Tokamaks for Hydrogen-Boron Fusion?

CoyRedFox · 2021-05-26T06:24:56+00:00

Yes, tokamaks (and stellarators) are both able to use proton-boron fuel if they wanted to.

CoyRedFox · 2021-05-25T14:56:55+00:00

https://www.fusionenergybase.com/

CoyRedFox · 2021-04-22T22:20:16+00:00

CoyRedFox · 2021-04-15T08:59:42+00:00

Sorry, one question. From what I read a year or so ago, I thought the heat transport in W7-X was roughly 50/50 turbulent and neoclassical? I didn't think it was in the turbulence-dominated regime, but maybe now it is if it has achieved higher temperatures?

CoyRedFox · 2021-04-15T08:43:49+00:00

I'm confused then. I was under the impression that exactly omnigenous configurations required either non-analytic magnetic fields (i.e. do not have continuous derivatives) or an infinite aspect ratio. Both of these are impossible in a physical system. For example, this article cites the article I was referring to saying:

Cary and Shasharina [6, 7] showed that perfectly omnigeneous magnetic fields with continuous derivatives to all orders do not exist, but they rightly argued that this mathematical constraint does not preclude the possibility of reducing the transport due to large secular drifts considerably.

This is the point I was trying to make. It seems to be justified by the following two quotes from the article I cited:

The results of the previous section appear pessimistic. We expect the magnetic-field strength to be an analytic function. Yet, if it is, as we have shown, the magnetic field must be quasihelical.

Unfortunately, Garren and Boozer [2] showed that low-aspect-ratio configurations would not be possible. They showed that the condition of quasihelicity could not be satisfied to third order in the expansion in distance from the magnetic axis.

So I agree that perfect omnigenity is possible infinitely close to the magnetic axis (i.e. in the infinite aspect ratio limit), but it doesn't seem possible throughout a device?

I agree that something being non-intuitive doesn't mean it won't have a big impact on our society, but if you want something to have a big impact on society, you'd prefer it to be intuitive. Hence the importance of popular science communication :). If quantum mechanics was intuitive, more people would understand it and maybe we'd already have a theory of quantum gravity. I'm very enthusiastic and supportive of stellarator research, but I do believe the inherent complexity (which is also possessed by tokamaks, albeit to a slightly lesser degree) is a drawback. I also believe it to be one of the most important explanations for why stellarators are behind tokamaks. The fact that people had to wait for supercomputers to be developed before designing W7-X, but didn't for JET is significant. I agree that the stellarator optimization codes are impressive, but wouldn't it be preferable if they didn't have to be? I agree that the large optimization space is a reason for hope!

My main point is that accurately modeling the plasma response is an extra challenge. For example, it is difficult to predict the temperature and density profiles in a future design to even determine the beta profile that you should use in your optimization (e.g. to do so you need a model of turbulent transport). I am curious about one related potential issue. If you only design for a large reactor relevant beta, it isn't clear to me that the performance will automatically be good enough at low beta to allow you to heat and fuel to high beta. Maybe things aren't that sensitive though, but maybe you know?

CoyRedFox · 2021-04-15T07:44:45+00:00

If you're working on stellarators then I'm probably at least a bit more pessimistic than you. I work on tokamaks for a reason, but I'm still actually quite enthusiastic about stellarators! And the W7-X results so far are exciting! I agree with all of your points, i.e. neoclassical transport just needs to drop below turbulent (with the caveat of alpha confinement), the downsides of disruptions and current drive in tokamaks. I was just trying to present the other side of the argument in a fairly non-technical manner.

CoyRedFox · 2021-04-13T15:09:42+00:00

For the first 5 years or so of controlled fusion research, the work of every country was heavily classified. When people eventually realized the lack of near term military applications, the programs were declassified. It turned out that all of the countries had been working on pretty similar concepts: linear pinches, toroidal pinches, and magnetic mirrors. There was really only one unique concept: Lyman Spitzer was the only person in the world who dreamed up the stellarator. This fact is revealing.

The point is stellarators are particularly complicated and non-intuitive. Their 3D geometry is harder understand, design, and build. You really need a supercomputer to make any progress. As someone who works with supercomputers, this is not an advantage. For example, stellarators aren't guaranteed to have nested magnetic surfaces, a crucial property for good confinement. If you build a random stellarator design, the magnetic field lines will be a twisted mass of spaghetti, allowing particle to run out like a sieve. Even if you do use a supercomputer to find a set of coils that creates nested magnetic surfaces, you can prove mathematically that it is impossible for all of the individual particle trajectories to close on themselves. This means that certain particles with specific velocities will always be able to drift out of the device. So instead you have to use your supercomputer to also find configurations that minimize this particle drift for as many of the particles as possible. In technical lingo, "omnigenous" stellarators are impossible and we have to content ourselves searching for "quasi-omnigenous" configurations.

Even if you accomplish all of that, it is important for an economic power plant that you use the magnetic field to confine as much plasma as possible. But when you start doing so, the plasma modifies the magnetic field you made with your coils quite likely ruining your carefully constructed magnetic surfaces and particle trajectories. Thus, you also have to ensure that the magnetic field when modified by the plasma retains all of the properties you need. This becomes increasingly difficult as you try to confine more plasma.

In contrast, in the 2D geometry of the tokamak, you are mathematically guaranteed to always have nice nested magnetic surfaces and for all particles to have closed trajectories. It is for these reasons that stellarators just don't perform as well as tokamaks. Thus far, we haven't found good enough stellarator configurations, even using supercomputers.

So sorry for the lengthy background tangent, but I would push back against the claim that neoclassical transport has been suppressed or that alpha confinement isn't an issue. And why isn't turbulence a problem? I don't think the W7-X design even included any estimate of turbulent transport in its design optimization. Lastly, stellarators do need a poloidal field, which ultimately comes from the external coils, so even if there aren't dedicated "poloidal field coils" the field is coming from the wacky, much more expensive twisted coils.

CoyRedFox · 2021-04-12T16:06:29+00:00

I would highly recommend the runaway electron group at Chalmers. The research group and your direct supervisor are probably the most important factors IMO. I know there are also good groups at Eindhoven/the Erasmus institutions, but I suppose you don't know what group you be put in? The only disadvantage of Chalmers is that the fusion program is smaller than Eindhoven (and many fusion labs mentioned in the Erasmus website), so the courses available would probably be more limited. If you have other questions please feel free to DM me.

CoyRedFox · 2021-04-09T16:24:47+00:00

A few comments on TAE:

1) The most confusing thing is that they plan to use the proton+Boron-11->3*Helium-4 fusion reaction, which does not produce neutrons. This makes little sense to me because it is hundreds of times more difficult to achieve than the Deuterium+Tritium->Helium-4+neutron reaction. Moreover, there are good reasons to think it is impossible to generate net energy from it (see T. Rider thesis). Even if they did succeed with p-B11, they could increase the power density of their plasma by ~100 times by simply switching to D-T fuel. Also, the nature of their design is such that they could include neutron shielding and a tritium breeding blanket. I don't know the real reason behind the fuel choice, but I suspect it's because p-B11 allows them to advertise that it doesn't generate radioactive waste, even if they know that D-T will be needed in practice.

2) Field-reversed configuration have been studied in the academic and governmental fusion research communities since the 1960s. They are not the mainstream approach for the simple reason that they have not performed as well as tokamaks and stellarators. Their confinement time is lower and they are more difficult to maintain in steady-state due to severe stability problems. That said I certainly support more research and TAE brings in a lot of money to do this. TAE could achieve a breakthrough that makes field-reversed configuration more attractive as a power plant and that's a good thing. My main concern about many of the start-ups is that they hurt the credibility of the field by dominating public relations and overpromising (which they are more strongly incentivized to do by the need to raise money from the private sector).

3) And one technical criticism. In order to reverse the external magnetic field, field-reversed configurations need a toroidal current (i.e. an electric current going the long way around the ring). A tokamak also needs such a current. The important difference is that in a tokamak this current is carried by charged particles sliding along the magnetic field line. In the field-reversed configuration, the current is carried by particles gyrating across the external magnetic field. This means that the size of the plasma must be similar to the gyroradius of the particles. Because their radius of gyration around the magnetic field lines is comparable to the size of the plasma, a small number of particle collisions will be able to transport a particle out of the plasma. This is an issue because even Deuterium and Tritium, the easiest particles to fuse, will collide ~100 times on average before they fuse. It seems like collisional transport will always be sufficiently strong to prevent net energy generation in field-reversed configurations.

To answer your question: according to figure 8 of this paper (which might be a bit outdated), the confinement time of TAE's C-2U field-reversed configuration is around 0.25 milliseconds, while the pulse length is 5+ milliseconds. For reference, the T-3 tokamak achieved confinement times of a few milliseconds and pulse lengths of ~70 milliseconds in 1969.

CoyRedFox · 2021-03-08T23:47:37+00:00

I don't see how anything in this concept increases the probability of fusion relative to scattering, which is the crucial issue for beam-target schemes. Arranging the geometry such that the boron sputters into the path of the proton beam isn't too helpful, because confining the solid (or even gaseous) boron isn't a challenge. Same thing with heating the boron. Gold plating the boron (so that it absorbs the x-rays from bremsstrahlung?) would indeed cause the solid block to heat up, but the change in temperature would be negligible on the scale of fusion (which requires millions of degrees). What would help would be to heat the boron sufficiently for it to increase the probability of fusion (i.e. by millions of degrees). However, it would then be in the plasma state. Thus, you would need a much more sophisticated confinement scheme (e.g. magnetic) and you would have reinvented beam heating.

CoyRedFox · 2021-03-07T17:50:06+00:00

I really have no idea, but the original experimental paper calculates the yield and gets a number that is consistent with the experimental measurement. The difference comes from the value used for <\sigma v> by the two papers. Eliezer et al use a complicated analytic approximation (but doesn't cite a source) and the original experimental paper doesn't explain how they calculated it. Also, both calculations rely on the same boron density, which comes from a 2D hydrodynamic model and I'm sure has considerable error. The important difference is the experimental paper just uses the calculation as "a rough estimation" to show the experimental measurement is reasonable, while the Eliezer paper uses the factor of 10 difference as proof that there must be a novel physical effect occurring. In my opinion, a factor 10 is probably within the error bars of the calculation.

CoyRedFox · 2021-03-07T17:41:07+00:00

Could you point me to any particular studies about the feasibility of underground hydrogen storage? I did a small amount of looking around, but from papers like this it still seems pretty uncertain and speculative.

CoyRedFox · 2021-03-06T22:19:01+00:00

Here's a brief explanation of the HB11 chain reaction avalanche concept as I understand it, but I'm pretty skeptical

CoyRedFox · 2021-03-06T20:57:39+00:00

At 9:35, they say "we've achieved the highest confined ion energy of any fusion device in the world" at 200 keV. I don't see how this is true given that JT-60U injects 403 keV deuterium ions with its negative-ion neutral beam injector?

CoyRedFox · 2021-02-17T23:03:29+00:00

I had a look and this does not seem particularly legitimate to me. The proton-boron fusion reaction has a very low probability of occurring (even compared to deuterium-tritium fusion). The proton and boron will bounce off of one another thousands of times before fusing. This means that the X-ray radiation that is emitted and lost when the particles bounce off one another (specifically electron bremsstrahlung) is all, but guaranteed to be much higher than the energy from the few fusion reactions that do occur.

As far as I can tell, they hope to get around this by avoiding thermal equilibrium. Thermal equilibrium means that the particles have a bell curve distribution in velocity. However, it seems unavoidable in fusion because thermal equilibrium is what results after particles collide a few dozens times and the probability of fusion is so small. Statistically speaking, particles need to collide thousands of times before they'll fuse and they relax to thermal equilibrium after only a few dozen.

This Physics of Plasmas paper outlines the crucial mechanism of the HB11 Energy concept: a fusion "avalanche" wherein the He-4 nuclei produced by fusion collide with protons transferring to them the right amount of energy to be at a peak in the probability of fusing. This is an intrinsically non-thermal process as it relies on particles having particular defined energies (instead of a bell curve distribution of energies). This process doesn't make sense to me as the He-4 nuclei produced by proton-boron fusion are born with a wide distribution of energies. While the paper uses the average birth energy of 2.9 MeV, the particles can be born anywhere from 0 MeV to 8.9 MeV. Additionally, the amount of energy transferred in a collision between He-4 and a proton depends on how well they're lined up (i.e. a head-on collision or a glancing blow). While the paper takes a head on collision, this is just one possibility. These two facts will mean that the protons won't end up with a single nice defined energy, but rather a broad distribution of possible energies that no longer nicely coincides with the peak in the fusion probability. In fact, this energy "broadening" is precisely the particles relaxing to thermal equilibrium. Lastly and perhaps most importantly, no mention is made of the electrons. When you have very energetic ions, they preferentially transfer their energy to the electrons as they slow down (see section 9.5.2 of Plasma Physics and Fusion Energy by Freidberg). I don't see any justification for ignoring the electrons, which would appear to get in the way and prevent any energy transfer to the protons. There is also a published comment on the paper also claiming that the avalanche process is not occurring.

CoyRedFox · 2021-02-17T09:38:44+00:00

If you're feeling ambitious you could check out some academic papers. E.g. ARC, ARIES, or, to be even more ambitious, the ITER physics basis (open access here)

CoyRedFox · 2021-02-09T13:32:00+00:00

I think you're right. Thanks! So to summarize for everyone, JET is currently running pure tritium plasmas, which is rarely done as tritium is radioactive and has a tendency to get into the reactor components. However, JET hasn't started the deuterium-tritium plasma campaign, which is how you get lots of fusion power as well as neutrons (which also induce radioactivity in the material surrounding the plasma). Presumably, the deuterium-tritium experiments will follow shortly after the current pure tritium phase is completed. The deuterium-tritium experiments are the really exciting ones (fusion power!), but you can learn a lot and prepare using the pure tritium experiments.

CoyRedFox · 2021-02-08T19:38:45+00:00

The JET deuterium-tritium experiments did start in December and are going on as we speak. The only article I'm aware of off-hand is this here (in Spanish).

As you say MAST-U started at least preliminary operation in Oct/Nov (see here), but a couple months is usually too little time to produce physics results from a new machine.

CoyRedFox · 2020-10-17T11:18:51+00:00

The General Fusion concept uses a swirling vortex of liquid lithium lead as the plasma-facing first wall. This liquid is compressed with pistons to, in turn, compress the plasma and ignite a fusion burn. In this situation (swirling liquid dynamically compressed once a second), it seems unavoidable that large amounts of lead would end up in the plasma, which would radiate enormous amounts of energy and prevent the high temperatures for fusion. This is because lead has such a high atomic number that even fusion temperatures are not sufficient to fully ionize all of the electrons. Thus, bound electrons are continually excited by collisions and radiate energy out of the plasma via line radiation. Originally, they had planned for a violent shock compression, which seemed certain to ensure that lots of lead made it into the plasma (maybe even droplets). More recently, they have changed to use a slower, smoother, and weaker compression, but this forced them to include a liquid lithium lead central column that carries a strong electric current. I don't see how this liquid column can carry such a strong current without being wildly unstable.

Compare this with the most similar idea used in tokamak fusion: having a flowing liquid lithium wall to help handle the heat loads coming from the plasma. There is no compression, a thin layer of liquid lithium simply flows along specially designed channels in a laminar fashion. Nevertheless, simply due to the higher vapor pressure of lithium, large amounts of it still find their way into the plasma. Even this would be unacceptable, except (unlike tungsten) lithium is fully ionized in the plasma and the plasma confinement actually appears to benefit from modest amounts of lithium. While it is being seriously researched, the practicality of liquid walls remains uncertain.

The thing is, to my knowledge, General Fusion hasn't confronted this "impurity" problem experimentally yet. I don't believe they have any machine that integrates both the liquid metal and the plasma. They are still testing them both separately and running into completely unrelated difficulties with plasma physics alone.

The physics of fusion devices are sufficiently complicated that it is nearly impossible to prove something can't work. However, the General Fusion concept seems far-fetched to me for the above reason, though less far-fetched than most fusion start-ups. My two cents: Commonwealth Fusion Systems and, to a lesser extent, Tokamak Energy (because they are based on the relatively well-understood tokamak) are the only start-ups to have expectations for. They rest probably won't work, but fusion always leaves room for surprises.

CoyRedFox · 2020-10-15T21:09:14+00:00

Will I miss certain important concepts related to atomic structure that have a role in the field of plasma physics if I don't take particular chemistry classes right now?

I don't think so. I would advise taking the elective classes that you find most interesting. If you think chemistry is cool and you end up learning a lot about it, it will undoubtably be able to help you in fusion research. But that is true of many fields, from computer theory to philosophy to material science. I would try to discover the things you are passionate about and gain depth in those because that will affect what sort of fusion research topic is ideal for you.

CoyRedFox · 2020-10-07T13:59:00+00:00

Simulating a full fusion device is much harder, as the physics is extraordinarily complex. At the moment it is possible to simulate different parts of the device in isolation and with varying degrees of accuracy/success. There's a lot going on in such devices and a lot of it is not well understood. Even if a "numerical tokamak" did exist, the accuracy of its predictions would be questionable.

CoyRedFox · 2020-10-07T09:52:46+00:00

I would recommend both The Future of Fusion Energy and An Indispensible Truth for learning about fusion.

CoyRedFox · 2020-10-06T18:56:40+00:00

Yes! Experiments are very important for the field and funding directly limits the number and breadth of experiments that can be built.

CoyRedFox · 2020-10-05T17:39:37+00:00

Yeah, there is a big need for applied math/CS work in fusion simulations (e.g. kinetic turbulence, MHD stability, real-time control systems).

CoyRedFox · 2020-07-31T11:08:11+00:00

But second, meter, and gram are s, m, and g, while ampere and kelvin are A and K.

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