Controlled Nuclear Fusion
Controlled Nuclear Fusion
Our tour through plasma science finally returns to the hot plasmas of the stars. But now we are interested how to mimic the conditions in the interior of stars by hot plasmasconfinedinfusionreactors.Researchoncontrollednuclearfusionpromises an energy source that could provide the worlds growing energy demand in the 21st century and beyond. In the cold-war era after World War II, research on nuclear energy was done within secret programs. In the United States, the astrophysicist Lyman Spitzer (1914–1997) began building a stellarator device at Princeton University. Richard F. Post (1918–) was setting up a mirror machine at the University of California’s Livermore laboratory. In the Soviet Union, the tokamak concept was introduced by Igor Tamm (1895–1971) and Andrei Sakharov (1921–1989). In 1956, the Soviet research on controlled nuclear fusion was unilaterally disclosed to Western scientists by Igor V. Kurchatov (1903–1960). In short time, the road to a peaceful use of nuclear fusion energy opened in 1958 at the 2nd Atoms for Peace Conference in 1958, when scientists from around the world were allowed to share their results and laid the foundation for “one of the most closely collaborative scientific endeavours ever undertaken” [37]. The common goal of all these attempts is to use the energy resulting from the fusion of deuterium and tritium nuclei to operate a power plant. The reaction channels and associated energies are compiled in Table 1.5. A significant yield of fusion reactions can only be expected at such kinetic energies of the fusion partners that overcome the Coulomb repulsion between the likecharged nuclei. Figure 1.15 shows the fusion cross sections as a function of the particle energy in the center-of-mass system. The figure uses the tabulated values from [38, 39]. The fusion reactions set in between 10 and 100keV energy. Moreover, the crosssectionfortheD–Treactionisfound,atthesameenergy,muchlargerthanthat of the D–D or 3He–D reaction. This is the reason why all present experiments for igniting a fusion reaction use D–T mixtures. Actual concepts for obtaining nuclear
Table 1.5 Fusion reactions of the hydrogen isotopes 2D+ 2D → 3T + p + 4.0 MeV 2D+ 2D → 3He + n + 3.3 MeV 2D+ 3T → 4He + n + 17.6 MeV 2D+3He → 4He + p + 18.3 MeV
18 1 Introduction
Fig. 1.15 The cross section for D–T, D–3He and D–D fusion reactions as a function of the center-of-mass energy. The D–D cross section is the sum of both reaction channels
fusion are either based on magnetically-confined hot plasmas in so-called tokamak or stellarator devices, or on heating small pellets containing deuterium and tritium with ultra-intense laser beams.
1.5.1 A Particle Accelerator Makes No Fusion Reactor
Why can’t we simply operate a particle accelerator as a fusion reactor? Obviously, todayitisnobigtechnicalproblemtoaccelerateionsto(0.1–1)MeV.Letusassume that we shoot a beam of tritium ions with the optimum energy into a solid target of deuterium ice, which may be a cube of 1cm edge length that contains roughly 5.4×1019 deuterium atoms (Fig. 1.16). The probability p of hitting one of these target atoms is the ratio of the blocked area to the cross section of the cube, i.e., p = 2.7 × 10−4. This means, however, that 99.97% of the projectiles have not performed a fusion reaction. Let us further assume that the tritium beam represents an electric current of I = 1A, which is quite substantial at 100keV energy. Then the cube is hit by dNT/dt = I/e = 6.3×1018 tritium ions per second (e is the elementary charge). The product of this hit rate with the reaction probability and the fusion energy of 17MeV gives a respectable fusion power of 4.6kW per cubic centimeter. However, will this ion beam be able to penetrate a solid deuterium ice cube? Unfortunately, no. The interaction of the tritium ion beam with the electrons
Fig. 1.16 Cartoon of the deuterium ice-cube with an impinging tritium ion beam
1cm
D2 ice
tritium beam
1.5 Controlled Nuclear Fusion 19
of the densely packed deuterium atoms leads to a rapid energy loss, which is of the order of 4×105 eVcm−1. Hence, the initial energy of 100keV will be completely lostasheatwithintheicecube.Sincenoionenergyisleftontheexitside,wewould have to replenish the ion energy at a rate of 100kV×1A=100kW, which is much more than we would gain from fusion. This is why nuclear fusion uses a different concept. The trick is that the heat becomes not lost energy for the fusion processes. The magnetic confinement fusion approach starts with a hot gaseous plasma containing deuterium and tritium ions. Collisions between D+ and T+ ions, which do not lead to fusion, only scatter the collision partners but do not alter the heat content of the hot plasma. Admittedly, there is an energy leak by means of radiation losses (Bremsstrahlung), which are generated during the scattering process. However, different from the accelerator concept, where energy is dissipated in microseconds, the particle energy of the fusion partners in the hot plasma can be contained for fractions of a second. This is necessary to compensate for the lower density of the gaseous medium. The other approach, inertial confinement fusion (ICF), which will be touched in Sect. 1.5.6, achieves nuclear fusion in a highly compressed D–T target that has a density of 300gcm−3, about 1500 times the density of D–T ice. The plasma is confined, for a short time of the order of a nanosecond, by its own inertia. This concept was originally developed by John Nuckolls, in 1957, before the invention of the laser. A full concept using lasers to compress the plasma was published in 1972 [40]. Alternatively, heavy-ion beams were suggested for ICF [41].
Our tour through plasma science finally returns to the hot plasmas of the stars. But now we are interested how to mimic the conditions in the interior of stars by hot plasmasconfinedinfusionreactors.Researchoncontrollednuclearfusionpromises an energy source that could provide the worlds growing energy demand in the 21st century and beyond. In the cold-war era after World War II, research on nuclear energy was done within secret programs. In the United States, the astrophysicist Lyman Spitzer (1914–1997) began building a stellarator device at Princeton University. Richard F. Post (1918–) was setting up a mirror machine at the University of California’s Livermore laboratory. In the Soviet Union, the tokamak concept was introduced by Igor Tamm (1895–1971) and Andrei Sakharov (1921–1989). In 1956, the Soviet research on controlled nuclear fusion was unilaterally disclosed to Western scientists by Igor V. Kurchatov (1903–1960). In short time, the road to a peaceful use of nuclear fusion energy opened in 1958 at the 2nd Atoms for Peace Conference in 1958, when scientists from around the world were allowed to share their results and laid the foundation for “one of the most closely collaborative scientific endeavours ever undertaken” [37]. The common goal of all these attempts is to use the energy resulting from the fusion of deuterium and tritium nuclei to operate a power plant. The reaction channels and associated energies are compiled in Table 1.5. A significant yield of fusion reactions can only be expected at such kinetic energies of the fusion partners that overcome the Coulomb repulsion between the likecharged nuclei. Figure 1.15 shows the fusion cross sections as a function of the particle energy in the center-of-mass system. The figure uses the tabulated values from [38, 39]. The fusion reactions set in between 10 and 100keV energy. Moreover, the crosssectionfortheD–Treactionisfound,atthesameenergy,muchlargerthanthat of the D–D or 3He–D reaction. This is the reason why all present experiments for igniting a fusion reaction use D–T mixtures. Actual concepts for obtaining nuclear
Table 1.5 Fusion reactions of the hydrogen isotopes 2D+ 2D → 3T + p + 4.0 MeV 2D+ 2D → 3He + n + 3.3 MeV 2D+ 3T → 4He + n + 17.6 MeV 2D+3He → 4He + p + 18.3 MeV
18 1 Introduction
Fig. 1.15 The cross section for D–T, D–3He and D–D fusion reactions as a function of the center-of-mass energy. The D–D cross section is the sum of both reaction channels
fusion are either based on magnetically-confined hot plasmas in so-called tokamak or stellarator devices, or on heating small pellets containing deuterium and tritium with ultra-intense laser beams.
1.5.1 A Particle Accelerator Makes No Fusion Reactor
Why can’t we simply operate a particle accelerator as a fusion reactor? Obviously, todayitisnobigtechnicalproblemtoaccelerateionsto(0.1–1)MeV.Letusassume that we shoot a beam of tritium ions with the optimum energy into a solid target of deuterium ice, which may be a cube of 1cm edge length that contains roughly 5.4×1019 deuterium atoms (Fig. 1.16). The probability p of hitting one of these target atoms is the ratio of the blocked area to the cross section of the cube, i.e., p = 2.7 × 10−4. This means, however, that 99.97% of the projectiles have not performed a fusion reaction. Let us further assume that the tritium beam represents an electric current of I = 1A, which is quite substantial at 100keV energy. Then the cube is hit by dNT/dt = I/e = 6.3×1018 tritium ions per second (e is the elementary charge). The product of this hit rate with the reaction probability and the fusion energy of 17MeV gives a respectable fusion power of 4.6kW per cubic centimeter. However, will this ion beam be able to penetrate a solid deuterium ice cube? Unfortunately, no. The interaction of the tritium ion beam with the electrons
Fig. 1.16 Cartoon of the deuterium ice-cube with an impinging tritium ion beam
1cm
D2 ice
tritium beam
1.5 Controlled Nuclear Fusion 19
of the densely packed deuterium atoms leads to a rapid energy loss, which is of the order of 4×105 eVcm−1. Hence, the initial energy of 100keV will be completely lostasheatwithintheicecube.Sincenoionenergyisleftontheexitside,wewould have to replenish the ion energy at a rate of 100kV×1A=100kW, which is much more than we would gain from fusion. This is why nuclear fusion uses a different concept. The trick is that the heat becomes not lost energy for the fusion processes. The magnetic confinement fusion approach starts with a hot gaseous plasma containing deuterium and tritium ions. Collisions between D+ and T+ ions, which do not lead to fusion, only scatter the collision partners but do not alter the heat content of the hot plasma. Admittedly, there is an energy leak by means of radiation losses (Bremsstrahlung), which are generated during the scattering process. However, different from the accelerator concept, where energy is dissipated in microseconds, the particle energy of the fusion partners in the hot plasma can be contained for fractions of a second. This is necessary to compensate for the lower density of the gaseous medium. The other approach, inertial confinement fusion (ICF), which will be touched in Sect. 1.5.6, achieves nuclear fusion in a highly compressed D–T target that has a density of 300gcm−3, about 1500 times the density of D–T ice. The plasma is confined, for a short time of the order of a nanosecond, by its own inertia. This concept was originally developed by John Nuckolls, in 1957, before the invention of the laser. A full concept using lasers to compress the plasma was published in 1972 [40]. Alternatively, heavy-ion beams were suggested for ICF [41].
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