Maths pavingthe pathto Fusion Energy & ITER. Marseille, Maths master class, May 28 th 2018, Philippe GHENDRIH

Transcription

1 Maths pavingthe pathto Fusion Energy & ITER Marseille, Maths master class, May 28 th 2018, Philippe GHENDRIH

2 Maths & Physics A story of Fusion Energy What is Fusion Energy Research made of? MATHS & PHYSICS Kinetics in 1D-1V How is plasma special? Philippe GHENDRIH, Wuppertal, May 26th 2014 PAGE N /35 PAGE 2

3 Physics& maths: an oldcouple Symmetry no dependence on 1 variable conjugate variable is conserved identify these couples Emmy NOETHER L Symmetry = conservation laws in the plane cylindrical symmetry: L fixed, θ varies invariance origin of time = energy conservation: H = kinetic + potential θ Marseille, Maths master class, May 28 th 2018, Philippe GHENDRIH, 3/ 45

4 Equations: conservation & evolution Conservation equation (conjugate variable) g = 0 no dependence conserved conjugate variables: phase space = L θ Evolution equation differential equation Newton: Marseille, Maths master class, May 28 th 2018, Philippe GHENDRIH, 4/ 45

5 Symmetrybreaking: Maths Physics Mathematics: stepping by extension closed problem (well posed) Experimental evidence particular model A particular model B Physics: stepping by agglomeration? Unification: towards maths Simplification: effectiveness = towards engineering Making tools (Newton, Fourier, etc.) Threshold effects: changing model Symmetry breaking Marseille, Maths master class, May 28 th 2018, Philippe GHENDRIH, 5/ 45

6 Units: where worlds split? Different facets of units Identify an independent field example: current = A physics model equation adimensional equation Maths analysis 0 continuous discrete dimensional analysis control parameters Numerical analysis Identifya scale: milikilo, etc. identifies small(<< 1) and big(>>1) consequently: limits and derivatives Marseille, Maths master class, May 28 th 2018, Philippe GHENDRIH, 6/ 45

7 A STORY OF FUSION ENERGY Philippe GHENDRIH, Wuppertal, May 26th 2014 PAGE N /35 PAGE 7

8 1911: Discovering the atom matter is not "plum pudding" Walton Rutherford Cockcroft 1911: Discovering superconductivity He / α = commonfeature Marseille, Maths master class, May 28 th 2018, Philippe GHENDRIH, 8/ 45

9 Fusion energy& stars 1905: Einstein: E = mc2 + Brownianmotion 1908: Langevin, Jean Perrin Brownian motion = atoms : Nuclear fusion = energy of the sun(jean Perrin) 1 billion years(10 9 ) 1 second Marseille, Maths master class, May 28 th 2018, Philippe GHENDRIH, 9/ 45

10 Deuterium fusion Oliphant & Rutherford discover deuterium fusion, 1933 Marseille, Maths master class, May 28 th 2018, Philippe GHENDRIH, 10/ 45

11 a (political) story about FUSION The cold warforefront Early days(~1950): H bomb story Classified Research Marseille, Maths master class, May 28 th 2018, Philippe GHENDRIH, 11/ 45

12 Ça a débuté comme ça Céline LF "Voyage au bout de la nuit" Marseille, Maths master class, May 28 th 2018, Philippe GHENDRIH, 12/ 45

13 a (political) story about FUSION The cold warforefront Early days(~1950): H bomb story Classified Research 1957 Spoutnik effect, USA declassify 1958 IAEA = "International Cooperation" Euratom = European programme (+ Swiss!) 60 years 1960 URSS tokamak 1968 IAEA : tokamak T3, T e ~ K record! 1969 Tokamak performance isconfirmed(uk) Marseille, Maths master class, May 28 th 2018, Philippe GHENDRIH, 13/ 45

14 ITER, on the way to peace 1985 ending Cold War: Reagan / Gorbatchev summit ITER 1.5 GW device, cost10 Billion $ 4 partners: USA, USSR, Japan, EU Geneva Summit, 1985 Gorbachev, Reagan fusion as an inexhaustible source of energy for the benefit of mankind Marseille, Maths master class, May 28 th 2018, Philippe GHENDRIH, 14/ 45

15 ITER going international 1985 ending Cold War: Reagan / Gorbatchev summit 1.5 GW device, cost 10 Billion $: ITER 4 partners : USA, USSR, Japan, EU 1998 End of design (including technology research) 1998 USA pull-out 1998 New projectat 50 % cost: ITER-FEAT 3 partners: Russia, Japan, EU 2001 End of new ITER design 2003 Towards a decision, political of course 2005 Cadarache site is chosen 2014 The long and windingroad : 50 years Marseille, Maths master class, May 28 th 2018, Philippe GHENDRIH, 15/ 45

16 ITER: a very long way to go 2005 (+20 ears) Marseille, Maths master class, May 28 th 2018, Philippe GHENDRIH, 16/ 45

17 ITER: still a long way to go 2013 Marseille, Maths master class, May 28 th 2018, Philippe GHENDRIH, 17/ 45

18 ITER: building buildings... Marseille, Maths master class, May 28 th 2018, Philippe GHENDRIH, 18/ 45

19 ITER: coilmade in Japan Marseille, Maths master class, May 28 th 2018, Philippe GHENDRIH, 19/ 45

20 ITER: Cryostat base Marseille, Maths master class, May 28 th 2018, Philippe GHENDRIH, 20/ 45

21 ITER: complexity at work Paris, Marseille, SPICE Maths 21 avril master 2017 class, Philippe May 28 th GHENDRIH 2018, Philippe GHENDRIH, 21/15 45

22 ITER: a nuclearexperiment Paris, Marseille, SPICE Maths 21 avril master 2017 class, Philippe May 28 th GHENDRIH 2018, Philippe GHENDRIH, 22/15 45

23 New East -Old West EAST The new generationof superconducting tokamaks JT60-SA SST1 KSTAR Marseille, Maths master class, May 28 th 2018, Philippe GHENDRIH, 23/ 45

24 WHAT ISFUSIONENERGY RESEARCH MADE OF? Philippe GHENDRIH, Wuppertal, May 26th 2014 PAGE N /35 PAGE 24 Plasma & Large magnetic fields

25 a little Nuclear Chemistry D + T He + n D: hydrogen stable isotope T: hydrogen unstable isotope He: helium (stable ϕ& χ) n: neutron must be produced not key for ITER impact on device must be used to produce T not key for ITER Threshold condition for thermonuclear fusion interaction distance m E th 10 kev T K D + + T + He 2+ + n Ionised Media: PLASMA Langmuir 1928 Marseille, Maths master class, May 28 th 2018, Philippe GHENDRIH, 25/ 45

26 heat engine: insulation Energy production: self heated plasma at 10 8 K plasma energy balance 3.5 MeV helium ash (α particle) τ E heat confinement efficiency Lawson 1957 τ E low density n e τ E long magnetic confinement fusion P α + P add heat outflux on wall / plasma wall interaction Marseille, Maths master class, May 28 th 2018, Philippe GHENDRIH, 26/ 45

27 Newton equation / Lorentz force: adimensional: control parameter: Symmetries& work Work: Power: First integral: Larmor gyration in magnetic field Larmor radius: // motion = free Marseille, Maths master class, May 28 th 2018, Philippe GHENDRIH, 27/ 45

28 insulator = magnetic field B B Strong Magnetic Field: 5T Larmor radius ρ = v / Ω 10-3 m Drift in strong magnetic field Force //motion = free compressible motion = constrained incompressible Marseille, Maths master class, May 28 th 2018, Philippe GHENDRIH, 28/ 45

29 B-geometry: tokamak Free // motion: solution = torus centrifugal force = g-force drive of interchange instability vertical drift High Performance Magnetic Geometry: Tokamak ITER (alternative g-force) B 5T a= minor radius (R= A a) a 2 m A 3 aspect ratio ρ = ρ / a= 10-3 << 1 Marseille, Maths master class, May 28 th 2018, Philippe GHENDRIH, 29/ 45

30 Go big/ experimentalevidence ITER JET ITER size = cost $ = political Performance: Scaling law JET Manyopen questions: Uncertainty= small device weight? Scatter? Data selection Performance: empirical τ E Performance = size = cost Marseille, Maths master class, May 28 th 2018, Philippe GHENDRIH, 30/ 45

31 Vlasov equation (Boltzmann for plasmas) Kinetic equation 1-particle distribution function: f a collisions: VLASOV operator: a-dimensional form: Marseille, Maths master class, May 28 th 2018, Philippe GHENDRIH, 31/ 45

32 Maxwell equationsfor E& B Asymptotic limits in Maxwell equations Bisgiven(low βlimit) electrostatic limit Poisson equation Asymptotic limit = quasineutrality Nonlinear Gyro-kinetic (5D) simulations code = GYSELA Marseille, Maths master class, May 28 th 2018, Philippe GHENDRIH, 32/ 45

33 Large Basymptoticlimitof Vlasov 0; Asymptotic limit of Vlasov Gyrokinetic equation: expansion in ε High frequency (Ω) = particle motion gyroaverage ρ ρ 10-3 m Gyrokinetics : phase space 6D 5D Much better for the code Difficult framework Marseille, Maths master class, May 28 th 2018, Philippe GHENDRIH, 33/ 45

34 Plasma shaping: Work in progress New code version? GYSELA: a global code All the confined plasma volume? Why? Given the cost: mesh size + time steady state (= τ E ) No scale separation Importance of large scales: barrier physics Boundaries (no r-periodicity) No inner radius outer radius: SOL, heat sink Marseille, Maths master class, May 28 th 2018, Philippe GHENDRIH, 34/ 45

35 A guide to toroidal geometry ϕ Torus 2 angles + radial coordinate= r filament structure quasi 2D θ r θ ϕ Marseille, Maths master class, May 28 th 2018, Philippe GHENDRIH, 35/ 45

36 Steady-state & global WATT: Grand challenge OCCIGEN2 (8 Million CPU hours) o self-organised turbulence: avalanches + staircase(= large scale) o SOL corrugated boundary Marseille, Maths master class, May 28 th 2018, Philippe GHENDRIH, 36/ 45

37 KINETICS IN1D-1V HOW IS PLASMA SPECIAL?

38 Two species plasma: Vlasov-Poisson Reference species = electrons: α= e 1D in position, 1D in velocity= 1D-1V Frozen ion asymptotic limit: Preparedinitial state t = t 0 conditions: Marseille, Maths master class, May 28 th 2018, Philippe GHENDRIH, 38/ 45

39 Solutions of the dispersion equation with: Dispersion equation γ< 0 e γt 0 damping ω e iωt oscillations Marseille, Maths master class, May 28 th 2018, Philippe GHENDRIH, 39/ 45

40 Landau damping δf e Bulk: frequency of Langmuir waves Resonance: Ω/ k Exponential decay Electric potential Marseille, Maths master class, May 28 th 2018, Philippe GHENDRIH, 40/ 45

41 plasma echos (seealsospin echo) Plasma electric potential First perturbation Second perturbation Echo x-direction time Marseille, Maths master class, May 28 th 2018, Philippe GHENDRIH, 41/ 45

42 Bump on tail Marseille, Maths master class, May 28 th 2018, Philippe GHENDRIH, 42/ 45

43 Manykineticproblems Collisions, heat transfer, sheath physics, quasineutrality Marseille, Maths master class, May 28 th 2018, Philippe GHENDRIH, 43/ 45

44 Fusion promises Long term research in a changing world! (cold war to ITER) Safe, no waste, inexhaustible Complex technology Tayloring burning plasmas On the way to material science Science of complexity "infinitely normal" Large scale computing Big money science Funding innovation in industry What is the price of research? Marseille, Maths master class, May 28 th 2018, Philippe GHENDRIH, 44/ 45

45 Summary Strong need for first principle simulations Strong need for support from maths & applied maths Need for comparison to experiments Scaling law? Need for AMU support project AMIDEX TOP, leader Eric SERRE Needfor collaboration withmaths & AppliedMaths Commissariat à l énergie atomique et aux énergies alternatives Centre de Cadarache Saint Paul Lez Durance Cedex T. +33 (0) F. +33 (0) Etablissement public à caractère industriel et commercial RCS Paris B DSM IRFM SIPP