Why aren't fusion reactors using centrifuges?

If fusing of nuclei in stars requires pressure, heat, and gravity, why not use a centrifuge to increase the gravity? We currently have the technology to make diamonds, and generate immense temperatures. Thus surely if you increase the effective gravity, that would reduce the required temperatures! After all, as I understand it, the temperatures only need to be higher than a star, due to the lack of pressure - gravity!

• The answers given elsewhere don't really answer the question! Bear in mind, fusion can currently be achieved, it merely takes more energy than is produced! Fusion occurs when temperature, pressure are sufficient to fuse 2 or more atoms together. Current fusion reactor technology generates temperatures way beyond those even at the core of the sun, and the force of gravity on the sun is 1,280g! We can generate forces way beyond 1,280g. (Car crash sensors can easily be rated at 3000g. I've repaired them!) Thus claiming we cannot generate solar temperatures clearly is wrong! Aug 16, 2022 at 7:00
• So please, if you actually know why increasing the pressure/gravity won't reduce the temperature required on earth compared to current temps, please answer! Aug 16, 2022 at 7:00
• I don't know where you got that figure of 1280 g for the Sun's gravity. It's ~27.9 g at the surface, but it's much higher near the core, see this plot, which I created using the Standard Solar Model (BP 2004). Jul 22, 2023 at 7:51

The pressures required to force fusion to occur are so great that there simply is no material existing that is strong enough to apply such forces to a sample of matter to be fused.

Regarding the use of a centrifuge to apply compression to a fusion sample, the same comments apply: there is no material strong enough to make such a centrifuge out of.

In any case, note also that the pressure needed to trigger fusion has to be applied to the sample in all directions, something that centrifuges cannot do.

• Gravity on the sun is 1280g. Temperature of sun is 5,788k. The temperature in current fusion reactors are way beyond those of the sun! Thus that is a non-sequitur! Also the mere fact we CAN generate fusion on earth, it just takes more energy than it currently generates PROVES what you stated is simply untrue! The only thing we aren't currently generating on earth is the gravity - and a centrifuge increases gravity! Still need an ACTUAL reason why not using centrifuges! Aug 16, 2022 at 6:42
• Temperature inside the sun is of the order of millions of degrees. Your value of 5000K is for the atmosphere and has nothing to do with the fusion reaction.
– nasu
Aug 16, 2022 at 11:22
• The temperature and pressure in the center of the sun are 1.5E7K and 2.6E16pa. Jul 17, 2023 at 12:23
• I feel the core of the question is being missed! We CAN generate fusion, thus generating necessary heat is IRRELEVANT! a centrifuge simulates increasing the gravity (or pressure - O'm not a physicist - hence the question). Thus would increasing the force on the matter reduce the temperature required? Jul 22, 2023 at 2:43
• It's contained currently by magnets - thus your response is IRRELEVENT! How can adding additional kinetic energy to the process not aid the process? It's clear you don't understand the question! Jul 26, 2023 at 1:07

To add to @NielsNelsen's answer: it's not just that no solid material can withstand the needed pressure. The heat and heat capacity of the plasma are also problems. The plasma is high pressure primarily because of the high temperature, the density of the plasma is actually quite low (remember: $$P = k \,(\mathrm{number\ density})\, T$$). Because of this, if you allow the plasma to come in contact with the walls it would very quickly cool - low density means low heat capacity.

That's why just about every fusion reactor idea relies on either inertia or magnetic fields to confine the reaction. In inertial confinement, you use lasers (National Ignition Facility), explosions (think fusion bombs), or something similar to cause the temperature and pressure to suddenly reach insane levels faster than the hydrogen can fly apart. The reaction then proceeds until the density drops.

Magnetic field confinement relies on inventive and careful structuring of dynamic magnetic fields to hold the plasma away from the reactor walls. These are the tokamaks, stellerators, etc.

Why not just drop the temperature and up the pressure? Well, that won't work. Let's do some basic calculations. The fusion rate is going to be proportional to the number of collisions between nuclei that are above a certain energy cutoff $$E_c$$. The collision rate is proportional to the square of the number density (because you need the density of two nuclei being in the same place).

In an ideal gas you have $$PV = NkT$$. Divide both sides by $$V$$ and $$kT$$ and you get the following formula for the number density: \begin{align} \frac{N}{V} &= \frac{P}{kT} \end{align} Strangely, the density goes down with temperature, so you might think that you'd want the lowest temperature possible. Doesn't work, though. When the temperature gets low enough you just liquefy and then freeze the hydrogen, and you density stops going up at that point unless you apply more pressure mechanically.

Those kinds of pressures aren't feasible for physical things to exert, though. You're trying to force the nuclei of atoms together by pushing other atoms into them. Do you see the problem? The pressures needed to get fusion going in the fuel would exert enough mechanical back pressure to rip apart the bonds between the atoms of the walls, liquefying them, too. Even if you could keep the walls from breaking apart, if the atoms in the walls have lower atomic number than nickel/iron on the periodic table you're probably going to get them to start fusing with the hydrogen, too. If the walls have higher atomic number, you'll probably start catalyzing fission. Either way, no container made of atoms could withstand the demands this would place on it.

Even if we disregard that bit of physics, though, there's a huge problem with the fraction of atoms above the cutoff energy. The formula for that looks like \begin{align} f(E >= E_c) &= \frac{\int_{E_c}^\infty \exp\left(-\frac{E(p)}{kT}\right) \, p^2 \mathrm{d}p}{\int_{0}^\infty \exp\left(-\frac{E(p)}{kT}\right) \, p^2 \mathrm{d}p}, \end{align} where $$E(p)$$ is the energy of a nucleus with momentum $$p$$. This integral is a little complicated, but the key factor here is that as temperature drops the fraction of the exponential $$e^{-E/kT}$$ drops exponentially. To counteract that exponential drop you'd need to up the pressure exponentially to compensate, and that's just not feasible.

Notice, I didn't mention gravity. Because gravity is just the mechanism that allows the sun to achieve high enough pressure and density to get fusion at a lower temperature than we can achieve here. That, and the sun is stupendously huge, so fusion there is actually kind of slow, but it doesn't matter because there is so dang much sun. The power output per unit mass in the core of the sun is actually comparable to either your body or a compost heap rotting, I forget which. Because of its size, the outer layers can insulate the core to keep it hot, and the core just has enough mass that the total power output is huge even with the low density.

• That's all well and groovy, but doesn't answer the question! as I understand, heat pressure & gravity affect fusion. Thus if say AxBxC = fusion, A=temp, B=pressure, C=gravity. Thus if you increase B, A and/or C can be reduced. I'm sure there are practical issues, ultimately can you increase gravity or pressure and reduce the heat requirement? I'm sure I'm missing something, so what is it? Jul 22, 2023 at 2:50
• As I said here, the Sun's power in the core is roughly equal to a compost heap per unit volume. But the core density is ~150 g/cm³, so the power per unit mass is abysmal. ;) Jul 22, 2023 at 7:47
• @DodgyBob As Sean & Niels said, the gravity itself is only relevant because it creates pressure (via weight), and high pressure itself is only relevant because it causes high density. Your centrifuge can't create pressure without some kind of barrier that the plasma gets squeezed against. We normally confine fusion plasma using electromagnetic fields because solid matter can't withstand the high temperature, and would suck heat out of the plasma. Jul 22, 2023 at 8:02
• @DodgyBob BTW, the proto-Sun was hot from gravitational collapse converting gravitational potential energy to kinetic energy. It took hundreds of thousands of years to shed enough heat so that its core could achieve the density necessary for sustained p-p fusion. Jul 22, 2023 at 8:08
• @DodgyBob I'm explaining why if you attempt to add the pressure needed using a centrifuge you will fail. Yeah, if you had God's indestructible perfectly insulating hand, you could do exactly what you want. Us mere mortals have to work with real materials under real conditions, and those materials will both drain heat and break down. Jul 26, 2023 at 1:11

I answer only because the asker isn't satisfied with any of the currently existing five answers. And I think in some sense that's valid - nobody has directly addressed the concepts that they are asking about, although I think some answers contain correct and useful statements about how fusion actually works.

The question seems to assume that gravity plays some role in generating the pressure in fusion experiments, so if you were to effectively increase gravity, fusion would be easier to achieve. This is completely incorrect.

Gravity is involved in generating the pressure of the atmosphere in the following way: the sea level pressure of the atmosphere is the weight of a the entire column of air above us divided by the cross-sectional area of that column. So if we were to increase $$g$$, then the weight of each molecule of air would increase, and the pressure at sea level would increase. However, fusion experiments don't consist of physicists looking at the atmosphere at sea level and going "huh... why isn't it fusing already?"

For basically anything else, gravity plays no role in generating pressure. Consider a gas at high pressure in a container (for example we start with the atmosphere then compress it with a piston). The pressure is described by the ideal gas law $$P=nk_BT$$. So the pressure comes from the density and temperature and gravity has nothing to do with it. Putting the apparatus in a centrifuge will not change the pressure. Another way of seeing it is that the pressure comes from the force per area we can apply on the piston (leverage, gears, motors, etc.), and that's going to be a lot more force than we could ever achieve from a centrifuge.

So what about fusion experiments? As others have pointed out, for fusion experiments the plasma is too hot to be in contact with container walls, which would destroy the container walls and ruin the plasma at the same time. There are generally two kinds of particle confinement for fusion - magnetic confinement and inertial confinement. In magnetic confinement, charged particles are prevented from escaping by magnets which restrict the particle's motion. In inertial confinement we start with a solid mass and we compress it... really there's no confinement, but for a short period of time you have something really hot and denser than a solid. So like the situation with the piston-compressed air, gravity is playing no role in generating the pressure. We start with some initial density of gas (or solid for inertial confinement), then turn it into a hot plasma confined in some other way, which makes the pressure astronomically higher than the initial gas pressure.

It is true that fusion experiments rely on "pressure" (usually phrased as density) for success. A fusion experiment's efficacy can be parameterized by the "fusion triple product" - temperature times density times confinement time. Essentially, when this triple product increases, the likelihood increases that a charged particle will undergo a fusion reaction before it escapes from the plasma. Higher temperatures mean more collisions and the collisions are more likely to produce fusion, higher density means more collisions, and higher confinement time means more chances to fuse before being lost. Physicists are working as hard as they can to increase these three numbers. But since gravity never had anything to do with the pressure, increasing gravity using a centrifuge won't help.

Let's look at some numbers to see how this works. Below is a plot from this wiki page of different experiments' triple product. JET's confinement time is about a second, and its triple product is about $$10^{21}\text{ keV m}^{-3}\text{s}$$. So its density times temperature is $$10^{28}\text{ K m}^{-3}$$ (one keV is about 12 million Kelvin). When we plug this into the ideal gas law we get a pressure of about 1.3 atmospheres. But we can also find much higher pressures in inertial confinement experiments with much lower confinement times. NIF is one such experiment which boasts a triple product of $$10^{22}\text{ keV m}^{-3}\text{s}$$. Its confinement time is $$10^{-10}\text{ s}$$, so we get a pressure of about $$1\times 10^{12}$$ atmospheres.

• Gravity is a source of pressure! Thus it will have an effect! The five answers or whatever it is now state there is no material that can handle the heat - YET WE CAN PRODUCE FUSION - JUST NOT EFFICIENTLY! Thus all those people who googled a paper on fusion MISS THE POINT!!!!! Fusion requires pressure and temperature! The "basics" are simple, the practicalities aren't! Instead of re-posting papers you don't understand, explain WHY additional kinetic energy won't increase heat! This is physics 101! Stop pretending you know the answer if you don't! The responses don't understand the question! Aug 16, 2023 at 1:20
• @DodgyBob Gravity is a source of pressure... for the atmosphere. It is not the source of pressure in current fusion experiments. Fusion requires temperature, density, and confinement time, or you can phrase it as pressure and confinement time (see the triple product discussion in my answer). Additional kinetic energy will always increase heat... that's basically what heat is. I never said anything to the contrary. Honestly I suspect you didn't read any of my answer. Most of what you're saying is addressed in the answer or not in any way a response to anything I said in the answer. Aug 16, 2023 at 8:49

Thus surely if you increase the effective gravity, that would reduce the required temperatures!

It really doesn't. Temperature is effectively a measure of particles speed and KE (across a distribution). That tells you what fraction of them have sufficient energy to overcome the coulomb barrier.

Increased pressure or density might affect the rate of fusion, but it doesn't let you lower the temperature.

the temperatures only need to be higher than a star, due to the lack of pressure - gravity!

No, you need temperatures very similar to that of a star. There are a couple of things that will modify that need:

• Materials. D-T or even D-D fusion can happen at temperatures slightly cooler than necessary for proton fusion.
• Efficiency. Fusion happens at a relatively slow pace in the sun. If you want the energy to come out faster, then a higher temperature greatly increases the rate.
• A tokamak generates 100 million degrees celsius, the sun surface temp is under 5.8k, core temp is "only" 15 million ! Thus your temperature argument CANNOT be valid! Gravity on the sun is 1280G, Pressure to make diamonds is 725 kpsi. We can actually fuse atoms currently on earth, thus increasing the pressure and or gravity, will thus reduce any need for temperature! So why wouldn't a centrifuge make fusion occur at lower temperatures? Aug 16, 2022 at 6:51
• You can increase the rate with higher temperature (the rate of fusion in the sun is orders of magnitude too slow for commercial use). But you cannot remove the minimum temperature requirement with higher pressures. physics.stackexchange.com/questions/281082/… Aug 16, 2022 at 7:52
• Really? You can't quantum tunnel through that barrier? How else do you explain muon catalyzed fusion? en.wikipedia.org/wiki/Muon-catalyzed_fusion Aug 17, 2022 at 2:11
• All fusion rates already include tunneling. The required temperatures would be much higher without it. But it's still common to speak of "overcoming the coulomb barrier". Even with tunneling, the fusion rate is effectively zero below a critical temperature. The point is that realizable pressures don't lower that critical temperature. Aug 17, 2022 at 3:36
• fusionenergybase.com/article/… See the fusion triple product for an explanation of why density is considered one of three key parameters for successful energy-producing fusion reactions. The idea is essentially - all fusion reactors easily have high enough temperature for some fusion reactions to happen. The question is whether or not each nucleus is likely to undergo a reaction before it is lost. Increasing the density increases the number of collisions it sees, each giving a chance of fusion. Jul 20, 2023 at 10:20

Dodgy Bob, I just came across your question and wanted to pass along an experiment I set up years ago to test exactly what were asking in your asking specific to centrifugal fusion.

Here are some of the assumptions I was working with:

Specific to reproducing the Sun's G-force:

Using a pulley wheel that had a curved lip on each side of the wheel I poured deuterium onto the horizontally mounted wheel. The idea here was that, once the spinning started, the deuterium would be held in place within the curve of the wheel's "lip". The speed of the wheel could be tuned to match the required g-force and two copper rods were mounted on both sides of the wheel to allow for the plasma arc on both sides (horizontally). The copper rods were connected to a high voltage plasma generator.

You can see the experiment here at my YouTube site. I did not study physics in college so I still don't understand the results you see in the video. The radiation detector I mounted on the steel cabinet was picking up radiation but I can't say why. Ionized deuterium fused by high voltage is kind of an old school method of fusion that's been around a long time. It's possible that's what we are seeing here. My understanding is that if neutrons were being released they are not picked up by this type of radiation detector and have to be identified by a neutron "bubble detector" which I did not have available.

All in all it was very interesting!

Here is the video:

Centrifugal Fusion Video by Guy Cobb

Simply because gravity is attractive, while the centrifugal force is repulsive. You need a force from all sides in order to do the fusion process.

• The pressure we experience from the atmosphere is in all directions. This is despite the fact that it is generated by the earth's gravity, which only acts in one direction. A centrifuge does the same thing. It compresses a sample by applying a force in one direction, but as the material reaches equilibrium, it can be described as having a pressure, which will indeed be enhanced by the centrifuge. Jul 20, 2023 at 10:29
• Thanks for that. My concept is to provide additional force to achieve the required temperature for fusion. It may well be utterly impractical, it might use way too much energy to achieve. However, hypothetically, would a centrifuge aid fusion? Jul 22, 2023 at 3:01