# Fusion Nuclear Atoms

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What is fusion?

In these lecture notes fusion will refer to the controlled process in which two light atoms are fused together with the aim of producing energy. Fusion is a long sought after solution for the worlds energy needs, with the first research starting only shortly after the Second World War. In the early days it was thought that the solution was close at hand. Many problems have, however, since these first attempts been identified, and we are still a good distance away from a working reactor. For physics students this is not all bad news. The physics of a fusion reactor is an active and attractive area of research, with many unsolved problems, which (if my colleagues will forgive me) are not just of academic interest, and are nevertheless challenging.

the binding energy per nuclear particle in an atom as a function of the mass number A. For heavy elements the binding energy increases in the direction of lower mass number. Energy can therefore be released when a heavy atom is split into two (or more) lighter atoms. This is the reason behind the release of energy in fission reactors, were very heavy atoms (Uranium) are split through the interaction with neutrons. For sufficient small mass number the binding energy increases with increasing mass number. Energy can therefore also be released through the fusion of two light elements.

A typical fission reaction, base on Uranium, is shown in . 2. In every reaction several new neutrons are generated allowing for a continuous chain of reactions with the neutrons produced in one fission reaction catalyzing new reactions. This can unfortunately lead to an uncontrolled evallange of fission reactions with a large amount of energy released in a short time. This can lead to damages to the reactor and in the worst case to a large amount of radio-active material set free in the environment. Note that the reaction products are in general not (all) stable nuclei and therefore also the problem of nuclear waste must be faced. The disadvantages of a fission reactor are well known (not inherently safe, nuclear waste) and are hotly debated in public. It is outside of the scope of these lecture notes to evaluate the risks against the benefits. In view of the rest of these lecture notes I however feel that it is fair to point out that fission is a developed and working solution, whereas many of the alternatives are not.

Why fusion ??

The energy production through the use of nuclear fusion would have several advantages over current power plants.

present plan for the first fusion reactor is based on a burning plasma containing two isotopes of Hydrogen, namely Deuterium and Tritium.

To the cost argument, which is indeed rather popular, one should remark that it will not be the price of the fuel that will determine the price of the electricity. Nuclear fusion is not necessarily cheap due to the costs of the reactor itself, which is expected to be a rather complicated device, and has a finite lifetime due to the high neutron flux. With respect to the fuel it is, therefore, more important that it is present everywhere on earth. Consequently, it is of great interest to regions who currently have no access to oil or gas.

Of increasing importance is also the fact that nuclear fusion is CO2 neutral, i.e. it does not contribute to the greenhouse effect.

Of course fusion energy shares some of its advantages (and disadvantages) with fission energy. The advantages can be summarised as

- No risk of uncontrolled energy release

- Greatly reduced quantity of high level waste

- Greatly reduced threat to non-prol iferation of weapons material

Two main lines are pursued towards the realisation of thermonuclear fusion: inertial (ICF) and magnetic confinement (MCF). In both cases, a burn criterion must be satisfied which requires that a minimum quantity of fuel, represented by the fuel density *n*, be

maintained together for a minimum time span *E *(the energy confinement time) at a sufficiently high temperature *T*, brought together in the fusion triple product n tE T. Both of these lines have achieved considerable advances in recent years and in both instances the prospects for successful reactor application has been strengthened. In this lecture the basic principles of each of these lines are given, followed by a more in depth discussion of the conurations in which magnetic fusion research is pursued, with special emphasis on the tokamak.

II. INERTIAL CONFINEMENT

Inertial confinement fusion1 (ICF) uses laser or particle beams (called drivers) to heat frozen D-T pellets

(radius R), either directly or indirectly via conversion into X-rays, to the necessary fusion temperatures1. The heating pulses are typically 1 to 10 ns long. A reactor based on this concept is inherently pulsed and, hence, the basic reactor requirement should be to produce a substantial *target gain G*, defined as the energy yield of the fusion reactions divided by the energy of the driver. High yield depends on the number of fusion reactions that can occur in the time before the fuel disassembles i.e. during the time the fuel is confined on account of its finite mass. A good approximation for the inertial confinement time tE is

then the time it takes for an ion to move over the distance R, at its thermal speed *Vthi, *taken as the sound speed *(KT/m)1/2*. The ICF burn criterion is known as the *Rcriterion*, also called the high-gain condition, and is essentially obtained by requiring that almost all the fuel contained in the pellet is indeed burned, i.e. that the number of reactions that take place during the time interval *E *equals the number of fuel deuterons or tritons. The standard form reads2

*R 4 ( m K T)1/2 < v>-1 *(1)

where *m *is the mean ionic mass, the mass density *= n m*, and *< v> *is the fusion reaction rate constant. For D-T* R 3 g/cm2 *at *T = 50 keV*. The *R*-criterion can also berewritten in terms of density and confinement time, as *n E = < v>**-1*. The triple product that results from this putsthe reactor requirement typically 10 times higher than whatis asked for MCF, a consequence of the inherentinefficiency in assembling the fuel. Please note also thatin ICF the term ignition does not have the same meaningas in MCF, as it refers to the condition of efficient a-particle capture, a *R *value of at least 0.3 *g/cm**2 *beingrequired to slow the a-particles down in the pellet3.Since DT-ice has a mass density = 0*.*2 g/cm*3*,satisfying the *R*-criterion asks for massive targets,requiring for their heating unattainable amounts of driverenergies. An escape from this apparent impasse is howeverpossible. By compression of the pellet, can be increasedsignificantly. An increase by, for instance, a factor of 1000would lower the energy demand by 109, thus bringing it

in the range of what is technically achievable. In addition, it is not obvious that the total amount of heat that is needed to bring the fuel to fusion temperatures must be provided by the lasers or beams. It might be enough to ignite a fraction of the pellet and let the fusion energy, thus liberated, heat the rest. The latter requirement is also dictated by considerations of the energy economy of the scheme. It is easy to show that the intrinsic gain *G**i *of a uniformly heated D-T pellet, defined as the ratio of the energy liberated by fusion to the energy needed to reach the fusion conditions, is at most about 200. The efficiencies in the external systems of the power plant and the low efficiencies of the driver generation, ask for reactor target gains of about 100. Noting that *G = **T **G**i *requires in turn intrinsic gains of about 104 to account for a realistic coupling efficiency *T *of the driver. For inertial confinement to be attractive, it is

therefore mandatory to demonstrate that it is possible to burn the whole pellet after bringing just a small fraction to ignition temperature at the densities imposed by the *R*criterion.

The reader is referred to Refs. 1-3 for more details on pellet compression and hot spot creation.