Magnetic Confinement Fusion Energy Research: Past, Present and Future.

1. ZETA (UK), 1940 - 1950 Zero Energy Toroidal Assembly JET (EU), 1980 - Joint European Torus ITER (Earth), 2015 – International Thermonuclear Experimental Reactor Magnetic Confinement Fusion Energy Research: Past, Present and Future. November 3, 2005. Dr M. J. Hole, Department of Theoretical Physics, RSPSE

2. Contents (1) What is fusion energy? (2) Magnetic confinement concepts (3) Improvements in fusion plasma performance (4) Advances in Australian theoretical plasma physics research (5) The next step in fusion plasma physics (6) Summary and Discussion

3. 1.0 What is fusion ? Thermonuclear fusion : Nuclear fission : normally (3) U235 + n Xe134+ Sr100 + n + 200 MeV + soup of long-lived radionuclides, Sr90, Cs137 • Advanced fission cycles can reduce long-lived waste energy gain ~ 450:1 By comparison… simple to initiate, very low yield Coal combustion (anthracite, dry mass) (4) C6H2 + 6.5 O2 6 CO2+ H 20 + 30 eV (1) D2 + T3  He4+ n1 + 17.6 MeV

4. nDETi>3  1021 m-3 keV s • “Lawson” ignition criteria : Fusion power > heat loss Fusion triple product • At these extreme conditions matter exists in the plasma state 1.1 Conditions for fusion power • Achieve sufficiently high ion temperature Ti exceed Coulomb barrier density nD energy yield energy confinement time E 100 million °C

5. 99.9% of the visible universe is in a plasma state • plasma is an ionized gas Inner region of the M100 Galaxy in the Virgo Cluster, imaged with the Hubble Space Telescope Planetary Camera at full resolution. A Galaxy of Fusion Reactors. • Fusion is the process that powers the sun and the stars 1.2 The plasma state : the fourth state of matter

6. 2.0 Routes to Fusion Power : Hot Fusion Demonstrated Q = power out/power ~0.7 Laser confinement : (uncontrolled fusion) • Focusing multiple laser light beams to a target • Principally funded (US,France, UK) to continue nuclear weapons research following comprehensive test ban treaty. … concept designs for power plants do exist. Magnetic confinement: (controlled fusion) use of magnetic fields to confine a plasma : eg. tokamak

7. 2.1 Hot Fusion Power Plant designs Final Report of the European Fusion Power Plant Conceptual Design Study, April 13, 2005

8. “Breakeven” regime : Q = Pout /Pin ~1 • “Burning” regime : D2 + T3 He4 (3.5 MeV) + n1 (14.1 MeV) Pout ≥ Pin Q>5 ITER • “Ignition” regime, Q∞ : Power Plant. 3.0 Progress in magnetically confined fusion Eg. Joint European Tokamak : 1983 - 1997 : Q=0.7, 16.1MW fusion 1997- : steady-state, adv. confinement geometries

9. 3.1 Progress comparison to # CPU transistors per unit area Fusion progress exceeds Moore’s law scaling

10. 4.0 Some advances in Australian Theoretical Plasma Physics • Understanding magnetic perturbations • Advances in plasma modelling • Observation-lead theory development • Exploring the dynamics of turbulence • Frustrated Taylor relaxation • Burning Plasma Physics • Bushfires • Energetic Particle Mode physics

11. |n|=2 |n|=1 chirping |n|=1 4.1 Understanding Magnetic Perturbations : Blending diagnostics, interpretation and theory. M. J. Hole, L. C. Appel, R. Martin

12. Mirnov Coil Modelling and Design Graphite coated centre-column plasma Graphite shield - + • Diagnostic Transfer Function: MV coil/ transmission line Vo - + amplifier • Stray Capacitance modelling • M. J. Hole & L. C. Appel accepted IEE Proc. Ccts. Dev. Sys. - + Va A/D converter • System resonance, remote calibration • L. C. Appel, & M. J. Hole, Rev. Sci. Instrumen ts, 76(9)., Sep, 2005 + - Vf

13. f1 f2 f4 f3 q1 q2 q4 q3 Magnetic Eigenmode Detection M. J. Hole, L. C. Appel, R. Martin • A new approach to an old problem: poloidal (m) and toroidal (n) mode number identification in magnetic confinement • Motivation : Characterise magnetic perturbations, which can lead to • deterioration in confinement • disruption

14. Limitations of Standard Techniques (A) Phase counting of time series data Observed poloidal mode structure on centre column magnetic array for MAST shot 2952 R. J. Buttery et al., Contr. Fus. Plas. Phys. 25A pp. 597, (2001) (B) As above, but  mapped to straight field line coordinates Large aspect ratio approximations often used for  mapping Limitations : Data taken at different times, not all coils used at once (C) Singular Value Decomposition in time-series data : channels Polar plot of the first 2 SVD principal axes vs. *. Nardone C., Plasm. Phys. Con. Fus., 34 (9), 1992. time JET #23324 Limitations :Cannot resolve modes degenerate in n,m &/or .

15. 1 2 4 3 Fourier - SVD analysis resolves eigen-modes • For each coil, spectrogram gives complex Fourier transform : • For all coils: a1,...,aM = mode complex amplitudes n1,…,nM = mode numbers • Solve for a and {n1,n2,…,nm} s.t. is minimized for all modes with ninc, and nc =Nyquist mode number.

16. 1 2 4 3 P(r) for M=1, F=1 1.0 Im 0.8 F P(x r)=0.1 0.6 P(r) Fk 0.4 Fn 0.2 P(x r)=0.5 Re 0.0 0.0 0.2 0.4 0.6 0.8 1.0 r Statistical Analysis can quantify fit • Quantify r by comparing to significance levels generated by forming the pdf of noise. e.g. for M=1, M. J. Hole and L. C. Appel, Europhysics Conf. Abstract, 27A, P3.132. 30th EPS Conf. On Controlled Fusion and Plasma Physics. St Petersburg , Russia,2003.

17. 4836 400 -6 -7 300 f [kHz] -8 -9 200 -10 100 -11 -12 40 60 80 120 100 140 t=48.75 ms 6 4 4 || ( 10-7) 2 2 0 0 220 100 60 40 180 80 40 80 20 120 0.4 0.4 0.2 0.2 0 0 40 180 80 120 100 60 40 80 20 f [kHz] f [kHz] Mode identification with statistics log10|B[T]| shot #4636 : a beam-heated deuterium discharge t [ms] t=100 ms || ( 10-6) 220 10% level (one mode)

18. Aim: Find s.t. is maximised as 0. Is there an optimum coil placement ? plasma signal basis function mode number error New expression for rs(n) :

19. Method: Monte-Carlo sample • generate random arrangements for • Find rmin for each e.g. N=3, nc=40 200 160 e.g. 120  ( ) 80 40 0 0.5 0.4 0 0.1 0.3 0.2 Optimum locations related to density of rational numbers ? •  is not unique. Choose mapping to remove reflections and rotations Can these positions be generated by an algebraic mapping?

20. 4.2 Plasma Modelling : Equilibrium and Stability M. J. Hole and the MAST Team Mega-Ampere Spherical Tokamak BaselineAchieved (2002) Major Radius0.85 m 0.85 m Minor Radius0.65 m 0.65 m Elongation 2.5 2.4 Triangularity 0.5 0.5 Plasma Current 2 MA 1.2 MA Toroidal Field 0.51 T 0.51 T NBI Heating 5 MW 2.7 MW RF Heating 1.5 MW 0.8 MW Pulse Length 5 sec 0.5 sec

21. Plasmas are physics-rich (m,n) = (2,1) mode Ruby TS time #7085

22. Pressure fit: Inferring the magnetic topology : enabled by precision diagnostics … #7085 @ 290ms • ~300 point TS  ne, Te • Zeff ni= 0.78 ne • CXR Ti= 1.1 Te

23. … interpretation & ideal-MHD force-balance Kinetic reconstruction of #7085 M. J. Hole, PPCF • Boundary taken from EFIT • Pressure from kinetic fit • Ill = <J.B>/<B.> taken from EFIT: inconsistent with computed BS fraction

24. 1 Z(m) -1 1 R(m) Ideal MHD stability Linearized ideal MHD eigen-value equations for a plasma displacement can be written : Potential energy Kinetic energy • w2<0  secular growth • unstable low n external modes form hard performance limits. Proximity to instability determined by increasing pressure gradient, until plasma unstable. n=1

25. MAST equilibrium stable equilibrium unstable equilibrium Probing performance limits reveal new physics regimes Trajectories to disruption Conventional scaling limits : • Grayscaled data is a histogram of MAST operating space • M. J. Hole et al, Plasma Physics and Controlled Fusion, 47(4), 2005.

26. Pressing the limits of ideal MHD • Multiple energetic components, resolved by different diagnostics • Typical energy schematic breakdown [1] • Rotational energy ~ 2% of WMHD, v /vth <0.7. [1] R. Akers et al. Plas. Phys. Con. Fus. 45, A174-A204, 2003

27. 4.3 Theory Development : Multiple Fluid Models G. Dennis and M. J. Hole • Modern fusion plasmas are not thermalized, but are energy pumped in a steady-state • Multiple energetic reservoirs • Energetic components have different rotation profiles Single thermalized, stationary fluid no longer sufficient

28. General idea : Reduce multiple single-fluid force balance Into two algebraic equations (Bernoulli + toroidal comp.) , and a generalized Grad-Shafranov (force – balance) equation Solve numerically, by modifying a single fluid code that handles rotation, FLOW [1] [1] L. Guazzotto, R. Betti, J. Manickam, S. Kaye, PoP 11, 604, 2004 Multi-fluid force balance - a first attempt • Consider multiple quasi-neutral fluids, such that : • fluids have independent temperature, and arbitrary flow • pressure for each species is isotropic, p=p|| • inter-specie collisions may be neglected • velocity distribution function for each specie is Maxwellian • Plasma has toroidal symmetry

29. Application to MAST-like discharge • Fast-ion nicore localized, rapid poloidal & toroidal rotation • improved resolution of fast-ion & thermal species in force balance thermal thermal Z [m] ni [1020 m-3] vpoloidal [km s-1] fast-ion R [m] R [m] R [m] fast-ion Z [m] v[km s-1] p [kPa] R [m] R [m] R [m]

30. 4.4 Turbulence : fundamental in nature R. Numata, R. L. Dewar, and R. Ball [NASA web site http://solarsystem.nasa.gov] • Turbulence is present at scales from coffee cup to universe. • Characterized by unpredictability, strong mixing effect, etc. • Research Aim : infer universality from complete complexity.

31. Zonal flows improves plasma confinement Destruction of electrostatic elongated radial fluctuations by zonal flow  transport suppression In 2D, large-scale, spontaneously-generated, coherent structures often observed. Example : Zonal flow in a tokamak plasma [Z. Lin et al, Science (1998)] • Zonal flow creation and transport suppresion due to the zonal flow is a key physics for plasma confinement. • Zonal flow also observed in other systems (e.g. geophysical fluids), with analogous forces (eg. Coriolis force)

32. Drift-wave turbulence simulations suggest “universality” : power law spectrum Dynamics described by fluid equations of motion … and explored by numerical simulations viscosity saturation eg: n, density perturbations Energy diffusion term linear growth toroidal resistivity Density profile scale length Time(c) energy input Energy inertial range k • If a =   drift waves • If a~ 1  • Small scale fluctuation grows linearly by drift wave instability (k ~ 1). • Large fluctuation amplitudes evolve nonlinearly, and may saturate • Observe an inertial range where energy spectrum obeys power law.

33. Turbulence suppression at low power input zonal flow ? Shear flow can grow as power input is withdrawn R. Numata, R. Ball and R. L. Dewar • Dynamical systems model for : • thermal energy W, • kinetic energy of turbulence N, and • shear flow v kinetic energy • Constant, but arbitrary power input Q • Equilibria surface plots reveal striking dynamics with increasing power input Motivation : Explore dynamics of turbulence with power input, and suggest experiment optimization R. Ball, Phys. Plas., 12, 090904-5, 2005

34. 4.5 3D Magnetic Confinement M. J. Hole, S. R. Hudson, R. L. Dewar

35. If a symmetry exists  magnetic field forms flux surfaces Eg. toroidal symmetry : • General Case : With solution and  constant on a field line  Singular nature of B.  . J =0 p=0 at rational  (or q) S. Kumar, PRL, PhD stduent • In 3D, regions of rational  (or q) do not collapse to form flux surfaces. • In regions of rational  , p=0. Do 3D ideal MHD equilibria with p0 exist ? Ideal MHD model + BC’s, eg.

36. KAM theory states: if tori are sufficiently far from resonance (ie. satisfy a Diophantine condition), some tori survive for  < c  If  sufficiently irrational, some flux (KAM) surfaces survive • In 1996, Bruno and Laurence derived existence theorems for sharp boundary solutions for tori for small departure from axisymmetry. (Existence of 3-D Toroidal MHD Equilibria with Nonconstant Pressure Comm. Pure Appl. Maths, XLIX, 717-764). But some flux surfaces survive… • Moser considered integrable Hamiltonian H0 with a torus T0, and a set of frequencies  with .m0 , with m an integer array. Kolmogorov Arnold Moser (KAM) Theory : outlined by Kolmogorov (1954), proved by Arnold (1960) and Moser (1962) • Perturb Hamiltonian by some periodic functional H1, and stepped pressure equilibria can exist

37. … P1 In-1 I1 V Pn In Stepped Pressure Profile Model - Spies et al Relaxed Plasma-Vacuum Systems, Phys. Plas. 8(8). 2001 - Spies. Relaxed Plasma-Vacuum Systems with pressure, Phys. Plas. 8(8). 2003 Generalization of single interface model : • System comprises: • N plasma regions Pi in relaxed states. • Regions separated by ideal MHD barrier Ii. • Enclosed by a vacuum V, • Encased in a perfectly conducting wall W W potential energy functional: helicity functional: mass functional: loop integrals conserved

38. 1st variation Taylor “relaxed” equilibria Setting W=0 yields: Energy Functional W: n = unit normal to interfaces I, wall W Poloidal flux pol, toroidal flux t constant during relaxation:

39. Tokamak like relaxed equilibria can exist Eg. 5 layer equilibrium solution Contours of poloidal flux p • q profile smooth in plasma regions, • core must have some reverse shear • Not optimized Work in progress: • 2nd variation stable equilibria • Application to transport barrier modeling M. J. Hole, S. R. Hudson and R. L. Dewar, INCSP and APPTC, Nara, August 2005

40. 4.6 Spectrum of3-D ideal MHD R. L. Dewar and B. McMillan • Problems unique to 3D • Wave equation non-separable • Statistical characterization sensitive to spectral truncation method (“regularization”) Eg. W-7X • Strategy • Look at integrable and near-integrable cases to provide baseline for fully 3D cases

41. Eigenvalue equation for interchange modes in cylindrical (integrable) geometry • equations of motion  eigenmode equation for stream function linearized + averaged over helical ripple  MHD fluid displacement • Like quantum, microwave & acoustics spectral problems, ideal MHD on static equilibrium is Hermitian real eigenvalues  (= w2 — unstable modes have w2 < 0, w = ig).

42. Examples : • Details of spectrum determined by : • the rotational transform, iota • the pressure profile • interchange instabilities occur at resonant n,m. ie. Computing the interchange spectrum • Qualitatively, spectra looks like =2>0 =2<0 0  Alfvén continuum discrete modes accumulation points • The most unstable modes have no radial nodes (l=0) in the plasma

43. m, n space for most unstable l=0 modes   n/m - - At large m, eigenvalue depends only on slope,   infinite degeneracy at each rational unless we truncate spectrum

44. No avoidance of degeneracies Generic chaotic systems give pdf like randommatrices from a Gaussian Orthogonal Ensemble 2.5 Eg. Alfven eigenmode gaps in continuum of shear Alfven eigenmodes of a tokamak pklasma 2.0 Level repulsion 1.5 NAE gap  /A 1.0 EAE gap Generic integrable systems give Poisson distribution, as if random! (Eigenvalues uncorrelated) 0.5 TAE gap 0.0 0.2 0.4 0.8 1.0 0.6 0 n Statistics of nearest neighbour eigenvalues describes “universality” class of system • Suppose P(s)ds = probability of finding two consecutive eigenvalues n a distance s apart: • Shape of P(s) describes properties (eg. integrability) of system,

45. non-Poissonian statistics persist with finite m corrections Statistics of interchange modes reveal possible new universality class! • Ignore O(1/m) and higher terms [equivalent to Suydam condition], and apply abrupt truncation at mmax Data set consists of >32,000 of the most unstable eigenvalues: l = 0, m < mmax Separable system, but pdf is non-Poissonian — Is this a new universality class? Approaches a delta function as m

46. 2.5 2.0 1.5 1.0 0.5 0.0 0 0.2 0.4 0.8 1.0 0.6 n A. Sullivan, R. Ball, R. L. Dewar, M. J. Hole 4.7 Burning Plasma Physics  /A

47. Modelling the dynamics of a bushfire A. Sullivan, R. Ball, J. Gould, I. Enting no physics fast (4hrs in 1min.) detailed physics slow (1 min. in 2 days) Aim : develop a dynamical systems model of bushfire behaviour that is better than real-time for operational use. quasi-physical empirical physical • simplified processes • no chemistry • empirical response models, limited in scope. • detailed chemistry and physics of combustion and heat transfer

48. Modus Operandi : Benchmarked to reality! • Key ingredients : fuel, topography, atmosphere, fire. • Graph and network theory  abstract description of fire behaviour. • Datasets : grassland experiments conducted in mid-1980s will be used as basis of model development and testing.

49. For TAE’s, reduced ideal MHD equation for high-mode number shear Alfvén waves • Fourier decompose electrostatic potential  in poloidal harmonics with and with & • Toroidicity induced gaps in the Alfvén continuum appear • leads to coupling among poloidal harmonics. Fusion : the rise of Energetic Particles Modes M. J. Hole, L. C. Appel, S. Sharapov Eg. : Alfvén gap modes (in fusion, discovered by R. L. Dewar)

50. 2.5 2.0 1.5  /A 1.0 EAE gap 0.5 TAE gap 0.0 0 0.2 0.4 0.8 1.0 0.6 n r Continuum frequencies of Alfvén eigen-modes • TAE’s m=3 m=3 m=2  /A m=2 m=3 m=3 • Example of numerically computed continuum of eigen-modes