# Have light gases like hydrogen or helium been explored for ion propulsion?

This answer and discussion in comments below this answer mention that for an ion of mass $$m$$ and charge $$q$$ accelerated by a voltage $$V$$ the momentum it receives (impulse) is

$$p = \sqrt{2mqV} = \sqrt{2mE}$$

and the mass-specific impulse for one atom would be that divided by mass:

$$\sqrt{\frac{2qV}{m}}$$

This suggests that if you used 4He+ or 1H+ in an ion thruster or engine you could get about 5.7 or even 11.5 times more Isp compared to using 131Xe+ ions.

Xenon and krypton are popular despite their heavy mass because they are simply much easier to

1. put in bottles
2. ionize in the kinds of plasma conditions that are convenient to make on a small spacecraft
3. they are not very reactive with the materials used in the engines.

Has the "ion sorcery" for light gases like hydrogen and helium been explored experimentally for future ion propulsion technology? What about neon at least?

Just fyi iodine has also been explored because while heavy (bad) and easy-ish to ionize (good) like xenon, it can be stored as a solid and sublimated on-demand. While storing large quantities of liquid helium for long flights will be a challenge and require a sun shade, liquid and solid sources of gaseous hydrogen and hydrogen-containing gases are probably within reach.

• People make design choices for the performance of the mission by the craft. Fuel choices are made to maximize that. Heavier atoms give more thrust per energy (see your first equation) and that’s what the designer cares about when craft mass and power are limiters. Specific impulse matters when fuel mass is large and (combustion) energy comes from the fuel, but that’s not the ion case. Apr 13 '20 at 6:31
• @BobJacobsen The correct answer to "Have light gases like hydrogen or helium been explored for ion propulsion?" is "Yes they have!" and a good answer will explain it. Not every possible future mission will be clone of DAWN with DAWN's constraints. Imposing that seems counterproductive. Answering "No nobody has or would ever explore hydrogen or helium because all missions will be just like DAWN forever" seems to probably not be true.
– uhoh
Apr 15 '20 at 13:28
• Comments are not for extended discussion; this conversation has been moved to chat. Apr 15 '20 at 13:47
• But better ISP, this mean also less thrust per energy, isn't it? Although as an independent variable, more ISP is better, on a global mission profile, that choice could mean slower time to destination because thrust is lowered, I think. Apr 6 '21 at 7:47
• Isp reflects thrust per rate of mass use.
– uhoh
Apr 6 '21 at 8:15

(Top edit: The Question asserts "Xenon and krypton are popular despite their heavy mass" and asks about exploring H or He ion propellants for improved Isp. This answer shows that lighter is not better for ion thrusters, because Isp is not the proper measure of a power-limited situation. Hence, although lighter atoms have been explored for other reasons, they're certainly not explored because they provide better Isp.)

Typical ion thrusters have a small mass of propellant compared to the mass of the power generation system plus the rest of the spacecraft. In that case, the goal is to get as much thrust from the ions as possible given the power that's available.

Referring to the first equation from the Question:

$$p = \sqrt{2mqV} = \sqrt{2mE}$$

for a fixed amount of energy E, the greatest outgoing momentum hence greatest thrust comes from a larger mass atom. Switching from H to Xe is about a $$\sqrt{131} \approx 12$$ times increase in thrust, at the price of adding a couple kilograms to a much more massive spacecraft.

It's true that a heavier atom is ejected slower, as $$E =1/2 m v^2$$ means $$v = \sqrt{2E/m}$$. But that's more than made up for but the larger $$m$$ in $$mv$$.

Dawn is beyond the small-thruster regime into the ion engine region. It launched with 425kg of Xe on a 750kg spacecraft.

The Dawn spacecraft carried 425 kilograms (937 pounds) of xenon propellant at launch. Xenon was chosen because it is chemically inert, easily stored in a compact form, and the atoms are relatively heavy so they provide a relatively large thrust compared to other candidate propellants.

(Quote on this Dawn page)

The same number of H atoms would be only about $$425/130 = 3.3 \rm{kg}$$. But with the power available, the thrust would go down by a factor of 12 (although acceleration drops a bit less, as average total mass has gone down by about a sixth). That would have adverse impact on the mission. And the only way to restore the original thrust hence acceleration with H fuel would be to increase the size of the power provided by a similar factor of about 12. Dawn's solar arrays (which power the entire craft, not just the engines) are $$18\rm{m}^2$$ now; you'd be adding another $$100\rm{m}^2$$ or more, with consequent increase in mass, need for more thrust, etc. In discussion, it's argued that what matters is the velocity of the exhaust, not the momentum. This is only true in a specific approximation where the energy of the outgoing exhaust is not intrinsically limited by some other process. For example, if you're combusting 10kg of LOX LH2, then you want that mass to be ejected with as much speed as possible using as much of the combustion energy as possible. For a constant mass (flow), it is speed that matters. But ion propulsion is (so far? usually?) limited by available power, which is a different regime. You can't compare two different mass flows without taking into account how much the available power can accelerate them.

So how does the power limit come in? Here, a higher velocity of the charged particles in the exhaust works against you. The current is $$qv$$, so the power needed is $$qvV$$: Higher velocity is more energy needed per unit of charge. Since you're limited by the energy you can put in to the exhaust stream, the exhaust velocity is effectively fixed for the thruster.

Analytically, the available power is given by voltage and current (capital letters are electric quantities, lower case are mechanical, the $$i$$ subscript is per-ion): $$P = I V$$

Break down current into total charge per second and velocity:

$$P/V = I = q_i dN_i/dt v$$

where $$dN_i/dt$$ is the number of ions exhausted per second. Expressing this in terms of the ion's intrinsic charge to mass ratio:

$$P/V = I = (m_i dN_i/dt) q_i/m_i v$$

where the term in () is the total mass exhausted per second. Regrouping to highlight momentum:

$$P/V = q_i/m_i (dm/dt) v$$

$$P/V = q_i/m_i dp/dt$$

$$dp/dt$$ gives the thrust, so finally:

$$dp/dt = P/V (m_i/q_i)$$

More power and higher mass ions lead to more thrust; more specifically a higher mass/charge ratio is better.

• This is exactly the correct answer - it just doesn't make sense to use light gases because of power requirements to get the same acceleration. Nobody cares about dv alone, net acceleration is the crucial factor. Apr 13 '20 at 9:09
• @uhoh I don't see a wrong statement there. Heavy atoms are better. There is no way for any reasonably-sized, close-future technology probe to be better off using light ions. Apr 13 '20 at 11:12
• No, that's wrong. Xenon is chosen because it's heavy. Apr 13 '20 at 13:15
• This is the correct answer. Note that the energy $E$ is provided by the ion accelerator, and is the same regardless of ion mass (although increasing ion charge can increase the ion $E$, at the cost of not having nearly as many high charge state ions without a lot of trouble on the source side). Since momentum is key (conservation of momentum in the inertial frame), mass is good. Apr 13 '20 at 17:50
• I'm puzzled by the claims that this is the correct answer, given that it doesn't seem to address the title question at all. Apr 13 '20 at 19:08

Because this answer challenges my premise I'm going to review it here:

To go fast we want high exhaust velocity $$v_e$$ .

$$\Delta v = v_e \ln(m_f/m_i)$$

For a given potential difference (grid acceleration voltage) $$V$$ the energy of an ion of charge is $$E=qV$$:

$$E = qV = \frac{1}{2}mv_e^2$$

$$v_e = \sqrt{\frac{2qV}{m}}$$

This is the exhaust velocity of one atom, of any atom, of all atoms, of the exhaust. To get big $$v_e$$ we need small $$m$$.

Let's try it again:

$$F = \frac{dp}{dt} = v_e \frac{dm}{dt}$$

$$\frac{F}{\dot{m}} = \frac{\frac{dp}{dt}}{\dot{m}} = v_e \frac{\frac{dm}{dt}}{\dot{m}} = v_e$$

The mass-specific force or mass-specific impulse per unit time is the exhaust velocity, and for a given acceleration voltage light +1 ions are faster than heavy +1 ions by a factor of $$1/\sqrt{m}$$.

• Thrust comes from fuel momentum, not velocity. Acceleration comes from fuel momentum over craft mass. When craft mass ~ fuel mass, that division means velocity is key. When craft mass larger and constant, fuel momentum, not velocity, is key. Apr 13 '20 at 14:12
• @BobJacobsen all the prose in the world won't negate what we get when we integrate; to go fast we want high exhaust velocity because Tsiolkovsky said so; $\Delta v = v_e \ln(m_f/m_i)$
– uhoh
Apr 13 '20 at 14:22
• I don't know how to convince you. Xe was chosen over something else for a half-Billion dollar mission. You keep pointing to lighter => better without holding power constant. Those faster light ions are more current => more power => can't accelerate as many. Perhaps a Python program that does a simulation that show the effect of limited power? Apr 13 '20 at 14:49
• Aha! Maybe this will help: Why don't we use lasers pointing out the back of our rockets? They've got a fantastic exhaust velocity, firing out photons at c. Apr 13 '20 at 15:52
• Whatever, dude. The 2nd to last paragraph of your first cited paper makes the point quite well too. Have they been explored? Yes, and even though they have better Isp, they've been rejected because they're worse for an actual vehicle due to power (not just ionization). I'll leave the rest to the up and down votes. Apr 13 '20 at 21:53

### Have light gases like hydrogen or helium been explored for ion propulsion?

I'll quote @BobJabobsen:

Whatever, dude. The 2nd to last paragraph of your first cited paper makes the point quite well too. Have they been explored? Yes, and even though they have better Isp, they've been rejected because they're worse for an actual vehicle due to power (not just ionization). I'll leave the rest to the up and down votes.

Which is baffling because that's all that that answer ever says. Lighter gases will have better Isp, and so they might have been explored. The the indignation comes from pretending a different question was asked than what was actually asked, and the highly upvoted answer pretends that a different question was asked.

The question asks if they have been explored, and includes an explanation for why one might want to.

Rather than answer the question as asked with facts, there is a lot of chauvinistic opining why one would never do this in answers and in comments, and an inordinate amount of down voting on my answer post that elaborates on the premise.

Basically folks wanted to write answers to "Why didn't NASA use helium for Dawn?" and so they pretended that's what my question asked, which it did not.

There are other kinds of missions, other kinds of applications. Some orbits need only a tiny amount of delta-v for station keeping per year and have plenty of sunshine.

Just for an illustrative example, JWST will only need 2 to 4 meters per second of delta-v per year for station keeping. 1, 2 A cubesat in a similar orbit with some run-of-the-mill cubesat solar panes will have plenty of power. What it needs to be careful about is Isp and mass.

Not every spacecraft is a Dawn clone!

Arguments boil down to spacecraft being energy-limited rather than mass-limited, so if you are in a hurry you want to use heavier species. That's light-years away from what the question asks.

So I say the positions here are chauvinistic opining because they are all based on all space missions being exactly like historical ones; moderate distances and little patience.