Fusion Will it always be… The power source of the future
(Will we always have) Peak Oil Soon? In 1956 Shell correctly predicted that US oil production would peak around 1970. Various estimates of world rate of oil production
Statistics of oil production Oil exploration: nothing substantial has been discovered since 1970 New drilling techniques: consumed $billions already but no revolution Rising prices: but finite resource Alternatives are wind, tide, solar (limited) coal, gas (finite) nuclear fission and fusion
Safety and environmental impact / acceptability Fusion does not generate greenhouse gases Fusion has little potential for major accidents Fusion has no high-level waste problem The technology is almost totally unknown
Fusion and Fission Low and high mass nuclei are unstable
Nuclear Reactors on Earth Most of the heat in the core comes from fission … First uranium reactor…?? Oklo, Gabon, 1.5bn yrs ago, produced 100kW, ran for 100,000 years. 1943 Manhattan Project, Clinton Laboratory, Tennessee (now Oak Ridge)
Fusion Barrier Nuclei are kept apart by coulomb repulsion Only when they get close enough to feel the nuclear force do they attract, and fuse.
Getting Hydrogen together Gravity (Need a star mass, 10MK) Pressure (Need a fission bomb) Quantum Mechanics (need muons) Wishful thinking (sonofusion, electrolysis) Temperature (confined plasma, 100MK)
The Nuclear Reactions The sun p + p -> D + e + + ν p + D -> 3He + γ 3 He + 3 He -> 4 He + 2p Net result: 4p -> 4 He + 2e + + 2ν + 27 MeV Reactor Candidates D+D -> 3 He + n + 3.3MeV D+D -> T + p + 4.0MeV D+T -> 4 He + n + 17.6MeV D+ 3 He -> 4 He + n +18.3MeV n + 6 Li -> T + 4 He + 4.8MeV n + 7 Li -> T + 4 He + n – 2.5MeV the reactivity of stellar reactions is 3 x 10 -25 smaller than that for D+T
ITER – the Way Caderache, France, Open 2016 500Mw 400 seconds
ITER - costs Current estimate total 5 billion (JET on budget) Double LHC, Half SSC (at cancellation) 10% Space Station Indicative Single-year EU subsidies to existing generation methods 2001 (European Environmental Agency, 2004) Coal 13 billion Oil/gas 8.7 billion Nuclear 2.2 billion Renewables 5.3 billion
Making electricity Energy is primarily contained in neutrons, alpha particles. Capture these in a blanket, heat up water, sodium, Pb etc. Heat exchanger to run a steam engine. None of this will be done at ITER. Next Machine, DEMO, will make power
Materials Plasma facing material First wall Blanket Material Reaction pressure vessel Electronics… Magnets…
Challenges for fusion materials technology Low Activation – decommissionability Very high heat loads for materials facing the plasma Damage to the structure caused by high-energy neutrons Production of tritium in situ Helium embrittlement Sputtering on surface & poisoning of plasma by heavy ions
Radiation Damage Simulations Previous Edinburgh Funding: Four EU FP6/7 PDRA grants with various industrial partners (EDF, SCK, FZK) ITEM, PERFORM, PERFECT, GETMAT One EPSRC PDRA joint with Culham & Oxford Total value to Edinburgh ~£500,000 SUPA funding: none. Radiation damages the materials from which a reactor is made. This determines reactor lifetimes. A non-equilibrium process, it has unknown scaling with time and dose. Modelling required. Edinburgh: Graeme Ackland and Derek Hepburn First principles studies of primary damage (point defects). Simplified atomistic force models for metals. Molecular dynamics of evolution of damage, and emergent objects (dislocation loops, hardening, voids, etc.)
Dynamical system Radiation in Defects produced Defects recombine or migrate to sinks Sinks grow (voids lead to swelling) and may saturate (grain boundary segregation) Not at Thermodynamic Equilibrium Voids in Si after 10keV irradiation Vanadium swells (vacancies form voids) V + Fe brittle, doesnt swell V + Fe + Cr neither - but why?
International Fusion Materials Irradiation Facility (IFMIF)
Environments – First Wall Bombarded by 14MeV neutrons (alphas are contained by magnetic field). At 500 o C for commercial reactor. 200 dpa (five year lifetime) Immune to radiation damage in presence of He. Immune to transmutation to long lived isotopes. Weldable, formable, corrosion resistant etc. etc. Must not poison plasma, sputter
Candidates – First Wall Vanadium (+Cr,Ti). Ferritic/Martensitic Stainless Steel (FeCr) Oxide Dispersion Strengthening (ODS) SiC Diamond coating
Environment - Blanket Immediately behind the first wall Protect the magnets from radiation (ITER) Convert neutron energy to heat (DEMO) Produce tritium for reaction (DEMO) Liquid – avoid damage – water, LiPb
Environment – Pressure Vessel Contain coolant Resist neutron bombardment High temperature Stainless steel
Multiscale modelling of fusion materials Engineering properties depend on microstructures that depend on properties of defects that depend on interatomic interactions that depend on electronic structure of the material
Fusion Specific Problem 14MeV neutrons Massive local damage How does this differ from keV irradiation?
How materials deform Creep – 0D (point defects) My Video\nhcreep.mov Dislocations – 1D (line defects) My Video\dislox.mov
Edinburgh Speciality: Interatomic potentials Computational elegance -Want force on atoms as a function of atomic degrees of freedom only. Simulate billions of atoms (microns) Use insight from quantum mechanics – beyond pair potentials Energy as a functional of pairwise interactions Fit parameters of the functional to relevant properties of the material (phase diagram, defect formation etc)
Atomistic simulations Interstitial defects in body-centred cubic Fe diffuses slowly, quickly Not an atom moving - Impurities pin defects.
Radiation Damage When radiation hits metal – one atom acquires enormous energy. 3D billiards with a million balls Empty site – vacancy (red) Doubly-occupied site – interstitial (green) Clustering Cu 25keV cascade 100K 74FP.mov
Vacancies - the theory of nothing Vacancies cluster near initial event 3D void But … a 3D void comprising vacancies can collapse to form a 2D platelet Or, if top and bottom of platelet match, the only defect is a 1D loop around the edge. Vacancies are not conserved How to describe material transport?
Emergent interstitial features Interstitials form 2D platelets (anisotropic strain). But these are really 1D dislocation loops Simulation shows they move really fast Can sweep up defects as they go through the material (nanoscale cleaners?)
Which are the important defects? We dont know. Maybe all lengthscales are important? e.g. Ionic crystal Charged defects move and attract making Dipole defects move and attract making Static quadrupole defects, but capture Dipoles making 6-mers move and attract..
A dislocation loop containing 595 atoms Structure of defects
Nothing can stop dislocations! (vacancy pinning) 339V_sr5_100K.mov
Unknown unknowns Copper particles in Steel bcc, commensurate 9R then fcc Embrittling effect small, large, smaller
Voids observed near a grain boundary Drag impurities in, or out Formation and growth of voids
Helium Unavoidable in Fusion: D+T = He + n Helium hates being in metals – goes to voids, causes swelling attracts other He, emits interstitials. He voids nucleate on grain boundaries and cause embrittlement Introduce other sinks (precipitates) to capture He, or nanopipes to extract it to the surface – need to understand what attracts it.
Formation and growth of voids Experiment versus KMC theory.
Summary – not much known Radiation damage is a unique environment Driven, complex system – thermodynamics need not apply – extrapolation dangerous Experimental study of 14MeV neutrons expensive (IFMIF) but necessary Where can simulation focus, enhance, or replace experimentation? Who would believe it?
Functional Forms Must be such as to allow million atom MD Short-ranged (order-N calculation) Should describe electronic structure Motivated by DFT (a sufficient theory) Fitted to relevant properties
Dislocations Without dislocations, materials would be millions of times less ductile. Dislocations have infinite strain energy (so can only be created with other defects) Dislocation cores have infinite elastic energy (need atomistic level detail to remove it) Dislocation ends are topologically impossible - must end at a crystal imperfection
Radiation effects on crystals Want a material that can withstand radiation Google on crystals Radiation displaces atoms – how do they get back? What stops them? What are the timescales? Build a reactor and wait and see? Understanding would be better - theory
Heirarchies – where to start Schroedinger equation Quantum mechanics (nanometres) Effective interatomic forces (microns) Topological defects String theory (dislocations…) String theory (superstrings) Elementary particles Strong, weak gravitational force No significant advance in the theory of matter in bulk has ever come about through derivation from microscopic principles Tony Leggett, Nobel Laureate 2003 (physics)
Computational Physics at Edinburgh Work from first-principles Know only fundamental constants Computationally demanding….
History lesson 1930s Pair potentials 1980s Many body potentials 1990s Angle-dependence 2000s Onsite dependence:
What can empirical/MD do? Reproduce reliable energies – YES Predict reliable energies – NO Reproduce mechanisms and correlations – YES Predict unexpected mechanisms – YES
Potential developments Fill two bands Different widths Fixed offset Optimise wrt occupation of band locally.
Two Band Model Allows localised orbitals on atom to change state – e.g. s-d or Demonstrated for s-d transfer – gives a discontinuous isostructural transition. Work in progress for iron Minimisation done analytically => still Lennard Jones speed not Car-Parrinello.
Quantum Mechanics What electrons like to do… 1/ Be near to positive charges 2/ Not be too squashed up 3/ Not be near other electrons Quantum mechanics tells us how to apply these rules mathematically
Density Functional Theory Quantum mechanics tells us how to apply these rules mathematically For a many-body electron system… Energy is a functional of electron density only. Doesnt matter which electron, doesnt matter about individual wavefunctions. Kohn – 1998 Nobel prize
But what is the functional? Kohn-Sham equations Kinetic Energy Electron repulsion Ion-electron attraction Everything else
Calculate what you want Want energy differences between arrangements of atoms Dont mind systematic error in atoms themselves Avoid subtracting two large numbers Pseudopotentials (ion+core electrons) – large but systematic error in atomic energy
Computing and the new elegance * The pseudopotential plane wave method Write the wavefunction as a Fourier series Need hundreds of Fourier components, but Basis set is complete Operations can be done in real or k-space, whichever is quicker. Mathematically ugly – computationally elegant
UKCP A fifteen year mission 2004 - Commercially available plug n play code allows hundreds of academics to do quantum mechanics without the pain. Or the understanding… ? 1990 – Collaboration founded to write density functional theory software for parallel computing (Cambridge/Edinburgh Total Energy Package)
Cohesive term looks like Finnis-Sinclair with variable number of electrons in each band (second moment tight-binding) Plus extra energy associated with band centres being different Plus a pairwise potential (also dependent on occupation)
Problem: minimising total energy with respect to electron transfer at each site appears to be minimisation of N-variable function BUT, by writing energy as sum of atomic energies, and splitting the pair potential part between atoms appropriately, determining becomes local and analytic (i.e. as fast as pair potentials) in the absence of charge transfer W and U are sums of pair potentials E 0, N and T are constants (band centre offset, band capacities, total number of electrons/atom)
BETTER STILL… Force is variational in so can be evaluated locally (quickly) for MD. (Hellman-Feynman theorem!) Elasticity is non-local – great flexibility in fitting.
Two band model – caesium s-d transfer Isostructural phase transition Elastic anomalies d-like atom is smaller – favoured under pressure Correlation effect beyond DFT-GGA!
Electron transfer Optimise Ns-Nd Fit phase transition pressure, energy, volumes
Two-band model - transferability Parameters fitted to Cs describe all 6s5d metals! Suggests the physics is right
Composition dependent potentials For alloys, properties depend on Fermi energy. Potentials capture only local effects (e.g. pinning), not global effects (phase stability) Two-band model shows that the total number of electrons can be included in fit without extra computational cost For MD, composition-dependent potentials can be generated at start of each run with no computing cost.