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# Magnetic Nuclear Fusion in Tokamaks

## INTRODUCTION

The kind of nuclear fusion energy that powers the stars and the Sun became possible on our planet in the twentieth century, first in military applications. The aim of magnetic nuclear fusion is to make fusion energy available for peaceful industrial-scale energy production [1.1]. This energy source is nearly inexhaustible, no greenhouse gases are emitted, and the radioactive waste and other dangers of nuclear power are minimised. The possibility of achieving nuclear fusion on Earth exists owing to an exceptionally large cross-section (a measure of the ability to fuse) of a nuclear fusion reaction between the nuclei of hydrogen isotopes deuterium (D), consisting of one proton and one neutron, and tritium (T), consisting of one proton and two neutrons [1.2]:

This fusion reaction produces highly energetic helium-4 ion. He (also called alpha particle) with electric charge +2, and neutron, n. These products of the D-T fusion have birth energies in the centre-of-mass reference frame 3.52 and 14.1 MeV, respectively.

Other fusion reactions investigated in present-day magnetic fusion, which substitute much more demanding D-T operation, but may become essential in the future in their own right, are:

and

Here, each of D-D reactions (1.2), (1.3) has a probability of 50%, so the total D-D fusion rate is a sum of (1.2) and (1.3), giving the total D-D fusion rate twice that of D-D neutron rate.

The reaction (1.4) involving an extremely rare gas 'He generates alpha particle 4He with an energy of 3.67 MeV. Because this energy is close to the birth energy of alpha particle in (1.1) of 3.52 MeV, reaction (1.4) is used to study test alpha particles when complications associated with the use of tritium and/or the flux of D-T neutrons need to be avoided.

The cross-sections of main thermonuclear reactions (1.1)—(1.4) are shown in Figure 1.1 when the colliding D ion moves at high speed (the “projectile ion”), while the second colliding ion is stationary. Figure 1.1 shows that the fusion reaction between isotopes D and T has the largest cross-section and is therefore the “easiest” one to access in experiments. In magnetic fusion, for a plasma consisting of a mixture of D and T ions at equal temperatures, the yield of thermonuclear D-T reaction is maximised at a temperature of ~20 keV.

FIGURE 1.1 Cross-sections for fusion reactions D-T, D-D, and D-’He as functions of the D projectile energy.

The energy released in nuclear reactions is significantly larger than that in chemical reactions because the binding energy holding a nucleus together is far greater than the energy holding an atom (electrons and ions) together. The energy gained by adding an electron to a hydrogen nucleus (proton, deuterium, or tritium) is only 13.6eV. This value is less than one-millionth of the 17.6 MeV energy released in D-T nuclear fusion reaction. Next, in comparison with nuclear fission reactions, fusion reactions have a higher energy density. The fusion reactions produce far greater energy per unit mass even though individual fission reactions are generally much more energetic than individual fusion reactions. Only the direct conversion of mass into energy, such as that caused by the annihilation of matter and antimatter, is more energetic per unit mass than nuclear fusion.

The environmental advantages of fusion are largely determined by the type and accessibility of the reacting fuel species on Earth. The light isotope deuterium involved in all reactions (1.1)—(1.4) is naturally abundant on our planet as it constitutes 0.015% of all water. Tritium involved in (1.1) is radioactive with a half-life of 13 years, so it must be obtained first from lithium using neutron flux from a nuclear reactor via the reaction 6Li+n=T+4He. The raw materials for the most important D-T reaction are water and lithium, which are abundant and much less expensive than, for example, enriched uranium used in nuclear fission. The reaction (1.4), which is not a mainstream one, requires very rare ’He. This can be obtained from nuclear reactors or can be found in significant quantities on the Moon.

For comparison with other fuel types, one could assess what amount of fuel is required for generating 1 GW power for 1 year (this energy is equivalent to the one typically used in a large industrial city):

Coal: 2.5 Mtonnes - produces 6 Mtonnes C02;

Fission: 150 tonnes U - produces several tonnes of fission waste;

Fusion: 1 tonne Li+5 ML water.

In contrast to fossil fuels, fusion does not generate “greenhouse” gases. In contrast to fission, fusion is nearly free of radioactive waste. Of course, after operating in an intense neutron flux, the structure of a fusion reactor could become activated, but the fusion fuel cycle does not generate plutonium or other long-life (thousands of years) active waste. A careful selection of materials for fusion reactor could make the activation to decay to a safe level in less than 100years. Responsibility for the safety and integrity of a fusion facility at such a time scale could be taken without major problems as many buildings around us exist which are older than 100years.

How can we make the nuclear forces between D and T ions work without the help of gravity existing on Sun and stars? For the fusion reaction, D and T nuclei must approach each other to a “nuclear” distance of ~10~l3cm. However, the nuclei are both charged positively and need to overcome the Coulomb electrostatic force between them. One of the solutions to this problem is to provide the colliding nuclei with kinetic energy larger than the Coulomb potential energy. In other words, the fuel must be hot enough with the optimum fusion rate for a DT mixture achieved at Td=Tt=20 keV (200 Mdeg). At this temperature, the DT gas is ionised and becomes a plasma - a mixture of positively charged D and T nuclei, which are the plasma ions, and negatively charged plasma electrons compensating the positive ion charge so that plasma is quasi-neutral. At this point, one needs to consider a “confinement” criterion, which is especially important for discussing plasma properties in a laboratory device. Figure 1.2 shows a sequence of the phase transitions and the relevant states of some matter, for example, an ice cube, at an increasing temperature.

All states of matter in Figure 1.2 represent different types of organisation determined by values of binding energy of that matter versus the average kinetic energy per molecule given by the temperature. If the binding energy of molecules in a crystal form exceeds the average kinetic energy per molecule, a solid state is formed. If the average kinetic energy per molecule exceeds the binding energy (a fraction of an eV), the crystal structure breaks up either into a liquid or a gas. In liquid form, when increasing kinetic energy of molecules becomes high enough to break the van der Waals forces, the liquid vaporises into a gas. Finally, when the kinetic energy of the gaseous particles exceeds the ionising potential of atoms (usually a few eV), the gas becomes plasma.

Confinement of the matter, starting from a piece of ice, becomes increasingly difficult as its temperature increases and the matter goes through the sequence of phase transitions as Figure 1.2 shows. It is easy to keep a piece of ice in hands, but a bucket is needed to confine water when this ice melts, and a balloon is required for confining water vapour when temperature further increases. It is even more difficult to confine plasma consisting of electrically charged ions and electrons. In the Sun and stars, such ionised gas is confined for millions of years by the enormous gravity of the stars, and nuclei of light elements have sufficient time to collide inside this plasma and enter into fusion reactions. However, dimensions of such fusion systems are too large to be explored on our planet. In the inertial fusion represented by thermonuclear weapons, laser, and beam fusion, the plasma is confined at a very high pressure for very short time determined by the plasma expansion. However, release of fusion energy in such short time represents a significant difficulty for integrating pulsed energy source into electric circuits delivering electricity at a nearly flat rate.

In magnetic fusion, scientists explore the key property of plasmas to conduct electricity, so that plasma can be affected by electric and magnetic fields. Confinement of plasma by external magnetic fields is the focus of magnetic fusion. It is well-known that charged particles in magnetic field move on helical orbits, that is, they circle with Larmor radius perpendicularly to the field and move freely along the field. By bending the initially straight solenoid so that the two ends of the solenoid’s cylinder come together, one obtains a toroidal solenoid, as shown in Figure 1.3. Because this magnetic field toroidal topology has no open ends, charged particles flowing freely along the toroidal magnetic field move in circle Larmor orbits across the field and can remain inside the trap for a long time determined by transport processes across the magnetic field. If the toroidal loop with plasma is used as a secondary wing of a transformer, an electric inductive current IP starts flowing in the toroidal direction as plasma is a perfect conductor. This plasma current generates a so-called “poloidal” magnetic field BP in addition to the toroidal magnetic field B, induced by the solenoid coils. Schematically, this concept of a toroidal magnetic field machine with toroidal plasma current

FIGURE 1.2 Schematic representation of phase transitions with increasing temperatures.

FIGURE 1.3 Schematic representation of a toroidal solenoid with plasma current used for plasma confinement in magnetic fusion.

represents a tokamak [1.3]. Tokamaks were initially conceptualised in the 1950s by Soviet physicists I.E. Tamm and A.D. Sakharov and have become popular since 1970s [1.4].

Considering D-T plasma trapped in a magnetic confinement machine and generating fusion reactions (1.1) at a reasonable rate, one would use the 14.1 MeV (80% energy) neutrons generated by D-T fusion and leaving the machine for breeding new tritium and generating the energy output, while the charged alpha particle with an energy of 3.52 MeV generated in the fusion reactions should be further confined inside the plasma. If confined well, the highly energetic alpha particles would deliver its energy to electrons and ions of the bulk plasma via Coulomb collisions. This heat flux from the fusion- born alpha particles to the plasma increases, in turn, the fusion reactivity of the plasma, and the D-T plasma becomes self-heated. When alpha particles are generated in significant numbers and the plasma self-heating by these alpha particles exceeds plasma heat losses due to radiation and thermal conductivity, the thermonuclear D-T plasma ignites. Energy production becomes possible from such “ignited” plasma. The D-T plasma could be sustained in such a state by providing relevant levels of D and T fuels and removing He ash (cooled alpha particles after transferring most of their energy to plasma).

Fusion plasmas heated by some auxiliary heating systems, in addition to the alpha particles, are called “burning” plasmas. The role of auxiliary heating is the control of plasma burn in addition to the control of D and T fuelling. This could be a more effective option for controlling non-linear exothermal plasma self-heating by fusion-born alpha particles.

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