What limits thrust-to-weight ratio of ion thusters? (beside power density of energy source)

Question

If we consider nuclear-rocket technology not feasible (whether due to technological or political limitations), the second best options for future transportation in solar system are perhaps solar-electric ships... there are many concepts to use ion-thrusters in combination with photovoltaics in large scale - both historical and more recent.

Thin-film solar cells can ultimately provide power source with density something like 6W/g. In future it can be in principle developed may be up to 100-400 W/g (10-40% conversion efficiency in 1 micron foil at Earth orbit).

Therefore it makes sense to ask what are the inherent limits (maximum thrust-to-weight ratio) of the ion thruster, assuming the problem of sufficiently light power source is solved.

Now what about Ion thrusters? What makes them heavy? I guess current experimental realizations do not try to push thrust-to-weight up hard enough, simply because they don't have enough power to feed them. But in combination with these thin-film solar cell, the bottleneck starts to be the weight of thrusters.

Intuitively I assume classical ion thrusters with grid electrodes can be made lighter than Hall thrusters. While the grids can be made of thin metallic foils or wires, the Hall thrusters need quite heavy electromagnets. But I don't really know the engineering challenges which have to be solved in order to make them lighter.

What I really like with this respect is this concept where the thrusters are distributed over the solar array

Answer 1

The engines aren't particularly heavyweight, but we're handling lots of power in a very tiny volume. Lots of power means cooling. Gas accelerated to these energies becomes an extremely corrosive plasma, best held at bay by magnetic fields because otherwise the engine will be burning through itself. So - heavy electromagnets to guide the propellant. The electrical subsystems handle pretty high power at very high voltages, so again, not really lightweight. But overall, the engines aren't particularly much heavier than chemical engines of comparable power. The 'weight' part of thrust-to-weight is so-so, nothing really out of ordinary.

But now let's look at the thrust.

$E_k = {1 \over 2} m v^2 \ \ (1)$

$p = mv \ \ (2)$

These are the equations for kinetic energy and momentum.
Ion engines are all about maximizing performance; specific impulse. $I_{sp}={ v_e\over g_0}$.
To achieve maximum performance, you want to maximize the exhaust gas velocity. You only have a certain amount of energy to handle, your solar panels or other energy source as input. Take equation (1) To get as much performance - as much exhaust velocity of the gas, given constant accessible energy, you must reduce mass - specifically, take less propellant, apply same electric energy squeezing it into lower amount of propellant, achieve higher acceleration of the propellant, higher exhaust velocity. And still you're getting only $v = \sqrt{2E_k \over m}$ - a square root growth of velocity with both increase of energy/power or reduction of mass; diminishing returns although still worth it. In other words, an engine of twice the performance of another will either require 4x as much power, or 1/4 the fuel flow, the amount of propellant used per unit of time - and the engine, its power sources, the structure, doesn't get any lighter in the process of improving the performance.

And now let's look at how that impacts thrust. The rocket motion is based off conservation of momentum. There are many fancy equations that describe it in terms of differential time, change of mass over time etc, but it all boils down to the simplest approach, momentum from equation (2) is conserved: $v_{rocket} m_{rocket} = v_{exhaust} m_{exhaust}$.

Now what did we just do to get the most performance out of our engine? We reduced $m_{exhaust}$ linearly, to increase $v_{exhaust}$ in a square root proportion. The better performance the lower the right-hand term of the above equation. $m_{rocket}$ didn't improve, our engine is just as heavy as less efficient. Therefore $v_{rocket}$ suffers. Over a unit of time, our rocket gains less velocity, so it accelerated less - we lost thrust.

And this, the fact that with given a certain accessible engine power, increasing performance by a factor of $\sqrt{n}$ you reduce exhaust mass flow by a factor of $n$, leads inevitably to loss of thrust (and no weight savings), therefore the better the engine performance, for given power, the worse TWR is to be expected.

Answer 2

Ion thrusters need a power source. And power sources can be massive.

This was a major objection to Franklin Chang Diaz' claim that VASIMR could get to Mars in 39 days. He assumed an alpha of .5 kg/KWe. Which isn't doable with present day state of the art. So what would a power source look like that cranks out a kilowatt electricity per half kilogram? I tried to illustrate it. A screen capture from my The Need For A Better Alpha

Dominique is a 60 kilogram girl. If she had that kind of alpha she could do the work of a Ford Focus' engine along with the gasoline and oxygen.

I believe thin film photovoltaic arrays have the potential for a good alpha. If we can get solar arrays that deliver 250 watts per kilogram I believe 1 mm/sec^2 acceleration is doable.

Answer 3

There are 2 things that limit basically all electric rockets. One is the power supply. An electric rocket is only as good as it’s power supply. Whether it is solar or nuclear, in many designs, the weight of the power generation is so great that it usurps the advantage of needing little propellant. As you pointed out, the increasing performance and light weight of solar cells is encouraging.

The other big limitation is the density of the exhaust stream. Because these are extremely hot, they are naturally of low mass and large volume. So the problem becomes how to compress the exhaust stream so you can have more thrust.

I don’t know that the weight of the engine itself is as much of a problem. As you pointed out a design with magnetic coils (like the VASMIR) is heavier, but the coils enable it to squeeze the exhaust stream to make it more dense, so maybe it cancels out the weight burden.

Answer 4

I agree with the other comments regarding thin film photovoltaics being a good source of power. I built an ion thruster that is patented for lifting its power supply against Earth's gravity. A normal xenon ion thruster or "ion lifter," can't lift its power supply because the thrust to weight or mass ratio is too low. In a xenon thruster for instance, electrical energy is used to knock electrons loose from the xenon atoms which requires a fair amount of wattage and that creates power losses especially when considering the added losses in the electrical system and heat generated in the exhaust. Those engines also have erosion issues and normally must run for long periods of time to have much effect. "Ion lifters," were basically toys that required a large external power supply and rely on ambient O2 molecules primarily as the propellant.
The Ion Propelled Vehicle or Self-Contained Ion Powered "Aircraft," just adds electrons to a small percentage of either ambient O2 molecules or to O2 or SF6 supplied by optional onboard propellant tanks. O2 has a strong affinity for gaining extra electrons and so does not require the same ionization energy, it just absorbs electrons produced by the power supply. While the voltage of the power supply is much higher than in a xenon thruster, the current and wattage is far lower, so it was possible to reduce the mass of the power supply significantly. The erosion on the collector surfaces is minimized because it works by a different principal with very little wattage required.