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Fusion energy

Thermonuclear reactions are the main source of energy in the stars and play a very important role in astrophysical processes. In the nucleus of the stars the temperature and density of matter are so high that a large number of fusion reactions occurs. The main constituent of stellar matter, hydrogen (H), is converted into helium (He), in a process releasing a huge amount of thermal energy, electromagnetic radiation, particle flow (solar wind) and neutrinos.

The chain of reactions leading to a helium nucleus 4He (or α-particle, consisting of 2 protons and 2 neutrons) starting from two hydrogen nuclei through the formation of deuterium (2H = D, hydrogen isotope) and 3He, isotope of helium) is called proton-proton chain (pp). The total energy released to form a 4He nucleus is 26.72 MeV (1 keV = 11.6106 K). In large-scale stars whose core reaches about 16 million K, the carbon-nitrogen-oxygen chain (CNO) is the dominant process where four protons fuse, using carbon, nitrogen and oxygen isotopes as catalysts, to produce one α-particle, two positrons and two electron neutrinos. The energy released in this cycle of reactions is 27.07 MeV.

In the sun and stars, fusion reactions are favored by gravitational forces and extremely high temperatures that allow the formation of an energetic plasma.

In order to be able to replicate on Earth, a different approach is needed, relying on the use of two hydrogen isotopes - the deuterium (D, nucleus formed by a proton and 1 neutron) obtainable from water and tritium (T, nucleus formed by 1 proton and 2 neutrons). The following figure illustrates the concept of isotopes applied to the hydrogen case, which have the same chemical properties (due to the same atomic number Z) but different physical properties (due to the different mass number A).

Idrogeno, deuterio e trizio a confronto
L'idrogeno e i suoi isotopi pesanti: deuterio e trizio. Il diverso numero di neutroni presenti nei rispettivi nuclei ne determina una massa complessiva differente (immagine elaborata, fonte https://306physics.wikispaces.com/Nuclear+Physics).

 

The D-T reaction (shown in the figure below) 2H + 3H → 4He + n is the one that requires a lower temperature to occur and has higher cross-section and reactivity (average number of reactions per unit of time and volume) at laboratory temperatures. Therefore, this reaction is the one chosen in the first generation of fusion reactors. It provides  17.6 MeV in the form of kinetic energy of the resulting products (14.1 MeV carried by the neutron and 3.2 MeV by the α-particle).

Reazione di fusione D-T

 

Physics of nuclear fusion

The fundamental principle of fusion is the collision of energetic atomic nuclei: two nuclei positively charged (for example deuterium and tritium) must overcome the electrostatic repulsion existing between charges with the same sign in order to "fuse" each other.

Interazione coulombiana e plasma termalizzato

This can be efficiently accomplished only by exploiting the thermal motion in a high temperature gas, or plasma. In the fusion process of light atoms, an amount of energy associated to the overall mass defect of the reaction products is released according to the relation ΔE = Δm c2.

In order to have a sufficiently large number of fusion reactions to occur in a reactor, a significant amount of energy must be introduced into the confined plasma in order to increase its average energy, i.e. the temperature, up to 10-100 keV. The process of producing energy is convenient from the point of view of the overall balance if the power produced by the fusion reactions is greater than the power injected into the system to achieve the required plasma conditions. The gain factor Q is the ratio between the output power PFUS coming from fusion reactions and that input power PIN, Q = PFUS / PIN. The condition to be satisfied is therefore Q> 1 (Q = 1 is called break-even condition).

Another important parameter to quantify the efficiency of a nuclear reaction is the triple product n T τE where n is the plasma density, T is its temperature and τE the time of energy confinement (defined by the ratio of plasma energy over the additional power supplied).

When the triple product is greater than a given threshold (the threshold being a function of the temperature), the ignition is obtained, a condition in which the heat produced by the fusion reactions self-sustains the burning plasma.

 

Fusion technology

In the stars, the plasma is confined by the intense gravitational field generated by its mass. This is not possible in a laboratory, but the need of a confined plasma is essential to have the nuclear reactions sustaining the melting process. The confinement structure must be maintained at reasonably low temperatures, unlike plasma, which must be heated up to temperatures of hundreds of millions of degrees; in such conditions, any contact would lead to a cooling down of the plasma itself and the walls of the container would be damaged.

For this purpose, the two most promising options are magnetic confinement and inertial confinement.

Magnetic confinement uses strong magnetic fields that can constrain the motion of plasma charged particles to be confined to a limited region.

In magnetic confinement machines, the field is generated by electric currents flowing into coils placed around the plasma confinement zone and the chamber that contains it. An advantageous solution to limit leakage due to particle dynamics utilizes a toroidal shape that does not have open ends: within it, the field lines are closed rings. Actually charged particles in a non-uniform field are subject to transverse drift motions that cause the loss of their confinement. To overcome this problem, magnetic field lines of additional magnetic field are used, which are not simple circumferences but wind up on toroidal surfaces. Examples of this configuration are the tokamak and the stellarator.

In the inertial confinement scheme, a mixture of liquid deuterium-tritum contained in a hollow sphere of several millimeters diameter is bombarded with high power laser beams (hundreds of terawatts per tens nanoseconds) or energy particle bundles uniformly and simultaneously from different directions distributed over the solid angle, producing a rapidly expanding plasma on the surface of the target. By reaction, the internal region of the DT fuel-containing sphere is subjected to a strong compression force directed towards the center, until its density reaches very high values for a very short time (about 1000-10000 times the solid matter density for a few nanoseconds) and the temperature the ignition condition (about 100 million K).


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