Fusion in small spherical tokamaks could be available soon, say Colin Windsor, Alan Sykes and Melanie Windridge

The energy supply to heat the homes of our grandchildren remains uncertain. The options available to us have been detailed by David Mackay in his readable book Sustainable Energy, Without the Hot Air [1]. Mackay describes how at present we use around 125KWh per day per person, produced largely by CO₂-emitting coal, oil and gas. There is now no doubt that climate change is with us. As David King, our Chief Scientist from 2000 to 2007, said: "Climate change is the most severe problem that we are facing today, more serious even than the threat of terrorism." We have to change our ways. There is solar and wind energy, but the sun does not always shine nor the wind always blow. There is nuclear fission energy, which the UK pioneered and which has served us well, but it is not without risk and its public acceptance is fragile. Fusion is one remaining option for a sustainable, safe, CO₂-free, base-load energy source (Figure 1).

Figure 1: Nuclear power from fusion and fission. The graph shows the excess energy of different nuclei plotted against atomic mass. The very light atoms have a high excess energy and can become more stable by fusing together to produce larger nuclei. Heavy nuclei can become more stable by splitting up to produce fission products of intermediate mass.

The fusion reaction
Nuclear fusion is the reaction that powers our Sun. The fuel is hydrogen nuclei, protons, deuterons (D) and tritons (T). In the heat and gravitational 'bottle' of the Sun, these can be forced to overcome their electrostatic repulsion and join together to form the stable helium nucleus - or alpha particle - and a neutron (n), together with a great deal of energy: 14MeV flies off in the neutron, which may be used to heat up a water jacket to make electricity; the charged alpha particle, with 3.6 MeV of energy, remains in the plasma, giving up its energy and helping to sustain the following reaction.

²D+³T = ⁴He+n +17.6MeV

There are important differences in the safety issues for nuclear fission and fusion (Figure 2). At Chernobyl, the criticality accident only occurred because a fission reactor contains large reserves of fuel. In a fusion reactor the hydrogen fuel is continuously injected into the plasma so that it can only sustain fusion for seconds, and a 'criticality' accident is impossible. At Fukishima the reactor was properly shut down, but the meltdown occurred because spent fuel continues to produce heat, which could not be removed because of the flooded back-up generators. There is no such 'delayed' heat in a fusion reactor. At Three Mile Island, human error caused the meltdown but the problem was the high reactivity of the long-lived fission products that were allowed to escape. The fusion products are the benign helium and neutrons. The neutrons produce some activation in the structural materials, but with the correct choice of alloy materials this is a minor issue compared with the fission spent fuel which has proved so expensive to deal with.

Figure 2: The three accidents that changed public acceptance of fission power. In a fusion reactor there is no possibility of the 'criticality' at Chernobyl (a), the release of highly active 'fission products' at Three Mile Island (b), or the 'delayed heat' at Fukashima (c)

In defence of fission it must be said that the public mind tends to over-estimate the actual deaths and premature deaths (56 and 4000 respectively from Chernobyl according to Wikipedia), compared with, say, the seven million premature deaths per year estimated by the World Health Organisation to result from air pollution [2].

Figure 3: The ST40 tokamak. The plasma (violet) is the elongated toroid. The white coils produce the toroidal field along the direction of the plasma which helps to stabilise it. The blue coils produce the vertical fields that shape and help form the plasma. Wound around the brown central column is a solenoid that also helps drive the plasma current.

The tokamak magnetic bottle
In order to make the fusion reaction work on Earth, the gravitational confinement operating in the Sun must be reproduced in some way. The tokamak (Russian for magnetic bottle) provides a magnetic confinement that is able to hold the high-temperature plasma away from all walls. Figure 3 shows the typical tokamak design, specifically the ST40 spherical tokamak being built at Tokamak Energy. (Conventional tokamaks have a wider, ring-doughnut shape but similar configuration.) It has a toroidal vacuum chamber containing the plasma, and toroidal coils which produce a strong field parallel to the plasma direction.

Figure 4:The historical increase in the fusion Lawson 'triple product'. For three decades until 1997 the fusion triple product increased exponentially (points and blue line) with around a two-year doubling time, almost the same as the Moores's law for semiconductors (red dashed line). Only the JET and TFTR data points used tritium fuel, the other points are extrapolations from deuterium plasmas.

Since the earliest ZETA days a key problem of plasma physics has been the stability of the plasma. Any contained plasma must be 'pinched in' away from the container walls; however, the plasma column wiggles about and tends not to be stable. In a tokamak the toroidal coils form a strong magnetic field along the plasma path, which tends to improve its stability. How can progress towards fusion be measured? One answer was given by John Lawson in 1955 who, while working at Culham, devised the 'Lawson triple-product':

nTt_E > 2²¹ m^-3keVs
where n is the plasma density, T is the plasma temperature in keV, and t_E is the plasma 'energy confinement time', i.e. the mean time for energy to diffuse away from the plasma.

Figure 4 shows the increase in fusion triple product from the first T3 tokamak in Russia to the JET tritium runs in 1997. A doubling time of around two years was achieved largely by building ever-larger tokamaks. The JET tokamak has a major radius of three metres and achieved some 16MW of fusion power. Those were exciting days! Figure 5 shows the neutron emission profile as modelled from the nine vertical and ten horizontal neutron counters measuring the neutron emission profile along the lines shown [3].

Figure 5:The recordbreaking shot 42976 on JET. On the right is a reconstruction of the neutron emission as measured by the vertical and horizontal neutron cameras [3].

What can the physics say?
The increasing triple product curve stops at 1997, as the whole world looks forward to the ITER project with its 6.2 metre major radius. Its centre column alone weighs more than the Eiffel tower. The project is funded by Europe, Japan, Russia, USA, China, South Korea and India, and we all eagerly await its answers to the unknown conditions of a burning plasma. But ITER has already shown us that building bigger has its own problems. Can there be quicker way by building more compactly, to produce smaller power plants better suited to the energy market? The physics tells us of options that were not available in the 1990s when ITER was designed. The fusion power (P_fus) can be written as

P_fus ~ b²B_T⁴V
where b is the plasma pressure, B_t is the toroidal field and V is the volume. The ITER design had the conventional JET shape, largely defining the plasma pressure, and used the best low-temperature superconducting magnets available to give the highest possible toroidal field. Increasing the volume was the only option available then.

Figure 6: Two developments from the 1990s: (left) the START spherical tokamak; (right) the high-temperature superconducting 'REBCO' tape.

There were two developments in the 1990s which changed this. First, the START spherical tokamak at Culham, shown on the left of Figure 6, demonstrated that making the plasma the shape of a cored apple rather than a doughnut could give a higher plasma pressure. Secondly, the discovery of 'high-temperature' superconducting materials showed that the magnetic fields on the plasma could be much higher than previously thought. The right of Figure 6 shows the cross-section of the high-temperature superconducting tape. Most of the tape is copper stabiliser and substrate. The superconducting layer is only one micron thick.

Figure 7: The Tokamak Energy team at Milton Park.

TokamakEnergy.co.uk
Tokamak Energy was founded by the START pioneers Alan Sykes and Mikhail Gryaznevich, with David Kingham as chief executive officer. With just a small number of UK investors who actively guide the company, and the relatively tiny number of staff shown in Figure 7, it has been able to forge an alternative path to fusion energy based on rapid development using small prototypes. At their premises in Milton Park in Oxfordshire a small test tokamak, ST25, has been built to investigate innovative solutions to the key problems of novel controllable power supplies, plasma start-up and efficient plasma current drive.

A key challenge in the development of compact fusion is how to make reliable, high-field high-temperature superconducting (HTS) magnets. Their operation is quite different from conventional low-temperature superconductors. They can operate at 77K liquid nitrogen temperatures rather than 4K helium temperatures, but much higher fields can be generated if they are cooled to about 20K with helium, hydrogen or neon coolants. At present they are not available in the kilometre lengths required for a power plant.

New methods for joining them have recently been developed in house: they involve using hair straighteners, which have exactly the right temperature-controlled flat surfaces to bond the tapes nicely together. The quench properties of the HTSs are also quite different: they seem less prone to the catastrophic quench events that can occur with conventional superconductors. To test these technologies, the ST25HTS tokamak has been built at Milton Park. During July 2015, during the Royal Society Summer Exhibition, it was run successfully at Milton Park for over 24 hours, as shown in Figure 8.

Figure 8: Our small tokamak with hight-temperature superconducting (HTS) magnets, ST25HTS, hold a plasma for 29 hours, demonstrating the feasibility of HTS for tokamaks.

A key objective of Tokamak Energy is to design a pilot plant that would be small enough to manufacture as the first of a series of units that could be developed incrementally, and linked together to form a modular power station. This would provide continuity of supply, economy of mass production and other practical advantages. The key requirement is that each module should produce a high gain Q_fus in fusion power, where Q_fus = power released/power in.

But how small could the base module be? What are the limiting factors? What can theory say? What experimental measurements need to be done?

Figure 9: The figure from the paper by Costley et al. [4] showing that the fusion gain Q_fus is only weakly dependent on device size R but does depend on the fusion power.

A theoretical study by Alan Costley and colleagues [4] showed that when the plasma was operated in a steady state within reasonable fractions, say 0.8 of the Greenwald density limit and 0.9 of the Troyon beta limit, then the fusion energy gain (and triple product) depends mainly on the absolute level of the fusion power and the energy confinement, and only weakly on the device size, as shown in Figure 9. Further, they showed that the scaling law used to design ITER needs to be updated. In particular, a betaindependent scaling is needed to account for recent experiments.

This approach suggests that there is no problem with the physics of smaller tokamaks. But what about their engineering? It has long been realised that the slender centre column of the spherical tokamak is a problem. If made of superconductors they must be surrounded by a neutron shield, both to reduce the heat deposition and to reduce radiation damage. If made, instead, of copper, the ohmic heating is large. Either much energy must be wasted cooling the centre column, or its temperature must be allowed to rise during the experiment. This last solution is the one chosen for ST40, a larger machine under construction by Tokamak Energy. It is designed to be the world's highest field spherical tokamak and to establish the physical properties of these plasmas. ST40 will operate in hydrogen, and will not produce neutrons. The copper resistivity is lowered by cooling to liquid nitrogen temperatures, and a window of operation time several seconds long is available as the centre column heats up from, say, 77K to 200K. Of course there follows several minutes of cooling down before the next shot.

Figure 10: On the left is a section through the centre column of a pilot plant tokamak with a tie-rod (green) in the centre then a high temperature superconductor alloy (purple), a thermal gap (white) and layers of shield material (blue) and water-cooling (yellow). On the right is the heat deposition as a function of the thickness of the water-cooling layer.

For a power plant, there are many high-energy neutrons produced and this option is not possible. An efficient neutron shield must be designed. This is not easy. The 14MeV fission neutrons hitting its outer surface create cascades of high-energy gamma rays which need heavy elements to attenuate them. The fast neutrons bounce off these heavy elements and need light elements to slow them down and give up their energy. The Monte Carlo computations [5] have now been extended and it seems that the energy deposition could become a manageable 36kW or so using the shield comprising layers of tungsten carbide separated by cooling water, illustrated in Figure 10. The graph shows that the heat deposition increases if the water-cooling thickness is too small, leading to poor moderation. If the water-cooling thickness is too large there is insufficient gamma shielding. Better performance is given when the water thickness close to the core is thicker than that close to the plasma. Still better performance occurs if the layer of tungsten carbide closest to the core is replaced by tungsten boride, which can absorb the slower neutrons.

Towards a modular power plant
The power plant modelling by Costley et al. [4] suggested that a possible optimum size would be with a major radius of 1.35m. The 36kW of nuclear heating to the superconducting core could be removed by a cryoplant of around 2MW, which is not an unreasonable fraction of the 175MW fusion power. Such a pilot plant is illustrated in Figure 11, which shows a design developed in collaboration with Princeton Plasma Physics Laboratory, USA. It is large enough to be attractive as a unit to a utility company, and small and cheap enough to be constructed conventionally using available finance.

Figure 11: A possible modular fusion power plant designed in collaboration with the Princeton Plasma Physics Institute in the USA.

Tokamak Energy is breaking the problem of fusion down into a series of engineering challenges. Our ST40 experiment will give us the numbers, in particular the energy confinement time in high-field spherical tokamaks, to design the plant without large extrapolations. At present the HTS superconductors are expensive but the technology is developing and their price coming down. A big market will aid this development. Heat deposition and stresses in the centre column remain a problem, but new materials combining the advantages of shielding, strength and toughness are being developed to cope with them. None of these problems appear insuperable and fusion in small spherical tokamaks could be possible quite soon.

References
1. MacKay, D. Sustainable energy, without the hot air www. withouthotair.com
2. World Health Organisation (2014) New release, Geneva, 25 March 2014 www.who.int/mediacentre/news/releases/2014/ air-pollution/en/
3. Windsor, C.G. (1998) Validated neutron data for physics studies and their use in tomographic reconstructions from JET's DTE1 campaign. JET workpackage A14.2d report, F/PL/ WPA14.2d/CGW/1 March 1998
4. Costley, A.E., Hugill, J. and Buxton, P.F. (2015) On the power and size of tokamak fusion pilot plants and reactors. Nucl. Fusion 55, 033001
5. Windsor, C.G., Morgan, J.G. and Buxton, P.F. (2015) Heat deposition into the superconducting centre column of a spherical tokamak fusion plant. Nucl. Fusion 55, 023014

About the authors

Colin Windsor
Colin Windsor joined Tokamak Energy in 2013 after a career at Harwell working on materials using neutrons. He came to Culham in 1994 to work on control of the COMPASS-D tokamak and on the JET tritium campaign. He now works on the neutronics of high temperature superconductor tokamaks.

Melanie Windridge
Melanie Windridge is a physicist, speaker, writer and communications consultant to Tokamak Energy. Her PhD focused on vertical stability on the MAST tokamak at Culham Centre for Fusion Energy. She has published an introductory book on fusion called "Star Chambers" and a narrative science book called "Aurora".

Alan Sykes
Alan Sykes is one of the founders of Tokamak Energy and a pioneer of the spherical tokamak concept. He had a fruitful career in fusion energy at Culham Laboratory from 1965 to 2008 spanning theory and experiment and leading on the record-breaking START machine.