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Will Helmholtz coils allow fusion reactors?

Ariel Sharon died, RIP, the new (and optimal) Czech ambassador to Slovakia, Livia Klausová, is facing tons of vitriol from 95% of the Internet commenters – a screwed rabble – but I will talk about some potentially pleasant developments in the fusion research. (Some local good news: the babe MP who was the victim of a recent acid attack in Pilsen seems to be out of lethal danger. The tubes are gone, she can talk, and is interested in their puppy. Some extra good news: Google cooled its relations with an ex-German leader and freshly renamed Berlin's Adolf-Hitler-Platz to Theodor-Heuss-Platz.)

First, a political advance. Science Magazine mentions that the European grant agencies will no longer throw the money to the fusion research without any feedbacks. Instead, some of the sponsors have apparently realized that the construction of a working fusion reactor (before 2050) is a goal. The apparatchiks' brains must be really fast if they only needed 60-90 years for this realization. ;-)

The Z-machine (see the 8-minute intro video above) will be discussed below the following paragraph.

In unrelated news, MIT boasts that the 2010 MIT paper I-Mode: An H-Mode Energy Confinement Regime with L-Mode Particle Transport in Alcator C-Mod. by D.G. Whyte et al. (journal) has won a prize from the International Atomic [sic: should be Nuclear] Energy Agency. It's about an improved confinement technique, much like the story I want to focus on in the rest of this blog post.

The main story is about the Z-machine at the Sandia Labs in Albuquerque, New Mexico (see a 2006 TRF comment; don't confuse it with the NIF in Livermore) which managed to reduce the instabilities by a 19th century effect. See

Fusion instabilities lessened by unexpected effect (Sandia news release)

Fusion: Now With Less Instability, Thanks To A 19th Century Technique (
The improvement is simple and was explicitly stated and calculated by Hermann von Helmholtz in 1873.

What is the Helmholtz coil?

Well, it's simple. It's a pair of coils with the same current \(I\). Their radii are \(R\) and they're located in the planes \(x=\pm h/2\). What is the magnetic field and its derivatives near Sheldon's place \((0,0,0)\) (OK, I forgot another zero)?

Well, there is some magnetic field \(\vec B = (B,0,0)\) over there. But from the symmetry considerations, it follows that the odd \(x\)-derivatives vanish (the first one and the third one, for example). However, the second derivative \(\partial^2 B / \partial x^2\) doesn't vanish in general.

However, it may be calculated that for \(h=R\), when the side view of the coils looks like a 2-to-1 rectangle, we actually have\[

\frac{\partial^2 B}{\partial x^2} = 0\quad {\rm at}\quad x=0.

\] And that's cool because the magnetic field is really uniform near the origin. Just write down the magnetic field as a Taylor expansion and see how many terms are zero! Aside from the constant term, the expansion starts with the \(x^4\) term which is really small for \(x\to 0\).

Finally now, in the 21st century, they also had the idea to forget about all the illogical and speculative excuses and realize this observation by von Helmholtz in practice. The experimental result showed that the magneto-Rayleigh-Taylor instabilities (which apparently thrive on inhomogeneities) were really suppressed dramatically: PRL. So the macroscopic derivatives of the magnetic field, and not just its random wiggles, matter. What a "surprise".

Thomas Awe looks at the helpful coils.

These folks may ask your humble correspondent to propose a geometry that will guarantee that the fourth derivative of \(B\) will vanish as well, and the sixth one, and so on, so that they may add another cute experimental publication (if not a working reactor) sometime in the 23rd century.

It's great that this progress has occurred but the apparent previous inability to suppress the most evident sources of inhomogeneities and instabilities – something that is obviously the greatest engineering obstacle decelerating the construction of fusion power plants – fills me with a worry that the people employed in this research are insufficiently competent or clever.

TV, off-topic

I saw The Last Mimzy (2007) for the first time. Brian Greene starred as a top Intel scientist. It was a cute sci-fi movie and $27 million in the box office surely looks undeservedly low to me.

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reader Gene Day said...

Every physics grad student and most undergraduate physics majors are familiar with Helmholtz coils. I agree that it is disturbing that it took so long to come up with this application. After all, these folks spend most of their time thinking about the behavior of plasmas, don’t they?. There is something fishy here.

reader Luboš Motl said...

Right, Gene.

You may read the articles, e.g.

that explain why this was "assumed" to be a bad idea, without attempts. I find them unconvincing.

reader Curious George said...

How exactly does a very homogeneous external magnetic field help to confine a plasma? And does anybody have an idea how to use a plasma - should it be stabilized and confined - to generate energy (other than via a steam turbine)?

reader Andre said...

It is worth mentioning that the Z machine had a different purpose when it was designed.

reader Dilaton said...

It is better to have no reports about theoretical physics at all, than the distorted sensational dilettante ones you suggest ...

Actually, most of the popular media do exactly what you suggest (if they do not even outright attack theoretical physics to make things even more "interesting" and "controversial"), which is very harmful to the picture of fundamental physics in the lay public ...

reader Svik said...

The small constant field works like a cap and filters out transients. Better than busting stray fields

reader Rehbock said...

Too often what I find is that which would be easy to understand were it correctly understood and correctly explained is made confusing and controversial by such sloppy simplifications. It is much harder to unlearn.

reader Gene Day said...

The field is far too weak to aid in the plasma confinement, George. It serves only to reduce density variations at the very beginning of the compression process.
These initial fluctuations are probably quite small and due to unavoidable quantum effects, basically, the uncertainty principle. It is likely that a stronger applied field would yield even better results but strong magnetic fields are difficult to achieve with Helmholtz coils. I would be willing to bet, however, that there are other geometries that can produce a more optimum result while maintaining adequate homogeneity.

Similar quantum effects led to density variations in the early universe and are observed today as small variations in the blackbody temperature of the CMB (cosmic microwave background). Studies of the CMB have led to an astonishingly rich trove in our understanding of the early universe. It is just amazing!

reader Gene Day said...

After some thought I am more forgiving of these folks, Lubos. Frequently, that which seems obvious to an outsider is not so obvious to a person deeply immersed in the work. Detailed information may actually lead in the wrong direction, making this a real invention. I have seen this effect in patent prosecutions, for instance. Not seeing the forest for the trees is a real phenomenon.

reader BobSykes said...

Back in the late 1970's, Science had a three (?) part series on the tokamak design. The authors concluded that even if it worked, the electricity produced would be an order or magnitude more expensive than that from a fission reactor. At that time, fission reactors were very expensive; they're better now. The tokamaks would also be huge.

As a result, the tokamak would have no conceivable civilian or military use, Aliens not with standing. We are now 40 years into fusion research with literally no results for any of the proposed techniques. The tokamak fiasco has been especially embarrassing, and has wasted billions of dollars the professional lives of thousands of gifted physicists.

reader Ali Shehper said...

Is it the right sequence to learn bosonic and supersymmetric string theories first, then coming to topological string theory or the other way round - i.e. reading topological string theory from books like 'Mirror symmetry' by Hori et. al and then moving to Green/Schwarz/Witten or any other textbook of String theory for that matter?

reader Gene Day said...

It is a very tough problem. I consider it unlikely that my grandchildren’s grandchildren will enjoy the fruits of this research.

reader Gene Day said...

The applied field is not small; it is 7 teslas or 160,000 times stronger than the earth’s average magnetic field.

reader strictly speaking... said...

Tokamaks may not be very viable for cheap power generation, but that doesn't mean that they don't have their uses. A self-sustaining Tokamak fusing deuterium and tritium will produce a massive ammount of high energy neutrons - for free, since it's self sustaining.

This could be very useful for a number of applications. One military application would be exotic fission fuels such as Americium 242m, which could completely blow Plutonium out of the water for compact thermonuclear weapons.

Civilian application would include neutron-activating the most dangerous radioactive waste from nuclear power plants to speed up their decay.

Once you start looking at what Fusion reactors can do beyond generating power, you'll see that they are a very useful tool for nuclear scientists, which is why designs that are inherently impossible to use for power generation such as the US national ignition facility get massive DoD funding.

Of course, this is not something that would sound particularily enchanting to the general public, so most of the PR concentrates on cheap and clean power.

reader John Archer said...

@W. A. Zajc: Nice quote selection.

However, I found the article a bit of a curate's egg, and rather weird.

When reading it I veered between "Yeah, stick it to 'em!" and "WTF?!". I stopped reading halfway through and skimmed the rest as I got fed up with the dissonance.

A lot of the attitudes he describes and implies are mainstream in some way I simply don't recognise. (Maybe I don't read in the right areas? Yeah, that must be it. I probably need to read the Guardian more — f##k that!) But some I do. For example, giving Dawkins (albeit indirectly) a good kicking for his ranting atheistic dogmatism is laudable. But then Nagel, whom Gelernter applauds, we're told is an atheist himself! Unh? Anyway, how the fcuk do Nagel and Dawkins know*? In particular, Nagel himself is something of a dogmatist too, only (presumably) not as strident as Dawkins! Doh!

Oh well...

A quick mention in dispatches: Gelernter, however, scores lots of Brownie points with me for his italicising of unacceptable. I know EXACTLY what he means. Indeed I look forward to the day when a jackboot immediately stomps on the face of anyone who uses the word. The same goes for unhelpful and inappropriate.

* I see both theists and atheists as two sides of the same coin. My response is: "Why even bother having an opinion let alone expressing one as there's no way of telling either way?"

reader HelianUnbound said...

It's hard for me to understand why the European science community isn't screaming bloody murder over the gross waste of potential research money on a white elephant like ITER. Tokamaks will never be able to compete economically with fast breeders and other alternative power sources, at least for centuries to come. As for the military applications, I'll believe them when the weapons designers at LLNL and LANL show even a faint interest. The NIF's military applications are obvious, and are the main reason it was built. Not so ITER. A copious source of neutrons? I don't think so. They'll need all the neutrons they can get to breed the tritium they need to keep the thing running. Am242m?? I'd call that a bug, not a feature. There's certainly little if any military need for it, but terrorists would drool over it. The last I heard, they're not even planning to fuel ITER with tritium until 2028. Nothing like job security for welfare queens in white coats.

reader Luboš Motl said...

Sorry, Helian, I am confused. Breeder reactors are about fission and heavy nuclei, right? Tokamak is fusion (of light nuclei).

I surely consider fusion power plants, if constructed, a vastly superior source of energy/ And yes, so far, I think that tokamaks are still the most sensible path to a working prototype. So I don't understand your criticism of them.

The total cost of ITER issomething like 15 billion euros. I find it ludicrously low and would have no trouble with paying 10 times more than that, especially because hundreds of billions of euros are *annually* wasted on the carbon hysteria which is complete, utterly unscientific nonsense.

reader HelianUnbound said...

There is no question in my mind that both magnetic and inertial confinement fusion are scientifically feasible. However, IMHO neither of them will ever be cheap in comparison with, for example, fast breeders, not to mention coal, for centuries to come.

In the case of magnetic, the fuel won't be "free" because tritium must be bred. In other words, in addition to the enormously expensive super-conducting magnets, some kind of a blanket must surround the plasma that will breed tritium from the fusion neutrons. The tritium must then be somehow extracted in a way that allows none of the slippery stuff to escape to the environment, provoking the usual howls from the usual suspects. Structural materials will quickly be embrittled by the 14 plus MeV fusion neutrons, and must somehow be annealed in place or replaced. As you probably know, the current version of ITER has been dumbed down considerably from the original proposal, from a full reactor to what really amounts to just another, albeit bigger, JET or TFTR. The reason is cost. Add to the cost of the original version of ITER all the technology needed for tritium breeding, electricity production, etc., and there is no way it will ever be competitive, even if we start building lots of them. I will gladly make a bet with you that this will be as true 200 years from now as it is now, to be paid off by our closest genetic descendants. Of course, we won't be around to make them pay up, but we can always pronounce our ancestral curse on them if they don't.

Don't trust the official cost studies. I took part in such a study for inertial fusion reactors, funded by the US Department of Energy. It was simply understood that the cost would come out "right," and the real potential cost drivers were ignored. The same is undoubtedly true of the magnetic fusion reactor design studies. I can guarantee that they will inevitably return a competitive cost, which will inevitably be bogus.

Breeder reactors aren't a perfect solution to the problem, but there is no perfect solution. They have the advantage of being a mature technology, with manageable problems, capable of producing enough neutrons to burn the long lived transuranics and even the nastier fission products of current reactors, so that the waste will be less radioactive than the original ore in hundreds, not tens of thousands of years.

Meanwhile, some whiz kid may yet find a clever way to defeat the Coulomb barrier and enable fusion power using some as yet unknown technology that will actually be competitive with the alternatives. One must, of course, hope that he doesn't enable pure fusion weapons at the same time.

reader TomVonk said...

I have been discussing with a guy working on ITER a few years ago and to illustrate the huge engineering difficulties of building sustainable fusion reactors, he has shown me a mundane effect that most lay people don't even think about - the electromagnetic forces.
One of the potentially deadly consequences of plasma disruptions are induced torques and stresses.
While the stresses brutally appearing inside the material can be 300 bar what is big but manageable, the torques go almost instantaneously up to more than 10 tons.m.
Useless to say that these effects can utterly destroy, rip out and otherwise bend out of shape any metallic parts.
This is one of the reasons why plasma disruptions must be avoided at all costs.

See :

reader stringpyre said...

But you do UNDERSTAND exactly what Justin is saying. Bell's inequality has proved time and again there are no hidden variables. It is spooky and it directly challenges reality. The stringers hate it and we all know why. So Susskind their Lord of the strings belittles Einstein's accurate caricature because he cannot live in a spooky world where he is not the most evolved thing in it.

Bell created a genius way to test spooky action. Aspect et al created genius ways to perform the Bell test. Susskind will NEVER perform an experiment that will have real world application. He is more like Dr. Seuss than science.