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Chapter 5. Thermonuclear Fusion 1.Introduction 2.Thermonuclear Reactions and Energy Production 3.Fusion in a Hot Medium 4.Progress Towards Fusion Power 5.Stellar Burning Nuclear Fusion The Fusion Process Neutron proton Two nuclei combine into one nucleus plus a nucleon is called nuclear fusion, a nuclear reaction. Collision The picture here illustrates the fusion of 2D + 3T 4He + n that releases a lot of energy. Fusion Fusion 2 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 + Q Q = 17.6 MeV/fusion This amount is 3.5 MeV/amu compared to 0.8 MeV/amu for fission. Estimating Q is an important skill. Mass and mass excess can be used, the latter is usually given to unstable nuclides. 4 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 5 Effective Cross Section (mb) of Fusion Reactions 10000 1000 Nuclear Fusion Cross Sections D + T 4He + n Cross sections data from reactions studied using particles from cyclotron 100 D + D 3T + p 10 7Li (p, n) 7Be 3T (p, n) 3He 1H (t, n) 3He 2D (d, n) 3He 2D (t, n) 4He 3T (d, n) 4He D + D 3He + n 1. D + 3He 4He + p 0.1 10 20 30 40 50 60 60 keV Chapter 5. Thermonuclear Fusion 1.Introduction 2.Thermonuclear Reactions and Energy Production 3.Fusion in a Hot Medium 4.Progress Towards Fusion Power 5.Stellar Burning FUSION IN A HOT MEDIUM Maxwell-Boltzmann Distribution Fraction 0.003 0.002 is the probability that the speed lies between v and v + dv The kinetic energy corresponding to the most probable speed is kT 4 amu 50 K 0.001 4 amu 500 K 1000 2000 Speed (m/s) At room temperature, kT is about 0.025 eV 3000 Kinetic energies of particles in plasma follow the MaxwellBoltzmann distribution 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: nl particles 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. Is D-T reaction favourable? 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 4. Progress Towards Fusion Power 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 xaxis 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) Inertial Confinement Fusion(惯性约束聚变) Concept 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 25 For a significant burnup of f ~ 30%, D-T at 20 keV, s n ~ 26 Possible Drivers: Lasers (Best Shot) ~1000 large Optics: 192 beam lines: Engineering challeges at NIF Advantages: • Well advanced technology • Good control of energy release Disadvantages: • Bad energy conversion • Very expensive to build 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 11.6微米 Two Different Ways to Fusion Lawson Criterion: must be achieved Temperature must be around T = 6 ... 15 eV Two ways to fulfil Lawson criterion: (1) First solution (magnetically confined plasmas): increase confinement time (2) Other solution (inertial confinement fusion - ICF): increase density of fusion plasma Many similarities, but a few decisive differences! Chapter 5. Thermonuclear Fusion 1.Introduction 2.Thermonuclear Reactions and Energy Production 3.Fusion in a Hot Medium 4.Progress Towards Fusion Power 5.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–) + + + n 2D + 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 + 2 n + 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–) + + + n 13C + 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. 34 Nuclear Fusion in Stars Nuclear fusion reactions The hydrogen cycle The carbon cycle When temperatures at the center of the mass increase to 10,000,000 (ten million) K, the Others reactions hydrogen fusion cycle begins. 3He + 4He 7Be4 + Fusion energy causes the 7Be + H 8B5 + surface to heat up, and 8B 8Be + + eventually, energy escapes 8Be 2 4He + (major) from the mass as radiation 8Be + 4He 12C (minor) (heat and light). When energy Additional reactions released from fusion equals 12C + 4He 16O + 2.425 MeV the energy lost by radiation, 16O + 4He 20Ne + 4.73 Me the steady state is a star. 4He + 20Ne 24Mg + 9.31 MeV Fusion 35 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. E = mc2 1H, 2D 3T, 4He Energy stored in plants sustains animal lives, ours included. Fusion 36 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 37 The Sun Core: Radius = 0.25 Rsun T = 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 38 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 39 Recognizing energy Energy plays an important part And 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 energy Belongs to a little brown horse. A school verse by Richard Feynman Nobel laureate for physics Photo of Feynman and Murray Gell-Men 40 Mechanical Work Mass: m kg Acceleration: a m s-2 Force: F = m a N (Newton = kg m s-2) 0.1 kg Distance: s m Work: W = F • s J (N m or kg m2 s-2) 1N Potential energy Wp = m g h unites? Kinetic energy Wk = ½ m v 2 work out unites Think and deal with quantity of energy Energy & Nuclear Science 41 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 42 Explain state functions The Temperature Concept Objective comparison of energy flow potentials – temperature scales. 0th law of thermodynamics Two bodies each equal in temperature to a third body are equal in temperature to each other. Maxwell (19th century) N F C K 212 100 373.15 12 98 37 310 0 32 0 273.15 -40 233.15 -40 Temperature scales led to the concept of heat The science of heat thermodynamics. Newton (N), Fahrenheit (F), Celsius ( C), and Kelvin (K) temperature scales. Energy & Nuclear Science 43 Hot, Cold and Heat What are the differences between hot-cold temperature and heat? 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. 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. Energy & Nuclear Science Differentiate temperature from heat 44 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 particles Joseph Black (1728-1799) - is a typical additive quantity Is heat a fluid like water? - is different from hot - inter-convertible to mechanical work (same units) Energy & Nuclear Science 45 The Energy Concept Inter-conversion of Heat and Work Inter-conversion - discovered unexpectedly by Ben Thompson (1753-1814) while making cannons. Joule in his 20s Thermometer Conversion factor was determined by J. Joule (18181889) 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) mgh Joules experiment demonstrated the generation of heat by mechanical means. Energy & Nuclear Science 46 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 47 Forms of Energy Other driving forces Heat Mechanical work Waves (sound etc) Electromagnetic radiation (waves) Electrical (charge transfer) Chemical Mass (nuclear) Benefit chi determination encouragement inspiration love law motivation resolution scarcity What are the properties of energy in these forms and how to evaluate them? Energy & Nuclear Science 48 Electric Energy Electric energy, E Joule potential, V Volt charge, q Coulomb E=Vq E = hg m 1 J = 1 CV = 1 N m etc Be able to evaluate quantities of electric energy + + + + + + + - Electric field Gravitational field Energy & Nuclear Science 49 Simple electric energy calculations 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 i 2 (Joules law) Electric energy, E Joule potential, V Volt charge, q Coulomb E=Vq E = hg m 1 J = 1 CV = 1 N m etc Energy and power E = P t ( unit kilo-watt-hour) DC and AC Energy & Nuclear Science 50 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 51 What is light? Wave properties? Particle properties? Massless Interference Newton ring diffraction Law of reflection law of refraction move in straight line ?? Energy & Nuclear Science 52 Electromagnetic Radiation Electromagnetic radiation is transfer of energy by EM waves via no medium(?). EM waves travel in empty space at constant speed (c = 2.997925e8 m/s constant). EM waves are characterized by wavelength (or frequency n) Light is part of the EM spectrum. EM radiation has a very wide spectrum ( or n ). Energy & Nuclear Science 53 The EM Spectrum The EM Radiation Spectrum Long-wave Radio Broadcast radio band Short wavelength radio Infrared VISIBLE Ultraviolet X-rays Gamma rays Remember the order of these regions > 600 m 600 - 200 m 200 m - 0.1 mm 0.1 - 0.0007 mm 0.7 - 0.4 um 0.4 um - 1 nm 1 nm - 0.1 pm 0.1 nm Energy & Nuclear Science 54 The EM Wave Spectrum Energy & Nuclear Science 55 The Visible Spectrum Double rainbow A color pattern seen in an oil film Energy & Nuclear Science 56 Photons, E = hn Max Planck assumption, E = h n, was shown to be true by Einstein’s photoelectric experiment. Speed of light, c = 3e8 m s-1 wavelength, frequency of light, n = c / Planck constant, h = 6.62619e-34 J s energy of a photon E = h n. Max Planck (1858-1947) Nobel Prize (1918) A photon is a bundle of energy, and it’s like a particle of light. Use wave to show and n. Energy & Nuclear Science 57 The Photon Story Max Planck assumption, E = hn, was shown to be true by Einstein’s photoelectric experiment. I N T E N S I T Y Kinetic energy of electron Rayleigh’s Prediction Experimental curve and Planck’s prediction Wien’s Law Threshold Frequency Frequency Explain the photoelectric effect. Energy & Nuclear Science 58 Photon Energy Typical red light, n = 4.69e14 s-1 (Hz), =c/n = 3e8 m s-1 / 4.69e14 s-1 = 640 nm Wave number = 1 / = 1 / 6.40e11 m = 1.56e6 m-1 E=hn = 6.62619e-34 J s * 4.69e14 s-1 = 3.1 x 10-19 J (1 eV / 1.6 x 10-19 J) = 1.9 eV per photon find wavelength or frequency of a violet photon and carry out similar evaluations. Energy & Nuclear Science 59 Laser Light Amplification by Stimulated Emission of Radiation (LASER) Spontaneous decay Green photons Stimulated decay, Red laser Partial mirror Mirror Red laser Green pumping light Energy & Nuclear Science 60 4H + 2O 1469 kJ, bond energy Understand these terms on energy or enthalpy 2H2 + O2 484 kJ, energy of reaction 2H2O(g)373K 81 kJ, energy of vaporization 2H2O(l)373K 15 kJ, heat 2H2O(l)273K 2H2O(s)273K Chemical Energy enthalpy Bond energy energy of reaction energy related to temperature energy related to states melting, vaporization, phase transition mass loss in chemical reactions 12 kJ, energy of fusion Energy & Nuclear Science 61 Relative and Zero Masses Special theory of relativity (by Einstein) shows that mass m of a particle with velocity, v relates to the mass when v = 0, which is called zero mass, mo. m = mo v 2 1 - ( ) c Universal speed 299,792,458 m/s Energy & Nuclear Science 62 Mass and Energy Einstein further showed that the relativistic mass, m, of a particle exceeds its rest mass mo (m = m - mo). The increase in kinetic energy E and increase in mass are related by: E = m c 2 or E=mc2 Implication: Mass and energy are equivalent. Mass can be expressed in energy unit and vice versa. 241800 J = 241800/c 2 = 2.7 x 10-12 kg = 3 ng Energy & Nuclear Science 63 Power – rate of energy transfer The SI unit for power P is watt named after James Watt, 1 watt = 1 J s–1 Power = m g v, v, pulling velocity mgh Work out by heart 1 kilowatt-hour = __ J = __ cal = __ BTU Energy & Nuclear Science 64 The law of Conservation of Energy Energy converts among various forms without any loss or gain. Energy cannot be created nor destroyed. Conversions of energy in various forms have definite rates. These rates never change, and we have energy conversion factors. 1 amu = 1/12th of mass of a C12 atom 1 amu = (12 kg/k mol)/12 = (1 kg/k mol)/(6.022e26 (k mol)-1) = 1.661e-27 kg = 931.5 MeV Power = m g v, v, pulling velocity mgh Energy & Nuclear Science 65 Some conversion factors 1 eV = 1.602 x 10-19 J 1 eV/molecule = 23045 cal/mol 1 MeV = 1.602 x 10-13 J 1 amu = 1.66043 x 10-31 J = 931.4812 MeV 1 cal = 4.184 J 1 atm L = 101.3 J 1 J = 1 coulomb-volt 1 joule = 107 ergs 1 BTU = 252 cal Transmitting Energy by Sound Sound intensity (I, watt/m2), level (SIL) is SIL (dB) = SILo + 10 log (I/Io ) At 1000 Hz, the threshold SILo = 0 dB, I0 = 10-12 watt / m2) When I = 1 watt / m2 SIL = 120 dB (work out) Comfortable hearing is between 50 and 70 dB, whereas 10 dB is a bel (after A. G. Bell, 1847-1922). A shock wave is due to a sharp difference in pressure from (nuclear) explosions. Shock waves cause serious injuries to ears, and destroy buildings and structures. Energy & Nuclear Science 67 Thermodynamics Thermodynamics was derived from the Greek words therme (heat) and dynamis (force), intensely studied in the 19th century motivated by the need to convert heat into mechanical work. 0th law: if T of A, TA = T B, TB = TC, then TA = TC 1st law: law of conservation of energy, recognizing internal energy Ein = q – w. 2nd law: not possible for a machine to convert all the heat into work. 3rd law: changes are caused be energy decrease and entropy increase. These laws govern engineering of energy transfer. Energy & Nuclear Science 68 Energy Resources and Utilization What are possible energy resources? Solar energy Geothermal energy Nuclear energy ??? What technologies are available to utilize these resources? ??? How efficient are some of the technologies? ??? Energy & Nuclear Science 69 Energy crisis and social problems Level Demand These issues affect us all, and please apply basics and human natures to solve these problems so your generation will live happily hereafter. Cost Arbitrary Coordinate Energy & Nuclear Science 70 Chung, Chieh sprott.physics.wisc.edu/lectures/plasma.ppt Dirk O. Gericke, 1. Introduction Advantages of Fusion • Inexhaustible Supply of Fuel • Relatively Safe and Clean • Possibility of Direct Conversion The Sun The sun flare The corona during an eclipse The aurora corona during an eclipse Fusion 73