Would an ICE powered Hall thrusters be efficient?

[Stormer]

TL;DR Summary

Is ICE powered hall thrusters more efficient than using the fuel to power chemical rockets directly for a Mars mission?

Hall thrusters is generally considered to have a much higher specific impulse and higher max speed than chemical rockets for use in space. But that does not calculate in the power source use of fuel right? Because it is generally assumed that you will use solar panels or a nuclear reactor to power the hall thruster. But if you used a ICE powered generator to give power to the hall thrusters using the same fuel that would be used for a chemical rocket wold the hall thrusters then be more efficient in deep space than a chemical rocket even with all of the losses in the engine and generator? But still using Xenon or Krypton for the reaction fuel of the hall thrusters of course.

 

[mfb]

It would be far worse. You add conversion processes, extra propellant, and you don't have enough energy.

RP-1+LOX releases about 9.1 kJ/g at the stochiometric ratio. You don't want that in a rocket engine, but let's use that approximation. The physical limit is the full use of all that energy to propel the produced CO2 and H2O at a velocity of 4250 m/s, or an I_sp of 433 s. A real rocket engine won't reach that, but good engines reach ~350 s. It's quite close to an ideal use of the chemical energy. You have the gases anyway, so you might as well put all your energy into them to accelerate them away.

Energy requirements scale with the velocity squared while thrust is only linear in the energy, so you want to expel everything at the same speed.

Let's burn RP-1+LOX in an ICE. You get ~1/3 chemical to electric efficiency. If you use that to propel an equal amount of noble gas at 100% efficiency you can reach an exhaust velocity of 2450 m/s, or 250 s I_sp. But you used twice the amount of mass, so your effective I_sp is down to 125 s. That's atrocious. Even a magical 100% efficiency in the ICE would still halve the I_sp because you need extra propellant.

What if you want to expel propellant at a higher speed? Let's say 10 km/s, that's quite low for ion thrusters. You need 50 kJ/g, so you need 17 gram of RP-1+LOX for a single gram in the Hall thruster. That means we get an effective I_sp of 1000 s/18 = 58 s. It's even worse.
Increasing the speed more just makes it worse and worse because the amount of propellant you can accelerate goes down even more.

 

[Stormer]

Thank you for a great reply.
Another question: Wold using the exhaust gasses from the ICE and a nozzle as a "thruster" kind of like what they are doing with directing the exhaust gas up on top fuel dragsters do any significant effect to offset the poor efficiency of the ICE (of course it would still be a horrible total I_sp even at 100% ICE efficiency as you said)?

 

[mfb]

If that exhaust has any relevant speed you converted the ICE to a rocket engine.
Expelling the exhaust slower than a rocket engine can is a waste of mass.