The impact of fusion

Controlled thermonuclear fusion is one of the few energy supply options capable of supplying energy on a large scale for the twenty-first century.

According to recent estimates, the world population will grow to around 10 billion about halfway through the next century.

In 1990, the primary energy consumption per head per year in the industrial countries was about 2.2 x 10¹¹ Joules, or 5.1 t.p.e. (tonnes of petrol equivalent) and about 10 times less in the developing countries. Depending on the scenario for the evolution of the world energy demand, the primary world energy consumption might increase by a factor of two or three by the year 2050.

The energy sources having a capability of covering a substantial share of the energetic needs are the following:

• Fossil fuels: basically carbon, seeing as how the petrol and gas reserves will have diminished considerably in the next century.
• Nuclear energy: fission and fusion.
• Renewable energy: hidro-electric energy, solar, wind, wave, geothermal, biomass energy, etc ...

Nuclear Reactions

The atomic nuclei consist of protons and neutrons that are packed together in a tremendously compact way in a small region of space. These common building blocks of all nuclei are commonly called nucleons. Protons and neutrons possess a nearly identicall mass, which is 1836 times larger than the electron mass. The size (radius) of a nucleus is approximately given by the expression

where r=1.5 x 10^-13 cm and A is the number of nucleons in the nucleus.

Z is the number of protons in the nucleus; the variation of A-Z for any given Z gives rise to the phenomenon of isotopes. Two isotopes of hydrogen: deuterium and tritium, are very relevant to fusion at the moment, as we will see further on. Often the isotopes of a naturally occurring element are radioactive and transform spontaneously into other elements. E.g., tritium has a weak beta emission (with an average energy of 5.7 keV and a maximum energy of 18.6 keV) and with a half-life of 12.35 years. Yet this phenomenon is not of any great importance to fusion since the characteristic times at which the fusion process occurs is short enough for this decay to occur very often.

Inside the nuclei the repelling forces between the positively charged protons are much smaller than the nuclear attractive - or binding - forces that keep the nucleus together. In order to extract a nucleon from the nucleus, an amount of energy is necessary; and when a nucleon is captured by a nucleus, this same energy is released. The required energy depends on the atomic weight A, but has a maximum value of around 8 MeV for nuclei close to iron. In fission, heavy elemnts with binding energies less than 8 MeV break up into lighter nuclei, thus releasing energy since the resulting nuclei are closer to iron. In fusion, on the other hand, two light nuclei combine yielding a heavier one, which also is closer to iron. The latter process is the one which causes the stars to have an iron nucleus towards the end of their lives. Both in fission and in fusion, a considerable amount of energy is released, equivalent to the decrease in total mass of the product nuclei with respect to the initial mass. The mass difference is released as energy in accordance with the famous equation by Einstein:

To form a nucleus of more than one constituent, it is necessary for them to get close enough together for the nuclear attractive forces to work. In order to do so, they will have to surmount the Coulomb repelling force, which acts as a barrier, before the attractive nuclear forces can come into play. The repelling Coulomb force os proportional to the charge of the interacting nuclei, and therefore plasmas made up of nuclei of the hydrogen family are most adequate for the achievement of fusion. There exist various fusion reactions that may be useful from the energetic point of view. Of all the reactions that involve isotopes of hydrogen, the reaction deuterium-tritium has the largest cross section for relatively low temperatures and, therefore, is the easiest to achieve in a controlled fashion. The reaction produces a highly energetic neutron and a helium.

On our planet, deuterium abounds in seawater (30 g/m³), but tritium does not exist naturally, because of its radioactivity with a half-life of 12.36 years, and therefore it is necessary to produce it. In a fusion reactor, the neutrons, that carry away 80 % of the produced energy, will be absorbed in a breeding mantle which covers the central part of the reactor, where lithium will transform itself into tritium and helium:

Naturally occurring lithium (92.5% 7Li y 7.5% 6Li) is an abundant element in the earth's crust (30 ppm: parts per million), while smaller concentrations are also found in the seas. The mantle thickness must be sufficient (of the order of a metre) to slow down the neutrons (having 14 MeV) that are produced in the fusion process. The neutrons combine with the lithium to form tritium. In slowing down the neutrons, the breeding mantle heats up and the coolant that flows through it transfers the heat to an area external to the reactor, where it is used to vaporize water that finally is converted into electrical energy in a conventional manner.

The use of pure deuterium fuel is a long-range goal that has the following advantages: it is not radioactive, it is not necessary to employ a breeding mantle for its production, and it induces low-level radioactivity in the structural components. The reaction produces helium-3 and a neutron or tritium and a proton.

The reaction deuterium-helium-3 is attractive due to its cross section and because it doesn't produce neutrons. Helium-3 is very scarce on Earth, but is available in great quantities on the Moon.

Fusion plasmas

In order to surmount the electrostatic repulsion between nuclei that one wants to fuse under laboratory conditions, it is necessary to don them with much energy; this can be achieved by heating them to very high temperatures. Under such conditions matter is in a gaseous state of ionization exhibiting collective behaviour which we call plasma. 99% of the Universe consists of such plasmas, or ionized matter, but in nature exist a great variety of plasmas that do not necessarily possess the high temperature plasma conditions required for fusion.

In order to obtain a net positive result in a fusion reactor it is necessary to heat the plasma to sufficiently high temperatures and to reach densities, n, of the order of 10²⁰ particles/m³, during a time Tau_E that is of the order of seconds. That is to say, the product n Tau_E must be larger than a minimum value, denominated the Lawson criterium, at temperatures of the order of 100 million degrees centigrade. The final goal of the fusion research program is to achieve the ignition condition, i.e. to keep the plasma burning in a self-sustained way, through the energy contribution of the fusion products themselves that are confined in the plasma. In a deuterium-tritium (D-T) reactor, the kinetic energy of the helium ash will maintain the temperature needed for the continuation of the reactions without requiring external heating.

Two experimental roads towards the achievement of this goal are being investigated: fusion by magnetic confinement, in which a hot plasma is being confined by magnetic fields that act as a magnetic trap for the charged particles of the plasma - in this scheme, n = 10²⁰ m^-3 and Tau_E = 1 to 5 s; fusion by inertial confinement, in which a minute capsule of fuel is strongly compressed (to more than 1000 times the density of a liquid) until the fuel ignites in the core of the capsule and the flame propagates towards the exterior, where the fuel is colder. The ignition phase lasts only while the fuel is confined by its own inertia. Inertial confinement cannot be stationary - in this scheme n = 10³¹ m^-3 and Tau_E = 10^-11 s; Tau_E is the free expansion time of the matter.

One of the characteristics of a plasma is that it can be confined by magnetic fields. Effectively, the charged particles in the plasma are forced to describe spiral-like trajectories around the magnetic field lines.

The equation of motion of the particle is:

where m is the mass of the particle, e its charge and c the velocity of light. The component of v parallel to B is not affected by B, but the particle girates around B in circles, centred at a field line, with a radius rL (Larmor radius):

where is the component perpendicular to B.

The sum of the circular movement and the translation along B with velocity v_|| give rise to a helicoidal trajectory with a magnetic moment of:

where is the magnetic energy of rotation of the particle.

The magnetic moment of the particle is conserved, so that the magnetic energy of the particle increases with the magnetic field.

Nevertheless, the collisions between particles result in displacements across megnetic field lines and surfaces, resulting in an associated loss of magnetic confinement. This collisional transport is inevitable but does not impede that the particles can be confined; yet it does reduce their confinement time.

In the present, the research in the field of fusion by magnetic confinement is the most advanced with regard to the construction of a future fusion reactor.