Controlled Thermonuclear Fusion

Jean Louis Bobin

• Publisher: WSPC
• Year: 2014
• ISBN:
  9789814579773
• Topic: Technology & Engineering
• Subtopic: Mechanical Engineering
• Index: Technology & Engineering

The book is a presentation of the basic principles and main achievements in the field of nuclear fusion. It encompasses both magnetic and inertial confinements plus a few exotic mechanisms for nuclear fusion. The state-of-the-art regarding thermonuclear reactions, hot plasmas, tokamaks, laser-driven compression and future reactors is given.

Contents:

• Some Basic Physics
• Thermonuclear Reactions
• Plasmas
• Some Features of Magnetic Confinement
• Tokamaks
• ITER and Satellite Programs
• Some Features of Inertial Confinement — The Role of Lasers
• Big Drivers for Inertial Fusion
• Off the Main Trails
• The Fusion Reactor

Readership: Students as well as the general public with a background in physical sciences.

Some Basic Physics

1. Atoms

In the early years of the 20th century, the atomic structure as it is known today was unravelled through a famous experiment, in which alpha particles from a radioactive source were impinging onto metal foils and unexpectedly, some of the particles were backscattered. As Rutherford put it later: “it was as if you fired a 15 inch shell at a piece of tissue paper and it came back and hit you.” The effect can be readily explained by thinking of alpha particles as microscopic particles each carrying a positive electric charge. Each of them undergoes electrostatic repulsion from a small-sized nucleus, positively charged, sitting at the centre of the atom (Figure 1.1). This is now known as Rutherford scattering, which is actually a special case of Coulomb scattering (Box 1.1). Meanwhile, alpha particles were identified as helium nuclei.

An atom is made of a central nucleus whose positive charge is exactly compensated by the negative charge of the surrounding electron cloud. Now, the electric charge is quantized. The elementary charge, i.e. the smallest quantity that can be isolated, is denoted by e = 1.6 × 10⁻¹⁹ coulomb. An electron carries a charge of −e. The charge of a nucleus is an integer Z times e. Every atomic number Z corresponds to a given chemical element.

Figure 1.1. The scattering of helium nuclei (α particles) by an atom. In the electron cloud, negative charges are smeared within a 10⁻¹⁰ m radius sphere. Their influence on incoming charged particles is negligible. On the contrary, in the heavy nucleus, the electric charge is concentrated in a sphere of radius 10⁻¹⁵ m. In most collisions, the projectile remains far from the target and is hardly deviated. Whenever it comes closer to the nucleus, it is backscattered.

Figure 1.2. Coulomb collisions in the target’s frame: a) both particles have the same sign, repulsive force; b) particles have opposite sign, attractive force. χ is the scattering angle depending upon the direction and the energy of the projectile.

Box 1.1. Coulomb scattering

Rutherford scattering is a special case of encounters between charged particles. The dynamics of the process are driven by the Coulomb electrostatic force, which follows the inverse square law, hence the name Coulomb collision. In the targets frame, trajectories follow branches of hyperbolas. They avoid the centre of force when the charges have identical signs, and they turn around it when the charges have opposite signs.

A familiar albeit misleading picture (Figure 1.3) shows the electron cloud as objects orbiting the nucleus the same way as planets orbiting the Sun. Actually, the atom is a complex structure obeying the laws of quantum physics. There are no such things as sharply defined trajectories. Electrons occupy quantum states corresponding to energy levels. Whenever a transition occurs from a given energy level to another one, a photon is emitted or absorbed whose frequency ν is proportional to the energy difference ∆E between the two level according to the well-known Planck’s formula:

Figure 1.3. Misleading planetary model of the atom: electrons (green dots) orbit the nucleus (orange dot). The figure is not drawn to scale: the radius of the nucleus is about 1/100000 of the atomic radius.

∆E = hν

where h (=6.63 × 10⁻³⁴ Js) is a universal constant.

An atom having lost at least one electron is ionised.

2. Nuclei

The nucleus is an assembly of nucleons: protons carrying the positive elementary charge e, and neutrons, which are electrically neutral as their name says it. The number of protons is equal to the atomic number Z. A proton and a neutron are both 2000 times more massive than the electron. Consequently, the greater part of the atomic mass lies in the nucleus. Since the radius of the nucleus is 10⁵ times smaller than the atomic radius, the density of the nuclear matter is 10¹⁵ times the solid-state density.

The zoo of nuclei is very rich. Each one is characterized by two numbers: the number of protons Z and the total number of nucleons A, which is also the atomic mass number. Given a chemical element, several mass numbers are available for a single atomic number. The corresponding nuclei are called isotopes. A nucleus is represented in short hand by a symbol with two indices on the left: the lower index is the atomic number Z, the upper one is the mass number A. Accordingly the deuteron, a heavy isotope of hydrogen, is represented by

. Many isotopes are stable: most isotopes are unstable and decay into smaller objects, according to various modes of radioactivity. On Figure 1.4, light nuclei are displayed on a Segré’s chart.

Figure 1.4. Light nuclei. In abscissas the number of protons, in ordinates the number of neutrons. Gray cells correspond to unstable isotopes. Beryllium-8 is by far the most unstable of light isotopes.

If only electrostatic repulsion and gravitational attraction, a small, almost negligible force, existed, a nucleus made of protons and neutrons would explode. A compensating force of a different nature is necessary to bind an assembly of nucleons together. It should be exceedingly intense and is named the strong nuclear interaction. Its range cannot extend much beyond the radius of the nucleus. Otherwise, Rutherford scattering of alpha particles by nuclei would not obey Coulomb’s law, as observed experimentally, whenever the incident particle comes closer to the target.

The electromagnetic interaction with infinite range is mediated by a massless particle, i.e. the photon. Due to its short range, the strong nuclear interaction is, on the contrary, mediated by massive particles: pions which are created and used in high energy physics experiments. They are either neutral or charged (either sign). Their mass is about 200 times the electron mass, hence the name meson which stands for an intermediate between electrons and nucleons. Nucleons and pions are themselves made of smaller entities — quarks, which are quoted here for the sake of completeness. Actually, an assembly of nucleons stuck by pions is the most adequate picture in the realm of man-made nuclear energy.

In nuclear processes such as the neutron decay (β radioactivity)

electrons and neutrinos (ν₀) are involved. Since these particles are insensitive to the strong interaction, the above nuclear reaction cannot depend on the strong force. Another nuclear force is necessary. It turns out to be far less intense and for that reason is called the weak interaction.

As far as we know it, only four forces do exist in nature: gravitation and electromagnetic interaction which have infinite range and the two nuclear interactions whose range is comparable to the size of a nucleus. Inside many nuclei, the strong nuclear force is more intense than the electrostatic repulsion. Nucleons stay confined inside a potential well. On the contrary, when Z is larger than 82 (Pb), the global electrostatic field is a sizable fraction of the strong attractive field. Heavy nuclei are thus unstable (radioactive).

3. Nuclear reactions

In some chemical reactions, atoms combine to build up more or less complex molecules. In other chemical reactions, molecules exchange atoms or group of atoms. Such processes absorb or release energy. By the same token, nuclei interact and exchange nucleons whilst absorbing or releasing energy. For instance, an alpha particle striking a nitrogen nucleus transforms the latter into an oxygen nucleus and a proton is emitted. Such a transmutation is written the same way as a chemical reaction. In a nuclear reaction, the number of nucleons and the total electric charge are conserved.

The probability of the reaction is represented by a quantity whose dimensions are those of a surface: the cross section. This definition applies to any binary processes.

Box 1.2. The probability of a microscopic event and cross section

Most nuclear reactions are binary since they have two reactants. Every event has a probability of occurrence. Let J_p be the flux of particles in a parallel beam, all with the same velocity. The beam impinges normally onto a slice of matter with thickness dx containing n_c targets per unit volume. Provided an incident particle undergoes no more than a single collision to produce a giv...