Why does fusion need to be so hot?

The topic of fuels for fusion is much talked about in the fusion start-up community. What fuel are you using is a common question, particularly from US VC investors.  Yet it is barely discussed in the publicly funded fusion programmes, neither magnetic nor inertial. This post is part of a series where I will outline why it is not discussed in the mainstream of fusion. To me, the answer is simple; it is because deuterium-tritium is the only viable fuel. I will present the analysis and you can make up your own mind.

  1. What are the options?
  2. Why does fusion need to be so hot? – you are here!
  3. The fusion gain limit

The ideal ignition temperature

In the first post in this series, we established the four candidate fuels for fusion power. These fuels have the highest reactivities at the lowest temperatures. The higher the reactivity the more fusion reactions per second, with all else being equal. And we showed that the deuterium-tritium (DT) reaction offers the highest power density across the whole temperature range.

The four different candidate fuels

But how did I decide what range to plot? It was a pretty serious range, from 1 keV (or 10 million degrees) all the way up to 1000 keV (a scorching 10 billion degrees). The centre of the Sun is only 15 million degrees, and the surface a measly 5800 K. Although it’s not the surface that does any fusing, 99% of the Sun’s energy comes from its middle 25%.

The reactivities definitely imply the need for high temperatures. The peak of the DT reactivity is at 65 keV. At this temperature we would get the highest fusion power. If it is colder, we get less fusion, if it is hotter, we also get less fusion. We need to establish, however, what is needed for energy gain. We have to invest energy heating the fuel up to the required temperature, we need to get a return on that investment. And we’re not looking for a 5% interest rate here, that isn’t going to deliver economic power production. We need high gain, many times the amount of energy coming out as going in.

A prerequisite for high gain is “ignition” or “self-heating”. There are many processes taking place inside the fuel. Some of these add energy, like the external heating. In magnetic fusion the external heating is supplied by intense radiowaves and microwaves, and so-called neutral beam heaters, which fire high energy particles into the plasma, normally deuterium atoms. In inertial fusion, it is the implosion itself that provides the heating. The implosion does thermodynamic work, pdV work, on the fuel.

The four main processes important for fusion. Two heat the fuel, the external heating and the self-heating by the fusion process itself, and two take energy away from the fuel, the conduction and radiation losses

There is a second heating mechanism, which is the fusion process itself. Some of the energy released escapes the fuel, some remains. That which remains contributes to the energy balance, helping to heat the plasma.

These two heating mechanisms are balanced by two main processes that take energy away from the fuel. The first of these is conduction of heat to the surroundings, the nature of which differs substantially between approaches. In inertial fusion, the fuel might be surrounded by a shell of much colder material, which means conduction loss will be very important. Or it might be that the fuel is assembled, at the final moment, in vacuum by itself. Conduction needs a material for the heat to flow into, if there is nothing there, there is no conduction. In magnetic fusion, the magnetic fields themselves inhibit conduction, this is almost the point of the approach. Energy is still lost though, the processes involved are complicated, but the end result is that the magnetic bottle is leaky.

The second major energy loss mechanism is universal, present in all approaches, and thankfully it is easier to quantify. This is the energy lost by radiation, which is to say, electromagnetic radiation, photons, light, although not visible. Think about the feeling of warmth you get sitting in front of a fire or stove. You are feeling infrared radiation, light of a particular frequency, and energy is conserved, the light gives energy to you, warming you up, and takes that energy away from the stove. The hotter the fire, the warmer it feels. Or looked at the other way around, the hotter the fire, the more energy it loses by radiation.

In a fusion plasma there is one dominant mechanism producing radiation, which is bremsstrahlung radiation. This word is actually German portmanteau meaning “braking radiation” and in a fusion plasma it occurs whenever an electron is deflected by the presence of an ion. As discussed in the first post, the microphysical picture in the plasma is one of dynamic equilibrium. The ions are flying about crashing into each other, sometimes fusing, sometimes bouncing off. But the electrons are still there too, they can’t disappear, you can’t get rid of them.

When a negatively charged electron encounters an ion, it is deflected on its flight path by the positive charge. The electron can change velocity and direction substantially whilst the ion is basically unaffected. The ion is 3600 times heavier; the electron is like a ping pong ball bouncing off a bowling ball. The energy lost by the electron is converted to photons, which escape the plasma, carrying the energy with them. And at the temperatures for fusion, these are x-ray photons.

We can now put together a simple criterion which will allow us to find the temperature needed for ignition. At low temperatures, the fusion rate has not ramped up yet, and the energy lost by radiation is dominant, meaning that without external heating the fuel would cool down. The point where the fusion energy released first exceeds the radiation loss is called the ideal ignition temperature. It is ideal in the sense that all we are doing here is balancing the fusion power with one specific individual mechanism that produces radiation. A fuller analysis including more losses is going to give a more pessimistic assessment, a higher required temperature.

The ideal ignition temperature also makes assumptions about the fusion energy released. Charged particles produced by fusion, like the alpha particle from the DT reaction, are assumed to stop within the fuel, transferring 100% of their energy into self-heating. The neutrons, on the other hand, are assumed to escape, contributing nothing.

Our criterion is that the energy released by fusion is greater than the energy lost to bremsstrahlung radiation. We can express both processes as power densities, energy released per unit volume per unit time. The answer we will get then doesn’t depend on the plasma geometry in any way, nor on the confinement time. And helpfully both processes depend on density squared, which means that the density cancels out and the result doesn’t depend on whether we at the tenuous densities of magnetic fusion, or the extremes of inertial fusion.

The ideal ignition temperature is the temperature where the fusion power first exceeds the energy lost to radiation, specifically bremsstrahlung radiation. The different fuels, compared to DT, have lower reactivity and lower fusion power density, and DHe3 and pB also have a higher average atomic number and higher radiation loss.

For the different fuels, two parts of the equation change. First, the reactivity is different for the different fuels, and highest for DT. And second, the bremsstrahlung loss depends on the average atomic number of the elements involved. The higher the atomic number, the higher the charge of the ion, the stronger the deflection of a passing electron, and the more energy lost to radiation.

And the answer is that DT needs a temperature of 4.3 keV to ignite, DHe3 comes in second needing 31 keV, and then DD needs 45 keV. The last “option” on the other hand, pB, has no solution, the fusion power never exceeds the radiation loss at any temperature.

Fusion power and radiation loss plotted vs temperature for each of the four fuels, allowing the ideal ignition temperature in each case to easily be seen. The required temperatures for DD and DHe3 are higher than DT, and with pB the fusion power never exceeds the radiation loss at any temperature.

It is also interesting to look at the ratio of the fusion power to the radiation loss. This gives a sense of the margin that we have in hand. There is conduction to account for, and other mechanisms of radiation emission that add on top of the bremsstrahlung number.

One example of an additional process is radiation from impurities; impurities make the bremsstrahlung loss worse. Impurities will have a higher atomic number. Tungsten, for example, which is used on the inside of tokamaks, has an atomic number of 74, meaning that the Z squared factor in the equation is about 22,000, implying that with only 0.02% admixture the radiation loss would be doubled.

Depending on the margin that might not be fatal. For DT the maximum ratio of fusion power to bremsstrahlung loss is 33, fusion is 33 times more powerful, and this occurs at a temperature of 39 keV, not much more than the table stakes for the other two fuels. For DHe3 the maximum is 6.5 and for DD it is 2.9, both occurring at extreme temperatures. I really don’t like the idea of a margin less than 10, and less than 3, it isn’t going to work. And for what it’s worth, the maximum ratio for pB is 0.43.

The ratio of the fusion power to the radiation loss, showing the margin that each fuel has to cope with deleterious additional processes not included this simple analysis.

To close, in the first post we identified the four fuels with the highest reactivities. DT had the highest power density, but we didn’t know what else we needed, any of the fuels might have worked even if DT produced the most power. In this post we’ve seen that the need to exceed the radiation loss has boxed us in hugely. DT is still looking good, but the other fuels require higher temperatures and are significantly more marginal. The advantages of DT are stacking up. In the third and next post, we will finally talk about energy gain.

And I will return to pB. Whilst the nail put in the coffin here is pretty big, we’ve not yet considered everything.

19 thoughts on “Why does fusion need to be so hot?”

  1. Thanks for another great post, this really is a great justification for DT fusion. So when you say, having a low Bremstrahlung radiation to Fusion energy ratio “won’t work” that means the reaction, at least within the reacting core, is cooling down. So unless new energy is injected from outside it will start to stop fusing soon. So it seems the key here is how quickly that detrimental cooling occurs and how quickly you can put that energy back in again.
    For first light fusion it seems you have only one shot per target to attain that heating so DT is ideal. You may well also benefit, at least partially, from Bremstrahlung radiation heating the Lithium shower. It is not so clear to me what happens for the other approaches. I can imagine this is particularly critical for Helion’s aneutronic DHe3 approach. They can’t get that heating by adding more DT reactions in the mix because their design approach is to avoid neutrons. The fact that they extract energy from induced current from charged-ions fusion-products means the significant energy created by Bremstrahlung radiation will just be lost. Would you agree, that if they can get their approach to work, it would appear to be on very slender energy margins? Or am I missing something?


    1. I think these things will make more sense with the next post. I just asserted the need for ignition here. The reason why will become clearer when we look at what is needed for gain. I’ll also make sure to discuss what energy can be captured by which method. X-ray energy can’t be captured by direct conversion from the plasma, exactly as you have it. Please keep the questions coming! I’m going to collate and answer them all together as the final post in the series.


  2. The other thing that I wondered about was that you use PMMA plastic for the targets. I assumed this was originally for ease of prototyping. You would move onto something more inert like glass or ceramic for the eventual power station, as it might produce gases that may be difficult to pump out in time, or leave moving sirfaces with hard to clean residues. Now I see PMMA with Carbon Hydrogen and Oxygen might be ideal in terms of Bremmstrahlung radiation. I just wondered if you could share some thoughts on the choice of target material in terms of this and its impact on machine uptime and ignition frequency.


    1. I think adjusting D-He3 for potential high efficiency energy recovery would give it an effective margin of about 10 relative to D-T. It does seem to have only one reactor design with a shot at working for it but to that extent I think it can be said to exist as a fuel candidate

      I have heard a few mentions of pB11 and D-He3 recovering brehmsstralung with solar panel like converters. This probably still doesn’t make pB11 a likely candidate but it sounds interesting for D-He3


      1. Hi “da Wolfe”, Thanks for replying. It would be great to understand where you got that 10x number from. None of the physics Nick describes would account for that. so what is missing from the equation?


      2. Steam engine efficiency is 35-40% for Lithium blamnket approach, so that only gives at most a 2.5x efficiency gain.


      3. Solar panels don’t work for x-rays I’m afraid. And I’m not sure what you mean with the factor of 10. I’ll be going through the energy balance stuff in the next post.


      4. Yeah, sorry for the early twenties somewhat edgy username, I couldn’t change it when I went to make the comment lol

        The 10x number is referring to the maximum ratio of fusion power to bremsstrahlung loss. 33 for DT, 6.5 for D-He3. If D-He3 for Helion can recover the energy 2x better then normalizing the ratio gives you 33 – 13

        For a favorable engineering design like First Light that makes DT look better while a tokamak with high construction and maintenance costs might look worse than D-He3 for Helion. I’ve heard some rumors that Trenta’s physics performance means at this point it also doesn’t have a relative physics risk to tokamaks


    2. If those elements got into the fuel, they would increase the radiation loss, which would be a bad thing. In our system, basically all the target material is going to react with the lithium after the shot and will need be extracted from there.


      1. For the eventual Powerplant does it make economic sense to purify the lithium and extract tritium all in a closed cycle system on site, or would you eventually have some central processing service serving multiple fusion reactors?


  3. General fusion uses lead in its blanket which has a Z of 82 compared to 22 for Titanium. While they should be able to capture the heat this heat in the blanket, it suggests the increased bremsstrahlung radiative cooling of the fusion reagents may be a challenge.


    1. Maybe the lead is useful for absorbing the bremsstrahlung radiation and converting it to heat. Lead is a preferred material for absorbing X rays.


      1. In a recent r/fusion post “3 recent Fusion vendors presentations from PPPL Colloquium” Michel Laberge mentioned the choice of lead for General Fusion. In the FDP demo plant they’ll use lithium for maximum velocity for the purpose of getting to the physics parameters they want, but lead is probably needed in a power plant to increase the dwell time of the implosion allowing for more fusion before the plasma expands again

        They are worried about lead getting into the plasma but at least sound confident they can clear it between shots


    1. As I understood their argument, this is possible because most of the heat is in the ions and not the electrons. and this was due to the high beta configuration. Just wondered what others opinion was on this.


      1. The different ion and electron temperatures will affect the brem loss, which is a function of the electron temperature. I’ll explore this in a future post. Being high-beta itself will not change the brem loss, you can’t stop particles from bashing into each other. At least, it won’t affect it a huge deal, the specific formula should indeed be different but I doubt it changes the picture substantially. What is going on here is that David is describing changing the temperature of the system but at the same plasma pressure. If the plasma is hotter but the same pressure, the density must be lower. So as you go from left to right on this plot density is sort of a hidden variable, and it is decreasing. The brem depends on temperature to the power half but density squared, so density wins and the brem goes down


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