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Home , ETE (tokamak), Heavy ion fusion, Joule, Large Helical Device, Magnetized target fusion, Nuclear fission

Chapter 1. Introduction

Magnetic Fusion Thomas J . Dolan

NPRE 421 University of

2011

dolan 2010 1 Some Forms of

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 (tractor, chemicals, transportation)  One of

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 = , AL = Australia, AU = Austria, BR = , CA = Canada, CH = , CZ = Czech, DE = , FR = France, GR = , HU = Hungary, ID = Indonesia, IN = India, .IR = , IT = , JA = , MX = Mexico, NO = Norway, PK = , RU = Russia, SA = South Africa, SP = , SW = Sweden, SZ = , TU = Turkey, UK = , 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

Power Limits, TW Resources Current Ultimately Solar 13.5 1580 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

ELiitEnergy Limits Recoverable Fossil Joule TW-years and Lignite (9.09E11 ) 2.4x1022 753 Crude Oil (1.34E12 barrels) 7.9x1021 249 (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 Fuels Joule * TW-years U-235 (3 . 88E4 ) 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 in ocean (2.3E14 tonnes) 1.4*1031 4.2*10^11 Lithium on (2. 84E7 tonnes) 17*101.7*1024 5. 2*10^4 (5.17E13 tonnes) 1.6*1031 5.1*10^11

dolan 2010 10 Why develop fusion reactors?

dolan 2010 11 Fusion reactions the and other

Dolan - Energy Sources 12 World energy flows, TW

Mankind uses ~ 20 TW

dolan 2010 13 per vs.

E = Mc2

Fe

dolan 2010 14 Why develop fusion reactors? Deuterium & lithium are • Abundant 1 L(H2O) = 300 L() • Cheap • Available to all nations. Safe – no supercriticality or meltdown hazard Materials No fission fragments or No high level (but much low level radioactivity) Recycling of , lithium and vanadium Fusion could help reduce pollution competition for fossil fuels threa t of war

Dolan - Energy Sources 15 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 are there in one liter of , 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/) / (18 g/mole) = 3.34x1025 molecules/liter.

Deuterium ~ 1.53x10-4 of 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

6Li + n(thermal)  4He(2.05) + T(2.73) 4.78 MeV

7Li + n(fast)  4He + T + n -247MeV2.47 MeV endothermic

Na tural 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 emission all reaction products are charged particles direct conversion to 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 Company U-235 0.2 U-238 0.0014 Los Alamos 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 Magnetic fusion reactor power plant

blanket turbine shield IHX steam generator

magnet

Dolan - Energy Sources 27 Need for Heating

T = 10 keV (120 Million ). positive fuel repel each other hig h vellitiocities  approach close for reactions to occur. fuel becomes “” = fully ionized gas, stars fluorescent arcs flames ionosphere idindus tiltrial plasma processing ddievices gaseous experiments

dolan 2010 28 Plasma requirements for a fusion reactor

Heating T > 10 keV to overcome repulsion

Confinement n > 1020 m-3s “”

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. beams  fuel pellet  extremely high density. Inertia limits expansion rate for times ~ 1 ns.

* electrostatic fields. Spherical High grids

* magnetic fields. Lorentz F =  and ions spiral around B field lines.

* electromagnetic waves. Radiofrequency waves and

dolan 2010 30 Toroidal

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 ati on aadnd bberem sstasstrahl un g radi ati on

Magnetohydrodynamic (MHD) instabilities (plasma shape) driven by gradients of 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 heating

dolan 2010 33 Plasma

 = (plasma pp)/(gressure)/(magnetic field p)pressure)

2  = p/(B /2o)

If B = 1 , then

2 B /2o = 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 density, m-3 T = ion temperature, keV  = energy confinemen t ti me, 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)n 2 <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+DH+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. 2x105 W/m3 = 072MW/m0.72 MW/m3

2 PDD = (½)n [<v>ddnWddn + <v>ddpWddp] = 050.5x 1040 [ 0 .626 x 10-24 524105.24x10-13 + 0. 582x 10-24 646106.46x10-13 ] = 0.0035 MW/m3

2 40 -24 -12 Pcat ≈ (½)n <v>ddWcat = (½)10 1.21x10 3.46x10 = 0.021 MW/m3

Dolan 2010 44 Plasma Pressure p = sum of of (fuel ions + electrons + impurity ions)

p = niTi + neTe + nzTz

If nz = 0 and T i ≈ Te = T, then

p ≈ 2nT

Example: n = 1020 m-3, T = 10 keV p ≈ 2x1020 m-3 10 keV 1.602x10-16 J/keV = 3.2x105 Pa = 0.32 atm Optimum Temperature p = 2nT  n = p/2T

2 2 PDT = (¼) n <v>WDT = (¼) (p/2T) <v>WDT At a given pressure, what T maximizes PDT ? T, keV <v> (10-22 m3/s) <v>/T2 5 0.129 0.0052 8 0.594 0.0093 10 1.09 0.0109 15 2.65 0.0118 20 4.24 0.0106 25 5595.59 0.0089 30 6.65 0.0074 35 7.45 0.0061 40 8.03 0.0050 Reactor Power Balance

dolan 2010 47 Toroidal coordinate system

dolan 2010 48 Definitions of a, b, c

2 2 minimize Vbsc = 2Ro  [(a+b+c) –a]

dolan 2010 49 Estimation of required b, c

Tritium breeding ratio > 1 and CilCoil shie lding factor 10‐6  b ~ 112.2 m magnet coil stress < 300 MPa, and coil volume minimized  c ≈ 0.25(a+b)

(Freidberg, 2007)

dolan 2010 50 Optimization of R, a

2 V = 2Roa S = 2Ro2a

Neutron wall power : 2 Pw = 080.8 (fusion power density)V/S < 4 MW/m

Electrical power

PE = 1.2 e (fusion power density)V

2 2 Vbc/PE = 2Ro  [(a+b+c) –a] / (3SPw e /2)

Minimizing this ratio  a = (5/3)b = 2.0 m, c = (a+b)/4 = 0.8 m 2 If Pw = 4 MW/m , and PE = 1000 MWe, then R o = 0.04 PE/aPw ≈ 5 m

(Freidberg, 2007)

dolan 2010 51 Determination of reactor parameters

Nuclear cross sections  b ~ 1.2 m

Bmax and stress limit  c (a+b)/4 Cost optimization  a 2 m

Electrical power & neutron wall loading  Ro 5 m Fusion power &  p Maximization of fusion power density  optimum T High‐Q or ignition  required value of  Plasma pressure and B  required value of 

(Freidberg, 2007)

dolan 2010 52 What Experiments Are Underway? http://www.iterbelgium.be/en/system/files/upload/n___Fusion_research_in_Belgium_dolan 2010 ‐_R__Weynants.pdf 54 Joint European (JET)

Culham Laboratory UK Tokamak Fusion Test Reactor (TFTR) Large

D III-D JT-60 JET Location R m 1.66 3.4 2.96 a m 0.67 1 0.96 BTB, T 222.2 424.2 4 current I, MA 35 6 ECH, MW 64 -- ICH, MW 51012 NBI, MW 20 40 24 LH, MW -- 8 7 Achievements  > 12% long pulses ~ 28 s P(DT) = equivalent Q > 1. 15 MW bibeing upgrad dded BllBe walls

dolan 2010 57 Plasma Shapes R/a =“ Aspect Ratio”Ratio

a a R R

Ordinary Spherical Compact Tokamak Tokamak R/a ~ 4 R/a ~ 1.4 R/a ~ 6 MegAmpere (MAST)

------ R = 0.85 m National Spherical Torus Experiment (NSTX)  = (plasma pressure) / (magnetic field pressure) ~ 0.3 Simulation of IRE in ST

National Institute of Fusion , Japan

Growth of helical perturbation Globus-M aa0=024m.24 m R=0.37 m Ioffe Institute, St. Petersburg, Russia Bt = 0.35 T I = 025MA0.25 MA (future 0.5 MA)

V = 4V Pulse ~ 60 ms (future 200 ms) Experimento Tokamak Esférico (ETE) Brazilian National Space Science Institute, INPE Assembly of SUNIST Website “All the world’s tokamaks” http://www.toodlepip .com/tokamak/

Conventional stellarator torsatron or heliotron

dolan 2010 66 LHD coils

dolan 2010 67 LHD helical coils

dolan 2010 68 LHlilLarge Helical Device, Toki, Japan Wendelstein 7‐X coils

dolan 2010 70 W7X Stellarator W7X Modular Coil Large stellarators LHD, Japan W7W 7-X, Germany Location R, m 3.5-3.9 5.5 a, m 0.6 0.53 B, T 2 - 3 3 number of helical 2 50 modular coils coils ECH, MW 2 10 NBI, MW 15 5 ICRH, MW 3 3 pulse length, s > 103 s at low n 1800 nT m-3keV-s 4. 4x1019 under construction

dolan 2010 73 National Compact Stellarator Experiment (NCSX) Potential advantages of stellarators over tokamaks

No disruptions

Current free operation  slower loss

Plasma current drive not required  lower input power, higher Q

dolan 2010 75 Alternative confinement concepts

Reversed field pinches (RFP)

field reversed configurations (RFC)

(MTF)

tandem mirrors

rotating plasmas

internal rings

dolan 2010 76 Alternative Concepts Reversed Field (RFP)

“Taylor Minimum Energy State”

oJ = xB = kB

Dynamo turbulence adjusts magnetic field components. Spheromaks 1. Magnetic field 2. Puff hydrogen 3. Apply V

4. Plasma 5. Plasma expansion 6. Sustained

Sustained Sppyp()heromak Physics Experiment (SSPX) a ~ 0.22 m,  ~ 5%, B ~ 0.25 T, Te ~ 200 eV for several ms. Field Reversed Configurations (FRC) Fluxcores Separation Coils F Coils EF Coils

Coaxial Gun .19m mm .19 Coaxial Gun 1.8m

OH Coil Torus Coils 1.8m Y. Ono, U. of Tokyo TS-4, U. of Tokyo: R ~ 05m0.5 m, R/a ~ 121.2-191.9, B ~ 04T0.4 T, I ~ 300 kA . Merging Two Spheromaks to Form an FRC

Y. Ono,,y U. of Tokyo Repetitively Merging Spheromaks

Shield Plug Over Vacuum Pumps Feedback Coils Vacuum Pump (4 total) Plasma Core ( Rotors) Plasma Sheath CT Formation S/C Coil (8 total) & Push Coils Separatrix

Central Core 1.2 m Blanket with Pumping Coaxial Accel.

Vacuum Pump (2 total) Inductive Accel. Region TitdTwisted First Wall Tubes Plates and C-X Neutrals Pumping Channel Structure

05 Hollow SPHACTIV R. BOURQUE Conducting Section Away From Pumps 12/98 meters Core

Magnetized Target Fusion (MTF) Plasma

Achieved n < 8x1016 cm-3, T ~ 300 eV, B ~ 3 T,  ~ 10 s. J. M. Tacetti et al., RSI 74 (2003) 4314-4232. Magnetized Target Fusion (MTF)

W = 5 MJ Magnetized Target Fusion (MTF) Magnetic Mirrors Inertial Confinement Fusion (ICF) Compression Methods National Ignition Facility – 192 beams Plasma around Target Sphere High Gain ICF Targets

FDTflFrozen DT fuel can be compressed to veryyg high densit y.

TaCHO pusher stops x-rays and hot electrons to prevent preheating fuel. NIF Target Chamber Interior

Laser MegaJoule (LMJ), France

240 beams, 1.8 MJ, 600 TW operation 2010 Osaka University Laser Room ICF Problems ICF Problems Diode‐Pumped Solid State Lasers (DPSSL)

Cooled by He gas flowing at Mach 0.1 Diode‐Pumped Solid State Lasers (DPSSL) MLYbSMercury Laser: Yb:S-FAP sl ab s  20 J per pu lse

Goal: 100 J, 10 ns, 10 Hz, 10% efficiency

Electra KrF Laser, NRL

Long- e lec tron beam ca tho de an d fo il Laser gas cooling system, long-life windos > 500 J in 100 ns pulses, scalable to higher energy Potential Advantages of

Beam coupling to target Atta ina ble energy an d curren t High repetition rates Efficiency > 20%

Issues Beam charge neutralization & focusing Accelerator cost What has been accomplished?

dolan 2010 103 Plasma research progress

1920s Langmuir ‐‐ gas discharges “plasma” Bennet – pinch equilbrium equation Landau – collisionless damping of waves 1940s Thomson ‐‐ patent of fusion reactor scheme 1950s Lavrentyev ‐‐ proposed electrostatic confinement in USSR Tamm & Sakharov – magnetic confinement England & USA –early experiments 1958 Geneva Conference on Peaceful Uses of many experiments were failing 1960s Ioffe ‐‐ stabilization with minimum‐B field 1968 Artsimovich ‐‐ IAEA conference T‐3 results 1970s Many tokamaks built. A few stellarators continued Success in tandem mirrors.

dolan 2010 104 Research Progress

1980s Good results from large tokamaks. Cancellation of Mirror Fusion Test Facility in USA Discovery of H-Mode in ASDEX (Germany).

1990s Strong plasma theory Excellent 3-D plasma simulations Cancellation of Tokamak Fusion Test Reactor in USA Fusion power plant design studies Design of International Thermonuclear Experimental Reactor (ITER) by Europe, Japan, Russia, USA

2000s Siting of ITER in France New ITER members China, Korea, India Beginning of ITER construction Large ICF experiments under construction Good results from in Japan W7-X under construction in Germany Cancellation of National Compact Stellarator Experiment in USA Triple Product vs. Year 22 nT 10 m-3keV•s 1021 1020 1019 1018 1017 1016 1015 1014 1013 1960 1970 1980 1990 2020

dolan 2010 106 Fusion triple product compared with semiconductors and accelerators

ITER

Year

dolan 2010 107 What are the future plans?

dolan 2010 108 Fusion Power Itilfi(lInertial fusion (lasers or ibion beams ) – ign ition in 2011 laser efficiency and cost chamber pppulse repetition rate

Tokamaks & Stellarators ~ 10 MWth produced in USA & UK ITER project  400 MWth, 400 s 2026

CttidCompact toroids – smaller, un deve lope d

Neutron source for materials testing

Development ~ 100 G$ needed. (= 2 months US military)

World < 2 G$/y Dolan - Energy Sources 109 International Thermonuclear Experimental Reactor (ITER) 1985 Mitterand, Gorbachev, Reagan ‐‐ International collaboration

1988‐1992 ITER Conceptual Design Activity, Europe, Japan, Russia, USA

1992‐1998 ITER Engineering Design Activity at 3 sites: Japp,an, Germany, USA

1998 Shortage of funds. Request for redesign to cut costs. US quits.

2003‐2005 US rejoins. China, Korea, India join.

2005‐2007 negotiations on siting in France or Japan.

dolan 2010 110 Reduction of ITER parameters

Ignition 1998 “High‐Q” 2005

Q ∞ (Ignition) 10

Pf, MW 1500 400 Burn, s 1000 400 R/a, m8.1 / 2.8 6.2 / 2.0 I, MA 21 15

Bf, T5.75.3 # TF coils 20 18  ripple problem

dolan 2010 111 ITER

dolan 2010 112 TF coil

central solenoid

blanket modules

access port plug

divertor

cryopump

person dolan 2010 113 ITER operation phases H Phase – studies of plasma control, stability, transport, heat flux, divertor, runaway electrons, electromagnetic loads, diagnostics, etc.

D Phase – deuterium operations, nuclear reactions, small amounts of tritium, shielding performance.

DT Phase –full fusion power operation, tritium control, non‐inductive, steady‐state current drive, long‐term burn, blanket module testing, high‐heat‐flux and neutron fluence testing.

dolan 2010 114 Japanese fusion power plant design

dolan 2010 115 Strong Economy of Scale Available

13 COE, Yen/kWh beta = 2% 12

11 Hiss = 2 10 1.7 9 3% 1.5 8 7 4% 6 5% 5 4 00.511.522.533.5 PGWPe, GWe

dolan 2010 116 ICF Chamber Protection

Lithium or Pb-Li streams (dashed lines) protect the walls from blast damage and absorb to breed tritium.

The is collected in a pool at the bottom and pumped back to the top.

“High Yield Lithium Injection Fusion Energy (HYLIFE) ”. Conclusions Fusion energy – safe, environmentally friendly Enormous potential : 1 liter water = 300 liters gasoline Very difficult : T ~ 100 million K Require nTt > 3x1021 m-3 KeV s NIF ignition in 2011, but efficiency and repetition rate problem ITER should demonstrate 400 MW for 400 s in 2026 Next step = demonstration power plant ~ 100 G$ needed to develop fusion energy World spending ~ 2 G$/year

dolan 2010 118 Fusion energy  cost competitive if: •High prices •Difficulty with coal transportation and waste •Tax on emissions •Nov el f usio n r eactor success f ul (sph er om ak , … ) •Economy of scale utilized (1 3 GWe) •Fusion-fission hybrids deployed •Difficulty siting fission power plants (protests, …)

dolan 2010 119 The Nuclear Industry Faces Protests

“We’ re here to s ing our pro tes t songs. Plug this in for me, will you, fella?”

dolan 2010 120 She mayyygyy, look like somebody’s granny to you, but she was instrumental in putting a $4-billion plant in the deep freeze.

dolan 2010 121 Extra Slides

dolan 2010 122 dolan 2010 123