Thursday, September 15, 2016

Xenon

Xenon The Noble Gas

Xenon is one of heavier Noble Gases

Screen capture from ChemicalElements.com

The noble gases are the orange column on the right of the periodic table. These are chemically inert. Which means they're not corrosive. This makes them easier to store or use.

Low Ionization Energy

Per this graph is from Wikipedia, Xenon has a lower ionization energy than the lighter noble gases.


Ionization energy for xenon (Xe) is 1170.4 kJ/mol. Ionization for krypton (Kr) is 1350.8 kJ/mol. Looks like about a 15% difference, right?

But a mole of the most common isotope of xenon is 131.3 grams, while a mole of krypton is 82.8 grams. So it takes 181% or nearly twice as much juice to ionize a gram of krypton.

Likewise it takes nearly 4.5 times as much juice to ionize a gram of argon.

The reaction mass must be ionized before it can be pushed by a magnetic field. Xenon takes less juice to ionize. So more of an ion engine's power source can be devoted to imparting exhaust velocity to reaction mass.

Big Atoms, Molar Weight

Low molar weight makes for good ISP but poor thrust. And pathetic thrust is the Achilles heel of Hall Thrusters and other ion engines. The atomic weight of xenon is 131.29 (see  periodic table at the top of the page).

Tiny hydrogen molecules are notorious for leaking past the tightest seals. Big atoms have a harder time squeezing through tight seals. Big whopper atoms like xenon can be stored more easily.

Around 160 K, xenon is a liquid with a density of about 3 grams per cubic centimeter. In contrast, oxygen is liquid below 90 K and a density of 1.1. So xenon is a much milder cryogen than oxygen and more than double (almost triple) the density.

Abundance

Ordinary atmosphere is 1.2 kg/m3 while xenon is about 5.9 kg/m3 at the same pressure. Xenon has about 4.8 times the density of regular air.

By volume earth's atmosphere is .0000087% xenon. 4.8 * .000000087 = 4.2e-7. Earth's atmosphere is estimated to mass 5e18 kg. By my arithmetic there is about 2e12 kg xenon in earth's atmosphere. In other words, about 2 billion tonnes.

Page 29 of the Keck asteroid retrieval proposal calls for 12.9 tonnes of xenon. Naysayers were aghast: "13 tonnes is almost a third of global xenon production for year! It would cause a shortage." Well, production is determined by demand. With 2 billion tonnes in our atmosphere, 13 tonnes is a drop in the bucket. We throw away a lot of xenon when we liquify oxygen and nitrogen from the atmosphere.

In fact ramping up production of xenon would lead to economies of scale and likely cause prices to drop. TildalWave makes such an argument in this Space Stack Exchange answer to the question "How much does it cost to fill an ion thruster with xenon for a spacecraft propulsion system?" TildalWave argues ramped up production could result in a $250,000 per tonne price. That's about a four fold cut in the going market price of $1.2 million per tonne.

Radon

If you examined the periodic table and ionization tables above you might have noticed there's a heavier noble gas that has an even lower ionization energy: Radon a.k.a. Rn.  Radon is radioactive. Radon 222, the most stable isotope, has a half life of less than 4 days. If I count the zeros on the Radon page correctly, our atmosphere is about 1e-19% radon -- what you'd expect for something with such a short half life. Besides being rare, it wouldn't last long in storage.

Where xenon excels


Great for moving between heliocentric orbits

Ion thrusters can get 10 to 80 km/s exhaust velocity, 30 km/s is a typical exhaust velocity. That's about 7 times as good as hydrogen/oxygen bipropellent which can do 4.4 km/s. But, as mentioned, ion thrust and acceleration are small. It takes a looong burn to get the delta V. To get good acceleration, an ion propelled vehicle needs good alpha. In my opinion, 1 millimeter/second2 is doable with near future power sources.

If the vehicle's acceleration is a healthy fraction of local gravity field, the accelerations resemble the impulsive burns to enter or exit an elliptical transfer orbit. But if the acceleration is a tiny fraction of the local gravity field, the path is a slow spiral.


Earth's distance from the sun, the sun's gravity is around 6 millimeters/second2. At Mars, sun's gravity is about 2.5 mm/s2 and in the asteroid belt 1 mm/s2 or less. Ion engines are okay for moving between heliocentric orbits, especially as you get out as far as Mars and The Main Belt.

Sucks for climbing in and out of planetary gravity wells

At 300 km altitude, Earth's local gravity field is about 9000 millimeters/second2. About 9 thousand times the 1 mm/s2 acceleration a plausible ion vehicle can do. At the altitude of low Mars orbit, gravity is about 3400 millimeters/sec2. So slow gradual spirals rather than elliptical transfer orbits. There's also no Oberth benefit.

At 1 mm/sec2 acceleration, it would take around 7 million seconds (80 days) to climb in or out of earth's gravity well and about 3 million seconds (35 days) for the Mars well.

Mark Adler's rendition of an ion spiral
where the thruster's acceleration is 1/000 that of local gravity at the start.

The general rule of thumb for calculating the delta V needed for low thrust spirals: subtract speed of destination orbit from speed of departure orbit.

Speed of Low Earth Orbit (LEO) is about 7.7 km/s. But you don't have to go to C3 = 0, getting past earth's Hill Sphere suffices. So about 7 km/s to climb from LEO to the edge of earth's gravity well.

It takes about 5.6 km/s to get from earth's 1 A.U. heliocentric orbit to Mars' 1.52 A.U. heliocentric orbit.

Speed of Low Mars Orbit (LMO) is about 3.4 km/s. About 3 km/s from the edge of Mars' Hill Sphere to LMO.

7 + 5.6 + 3 = 15.6. A total of 15.6 km/s to get from LEO to LMO.

With the Oberth benefit it takes about 5.6 km/s to get from LEO to LMO. The Oberth savings is almost 10 km/s.

10 km/s is nothing to sneeze at, even if exhaust velocity is 30 km/s. Climbing all the way up and down planetary gravity wells wth ion engines costs substantial delta V as well as a lot of time.

Elevators and chemical for planet wells, ion for heliocentric

So in my daydreams I imagine infrastructure at the edge of planetary gravity wells. Ports where ion driven driven vehicles arrive and leave as they move about the solar system. Then transportation from the well's edge down the well would be accomplished by chemical as well as orbital elevators.



Other possible sources of ion propellent.

Another possible propellent for ion engines is argon. Also a noble gas. Ionization energy isn't as good as xenon, but not bad. Mars atmosphere is about 2% argon. Mars is next door to The Main Belt. I like to imagine Mars will supply much of the propellent for moving about the Main Belt.

12 comments:

Jim Baerg said...

About 20% of fissions result in a stable isotope of xenon.

Used nuclear fuel would be a good source of xenon when reprocessed.

Hollister David said...

Jim, I'm happy to hear that!

I believe solar can provide good alpha in the neighborhood of earth and even Mars. But as we go further from the sun, NEP will become preferable over SEP. So there might be a whole lot of fission going on.

Chris Wolfe said...

Xenon's ionization energy is 1170 kJ/mol. Xenon's standard atomic mass is 131.29, yielding 131.29 g/mol or 7.62 mol/kg. That means you need 8915 kJ/kg for the atoms at first ionization. That might be easier to use as 8.9 J/mg given the low mass flows of electric engines.

Argon's ionization energy is 1521 kJ/mol. Argon's standard atomic mass is 39.95, yielding 39.95 g/mol or 25.03 mol/kg. That means you need 38,071 kJ/kg for the atoms at first ionization. That might be easier to use as 38 J/mg given the low mass flows of electric engines.

For the first stage of an ion thruster, argon requires about 4.3 times the power to ionize vs. xenon on a mass basis. On a molar basis argon requires 30% more power to ionize.

Consider a 200 kW VASIMR thruster (link at end) pushing argon. This is a plasma thruster, so the doubly-ionized problem doesn't really apply. 28 kW is applied to producing 107mg/s of plasma; this power must be spent to produce a stable mass flow regardless of the power setting of the acceleration stage. The remaining 172 kW is spent on acceleration at maximum power output. This produces 5.8 N of thrust with an exhaust velocity of 48km/s (Isp of 4900). That's a beam power of 123 kW, an acceleration stage efficiency of 71.5% and an overall efficiency of 61.5%.

Suppose the same device were to push xenon. The plasma stage would ionize 30% more propellant on a molar basis thanks to xenon's lower ionization energy. That plus xenon's higher molar mass means the engine processes 457 mg/s of plasma, around 4.3x the mass flow. Assuming the beam power remains the same (and by definition the efficiency), the exhaust velocity would be 23.2km/s (Isp 2365) and thrust would be 10.6 N.

80% better thrust at the cost of four times the fuel consumption makes sense for certain use cases like GTO to GEO (where the opportunity cost of a commsat's unavailability during transit is high) or manned heliocentric transfers (where the reduction in supplies and required shielding due to fast transit might be a net benefit), but for cargo or really anything that isn't time sensitive the argon propellant is superior. I suspect NASA and others use xenon because their engine thrust levels are just barely adequate for their mission with all available power and every astrodynamics trick in the book; if there was more power available on the craft then a change in propellant could greatly increase total dV for the same mass and thrust. To paraphrase hop, we really need better alpha if we want to get serious about deep space.

What if we cut the propellant flow in half? That would drop the ionization power to 14 kW. Argon exhaust velocity would be 67.8km/s (Isp 6912) and 3.6 N of thrust. Xenon exhaust velocity would be 32.8km/s (Isp 3345) and 7.5 N of thrust. Overall efficiency would rise to 66% in both cases, with a 41% increase in Isp and a 30-40% decrease in thrust (lower loss for xenon, higher for argon).

The ionization stage efficiency is reportedly about 87%. Ionizing the amount of argon they describe should only require 4 kW of coupled power, so the ionization stage is pumping about six times that much energy into the plasma and contributing to the useful output power. That means my simplistic comparisons may not be completely accurate. 20 kW into 107mg of argon would be a v of 19.3km/s (Isp 1970) and thrust of 2 N, making the ionization stage a respectable plasma thruster in its own right. I must be missing something. Most likely it is that this is a plasma device, essentially using heat rather than electricity. The kinetic energy of individual atoms is increased to the point where they dissociate into a neutral plasma; powerful magnetic fields are used to direct the plasma to the next stage where they are further heated and accelerated through a magnetic nozzle. If so, xenon as a propellant would have a somewhat lower exhaust velocity (thus lower thrust and Isp) than presented above.

source of VASIMR numbers: http://pepl.engin.umich.edu/pdf/AIAA-2012-3930.pdf

Hollister David said...

Chris, I had missed that chemical ionization energy is per mole. And a mole of Krypton is more than triple the mass a mole of Argon. So per kilogram, the ionization energy is a lot more dramatic than graphic I've published. There's a lot more to digest in your post. Am moving through it a little at a time. As usual, thanks for your input.

Kenneth Ferland said...

The in between gas Krypton is likely to be brought into service before scaling up of Xenon production as it's already available as a similar byproduct of atmospheric separation plants and is available in 4-5 times the volume of Xenon.

Also their are some concepts for thrusters that get around ionization energy, the Eletrodless Lorentz Force thruster ELF is intended to entrain neutral gas within a plasmoid which is ejected like a smoke ring. This would allow both higher thrust and efficiency from a propellant mixture of which only a fraction needs to be ionized.

Matter Beam said...

How could I have missed this blog? It's a treasure trove of information!

With regards to fission sourced Xenon: worldwide uranium consumption is in the tens of thousands of tons per year. Lots of xenon is being produced. However, it is a neutron poison that reactors are designed to 'burn' Xenon 135 into caesium.

If Xenon production becomes a priority, all we'd need is a redesign of nuclear reactors, instead of new atmospheric extraction equipment.

Hollister David said...

Matter Beam, Jim Baerg above also mentioned xenon is a fission product.

I was enthusiastic about Martian argon until Chris Wolfe pointed out the ionization energy is per mole. So kilogram per kilogram, argon takes 4.5 times as much juice to ionize as xenon.

I would imagine if we settle the Main Belt that fission nuclear power would be big. Even more so at the Trojans since solar falls with inverse square of distance from the sun. Do you have any idea how much xenon could be produced per watt?

So in my daydreams I like to imagine nuclear power plants on Ceres or 624 Hektor cranking out xenon as well as watts.

Also the space ships. As we get further from the sun, nuclear electric propulsion is more desirable than solar electric propulsion.

Doug Space said...

Cargo doesn't have to be time sensitive. One could stockpile large amounts of it at certain destinations prior to crewed missions. So, could we simply use the cheapest approach to launch (e.g. partially-reusable FHs) followed by ion propulsion for slow transport of cargo to other points such as an EML staging point, LLO, and LMO?

Chris Wolfe said...

Using internet numbers I see a uranium consumption of about 1200kg per GWe per year. (That's gigawatt, electric). Roughly 10^20 U235 fission events per second for a year. If 40% of those events result in Xenon then this reference reactor would produce 52,367 mol of Xe or about 6,875 kg with perfect recovery.
Assume a moderate Isp of 2500 (since thrust is desired for this application, that seems to be a reasonable value). Also assume a 6km/s dV budget for a one-way Earth-Mars heliocentric transfer. Using the rocket equation I get a 'leverage'* of 3.6, so this amount of Xe could propel 24.8 tons of dry mass. Let's be generous and assume that the entire dry mass is useful cargo.
I have trouble imagining a scenario where a colony using a gigawatt of electricity only needs 25 tons of supplies annually, or only produces 25 tons of exports. Such a colony could import highly-enriched U235 using only radiogenic xenon as propellant and still have surplus cargo capacity, but that seems like an arbitrary metric.

Argon works and is quite efficient. The problem is finding an efficient power source to put it to work. Krypton is indeed a 'middle ground' in terms of mass, ionization energy, thrust and Isp for a given amount of electrical power and could be one of several electric propellant choices.

* Leverage is similar to 'gear ratio', but in reverse. A chemical rocket is typically measured in tons of propellant per ton of cargo (gallons per mile). Electric rockets commonly deliver more than one ton of cargo per ton of propellant, so it makes sense to use the inverse value and express the number of tons of cargo per ton of propellant (miles per gallon) for a given route or mission.
To get the figure of 3.6 I used Mf = 1 - e^-(dV/Ve) to get the propellant mass fraction and then took (1 / Mf) - 1 to get units of dry mass per unit of propellant.

Doug Space said...

Your diagram illustrates wells concept which I call META (most efficient transportation architecture). In a nutshell, from planetary surfaces to their low orbits we use reusable ferries refueled from the resources on the planet. From LEO to the other low orbits we use SEP. The exception would be for crew which would go chemically to and EML staging point and then a small chemical kick for them and their cargo BLEO.

I would say that such a system could be near-term with only modest development. I don't know if tethers are as near-term.

Hollister David said...

Doug, thanks!

There is another type of vehicle: nuclear thermal rockets. My friends Winchell Chung and William Black have been proponents.

For space craft we want high energy density. Therefore weapons grade fissionables are desirable. I was opining to William that should such vehicles become common, proliferation would be a nightmare. William pointed out to me that horse is out of the barn and that nuclear powers have had good security over the stock piles for the last fifty years. I might take a look at reincarnations of NERVA and similar notions. Better ISP than chemical and better thrust than ion.

Also alpha is a whole lot better for thermal watts than electric watts.

We haven't invested that much on tethers so I think it's too soon to write them off. I wish NASA would toss Tethers Unlimited and Liftport some funding.

Matter Beam said...

"In a nutshell, from planetary surfaces to their low orbits we use reusable ferries refueled from the resources on the planet."

I think this is an exception for Earth. If we start capturing water-rich asteroids and comets, we can crack it with solar power and drop hydrogen onto extraplanetary surfaces. I think I read the 'Bring your own hydrogen' concept on selenianboondocks blog. The hydrogen will allow chemical propellants to be made in water-poor environments that have access to hydrogen. For example, imagine the freedom a lunar mining operation would have not being tied to a permashadow crater.

"For space craft we want high energy density"

Nuclear fuel mass is such an incredibly small fraction of the propulsion system that I doubt weapons-grade will ever exist in space. Nuclear bomb's aren't terribly useful in space, and completely useless in space-to-space combat*. I believe it is much more likely nuclear rockets will use whatever fissiles they can extract from rocky asteroids.

Could I suggest a comparison between tethers and beamed power. If lasers with modest powers and focusing arrays are used to transmit power at the same distances tethers operate at, SEP could receive the necessary boost to power that would allow for a burst of higher acceleration during the capture burn...