Chapter 1. Introduction Magnetic Fusion Technology Thomas J. Dolan NPRE 421 University of Illinois 2011 dolan 2010 1 Some Forms of Energy Dolan - Energy Sources 2 Some Forms of Energy Dolan - Energy Sources 3 Energy usage in the USA Industrial 41 % Transportation 25 % Residential 19 % Commercial 14 % Dolan - Energy Sources 4 Energy to agriculture and manufacturing ~ 8 Joules (tractor, chemicals, transportation) One Joule of food Processing energy costs are > 30% of following product costs: •steel •aluminum •glass •cement •paper. dolan 2010 5 GDP vs. Energy Cosumption 103 $/cap 60 50 40 30 20 10 0 0 2 4 6 8 10 12 kW/cap AG = Argentina, AL = Australia, AU = Austria, BR = Brazil, CA = Canada, CH = China, CZ = Czech, DE = Germany, FR = France, GR = Greece, HU = Hungary, ID = Indonesia, IN = India, .IR = Iran, IT = Italy, JA = Japan, MX = Mexico, NO = Norway, PK = Pakistan, RU = Russia, SA = South Africa, SP = Spain, SW = Sweden, SZ = Switzerland, TU = Turkey, UK = United Kingdom, US = USA. dolan 2010 6 International Energy Outlook W 25 n, T n, oo 20 20 TW sumpti 15 y Con 10 gg Ener 5 0 1980 1990 2000 2010 2020 2030 Year dolan 2010 7 World energy resources Power Limits, TW Renewable Energy Resources Current Ultimately Solar 13.5 1580 Biomass 1.74 8.56 Wind 0090.09 130 Wave and Tidal 0.05 1-10 Hydro 0.75 11 Geothermal 0.01 0.3 Organic Waste 0.02 0.1 dolan 2010 8 World energy resources ELiitEnergy Limits Recoverable Fossil Fuels Joule TW-years Coal and Lignite (9.09E11 ton) 2.4x1022 753 Crude Oil (1.34E12 barrels) 7.9x1021 249 Natural Gas (1.7E14 m^3) 6.6x1021 208 Tar-Sand Oil (3. 7E12 barrels) 2. 2x1012 703 Shale Oil (3.33E12 barrels) 1.9x1022 613 dolan 2010 9 World energy resources Nuclear Fission Fuels Joule * TW-years U-235 (3. 88E4 tonnes) 2. 5x1021 95 U-238 (5.43E6 tonnes) 3.5x1023 13000 Th-232 (2.57E6 tonnes) 1.7x1023 6300 Nuclear Fusion Fuels Joule TW-years Lithium in ocean (2.3E14 tonnes) 1.4*1031 4.2*10^11 Lithium on land (2. 84E7 tonnes) 17*101.7*1024 5. 2*10^4 Deuterium (5.17E13 tonnes) 1.6*1031 5.1*10^11 dolan 2010 10 Why develop fusion reactors? dolan 2010 11 Fusion reactions power the sun and other stars Dolan - Energy Sources 12 World energy flows, TW Mankind uses ~ 20 TW dolan 2010 13 Mass per nucleon vs. atomic number E = Mc2 Fe dolan 2010 14 Why develop fusion reactors? Deuterium & lithium are • Abundant 1 L(H2O) = 300 L(gasoline) • Cheap • Available to all nations. Safe – no supercriticality or meltdown hazard Materials No fission fragments or actinides No high level radioactive waste (but much low level radioactivity) Recycling of tritium, lithium and vanadium Fusion could help reduce pollution competition for fossil fuels threa t o f war Dolan - Energy Sources 15 Temperature units T K kT J k = 1.381x10-23 J/K kT/e eV e = 1. 602x10-19 C It is common to speak of T in units of kVkeV. 1 eV = 11605 K 1 keV = 11.605 MK Dolan - Energy Sources 16 Energy released by fusion reactions D+T 4He(3.52) + n(14.1) 17.59 MeV D+D 3He(0.82) + n(2.45) 3.27 MeV D+D T(()()1.01) + H(3.02) 4.03 MeV D+3He 4He(3.66) + H(14.6) 18.3 MeV T+T n + n + 4He 11.3 MeV H+6Li 4He + 3H402MVHe 4.02 MeV H+11B 4He + 4He + 4He 8.68 MeV Dolan - Energy Sources 17 dolan 2010 18 Example Problem How many deuterium atoms are there in one liter of water, and how much energy could they produce in a cataldlyzed DD reactor (7. 2 M/dMev/deuteron )? 23 N(water) = Nav/M = (1000 g/liter) (6.02x10 molecules/mole) / (18 g/mole) = 3.34x1025 molecules/liter. Deuterium ~ 1.53x10-4 of hydrogen atoms. N(deuterium) = 2 (3.34x1025) 1.53x10‐4 = 1.02x1022 atoms The energy released is W = 1.02x1022 (7.2 MeV) 1.60x10‐13 J/MeV = 1.18x1010 J = 11.8 GJ. dolan 2010 19 Main reactions for breeding tritium fuel 6Li + n(thermal) 4He(2.05) + T(2.73) 4.78 MeV 7Li + n(fast) 4He + T + n -247MeV2.47 MeV endothermic Na tura l lithium = 7. 42% 6Li an d 92. 58% 7Li Dolan - Energy Sources 20 Catalyzed DD fuel cycle D+D 3He(0.82) + n(2.45) D + 3He 4He(3.66) + p(14.6) D+D T(1.01) + p(3.02) D+T 4He(3.54) + n(14.05) _____________________________ Net: 6D 2n + 2p + 2(4He) + 43.2 MeV dolan 2010 21 H + 6Li and H + llB reactions no neutron emission all reaction products are charged particles direct conversion to electricity but low power densities and cross sections very high temperature operation Ignition difficult or impossible Dolan - Energy Sources 22 Approximate Fuel Costs, 2009 $/GJ Fossil Fuels Crude Oil 10.18 OPEC Natural Gas 5.19 EIA Macquarie Group Coal Limited Thermal 2.6 Coke 3.82 Fission Fuels Ux Consulting Uranium Company U-235 0.2 U-238 0.0014 Los Alamos Thorium 0.066 National Laboratory Fusion Fuels Sigma-Aldrich Deuterium 0150.15 Corporation Sigma-Aldrich Lithium 0.038 Corporation dolan 2010 23 Fusion advantages over fission * No supercriticality hazard * no emergency core cooling systems * no fission products or long‐lived high‐level radioactive waste (there would still be lower‐level radioactive wastes) * possible recycling of materials (such as V‐Cr‐Ti alloy) * widespread availability and easy transport of fuels * low cost of fuels. dolan 2010 24 How can we make a fusion reactor? dolan 2010 25 Fusion Power Plant Magnetic fusion reactor power plant blanket turbine shield IHX steam generator magnet Dolan - Energy Sources 27 Need for Heating T = 10 keV (120 Million Kelvin). positive fuel ions repel each other hig h velitilocities approach close for reactions to occur. fuel becomes “plasma” = fully ionized gas, stars fluorescent lights welding arcs flames ionosphere idindus tiltrial plasma processing didevices gaseous lasers nuclear fusion experiments dolan 2010 28 Plasma requirements for a fusion reactor Heating T > 10 keV to overcome Coulomb repulsion Confinement n > 1020 m-3s “Lawson Criterion” Magnetic confinement n ~ 1020 m-3 ~ 1 s Inertial confinement n ~ 1029 m-3 ~ 1 ns Dolan - Energy Sources 29 Confinement Long enough for a few percent of the fuel to “burn”. * solid walls. Low‐temperature plasmas, such as fluorescent lights. * gravity. Stars * inertia. Laser beams fuel pellet extremely high density. Inertia limits expansion rate for times ~ 1 ns. * electrostatic fields. Spherical High voltage grids * magnetic fields. Lorentz force F = electrons and ions spiral around B field lines. * electromagnetic waves. Radiofrequency waves and microwaves dolan 2010 30 Toroidal magnetic field dolan 2010 31 Plasma energy loss mechanisms Plasma flow along B – open magnetic systems Plasma Drift across B, caused by E, B, magnetic field curvature, … Heat Transport – conduction and convection Radiat io n Losses– line radi atio n aadnd bberem sstasstrahlu n g radi ati on Magnetohydrodynamic (MHD) instabilities (plasma shape) driven by gradients of pressure or current density Microinstabilities –interactions of particles and waves Charge exchange (neutralization of hot ions, allowing their escape) dolan 2010 32 Plasma Heating Methods Ohmic Compression Charged particle injection Alpha particle heating Neutral beam injection Radiowave and microwave heating dolan 2010 33 Plasma beta = (plasma p)/(gpressure)/(magnetic field p)pressure) 2 = p/(B /2o) If B = 1 Tesla, then 2 B /2o = 0.4 MPa = 4 atmospheres dolan 2010 34 Energy gain ratio Q Q = (fusion pp)ower) / ((pinput pp)ower) Q ≈ 5(nT) / [ 5x1021 -nT ] n = fuel ion density, m-3 T = ion temperature, keV = energy confinemen t time, s dolan 2010 35 Energy gain ratio vs. triple product 1000 Q 100 10 1 0.1 012345 nTt , 1021 m-3keV-s dolan 2010 36 Typical values for triple product * magnetic confinement fusion: n ~ 1020 m‐3, T ~ 10 keV, ~ 1s. * inertial confinement fusion: n ~ 1029 m‐3, T ~ 10 keV, ~ 1 ns. dolan 2010 37 Reaction Rate with Two Maxwellian Distributions r(x,t) = n1(x,t) n2(x,t) <v> If nD = nT = ½ n, then 2 r=¼nr = ¼ n <v>DT Dolan 2010 38 Interactions among like particles N = n(n-1)/2 ≈ n2/2 if n>>1 For DD reactions r = (½)n2 <v> Dolan 2010 39 Fusion Power Density nD = nT = ½ n 2 PDT = (¼) n <v>WDT 2 PDD = Pf = (½)n [<v>ddnWddn + <v>ddpWddp] 2 ≈ (½) n <v>ddWdd 2 Pcat ≈ (½) n <v>ddWcat The factor of ½ avoids counting the same DD reaction twice. Catalyzed DD fuel cycle D+D 3He(0.82) + n(2.45) D + 3He 4He (3. 66) + p (14. 6) D+D T(1.01) + p(3.02) D+T 4He(3.54) + n(14.05) _____________________________ Net: 6D 2n + 2p + 2(4He) + 43.2 MeV Each DD reaction results in consumption of 3 deuterons, yielding 21.6 MeV = 3.46x10‐12 J. dolan 2010 41 Reaction rate Parameters <v> 1. D+T 2. D+3He 3. D+DH+T 4TT4. T+T 5. T+3He 6. H+11B Dolan 2010 42 Reaction Rate Parameters 3 3 TkeVT, keV <v>DT, m /s <v>DD, m /s 8 5.94E-23 6.90E-25 10 1.09E-22 1.21E-24 15 2.65E-22 2.97E-24 20 4.24E-22 5.16E-24 25 5.59E-22 7.60E-24 30 6.65E-22 1.02E-23 Fusion Power Density Example: n=2x1020 m-3, T = 10 keV 2 PDT = (¼) n <v>WDT 40 -22 -12 PDT = ¼ (10 ) 1.09x10 2.82x10 = 7.