Thermonuclear Fusion and Pulsed Power: solving the global energy problem. Part I

Introduction to the problem

Sustainable energy is the engine of economic and the foundation of humanity's technological development. However, the limitations of the Earth's traditional energy sources are becoming increasingly apparent as a significant portion of the resources currently used by humans are exhaustible. The dynamics of global energy consumption (Figure 1) shows that at the current stage of human development, hydrocarbon fuels (coal, oil, and natural gas) are one of the main sources of energy: the share of global energy produced by their combustion is 77% (based on data for 2021).

According to Oil & Gas Journal's annual assessment, as of 2022, the world's proven oil reserves totaled 279,363 megatons and natural gas reserves totaled 208,768 billion cubic meters: enough reserves to last about 50 years if production remains at current levels.

According to British Petroleum (Statistical review of world energy, 2020), the world's proven coal reserves amount to 1,069,636 megatons: these reserves, according to conservative estimates, will last for 270 years.

These projections, it is worth noting, do not consider the constant growth in energy consumption due to the active development of technology, the increase in the world's population and its standard of living. Global energy consumption increased by 25% between 2000 and 2010, and a further 10% between 2010 and 2020. The 25-year record demand for energy has led to energy shortages: evidence pointing to a global energy crisis is mounting.

The situation is aggravated by the rapidly deteriorating environmental situation. The trend in global CO? emissions from fossil fuel combustion shows a more than fivefold increase between 1950 and 2004 (Figure 2).

According to the World Meteorological Organization, the concentration of carbon dioxide in the Earth's atmosphere from the burning of fossil fuels has increased by 46% by 2017 compared to the pre-industrial era (1750).

At the same time, 45% of total CO? emissions accumulate in the atmosphere, 31% are absorbed by plants and animals, and 23% accumulate in the oceans.

Burning hydrocarbons does not only release carbon dioxide into the air. According to the UN, 7 million people die every year from diseases caused by polluted air. The accumulation of CO? in the atmosphere also increases the greenhouse effect on the planet and leads to significant climate changes – winters become harsher, and summers become drier and hotter, the frequency and destructive power of natural disasters (droughts, floods, storms, hurricanes, etc.) increase. According to the UN, the Earth's temperature in 2020 reached the highest level in 3 million years. Already there are periodic floods with about 148 million people living in the zone. Between 3.3 billion and 3.6 billion people live in environments that are highly vulnerable to climate change. If current CO? emissions continue, rising global average temperatures will lead to catastrophic climate change.

According to UN Secretary General António Guterres , “Our fragile planet is hanging by a thread. We are still knocking on the door of climate catastrophe. It is time to go into emergency mode — or our chance of reaching net zero will itself be zero” [1].

It is about achieving carbon neutrality by 2050: carbon neutrality – is the reducing to zero emissions of carbon dioxide and its analogs from all production activities or offsetting these emissions through carbon-negative projects.

Thus, one of the main tasks of mankind at its current stage of development is the search for energy sources alternative to hydrocarbons. Such alternative sources are, for example, energy from falling water; energy released from the decay of heavy element nuclei; wind energy; solar energy and the like.

All these sources, for one reason or another, are unable to fully replace hydrocarbon fuels for mankind.

Hydropower has a few advantages over other energy sources, such as low production costs (about 4 times cheaper than Thermal Power Plants (TPPs) energy) and quick payback, nevertheless, even with the full development of the potential of all rivers of our planet, it is possible to provide only 25% of the energy needs of mankind [2].

The use of nuclear energy involves risks of accidents and radioactive contamination of the environment. In addition, the use of nuclear energy does not provide a radical solution to the environmental problem: studies of all stages of its production (uranium ore mining, uranium enrichment and radioactive waste disposal) show that the carbon footprint of Nuclear Power Plants (NPPs) operation is about 10 times smaller than that of a coal-fired TPPs, but still an order of magnitude larger than that of Solar and Wind Power Plants (SPPs and WPPs). Environmental Progress estimates that a typical 1 GW nuclear reactor produces 27 tons of waste annually. Yes, there are projects for nuclear power plants based on the so-called "closed fuel cycle" – such plants are theoretically capable of using this radioactive waste as fuel, but now only two such Russian reactors are active – BN-600 and BN-800 (I'll talk about these projects in a separate article). Due to enormous technological and economic difficulties, such plants are not widely used.

According to the World Nuclear Industry Status Report (WNISR, 2019), nuclear power is 3 to 4 times more expensive than solar and wind power: it is much more expensive to reduce emissions with nuclear power plants than it is to do so with renewable energy.

Complicating the situation is the fact that the average construction time for new nuclear power plants is 5 to 17 years longer than that of a solar plant or onshore wind farm (according to the 2019 State of the World Nuclear Industry report).

Wind Power Plants (WPPs) can only produce a small amount of electricity on a regular basis because wind is a highly intermittent energy source. The period of operation of wind for electricity generation is between 25% and 40% of the total operating time of a WPP, depending on the geographical location and turbine design. Disputable economic efficiency, which is still under research, high payback period and low reliability of energy generation compared to other methods excludes WPSs from the list of main energy sources but allows considering them as additional sources.

Solar power, like wind power, is intermittent: sunlight is absent at night and on cloudy days, resulting in the need for energy storage. Manufacturing batteries requires specialized technology, sophisticated equipment, and reliable suppliers of raw materials, which is why batteries are highly expensive. Solar Power Plants (SPPs) are categorized as environmentally friendly because they have little or no pollution during operation, but they can cause environmental damage during the manufacturing and disposal stages of battery and solar panel production. Toxic metals such as lead and cadmium are used in the production of solar panels, and the manufacturing process also emits greenhouse gases. While the disposal of nuclear waste is strictly controlled, waste from the use of SPP in most countries outside Europe now finds its way into a large e-waste stream, from where it can enter drinking water sources. In addition, SPPs are characterized by a relatively low average power density, i.e., the amount of energy that can be obtained from a unit area of the energy carrier. All this excludes SPPs from the list of main energy sources, but there is still a possibility of their application as additional sources.

Imitating the stars

Now the only worthy alternative to hydrocarbon fuel is reactors operating on the principle of controlled thermonuclear fusion. Thermonuclear reactions are the main source of energy in the modern universe. The energy reserve of these types of reactions is enormous: thermonuclear fusion releases nearly four million times more energy than the same amount of oil, gas or coal, and four times more energy than conventional nuclear power. Thanks to these reactions, stars and our Sun exist, whose radiation flux makes life on Earth possible. The ominous demonstration by man of the possibility of realization of uncontrollable reactions of this type were repeated explosions of hydrogen bombs, made first by the USA (the world's first explosion of a thermonuclear bomb was made in 1952), and then by the USSR (the largest exploded hydrogen bomb, "Tsar-bomb", 1961). In them, the start of the thermonuclear process is provided by the preliminary explosion of an atomic bomb, which is part of the hydrogen bomb. The measured explosive power of the "Tsar-bomb" was 58.6 megatons in TNT equivalent (so that's the equivalent of detonating 58.6 million tons of TNT simultaneously)! Where does such colossal energy come from?

As is known, the nuclei of atoms of chemical elements consist of nucleons – protons and neutrons. It has been experimentally established that the mass of the nucleus mn is less than the mass of its constituent nucleons m_npsum = Z?m_p + N?m_n, where mp is the mass of a proton, Z is the number of protons in the nucleus, mn is the mass of a neutron, N is the number of neutrons in the nucleus. The mass difference is called the mass defect and is defined as Δm = m_np-sum – m_n. How is this possible?

Modern physics says that in fact some of the mass of the nucleons when they combined into a single nucleus turned into energy – radiation, kinetic energy, and so on. Mass and energy are interrelated – this is the most important conclusion of the special theory of relativity developed by A. Einstein. Mass can convert to energy, and energy can convert to mass. A body of mass m has an energy called rest energy E_o?=?mc^2, where c is the speed of light in a vacuum, equal to approximately 3?10^8 m/s (is a pretty big multiplier to convert mass to energy!). It is one of the most famous formulas in physics today. The energy released during such a nucleon mass transformation is called the binding energy and is defined as E_bind = Δmс^2. The ratio of the binding energy of the nucleus Ebind to the number of nucleons in the nucleus A?=?Z + N is called the specific binding energy, i.e., the binding energy per nucleon, and is defined as ε = E_bind/A. Knowing the masses of nuclei of different chemical elements and the masses of proton and neutron (they are set experimentally with the help of special detectors) it is possible to determine the binding energies of the nuclei of these chemical elements (Figure 3).

In nuclei, nucleons are held together by nuclear forces. These forces are short-range: they are significant at distances on the order of the size of a nucleon, 10^(–15) meters, a thousand times smaller than the smallest atoms. At such distances, the nuclear forces far exceed the electrostatic repulsive forces acting between protons, which are relatively long-range. In order to "disassemble" the nucleus into separate nucleons, it is necessary to expend energy equal to the binding energy of all nucleons, because otherwise, without attracting this energy, the nucleons of the nucleus "do not have enough mass" to exist in the separated state. When a nucleus is formed from individual nucleons, on the contrary, the binding energy of the nucleons is released: the "extra mass" of nucleons is converted into energy and leaves the system.

The binding energy of the nucleus per nucleon is greater the more compactly the nucleus is "packed", i.e., the closer the nucleons are to each other and the more symmetrically they are located relative to the center of the nucleus. The shape of the lightest nuclei, containing only a few nucleons, is asymmetric, and the specific binding energy in such nuclei is small. Nuclei with large atomic weights, as a rule, have a "loose" structure, and the specific binding energy in such nuclei is also relatively small. Medium-sized nuclei have the highest specific binding energy: the rare nickel isotope with atomic weight 62 (8,794 KeV), the iron isotope with atomic weight 58 (8,792 KeV), and the most common iron isotope (it makes up about 92% of all iron) with atomic weight 56 (8,790 KeV). Their nuclei are maximally densely "packed", they are very stable and most strongly bound (Figure 3). By the way, this is why the cores of stars consist of nickel and iron: they simply have nowhere to transform further, thermonuclear transformations basically end here.

A change in the composition of the nucleus is called a nuclear reaction. Positive energy balance, thus, has those nuclear reactions that are directed towards the formation of medium-sized nuclei: either by fission of heavy nuclei or, on the contrary, by fusion of light nuclei. The first reaction is called a nuclear decay reaction; the second is called a fusion reaction. Both reactions can be used to produce energy.

How do you fuse two nuclei? Interacting nuclei are positively charged and strongly repulsive, so for the nuclei to get closer to the distance of action of nuclear forces, they must overcome the potential barrier created by the forces of Coulomb repulsion.

By the way, here's a link to my short article on Coulomb's research: https://www.dhirubhai.net/pulse/fundamental-electromagnetism-simple-interesting-part-i-vasiliev-ma30c/?trackingId=gJMOS%2FXOSjKckuosG23HFg%3D%3D

This is only possible when the relative velocity of the particles is large. One of the ways to achieve such speeds is to strongly heat the matter, because of which the reactions are called thermonuclear.

The height of the Coulomb barrier between two nuclei, i.e., the force of their pushing apart, is determined by the number of protons in each of the nuclei and, therefore, is proportional to the product of the atomic numbers of the nuclei. Therefore, it is easiest to realize the convergence of the lightest nuclei having atomic number 1. Of the single-charged nuclei, the nuclei of the "heavy" isotopes of hydrogen enter the fusion reaction: deuterium D (having a nucleus of a proton and a neutron) and tritium T (with a nucleus of a proton and two neutrons). We emphasize that there are other types of thermonuclear reactions in which particles with a larger charge participate, but their rates are several orders of magnitude smaller, and they become noticeable at very high temperatures, of the order of 10^9 °C. Therefore, their implementation is considerably more complex.

Deuterium is stable and is part of the heavy water molecules D?O contained in ordinary seawater at a ratio of 1:6500 (about 1 g of deuterium per 60 liters of water). Since water is available in virtually unlimited quantities (unlike, for example, natural uranium), deuterium is much easier to produce than nuclear fuel. Tritium is unstable with a half-life of 12.4 years, so there are no reserves of it on Earth. However, it can be produced, for example, from lithium by irradiation with fast neutrons, or in the process of fusion of deuterium nuclei. Consider the equation of the fusion reaction of two deuterium nuclei (these nuclei are called deuterons; Figure 4):

As a result of the collision of two deuterium nuclei, one of two processes can occur: one – with the formation of the helium isotope nucleus 3He and neutron n; the other – with the formation of the tritium nucleus T and proton p. In the first case, the elementary act of nuclear fusion releases energy of about 3.3 MeV; in the second – about 4 MeV (note that the energy of 1?MeV corresponds to a temperature of 11.65 billion °C). The energy in the indicated quantities is carried away mainly in the form of neutron kinetic energy. To convert this energy into heat and further into electrical energy, these neutrons must be absorbed by the coolant.

The formed tritium can enter a fusion reaction with deuterium according to the following scheme:

which produces helium-4 atom nuclei (such a nucleus is a positively charged particle formed by two protons and two neutrons; they are called ∝-particles) and fast neutrons n. In such a reaction, 17.7 MeV of energy is released. It is an interesting fact that to bring tritium and deuterium nuclei together, it is sufficient to give them an energy of the order of KeV units; the products of the reaction have energies of the order of MeV units, i.e., thousands of times greater! Note that the formation of about 1 g of helium releases energy of the order of 200 MW×h (720?GJ), which is equivalent to the energy released in the explosion of 160 tons of trinitrotoluene.

While nuclear fission reactions produce radioactive isotopes in large quantities, fusion reactions do not produce such products in significant quantities (radioactive waste is produced not during the reaction itself, but because of bombarding the surrounding equipment with fast neutrons). The availability of raw materials (practically unlimited amount of initial fuel) and comparative environmental cleanliness make thermonuclear energy extremely attractive. On the one hand, the Earth's water supply is very large; on the other hand, water for such reactors requires very little. The amount of this pineapple-sized fuel is equivalent to 10,000 tons of coal (about 200 full railway carriages)! Deuterium contained in 1 liter of water can provide energy equivalent to burning 300 liters of gasoline.

However, simply heating the fuel to the right temperatures is not enough to initiate a fusion reaction. The fact is that the probability that the nuclei will simply hit each other and fly apart is 10^6 times greater than the probability of a thermonuclear reaction [4]. This means that having heated the fuel to the required temperature, it is necessary to keep this high temperature for such a time, during which the nuclei, dispersing millions of times, would still take part in the thermonuclear reaction in sufficient quantity. Therefore, in order to start a thermonuclear reaction and obtain a positive energy yield from it, two criteria must be satisfied: 1) to provide heating of the fuel to thermonuclear temperatures; 2) to maintain this temperature long enough for such a number of nuclei to take part in the fusion reaction that the total energy yield of all these reactions exceeds the energy spent on heating and holding the fuel.

Fusion reactions in deuterium, occurring according to the above scheme, have appreciable intensity only at temperatures exceeding 2.5 million degrees; for the excess energy released to be of practical interest, a temperature of several hundred million degrees is required. At this temperature, deuterium is no longer a neutral substance, but becomes a highly ionized plasma composed of fast deuterons and fast electrons. In this case, the main difficulty is to isolate this plasma from the walls of the apparatus in which it is located (to keep the plasma from flying away), otherwise the plasma because of its high thermal conductivity cannot be heated even to a few hundred thousand degrees, because all the energy reported to it will immediately go to the walls.

Such a dual requirement is described by a special mathematical equation first formulated by the English physicist John Lawson in 1957 and given his name "Lawson's criterion". Since the fuel temperature determines the speed of colliding nuclei, it also determines their concentration n (usually expressed in the number of nuclei in 1 cm^3). Therefore, the Lawson criterion for the deuterium-deuterium reaction at temperatures on the order of 100 million degrees Celsius, or 10 KeV, is often written in the form nτ?≥?10^16 s/cm^3, where τ is the time to keep the plasma from flying apart (expressed in seconds). For the deuterium-tritium reaction, the criterion is nτ?≥?10^14?s/cm^3. When it is performed, about 0.7% of the fuel nuclei enter the fusion reaction [5]. In practice, the only facility in the world today that has been able to fulfill this criterion is the #NIF (Nation Ignition Facility) at Lawrence National Laboratory in Livermore (USA), which is a huge achievement, and we will talk about it, but a little later.

So, we have considered the essence of the problem of modern energy and one of the most promising ways to solve it - thermonuclear fusion. In the next part we will consider ways of fusion realization – (i) gravitational, (ii) magnetic and (iii) inertial. And in the third and final part, we will consider one of the very promising technologies for the realization of controlled thermonuclear fusion, which is proposed by Pulsed Power – Linear Transformer Driver Technology.

SOURCE CITATIONS:

[1] https://www.un.org/sg/en/content/sg/statement/2021-11-13/secretary-generals-statement-the-conclusion-of-the-un-climate-change-conference-cop26

[2] Kartamysheva, N. S. Ecological consequences of solar energy development / N. S. Kartamysheva, E. S. Kartamysheva, I. A. Vakhrushin, Y. V. Treskova // Technical Sciences: problems and prospects: proceedings of the III International Scientific Conference (St. Petersburg, July 2015). — St. Petersburg: Svoye publishing house, 2015. — С. 59-62. [in Russian]

[3] Atomic Mass Data Center. The AME 2020 atomic mass evaluation / Chinese Phys. C 45 030003 (2021).

[4] James J. Duderstadt, Gregory A. Moses. Inertial Confinement Fusion / John Wiley and Sons, New York, 1982.

[5] Basov N. G., Lebo I. G., Rozanov V. B. Physics of laser thermonuclear fusion / M.: Znanie, 1988. [in Russian]