeton page, MPD's could prove an exhaust velocity of up to and beyond 110,000 m/s - which is triple the value of current xenon-based ion thrusters. So yes, it would be great for space applications.

Here's the problem: The crazy things take a lot of power. As in a lot. Here's the gist of the problem, from this paper:

The MPDT has demonstrated its capability of providing specific impulses in the range of 1500–8000 sec with thrust efficiencies exceeding 40%. High efficiency (above 30%) is typically reached only at high power levels (above 100 kW); consequently, the steady-state version of the MPDT is regarded as a high-power propulsion option.

When the thruster is operated below 200 kW, the self-induced magnetic field becomes only marginally sufficient to provide the desired body force, and external fields are frequently added to enhance performance in this range.

Of course, spacecraft wouldn't be able to add the external field in an efficient manner - at this point, it would be more power efficient to use another option.

In addition to the present unavailability of high power in space, the cathode erosion rates of the steady-state MPDT (which can be as high as $0.2\frac{\mu g}{C}$), have slowed the evolution of steady-state MPDTs toward flight applications.

There is still hope, though, in the form of a varied system - a steady-state MPDT, called the lithium Lorentz-force accelerator (Li-LFA):

Li-LFA shot

An Li-LFA thruster.

The lithium Lorentz-force accelerator ($\rm{Li}$-LFA) uses a multichannel hollow cathode and lithium propellant to substantially reduce the cathode erosion problem while significantly raising the thrust efficiency at moderately high power levels. For example, a 200-kW $\rm{Li}$-LFA has demonstrated essentially erosion-free operation over 500 hr of steady thrusting at 12.5 N, 4000 sec $I_{sp}$, and 48% efficiency. Since no other electric thruster has yet shown such a high power processing capability, the $\rm{Li}$-LFA is at the forefront of propulsion options for nuclear-powered deep-space exploration and heavy cargo missions to the outer planets.

The paper is a great resource on the subject - there are many more nice little gems in it that I didn't cover here. Highly recommended!

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    $\begingroup$ Bottom line: you need a space nuclear reactor. If you want this kind of performance, you need to solve the problem of providing the power source first, since that problem is much more expensive to solve. Playing around with plasma thrusters is fun and relatively cheap, but it is completely pointless unless you're working on a power source. $\endgroup$ – Mark Adler Nov 11 '13 at 19:13
  • $\begingroup$ exactly, and NASA is not spending a penny on nuclear power sources for space. Which is what led Zubrin to say that VASIMR is a hoax. spacenews.com/article/vasimr-hoax $\endgroup$ – lurscher Nov 13 '13 at 5:31

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