Nuclear engineering

In a nuclear reaction, whether it be fission or fusion, some of the potential, configuration energy (in this case, usually going under the name of binding energy) of the initial atomic nuclei is released when the reaction products are formed. It turns out that the nucleus of an atom of somewhere around Z=26 requires the least amount of binding energy, pro rata for the number of nucleons. Therefore a fission reaction that breaks up a large atomic nucleus into medium sized nuclei ends up (in the typical case) requiring less binding energy in its reaction products than was required in the original nucleus. Meanwhile, a fusion reaction that combines two small atomic nuclei into a medium sized nucleus also ends up (in the typical case) requiring less binding energy in its reaction products. The surplus binding energy is transferred to the kinetic energy of the reaction products. In the case of nuclear fusion, two protons and three neutrons (as an example) need more binding energy to hold them together as a deuterium and plus a tritium nucleus, than they do as a helium nucleus plus a neutron; so the helium nucleus and neutron are sent off at high speed. If you go to measure the masses of the deuterium and tritium atom, you get a reading that accounts for the two protons, three neutrons, two electrons, AND the larger binding energy; while if you measure the masses of the helium nucleus and neutron, having stripped them of their kinetic energy in the water blanket surrounding the reactor vessel, you get a reading that accounts for the two protons, three neutrons, two electrons, AND the slightly lesser binding energy. (As with all short descriptions, the above has had to appeal to all sorts of simplification and semi-classical hand-waving,)

Implications

Plotting the binding energy against the atomic number produces a roughly U-shaped curve, with Z=26 (iron) roughly at its point of minimum. This explains why man-made nuclear reactors are normally built to use the elements at the extremities of the periodic table, such as isotopes of uranium (Z=92) for fission reactors, and isotopes of hydrogen (Z=1) for fusion reactors.

It also goes a long way to explaining why stars, novae and supernovae, kilonovae, or collapsars (NS, 24-Jul-2021, p46) end up producing so much iron. Iron appears to be the mean value of their eventual production, with other elements (including all the heavier ones) explained by the standard deviation.

However, if the atomic nucleus of iron is the most stable in the context of binding energy, it could be asked why it was not this that was produced in the big bang. One way of looking at this is that it was, but that that we happen to have caught the process part way through: hydrogen and helium were the natural, initial temporary steps in the production of iron.

Another implication is that, though mass and energy are equivalent, an outside view of a system as a black-box sees a collection of mass and energy only as mass. It takes an inside view, of the individual moving parts, to see some of that mass manifesting as the kinetic energy of the component parts. The mass of a proton (or neutron) illustrates this well, with only 1% of the mass being accounted for by the rest mass of the component quarks.

Nuclear fusion technology

One of the major hurdles in sustaining a controlled nuclear fusion reaction is that the input reactants are all positively charged, and repel each other, and so are difficult to bring together in a fusion reaction. The solution is to get those input components moving extremely fast. Being electrically charged, one well developed technology for doing this is through varying magnetic fields. Since fast moving particles are, by definition, hot particles, they need to be kept away from the walls of the reactor vessel, and this can also be achieved by adding other magnetic fields.

This is why one promising technology (albeit not the only one) is the tokamak, such as the one being constructed for the ITER project (NS, 10-Oct-2009, p40). In effect, a tokamak is just a giant test-tube, but bent round into a torus so that it joins at its two ends. The advantage of this over a linear tube is that it removes the inefficiency of having to accelerate the particles, only to have to slow them down, and to reflect them back again, at each end.

A bibliography

Since the particles are fast moving, they appear hot: the initial isotopes of hydrogen are heated to the point of being a plasma, with the atomic nuclei accelerated round the torus in one direction, and their electrons having been separated off, and accelerated round the torus in the opposite direction. (This does emphasise that, when viewed from the outside, a plasma is still, overall, electrically neutral.) This acceleration is achieved by a solenoid running up through the centre of the torus: in effect, this solenoid acts as the primary winding of a transformer, with the electrically conducting plasma acting as a single turn of a secondary winding. The series of magnets that are looped round the test-tube (there are 18 of them for ITER) are the main ones to keep the plasma from touching the walls of the test-tube, and for keeping its constituent particles confined within the plasma.

There is a distinction between current drive and heating. Simply accelerating all the particles together to circle round the torus merely manifests as a large electric current (perhaps of the order of 17 MA) with few collisions between the particles. However, with all the magnetic fields inside the torus, the particles do not travel in simple paths alongside each other, but in tight little corkscrew paths round the torus. Thus, just as in a balloon of gas moving through space, there is a distinction between the velocity of the whole mass of gas (the current) and the internal velocities of the component particles (the temperature).

Even having accelerated the atomic nuclei up to high speeds, most collisions are still thwarted by the electrostatic repulsion of the two positively-charged particles. So, confinement is important for keeping the particles from speeding away too far, and being able to be brought back for multiple attempts at collision. Tokamaks use magnetic confinement to achieve this, and laser ignition nuclear reactors use inertial confinement to achieve it. Stars like the sun use gravitational confinement, but require astronomical volumes of space to do so, so this is not an option for man-made nuclear fusion reactors on the planet's surface. Furthermore, the engineering sweet-spot for the fusion of deuterium and tritium in a tokamak, is around 150 million degrees Kelvin, and that this is ten times the temperature of the core of the sun. The implication is that the sun is operating at a greatly sub-optimal rate, which is just as well since that means that its fuel supply can last for billions of years, and its output is not so great as to fry its nearest planets.

As noted earlier, the reaction products of the fusion reaction acquire extra kinetic energy, and this can be captured in a water jacket surrounding the reaction vessel. This causes the water to heat, and to be available to turn a steam turbine. One intriguing possibility is to cut out the mechanical parts of the steam turbine and copper coils of the generator, and to use the movements in the magnetic fields, of the highly conducting plasma, to do the job more directly. Such magnetohydrodynamics (MHD) is indeed required as a means of heating the plasma, but is presently just one technology too far for use in the electricity generation. Thus, for the present, despite all its sophistication, and modern-world image, a nuclear reactor (whether fission or fusion) is just a new way to heat the water in the boiler of a steam engine. In this respect, the technology really has not advanced that much in 150 years.

Need for sources of clean energy

Harnessing economically viable energy generated from nuclear fusion has proven to be extremely difficult to achieve. It is still tantalisingly promising to be achieveable, and hence worth pursuing just that bit further. Not least, our greedy, energy-guzzling species is desperately in need of new, economically viable sources of ever-increasing amounts of energy in the future. No international treaties are ever going to change that: at best, those treaties can only ever hope to wean governments off the use of bad methods, and on to less-bad methods of energy production. In any case, the aim is not to offer nuclear fusion as the way to produce all energy in the future, but to be available in the list of options on energy generation, for the next generation to be able to select or unselect in each specific context.

As well as needing to feed an ever increasing need for energy, for ever newer applications, the world is not short of needs of greater amounts of energy to solve existing problems. As well as wars and famines, the world is faced with a growing list of gmobal problems: the wake-up realisations of the global impact of the hole in the ozone layer, the imminence of last oil, depleting marine fish stocks, acid rain, land-fill and pollution, the greenhouse effect, plastic waste in the oceans and on land, the shortage of rare metals, and of fresh water (for irrigation, drinking and industry). Most of these could be resolved, or at least eased, by the availability of new, cheap energy sources (for example for fishing plastic waste out of the ocean, scrubbing the atmosphere of exess carbon dioxide, mining landfill sites for rere metals, and desalinating water and pumping it to where it is needed, since sea-water is not one of the commodities that the planet is short of).

Particle colliders

Lastly, a final comment can be made about the connection with particle colliders. Despite sounding as though it is doing something similar, by accelerating particles round a ring by the use of magnets, and then colliding them together, a particle collider is in fact doing the opposite to a tokamak: it is converting energy back mass, in the form of a flurry of new particles. Most of these new particles are ordinary and already well studied, so the challenge is to sift past all these, to spot the rare exotic particle that warrants further study.