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## Chapter 5. Thermonuclear Fusion

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**Chapter 5. Thermonuclear Fusion**• Introduction • Thermonuclear Reactions and Energy Production • Fusion in a Hot Medium • Progress Towards Fusion Power • Stellar Burning**Nuclear Fusion**Neutron proton Two nuclei combine into one nucleus plus a nucleon is callednuclear fusion, a nuclear reaction. The picture here illustrates the fusion of 2D + 3T 4He + n that releases a lot of energy. Fusion**Penetration through a rectangular energy barrier (height B)**of a particle beam, of kinetic energy E (< B), incident from the left. The form of the wave functioni, Ψ is sketched In the upper part of the figure. Inside the barrier, Ψ is an exponentially decaying function of x. The Coulomb barrier between two hydrogen nuclei is about 200 keV**Nuclear Fusion Energy for D-T Fusion**Estimate the fusion energy for D + T 4He + n Estimate the fusion energy Q The mass excess (MeV) are given below every species. D + T 4He + n + Q 13.136 + 14.950 = 2.425 + 8.070 + QQ = 17.6 MeV/fusion This amount is 3.5 MeV/amu compared to 0.8 MeV/amu for fission. Estimating Qis an important skill. Mass and mass excess can be used, the latter is usually given to unstable nuclides.**Nuclear Fusion Energy for Fusion Reactions**Common fusion reactions and their Q values D + D 4He + n + 23.85 MeV H + H D + + + n + 1.44 MeV D + T 4He + n + 17.6 MeV D + 3He 4He + p + 18.4 MeV D + D 3He + n + 3.3 MeV D + D 3T + p + 4.0 MeV See Interactive Plasma Physics Education Experience : http:// ippex.pppl.gov/ Fusion**Nuclear Fusion Cross Sections**Cross sections data from reactions studied using particles from cyclotron 7Li (p, n) 7Be3T (p, n) 3He1H (t, n) 3He2D (d, n) 3He2D (t, n) 4He3T (d, n) 4He**Chapter 5. Thermonuclear Fusion**• Introduction • Thermonuclear Reactions and Energy Production • Fusion in a Hot Medium • Progress Towards Fusion Power • Stellar Burning**FUSION IN A HOT MEDIUM**is the probability that the speed lies between v and v + dv The kinetic energy corresponding to the most probable speed is kT Kinetic energies of particles in plasma follow the Maxwell-Boltzmann distribution At room temperature, kT is about 0.025 eV**Nuclear Fusion and Plasma**D and T mixtures have to be heated to 10 million degrees. At these temperatures, the mixture is a plasma. A plasma is a macroscopically neutral collection of charged particles. Ions (bare nuclei) at high temperature have high kinetic energy and they approach each other within 1 fm, a distance strong force being effective to cause fusion.**Reaction rate**Consider a mixture of two gases consisting, respectively, of nl and n2 particles per unit volume. The probability for a particle in the first gas to react with one in the second, per unit distance travelled, is The distance travelled per unit time is the speed v of the particle The reaction probability per unit time is total reaction rate per unit volume is Assume: nlparticles have the same speed and that the n2 particles of the second gas are stationary Reality: Maxwell- Boltzmann distribution**Qualitative plots showing the variation with speed of the**Maxwell-Boltzmann probability distribution p(v) and the fusion reaction rate vσ(v). Their product R(v) (shown dashed), which has a maximum at vm, corresponding to an effective thermal energy Em.**Performance criteria**The plasma will radiate energy to its surroundings at a rate that depends on its temperature T. The primary mechanism for this power loss is bremsstrahlung.**Lawson criterion**A preliminary stage on the way to either the break-even or ignition points is to be able to confine a hot, reacting plasma long enough that the nuclear energy produced exceeds the energy required to create the plasma. fusion energy output There are n ions and n electrons in the plasma and, in equilibrium, each has to be given the same initial, average kinetic energy 3/2kT. So, the energy required to create the plasma is Lawson criterion**D-T plasma, kT = 20 keV,**D-D plasma, kT = l00 keV**Requirements for Fusion**• High Temperatures • Adequate Densities • Adequate Confinement • Lawson Criterion: nt > 1020 s/m3**Magnetic Confinement**At P, the magnetic field B is uniform in the x direction and so the magnetic. force F acts vertically downwards. However, at point Q, B has a vertical component, which results in the force having a component parallel to the x-axis directing the particle towards the region of lower field**plasma particles constrained in a uniform toroidal field**could circulate endlessly Tokamak : 环形(toroidal)、真空室(kamera)、磁(magnit)、线圈(kotushka)**The rate of depletion of fuel atoms dn/dt = -2R**After a time t = Γ, the number remaining n(Γ) certain fraction f of the fuel be consumed in the time Γ**Possible Drivers: Lasers (Best Shot)**~1000 large Optics: Advantages: • Well advanced technology • Good control of energy release Disadvantages: • Bad energy conversion • Very expensive to build 192 beam lines: Engineering challeges at NIF**Compare Driver to Target Sizes!**real NIF target DT capsule Schematic**Micro- PIXE**PS(聚苯乙烯)靶内壳材料中掺入过渡金属元素Br**Two Different Ways to Fusion**• Lawson Criterion:must be achieved • Temperature must be around T = 6 ... 15 eV • Two ways to fulfil Lawson criterion: • First solution (magnetically confined plasmas): increase confinement time • Other solution (inertial confinement fusion - ICF): increase density of fusion plasma • Many similarities, but a few decisive differences!**Chapter 5. Thermonuclear Fusion**• Introduction • Thermonuclear Reactions and Energy Production • Fusion in a Hot Medium • Progress Towards Fusion Power • Stellar Burning**Nuclear Fusion of Protons - hydrogen cycle**The Sun derives energy from fusion of protons. There are many possibilities, but two detailed cycles were proposed. The hydrogen cycle: H + H 2D (+e–) + + + n2D + H 3He + 3He + 3He 4He + 2 H These steps take place in the deep interior of the stars net 4 H = 4He (+ 2e–) + 2+ +2 + 2n + 26.7 MeV The energy released is slowly transmitted to the star surface, from which energy is lost by way of radiation**Nuclear Fusion of Protons - carbon cycle**fusion of four hydrogen atoms to form a 4He nuclide could be accomplished with the help of the 12C nuclide. The 12C undergoes a cycle of reactions: The carbon cycle: 12C + H 13N + 13N 13C (+ e–) + + + n13C + H 14N + 14N + H 15O + 15O 15N (+ e–) + + + n 15N + H 12C + 4He + net 4 H = 4He (+ 2e–) + 2+ +4 + 2 n + 26.7 MeV (similar to the hydrogen cycle) carbon is at both the start and the end of the cycle. Thus, 12C is considered a catalyst in the fusion reaction.**Nuclear Fusion in Stars**Nuclear fusion reactions The hydrogen cycleThe carbon cycle Others reactions 3He + 4He 7Be4 + 7Be + H 8B5 + 8B 8Be + +8Be 2 4He + (major) 8Be + 4He 12C (minor) Additional reactions 12C + 4He 16O + 2.425 MeV16O + 4He 20Ne + 4.73 Me 4He + 20Ne 24Mg + 9.31 MeV When temperatures at the center of the mass increase to 10,000,000 (ten million) K, the hydrogen fusion cycle begins. Fusion energy causes the surface to heat up, and eventually, energy escapes from the mass as radiation (heat and light). When energy released from fusion equals the energy lost by radiation, the steady state is a star. Fusion**Nuclear Fusion in Stars**Stars are giant fusion reactors. Nuclear fusion reactions provide energy in the Sun and other stars. Solar energy drives the weather and makes plants grow. Energy stored in plants sustains animal lives, ours included. Fusion**Nuclear Fusion and the Sun**The birth of the 4.5e9 year old Sun Sun-Earth Distance (149,597,870.7 km or 8.3 light minutes) is an Astronomical Unit (AU). Alpha (A+B+proxima, Centauri triple star system nearest to the sun parallax angle of 0.76-arcsec) is 4.35-4.22 light years from the Sun. Sun Mass is 333,000 times that of the Earth. The sun is a big nuclear fusion reactor, 75% H and 25% He. Sun radius (695000 km) is 109 times that of the Earth (6.4e3 km). Sun emits 3.861026 watts, ~ 8 kwatt/cm2, 0.14 watt/cm2 reach the earth atmosphere (solar constant). Fusion**The Sun**Core:Radius = 0.25 RsunT = 15 Million K Density = 150 g/cc Envelope: Radius = Rsun = 700,000 km T = 5800 K Density = 10-7 g Life of Star:tug-of-war between Gravity & Pressure Fusion**Energy – driving force of change**Change is the only constant in the universe. Changes: winds, rains, storms, thunders, forest fires, earthquakes, waves, plant growth, food decay, ocean tides, formation and melting of ice, combustion, and growing old ... more example please. What are physical and non-physical changes? What causes changes? Heat elasticity gravity electromagnetic wave … Identify changes and energy in everyday events**Recognizing energy**Energy plays an important partAnd it’s used in all this work;Energy, yest energy with power so great,A kind that cannot shirk. If the farmer had not this energy,He would be at a loss,But it’s sad to think, this energyBelongs to a little brown horse. A school verse by Richard Feynman Nobel laureate for physics Photo of Feynman and Murray Gell-Men**Mechanical Work**Mass: m kg Acceleration: a m s-2 Force: F = m a N (Newton = kg m s-2) Distance: s m Work: W = F • s J (N m or kg m2 s-2) Potential energy Wp = m g h unites? Kinetic energy Wk = ½ m v 2 work out unites 0.1 kg 1 N Think and deal with quantity of energy Energy & Nuclear Science**Properties of PE and KE**PE and KE are state functions – depending on only the final conditions not on how the conditions were arrived (path). Changes of PE and KE depend on only the initial and final conditions, not on the paths. PE and KE are inter-convertible, but not destroyed. Do you know any other properties? Energy in amusement parks Explain state functions**The Temperature Concept**Objective comparison of energy flow potentials – temperature scales. 0th law of thermodynamicsTwo bodies each equal in temperature to a third body are equal in temperature to each other. Maxwell (19th century) Temperature scales led to the concept of heat The science of heat - thermodynamics. Energy & Nuclear Science**Hot, Cold and Heat**What are the differences between hot-cold temperature and heat? Heat, transfers from object to object, elusive. When heat is transferred between objects, their temperatures change. Heat is an extensive property as are electric charge, length, mechanical work, mass, mole, time, etc. Heat is measurable in quantities, units being btu, cal, kcal, J, kJ, kwh, etc.An amount of heat required to raise the temperature of 1.00 g of water from 288.5 to 289.5 K is defined as 1.00 calorie or 4.184 J. Temperatures (hot and cold) indicate potential for heat flow. They are intensive properties as are color, electrical potentials, concentrations heat capacity, pressures, etc. Temperature scales made hot-cold measurements quantitative, but they are not quantities to be added or subtracted. Energy & Nuclear Science Differentiate temperature from heat**The Concept of Heat**• Heat is evidently not passive; it is an expansive fluid which dilates in consequence of the repulsion subsisting among its own particlesJoseph Black (1728-1799) • - is a typical additive quantity • is different from hot • inter-convertible to mechanical work (same units) Energy & Nuclear Science**The Energy Concept**Inter-conversion of Heat and Work Inter-conversion- discovered unexpectedlyby Ben Thompson (1753-1814) while making cannons. Conversion factor was determined by J. Joule (1818-1889) 1 cal = 4.184 J This entity was called effort, living force, and travail, before the term energy was coined by Thomas Young (1773-1829) Joule in his 20s Energy & Nuclear Science**Energy**Heat and work are really energy being transferred. Energy stored in a body is neither heat nor work.Kinetic energies of gases are proportional to their temperature. Once absorbed, the nature of heat has changed. Motion of gas molecules gave rise to pressure - Daniel Bernoulli (1700-1782). Rudolf J.E. Clausius (1822-1888), James Clerk Maxwell (1831-1879), W. Thomson, and Ludwig E. Boltzmann (1844-1906), studied the relationship between temperature and energy of molecular motion. Many elegant theories have been developed as a result. Energy & Nuclear Science**Forms of Energy**Other driving forces Benefitchideterminationencouragementinspirationlovelawmotivationresolutionscarcity HeatMechanical work Waves (sound etc) Electromagnetic radiation (waves)Electrical (charge transfer)ChemicalMass (nuclear) What are the properties of energy in these forms and how to evaluate them? Energy & Nuclear Science**Electric Energy**Electric energy, EJoulepotential, V Voltcharge, q Coulomb E = V q E = hg m1 J = 1 CV = 1 N m etc Be able to evaluate quantities of electric energy Energy & Nuclear Science**Simple electric energy calculations**Electric energy, EJoulepotential, V Voltcharge, q Coulomb E = V q E = hg m1 J = 1 CV = 1 N m etc Potential difference, V, current i ( = q / t ) and resistance R.V = i R (Ohm’s law) Power P, (I/o)P = V q / t = V i( i = current )= R i2 (Joules law) Energy and powerE = P t ( unit kilo-watt-hour) DC and AC Energy & Nuclear Science**eV – a special energy unit**Electron-volt, eV, is a very special energy unit, although we have not discussed electricity and electrons yet. Charge of an electron = 1.6022e-19 C (one of the fundamental physical constants). The energy required to increase the electric potential of an electron by 1 V is 1 eV = 1.6022e-19 J (J = C V). Other units used in nuclear energy are keV (1000 eV) MeV (1e6 eV) GeV (1e9 eV) Be able to inter-convert energy quantities in various units Energy & Nuclear Science