# how is nuclear fusion used

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```					M. Moodley 2008

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Nuclear Fusion

In a nuclear fusion reaction, two or more small light nuclei come together or fuse, to form a larger nucleus: • the mass of the ﬁnal nucleus is less than the combined masses of the orignal nuclei • therefore there is a loss of mass accompanied by a release of energy

7.1

The Proton-Proton Cycle
2 + 1 1 1H + 1H → 1H + β + ν 2 1 3 1 H + 1 H → 2 He + γ 1 1 3 3 4 2 He + 2 He → 2 He + 1 H + 1 H

Consider the following energy-liberating fusion reactions: (1) (2) (3)

• in (1), two protons combine to form a deuteron (2 H) with the emission of a positron (β + ) and a neutrino • in (2), a proton and deuteron combine to form the nucleus of the light isotope of helium (3 He) with the emission of a gamma ray (γ) • interactions (1) and (2) have to occur twice in order to provide the two 3 He nuclei needed in interaction (3) to form an alpha particle (4 He) and two protons Together the reactions make up the process called the proton-proton cycle/chain.

Figure 1: The proton-proton cycle The net eﬀect of the chain is the conversion of 4 protons into • 1 alpha particle • 2 positrons • 2 neutrinos • 2 gamma rays The net process can be written as: 41 H → 4 He + 2β + + 2ν + 2γ 1 2

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Energy release (Q value) for this process: • the mass of 1 alpha particle plus 2 positrons is the mass of neutral 4 He • the neutrinos have zero (or negligible) mass • gamma rays have zero mass mass of 4 protons = 4.029106 u mass of 4 He = 4.002603 u mass diﬀerence = 0.026503 u energy release = (0.026503 u)(931.5 MeV/u) = 24.69 MeV But what about the positron? • the 2 positrons that are produced during interaction (1) of the protonproton chain collide with 2 electrons • mutual annihilation of the 4 particles takes place • their energy 4×(5.486×10−4 u)(931.5 MeV/u) = 2.044 MeV is converted to gamma radiation Therefore the total energy release is: Q = 24.69 MeV + 2.044 Mev = 26.73 MeV The proton-proton cycle takes place in the interior of the sun and other stars: • these reactions take place at temperatures of 15 × 106 K • only such high temperatures can sustain these reactions =⇒ called thermonuclear fusion reactions • each gram of the sun’s mass contains about 4.5 × 1023 protons - if all of these protons were fused into helium, the energy released would be about 130 000 kWh

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Fusion Reactors

The proton-proton interaction (as for the sun) is not suitable for use in a fusion reactor because this requires very high pressures and densities of protons. The most promising reactions that can be used in a fusion power reactor involves: • deuterium • tritium
2 1H 2 1H 2 1H

+ 2H → 1 + +
2 1H 3 1H

→ →

3 1 2 He + 0 n 3 1 1H + 1H 4 1 2 He + 0 n

(Q = 3.27 MeV) (Q = 4.03 MeV) (Q = 17.59 MeV)

The last reaction known as the D-T reaction has the largest energy release and is the best candidate.

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When deuterium gas is heated to high temperatures • the atoms become ionized • the resulting gas of hot ionized particles is called a plasma To increase the probability of collisions between the ions that would result in fusion, there are three requirements: 1. a high density n, so that the particles have a high probability of collision 2. a high temperature T, in the range of 108 K, which increases the probability for the particle to overcome their mutual Coulomb barrier 3. a long conﬁnement time τ , during which the high temperature and density must be maintained. Energy considerations: • the energy required to heat the plasma is proportional to the ion density n, whereas the energy generated by the fusion process is proportional to the product n2 τ . • therefore the density and conﬁnement time must both be large enough so that more fusion energy will be released than is required to heat the plasma. • the condition for the fusion power to exceed the input power is nτ ≥ 1020 s.m−3 which is known as Lawson’s criterion How can we conﬁne a plasma at a temperature of 108 K for times of the order of 1s? The two basic techniques under investigation to conﬁne plasmas are • magnetic conﬁnement • inertial conﬁnement Magnetic conﬁnement: The device used in this method is called a tokamak (Russian acronym for ”toroidal magnetic chamber”) • has a doughtnut-shaped geometry ( a toroid) • two magnetic ﬁelds are used to conﬁne and stabilize the plasma; one along the toroid axis and another around the axis • together these ﬁelds produce a helical ﬁeld along the toroid axis and the charged particles are conﬁned as they spiral about the ﬁeld lines • the current that passes through the plasma heats it

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Figure 2: Schematic of a typical tokamak. Inertial conﬁnement: Here the fuel is compressed to high densities for a very short conﬁnement time ( 10−11 to 10−9 s ) • because of their own inertia, the particles do not have a chance to move appreciably from their initial positions • the most common method is the laser fusion technique

Figure 3: Inertial conﬁnement using laser fusion. Advantages of Fusion: • the low cost and abundance of the fuel (deuterium) • the absence of weapons-grade material • impossibility of runaway accidents • a lesser radiation hazard than ﬁssion

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Problems and disadvantages of fusion: • its as yet unestablished feasibility • the very high proposed plant costs • the possibility of the scarcity of lithium which is used as a heat exchanger • the limited supply of helium and superconducting materials that are needed in the tokamak-type reactors

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