Tag: nuclear fusion

Notes on the NIF nuclear fusion breakthrough

My explainer/analysis of the US nuclear fusion breakthrough was published today. Some stuff didn’t make it to the final draft for space and tone constraints; I’m publishing that below.

1. While most US government officials present at the announcement of the NIF’s results, including the president’s science advisor Arati Prabhakar (and with the exception of energy secretary Jennifer Granholm), were clear that a power plant was a long way off, they weren’t sufficiently clear that the road from the achievement to such a power station was neither well-understood nor straightforward even as they repeatedly invoked the prospect of commercial power production. LLNL director Kim Budil even said she expects the technology to be ready for commercialisation within five decades. Apart from overstating the prospect as a result, their words also created a stark contrast with how the US government has responded to countries’ demand for more climate financing and emissions cuts. It’s okay with playing up a potential source of clean energy that can only be realised well after global warming has shot past the Paris Agreement threshold of 1.5º C (if at all) but dances all around its contributions to the $100 billion fund it promised it would contribute to and demands to cut emissions – both within the country and in the form of investments around the world – before 2050.

Also read: US fusion bhashan

2. A definitive prerequisite for a fusion setup to have achieved ignition [i.e. the fusion yield being higher than the input energy] is the Lawson criterion, named for nuclear engineer John D. Lawson, who derived it in 1955. It stipulates a minimum value for the product of the ion density and the confinement time for different fuels. For the deuterium-tritium reaction mixture at the NIF, for example, the product must be at least 1014 s/cm3. In words, this means the temperature must be high enough for long enough to allow the ions to get closer to each other given they are packed densely enough, achieved by compressing the capsule that contains them. The Lawson criterion in effect tells us why high temperature and high pressure are prerequisites for inertial confinement fusion and why we can’t easily compromise them on the road to higher gain.

3. Mentions of “gain” in the announcement on December 13 referred to the scientific gain of the fusion test: the ratio of fusion output to the lasers’ output. Its value is thus a reflection of the challenges of heating plasma, sources of heat loss during ignition and fusion, and increasing fusion yield. While government officials at the announcement were careful to note that the NIF result was a “scientific breakthrough”, other scientists told this correspondent that a scientific gain of 1 was a matter of time and that the real revolution would be a higher engineering gain. This is the ratio of the power supplied by an inertial confinement fusion power plant to the grid to the plant’s recirculating power – i.e. the power consumed to create, maintain and heat the fusion plasma and to operate other facilities. This metric is more brutal than the scientific gain because it includes the latter’s challenges as well as the challenges to reducing energy loss in electric engineering equipment.

4. One plasma physicist likened the NIF’s feat to “the Kitty Hawk moment for the Wright brothers” to The Washington Post. But in a January 2022 paper, scientists from the US Department of Energy wrote that their “Kitty Hawk moment” would be the wall-plug gain reaching 1, instead of the scientific gain, for fusion energy. The wall-plug gain is the ratio of the power from fusion to the power drawn from the wall-plug to run the power plant.

5. The mode of operation of the inertial confinement facility at NIF is indirect-drive and uses central hotspot ignition. Indirect-drive means the laser pulses don’t directly strike the capsule holding the ions but the hohlraum holding the capsule. When the lasers strike the capsule directly, they need to do so as symmetrically as possible to ensure uniform compression on all sides. Any asymmetry leads to a Rayleigh-Taylor instability that rapidly reduces the yield. Achieving such pinpoint accuracy is quite difficult: the capsule is only 2 mm wide, so even a sub-millimetre deviation in a single pulse can tamp the output to an enormous degree. Once the laser pulses have heated up the hohlraum’s inside surface, the latter emits X-rays, which then uniformly compress and heat the capsule from all sides.

A schematic of the laser, hohlraum and capsule setup for indirect-drive inertial confinement fusion at the National Ignition Facility. Source: S.H. Glenzer et al. Phys. Rev. Lett. 106, 085004

6. However, this doesn’t heat all of the fuel to the requisite high temperature. The fuel is arranged in concentric layers, and the heat and pressure cause the 20 µg of deueterium-tritium mix in the central portion to fuse first. This sharply increases the temperature and launches a thermonuclear “burn wave” into the rest of the fuel, which triggers additional reactions. The wisdom for this technique arises from the fact that fusing two hydrogen-2 nuclei requires a temperature corresponding to 5-10 keV of energy (a few million kelvin) whereas the yield is 17,600 keV. So supplying the energy for just one fusion reaction could yield enough energy for hundreds more. Its downside in the inertial confinement contest is that a not-insignificant fraction the energy needs to be diverted to compressing the nuclei instead of heating them, which reduces the gain.

7. As the NIF announcement turns the world’s attention to the prospect of nuclear fusion, ITER’s prospects are also under scrutiny. According to [Shishir Deshpande of IPR Gandhinagar], who is also former project director of ITER-India, the facility is 75% complete and “key components under manufacturing” will arrive in the “next three to five years”. It has already overrun several cost estimates and deadlines (India is one of its funding countries) – but [according to another scientist’s] estimate, it has “great progress” and will “deliver”. Extending the “current experiments” – referring to the NIF’s tests – “is not a direct path to a power station, unlike ITER, which is far more advanced in being an integrated power station. Many engineering issues which ITER is built to address are not even topics yet for laser fusion, such as survival of key components under high-intensity radiation environments.”

US fusion bhashan

At 8.30 pm on December 13, US Department of Energy officials announced that the federally funded National Ignition Facility (NIF) at the Lawrence Livermore National Laboratory (LLNL) in California had conducted a fusion test in which the energy yield was greater than that supplied to start it.

All of them seemed eager to say that this is what US leadership looks like, that this is proof of the US gunning for what was once thought impossible, that the US is where the world’s most brilliant minds work, that according to Joe Biden the US is the land of possibility – and it was hilarious.

The announcement pertains to a scientific demonstration that the NIF’s mode of achieving controlled fusion, called inertial confinement, works. After this come more tests and modelling, manufacturing to key components to very high quality standards, scaling up from the bare essentials to bigger tests, leading up to designing a commercial facility, then building and finally operating it – assuming success at every step. LLNL director Kim Budil said at the presser that commercial inertial confinement could be three or four decades away.

All this said, the test is actually far removed from “zero-carbon abundant fusion energy powering our society”, in the words of energy secretary Jennifer Granholm. My forthcoming article for The Hindu (Thursday) explains why. One important requirement is the energy gain: the ratio of the output energy to the input. The new test achieved a gain of around 1.5 – but only relative to the energy that started the fusion reactions, not the energy that the lasers consumed to produce and deliver it.

More importantly, for inertial confinement fusion to be practicable, it needs to achieve a gain in excess of at least 100. If scientists at NIF find that they’re unable to go past, say, a gain of 50, that will be the end of the road for commercial ICF using the NIF’s setup. So there’s a long, long way to go even before researchers conduct a test that’s a faithful proof of concept for practical nuclear fusion power.

But even more importantly, it’s spellbinding how the US government will stake its claims to being the country that achieves the impossible, etc. but will make all sorts of excuses to disguise its failure of leadership to mobilise $100 billion a year from economically developed countries for poorer countries to use to weather the climate crisis; to disguise its attempts to undermine, modify or defy commitments made under the Paris Agreement; and to evade, stall and deny efforts to set up a ‘loss and damage’ fund at COP27.

It’s a shame that the Conferences of the Parties to the UN FCCC have been spending bigger chunks of their agenda of late just to push back on the recalcitrance of the US et al. Yet here we are, with government officials blaring their trumpets for a proof of a proof of concept with several caveats (as I spell out in The Hindu). Granholm even called the result “one of the most impressive scientific feats of the 21st century”, to applause from the audience, and said Joe Biden called it a BFD.

Of course it is. It’s an unexpectedly big umbrella that the US has got to unfurl over its climate action obligations.

Better nuclear fusion – thanks to math from biology

There’s an interesting new study, published on February 23, 2022, that discusses a way to make nuclear fusion devices called stellarators more efficient by applying equations used all the way away in systems biology.

The Wikipedia article about stellarators is surprisingly well-written; I’ve often found that I’ve had to bring my undergraduate engineering lessons to bear to understand the physics articles. Not here. Let me quote at length from the sections describing why physicists need stellarators, which also serves to explain how these machines work.

Heating a gas increases the energy of the particles within it, so by heating a gas into hundreds of millions of degrees, the majority of the particles within it reach the energy required to fuse. … Because the energy released by the fusion reaction is much greater than what it takes to start it, even a small number of reactions can heat surrounding fuel until it fuses as well. In 1944, Enrico Fermi calculated the deuterium-tritium reaction would be self-sustaining at about 50,000,000º C.

Materials heated beyond a few tens of thousand degrees ionize into their electrons and nuclei, producing a gas-like state of matter known as plasma. According to the ideal gas law, like any hot gas, plasma has an internal pressure and thus wants to expand. For a fusion reactor, the challenge is to keep the plasma contained. In a magnetic field, the electrons and nuclei orbit around the magnetic field lines, confining them to the area defined by the field.

A simple confinement system can be made by placing a tube inside the open core of a solenoid.

A solenoid is a wire in the shape of a spring. When an electric current is passed through the wire, it generates a magnetic field running through the centre.

The tube can be evacuated and then filled with the requisite gas and heated until it becomes a plasma. The plasma naturally wants to expand outwards to the walls of the tube, as well as move along it, towards the ends. The solenoid creates magnetic field lines running down the center of the tube, and the plasma particles orbit these lines, preventing their motion towards the sides. Unfortunately, this arrangement would not confine the plasma along the length of the tube, and the plasma would be free to flow out the ends.

The obvious solution to this problem is to bend the tube around into a torus (a ring or donut) shape.

A nuclear fusion reactor of this shape is called a tokamak.

Motion towards the sides remains constrained as before, and while the particles remain free to move along the lines, in this case, they will simply circulate around the long axis of the tube. But, as Fermi pointed out, when the solenoid is bent into a ring, the electrical windings would be closer together on the inside than the outside. This would lead to an uneven field across the tube, and the fuel will slowly drift out of the center. Since the electrons and ions would drift in opposite directions, this would lead to a charge separation and electrostatic forces that would eventually overwhelm the magnetic force. Some additional force needs to counteract this drift, providing long-term confinement.

[Lyman] Spitzer’s key concept in the stellarator design is that the drift that Fermi noted could be canceled out through the physical arrangement of the vacuum tube. In a torus, particles on the inside edge of the tube, where the field was stronger, would drift up. … However, if the particle were made to alternate between the inside and outside of the tube, the drifts would alternate between up and down and would cancel out. The cancellation is not perfect, leaving some net drift, but basic calculations suggested drift would be lowered enough to confine plasma long enough to heat it sufficiently.

These calculations are not simple because this how a stellarator can look:

The coil system (blue), plasma (yellow) and a magnetic field line (green) at the Wendelstein 7-X plasma experiment under construction at the Max-Planck-Institut für Plasmaphysik, Greifswald, Germany. Credit: Max-Planck Institut für Plasmaphysik

When a stellarator is operating and nuclear fusion reactions are underway, impurities accumulate in the plasma. These include ions that have formed but which can’t fuse with other particles, and atoms that have entered the plasma from the reactor lining. These pollutants are typically found at the outer layer.

An additional device called a diverter is used to remove them. The heavy ions that form in the reactor plasma are also called ‘fusion ash’, and the diverter is the ashtray.

It works like a pencil sharpener. The graphite is the plasma and the blade is the diverter. It scrapes off the wood around the graphite until the latter is fully exposed and clean. But accomplishing this inside a stellarator is easier said than done.

In the image above, let’s isolate just the plasma (yellow stuff), slice a small section of it and look at it from the side. Depending on the shape of the stellarator, it will probably look like a vertical ellipse, an elongated egg – a blob, basically. By adjusting the magnetic field near the bottom of the stellarator, operators can change the shape of the plasma there to pinch off its bottom, making the overall shape more like an inverted droplet.

The shapes of an egg and an inverted droplet, laid side by side to compare.
The shapes of an egg and an inverted droplet. Note that the shapes are illustrative and aren’t exact representations of the shape of the plasma. Credit: Good Ware/Flaticon

At the bottom-most point, called the X-point, the magnetic field lines shaping the plasma intersect with each other. At least, some magnetic field lines intersect with each other while others move towards each other without fully criss-crossing, but which are in contact with the surface of the reactor. (In the image below, the boundary between these two layers of the plasma is called the separatrix.)

Diverter plates are installed near this crossover point to ‘drain’ the plasma moving along the non-intersecting fields.

An illustration showing the effect of the diverter coils on the plasma, the X-point, the layer of plasma that will be 'scraped off', and the diverter plates at the bottom – in the Joint European Torus, a plasma physics experiment at the Culham Centre for Fusion Energy, Oxfordshire.
An illustration showing the effect of the diverter coils on the plasma, the X-point, the layer of plasma that will be ‘scraped off’, and the diverter plates at the bottom – in the Joint European Torus, a plasma physics experiment at the Culham Centre for Fusion Energy, Oxfordshire. Credit: EUROfusion 2016/United Kingdom Atomic Energy Authority
Note the placement and shape of the diverter coils and their effect on the shape of the plasma, at the Joint European Torus. Credit: Focus On: JET/Matthew Banks, EFDA JET

In the new study, physicists addressed the problem of diverter overheating. The heat removed at the diverter is considered to be ‘waste’ and not a part of the fusion reactor’s output. The primary purpose here is to take away the impure plasma, so the cooler it is, the longer the diverter will be able to operate without replacement.

The researchers used the Large Helical Device in Gifu, Japan, to conduct their tests. It is the world’s second largest stellarator (the first is the Wendelstein 7-X). Their solution was to stop heating the plasma just before it hit the diverter plates, in order to allow the ions and electrons to recombine into atoms. The energy of the combined atom is lower than that of the free ions and electrons, so less heat reaches the diverter plates.

How to achieve this cooling? There were different options, but the physicists resorted to arranging additional magnetic coils around the stellarator such that, just before the plasma hit the diverter, its periphery would detach into a smaller blob that, being separated from the overall plasma, could cool. These smaller blobs are called magnetic islands.

When they ran tests with the Large Helical Device, they found that the diverter removed heat from the plasma chamber in short bursts, instead of continuously. They interpreted this to mean the magnetic islands didn’t exist in a steady state but attached and detached from the plasma at a regular frequency. The physicists also found that they could model the rate of attachment using the so-called predator-prey equations.

These are the famous Lotka-Volterra equations. They describe how the populations of two species – one predator and one prey – vary over time. Say we have a small ecosystem in which crows feed on worms. As they do, the crow population increases, but due to overfeeding, the population of worms dwindles. This forces the crow population to shrink as well. But once there are fewer crows around, the number of worms increases again, which then allows more crows to feed on worms and become more populous. And so the cycle goes.

A plot showing the varying populations of predator and prey, as predicted by the Lotka-Volterra equations.
A plot showing the varying populations of predator and prey, as predicted by the Lotka-Volterra equations. Plot: Ian Alexander and Krishnavedala/Wikimedia Commons, CC BY-SA 4.0

Similarly, the researchers found that the Lotka-Volterra equations (with some adjustments) could model the attachment frequency if they assumed the magnetic islands to be the predators and an electric current in the plasma to be the prey. This current is the product of electrons moving around in the plasma, which the authors call a “bootstrap current”.

When the strength of the bootstrap current increases, the magnetic island expands. At the same time, the confining magnetic field resists the expansion, forcing the current to dwindle. This allows the island to shrink as well, receding from the field. But then this allows the bootstrap current to increase once more to expand the island. And so the cycle goes.

Competitive relation between magnetic island and localised plasma current derived with the predator-prey model. Increased current (bottom left) enhances the magnetic island. In turn, electric resistivity increases, which reduces the current (bottom right). Eventually, the magnetic island shrinks, which leads to reduction of the electric receptivity and increase of the current. Caption and credit: National Institute for Fusion Science, Japan

The researchers reported in their paper that while they observed a frequency of 40 Hz (i.e. 40 times per second) in the Large Helical Device, the equations on paper predicted a frequency of around 20 Hz. However, they have interpreted to mean there is “qualitative agreement” between their idea and their observation. They also wrote that they expect the numbers to align once they fine-tune their math to account for various other specifics of the stellarator’s operation.

They eventually aim to find a way to control the attachment rate so that the diverters can operate for as long as possible – and at the same time take away as much ‘useless’ energy from the plasma as possible.

I also think that, ultimately, it’s a lovely union of physics, mathematics, biology and engineering. This is thanks in part to the Lotka-Volterra equations, which are a specific form of the Kolmogorov model. This is a framework of equations and principles that describes the evolution of a stochastic process in time. A stochastic process is simply one that depends on variables whose values change randomly.

In 1931, the Soviet mathematician Andrei Kolmogorov described two kinds of stochastic processes. In 1949, the Croatian-American mathematician William Feller described them thus:

… the “purely discontinuous” type of … process: in a small time interval there is an overwhelming probability that the state will remain unchanged; however, if it changes, the change may be radical.

… a “purely continuous” process … there it is certain that some change will occur in any time interval, however small; only, here it is certain that the changes during small time intervals will be also small.

Kolmogorov derived a pair of ‘forward’ and ‘backward’ equations for each type of stochastic process, depending on the direction of evolution we need to understand. Together, these four equations have been adapted to a diverse array of fields and applications – including quantum mechanics, financial options and biochemical dynamics.

Featured image: Inside the Large Helical Device stellarator. Credit: Justin Ruckman, Infinite Machine/Wikimedia Commons, CC BY 2.0.

What is a fusion reaction?

The Copernican
February 21, 2014

Last week, the National Ignition Facility, USA, announced that it had breached the first step in triggering a fusion reaction. But what is a fusion reaction? Here are some answers from Prof. Bora – which require prior knowledge of high-school physics and chemistry. We’ll start from their basics (with my comments in square brackets).

What is meant by a nuclear reaction?

A process in which two nuclei or a nucleus and a subatomic particle collide to produce one or more different nucleii is known as a nuclear reaction. It implies an induced change in at least in one nucleus and does not apply to any radioactive decay.

What is the difference between fission and fusion reactions?

The main difference between fusion and fission reactions is that fission is the splitting of an atom into two or more smaller ones while fusion is the fusing of two or more smaller atoms into a larger one. They are two different types of energy-releasing reactions in which energy is released from powerful atomic bonds between the particles within the nucleus.

Which elements are permitted to undergo nuclear fusion?

Technically any two light nuclei below iron [in the Periodic Table] can be used for fusion, although some nuclei are better than most others when it comes to energy production. Like in fission, the energy in fusion comes from the “mass defect” (loss in mass) due to the increase in binding energy [that holds subatomic particles inside an atom together]. The greater the change in binding energy (from lower binding energy to higher binding energy), more the mass lost, results in more output energy.

What are the steps of a nuclear fusion reaction?

To create fusion energy, extremely high temperatures (100 million degrees Celsius) are required to overcome the electrostatic force of repulsion that exists between the light nuclei, popularly known as the Coulomb’s barrier [due to the protons’ positive charges]. Fusion, therefore, can occur for any two nuclei provided the temperature, density of the plasma [the superheated soup of charged particles] and confinement durations are met.

Under what conditions will a fusion chain-reaction occur?

When, say, a deuterium (D) and tritium (T) plasma is compressed to very high density, the particles resulting from nuclear reactions give their energy mostly to D and T ions, by nuclear collisions, rather than to electrons as usual. Fusion can thus proceed as a chain reaction, without the need of thermonuclear temperatures.

What are the natural forces at play during nuclear fusion?

The gravitational forces in the stars compress matter, mostly hydrogen, up to very large densities and temperatures at the star-centers, igniting the fusion reaction. The same gravitational field balances the enormous thermal expansion forces, maintaining the thermonuclear reactions in a star, like the sun, at a controlled and steady rate.

In the laboratory, the gravitational force is replaced by magnetic forces in magnetic confinement systems whereas radiation force compresses the fuel, generating even higher pressures and temperature, and resulting in a fusion reaction in the inertial confinement systems.

What approaches have human attempts to achieve nuclear fusion taken?

Two main approaches, namely magnetic containment and inertial containment, have been attempted to achieve fusion.

In the magnetic confinement scheme, various magnetic ‘cages’ have been used, the most successful being the tokamak configuration. Here, magnetic fields are generated by electric coils. Together with the current due to charged particles in the plasma, they confine the plasma into a particular shape. It is then heated to an extremely high temperature for fusion to occur.

In the inertial confinement scheme, extremely high-power lasers are concentrated on a tiny sphere consisting of the D-T mixture, creating tremendous pressure and compression. This generates even higher pressures and temperatures, creating a conducive environment for a fusion reaction to occur.

To create fusion energy in both the schemes, the reaction must be self-sustaining.

What are the hurdles that must be overcome to operate a working nuclear fusion power plant to generate electricity?

Fusion power is in the form of fast neutrons that are released, of an energy of 14 Mev [although MeV is a unit of energy, it denotes a certain mass of the particle according to the mass-energy equivalence; to compare, a non-excited proton has an energy of 938.2 MeV]. This energy will be converted to thermal energy which then would be converted to electrical energy. Hurdles are in the form of special materials that need to be developed that are capable of withstanding extremely high heat flux in a neutron environment. Reliability of operation of fusion reactors is also a big challenge.

What kind of waste products/emissions would be produced by a fusion power plant?

All the plasma facing components are bombarded by neutrons, which will make the first layers of the metallic confinement radioactive for a short period. The confinement will be made of different materials. Efforts are being made by materials scientists to develop special-grade steel to have weaker effects struck by neutrons. All said, such irradiated components will have to be stored for at least 50 years. The extent of contamination should be reduced with the newer structural materials.

Fusion reactions are intrinsically safe as the reaction terminates itself in the event of the failure of any sub-system.

India is one of the seven countries committed to the ITER program in France. Could you tell us what its status is?

ITER project has gradually moved into construction phase. Therefore, Fusion is no more a dream but a reality. Construction at site is progressing rapidly. Various critical components are being fabricated in the seven parties through their domestic agencies.

The first plasma is expected in the end of 2020 as per the 2010 baseline. Indian industries are also involved in producing various subsystems. R&D and prototyping of many of the high tech components are progressing as per plan. India is committed to deliver its share in time.