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

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 ? (1) D 2 + T 3  He 4 + n 1 + 17.6 MeV Thermonuclear fusion : Coal combustion (anthracite, dry mass) (4) C 6 H 2 + 6.5 O 2  6 CO 2 + H 2 0 + 30 eV By comparison… simple to initiate, very low yield energy gain ~ 450:1 Nuclear fission : normally (3) U 235 + n  Xe 134 + Sr 100 + n + 200 MeV + soup of long-lived radionuclides, Sr 90, Cs 137 Advanced fission cycles can reduce long-lived waste

4. 1.1 Conditions for fusion power Achieve sufficiently high ion temperature T i  exceed Coulomb barrier density n D  energy yield energy confinement time  E n D  E T i >3  10 21 m -3 keV s “Lawson” ignition criteria : Fusion power > heat loss Fusion triple product At these extreme conditions matter exists in the plasma state  100 million °C

5. 1.2 The plasma state : the fourth state of matter plasma is an ionized gas 99.9% of the visible universe is in a plasma state 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

6. 2.0 Routes to Fusion Power : Hot Fusion 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 Demonstrated Q = power out/power ~0.7

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

8. Q = P out /P in ~1 3.0 Progress in magnetically confined fusion “Breakeven” regime : Eg. Joint European Tokamak : 1983 - “Ignition” regime, Q  ∞ : Power Plant. D 2 + T 3  He 4 (3.5 MeV) + n 1 (14.1 MeV) “Burning” regime : ≥ P in Q>5  ITER P out 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. 4.1 Understanding Magnetic Perturbations : Blending diagnostics, interpretation and theory. M. J. Hole, L. C. Appel, R. Martin |n|=1 chirping |n|=2 |n|=1

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

13. 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 33 22 11 44 33 22 11 44 Motivation : Characterise magnetic perturbations, which can lead to  deterioration in confinement  disruption

14. Limitations of Standard Techniques (A) Phase counting of time series data (B) As above, but  mapped to straight field line coordinates 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) Large aspect ratio approximations often used for  mapping (C) Singular Value Decomposition in time-series data : channels time Limitations : Data taken at different times, not all coils used at once Polar plot of the first 2 SVD principal axes vs.  *. Nardone C., Plasm. Phys. Con. Fus., 34 (9), 1992. JET #23324 Limitations : Cannot resolve modes degenerate in n,m &/or .

15. Fourier - SVD analysis resolves eigen-modes Solve for a and {n 1,n 2,…,n m } s.t. is minimized for all modes with n i  n c, and n c =Nyquist mode number. For all coils: 33 22 11 44 For each coil, spectrogram gives complex Fourier transform : a 1,..., a M = mode complex amplitudes n 1,…,n M = mode numbers

16. Statistical Analysis can quantify fit 33 22 11 44 e.g. for M=1, Quantify r by comparing to significance levels generated by forming the pdf of noise. FkFk FF FnFn Re Im 0.00.20.40.60.81.0 0.0 0.2 0.4 0.6 0.8 1.0 r P(r) P(r) for M=1, F=1 P(x  r)=0.1 P(x  r)=0.5 M. J. Hole and L. C. Appel, Europhysics Conf. Abstract, 27A, P3.132. 30 th EPS Conf. On Controlled Fusion and Plasma Physics. St Petersburg, Russia,2003.

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

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

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

20. 4.2 Plasma Modelling : Equilibrium and Stability Mega-Ampere Spherical Tokamak M. J. Hole and the MAST Team Baseline Achieved (2002) Major Radius 0.85 m 0.85 m Minor Radius 0.65 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 Ruby TS time (m,n) = (2,1) mode #7085

22. Inferring the magnetic topology : enabled by precision diagnostics … ~300 point TS  n e, T e Z eff  n i = 0.78 n e CXR  T i = 1.1 T e Pressure fit: #7085 @ 290ms

23. … interpretation & ideal-MHD force-balance Boundary taken from EFIT Pressure from kinetic fit I ll = / taken from EFIT: inconsistent with computed BS fraction Kinetic reconstruction of #7085 M. J. Hole, PPCF

24. Ideal MHD stability Linearized ideal MHD eigen-value equations for a plasma displacement can be written :   2 <0  secular growth  unstable low n external modes form hard performance limits. Potential energy Kinetic energy Z(m) 1 1 R(m) n=1 Proximity to instability determined by increasing pressure gradient, until plasma unstable.

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

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

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. 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 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

29. Application to MAST-like discharge R [m] n i [10 20 m -3 ] R [m] v poloidal [km s -1 ] R [m] v  [km s -1 ] p [kPa] thermal fast-ion Fast-ion n i core localized, rapid poloidal & toroidal rotation improved resolution of fast-ion & thermal species in force balance R [m] Z [m] R [m] Z [m]  fast-ion  thermal

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

31. In 2D, large-scale, spontaneously-generated, coherent structures often observed. Zonal flow creation and transport suppresion due to the zonal flow is a key physics for plasma confinement. [Z. Lin et al, Science (1998)] Zonal flows improves plasma confinement Example : Zonal flow in a tokamak plasma Destruction of electrostatic elongated radial fluctuations by zonal flow  transport suppression 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 toroidal resistivityDensity profile scale length viscosity diffusion term If  =   drift waves If  ~ 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. linear growth saturation Time(  c ) Energy inertial range energy input Energy k eg: n, density perturbations … and explored by numerical simulations

33. Turbulence suppression at low power input 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 R. Ball, Phys. Plas., 12, 090904-5, 2005 Motivation : Explore dynamics of turbulence with power input, and suggest experiment optimization R. Numata, R. Ball and R. L. Dewar Shear flow can grow as power input is withdrawn zonal flow ?

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

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

36. But some flux surfaces survive… Kolmogorov Arnold Moser (KAM) Theory : outlined by Kolmogorov (1954), proved by Arnold (1960) and Moser (1962) Perturb Hamiltonian by some periodic functional H 1, Moser considered integrable Hamiltonian H 0 with a torus T 0, and a set of frequencies  with .m  0, with m an integer array. and stepped pressure equilibria can exist (Existence of 3-D Toroidal MHD Equilibria with Nonconstant Pressure Comm. Pure Appl. Maths, XLIX, 717-764). In 1996, Bruno and Laurence derived existence theorems for sharp boundary solutions for tori for small departure from axisymmetry. 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

37. Stepped Pressure Profile Model Generalization of single interface 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 potential energy functional: helicity functional: mass functional: loop integrals conserved System comprises: N plasma regions P i in relaxed states. Regions separated by ideal MHD barrier I i. Enclosed by a vacuum V, Encased in a perfectly conducting wall W … I1I1 I n-1 InIn VPnPn P1P1 W

38. 1 st variation  Taylor “relaxed” equilibria Energy Functional W: Setting  W=0 yields: 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: 2 nd 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. ● Strategy – Look at integrable and near-integrable cases to provide baseline for fully 3D cases 4.6 Spectrum of 3-D ideal MHD ● Problems unique to 3D – Wave equation non-separable – Statistical characterization sensitive to spectral truncation method (“regularization”) R. L. Dewar and B. McMillan Eg. W-7X

41. Eigenvalue equation for interchange modes in cylindrical (integrable) geometry equations of motion  eigenmode equation for stream function Like quantum, microwave & acoustics spectral problems, ideal MHD on static equilibrium is Hermitian  real eigenvalues (=  2 — unstable modes have  2 < 0,  = i  ).  MHD fluid displacement linearized + averaged over helical ripple

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

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

44. 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, Generic chaotic systems give pdf like random matrices from a Gaussian Orthogonal Ensemble Level repulsion Generic integrable systems give Poisson distribution, as if random! (Eigenvalues uncorrelated) No avoidance of degeneracies TAE gap EAE gap nn  /  A 0 0.2 0.4 0.6 0.81.0 0.5 1.0 1.5 2.0 2.5 0.0 Eg. Alfven eigenmode gaps in continuum of shear Alfven eigenmodes of a tokamak pklasma NAE gap

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

46. 4.7 Burning Plasma Physics A. Sullivan, R. Ball, R. L. Dewar, M. J. Hole  /  A nn 0 0.2 0.4 0.6 0.81.0 0.5 1.0 1.5 2.0 2.5 0.0

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

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

50. Continuum frequencies of Alfvén eigen-modes r TAE’s Example of numerically computed continuum of eigen-modes m=2 m=3 m=3m=3  /  A TAE gap EAE gap nn  /  A 0 0.2 0.4 0.6 0.81.0 0.5 1.0 1.5 2.0 2.5 0.0

51. D + driven Alfvén eigenmode activity MAST discharge 5586 exhibits multiple mode frequency activity – I p =600kA, B tor = 0.4 T,  =1.9,  =a/R=0.7 – 0.8 MW co-injected 34keV D, v || /v A = 0.5 (Z eff =3.9) Drive calculations require knowledge of ion distribution function [1] K. McClements et. al. PPCF, 41, pp661, 1999

52. TAE Drive: Analytic Calculations Wave-particle drive analysis for (m,n)=(4,3) modes r [m]  0 0.4 0.8 1.2  b (v || =v A /3,  =0)  74mm  m  14mm Power drive from particles to wave P , collapses to 1D integral over , and =constant describes the unperturbed orbit, l = poloidal mode number describing variation of  along orbit,  l =1/(1-2l), C l (p) = constants describing TAE eigenfunction, v A0 = Alfvén velocity at magnetic axis (~2.9 x 10 6 ms -1 ) p=1;  b >>  m p=2;  m >>  b bb r r (1) large aspect ratio, equilibrium scale lengths » mode scale length  m (2) circular flux surfaces and drift orbits (3) narrow orbit k  -1 >  b (4) radially localised mode, k  -1 >  m, (5) ignore FLR effects,  b >  L (6) neglect continuum damping (7) neglect energy gradients in f 0

53. v || =v A /5 v || =-v A /5 v || =v A /3 v || =-v A /3 Counter-passing particles Co-passing particles Calculation of  f 0 /  P  Distribution functions obtained from LOCUST : a gyro-orbit NBI fast particle simulation code  f 0 (R,Z,v, =v || /v) projections of resonant particle distribution onto , P  plane P  /P  0  [keV/T] P  /P  0 P  /P  0 P  /P  0  [keV/T]  [keV/T]  [keV/T]

54. Significant Wave drive, although beam sub-Alfvénic Counter- passing Co-passing Integrate over  to obtain TAE drive Significant TAE wave drive, even though

55. 5.0 What is the future of fusion energy? ITER is an international collaboration to build the first fusion science experiment capable of producing a self-sustaining fusion reaction, called a “burning plasma.” It is the next essential and critical step on the path toward demonstrating the scientific and technological feasibility of fusion energy. US. Department of Energy, Office of Sciences DOE Office of Science Strategic Plan February, 2004 “The President has made achieving commercial fusion power the highest long-term energy priority for our Nation.”

56. 5.1 The future is ITER Plasma conditions 15MAIp, plasma current 6.2m, 2.0mMajor,minor radius 10Q = fusion power/ aux.heating 500MWTotal Fusion power 80  10 6 °C 73MWAuxillary heating, current drive 837 m 3 Plasma Volume 5.3TToroidal field @6.2m

57. 5.2 ITER Objectives Programmatic ● Demonstrate feasibility of fusion energy for peaceful purposes Physics ● Produce and study a plasma dominated by  particle (self) heating ● Steady-state power gain of Q = 5, higher Q for shorter time ● “Grand Challenge” burning plasma science : plasma self-organization, non-Maxwellian and nonlinear physics, confinement transitions, exhaust and fuelling control, high “bootstrap” (self-current driven) regimes, energetic particle modes, plasma stability. Technology ● Demonstrate integrated operation en-route to a power plant ● Investigate crucial materials issue: First wall neutron flux loading > 0.5 MW/m 2 Average fluence > 0.3 MW years/m2 ● Test tritium breeding blanket for a demonstration reactor (DEMO) The first wall of a fusion reactor has to cope with the ‘environment from hell’ so it needs a “heaven sent surface”.

58. 5.3 ITER Scaling – Why so big? A. Power Balance M=n D (0)  E T i (0) >3  10 21 m -3 keV s Ignition criteria : P  > P L Auxiliary heating  heating power loss D-T collision cross section peaks at T i (0) ~100 million K (1) B. Energy Confinement Time : empirical scaling Confinement mode H-mode: H H ~1 Plasma current magnetic field major radius elongation = b/a aspect ratio (2) C. Density Limit : ~ empirical (4) (3) Subs. (2), (3) and Ti- into (1) Finite Q : For Q=  : (5)

59. F. Materials Limits : Superconducting NbTi or NbSn OH coilTF coilshieldplasma Radial Tokamak build shieldTF coil R coil  BS a R Divertor ablation limits during ELM’s, disruption Minimize neutron flux loading 5.3 Design determined by physics, technology E. Engineering Choices : D. Edge magnetic winding (or “safety”) factor f = plasma geometric shaping factor plasma unstable for q 95 < 2.5  q 95 ~ 3 Fold A – F + design objective Q>5 ~ITER Fusion Power P f ~ 500 MW n DT 10 20 m -3 R c,  BS, a, R 3.2, 1.0, 2.0, 6.2 Ip, plasma current15 MA

60. 5.4 Who is ITER? ITER is a consortium of 6 nations and alliances under the auspices of the IAEA

61. 5.5 ITER technology has been demonstrated

62. 5.7 ITER site selection June 28, 2005

63. 5.8 Fusion energy time-scales Source: Accelerated development of fusion power. I. Cook et al. 2005 Australian Government Energy White paper (2004).... 200520502020 materials testing facility ITER today’s experiments demonstration power-plant commercial power-plants

64. 5.9 Towards a Unified Australian Fusion Science Program Collection of scientists and engineers from multiple research disciplines supporting a mission orientated goal : controlled fusion as an energy source ITER distribution email list ~100 scientists and engineers Attendees at ITER Forum meetings ~ 30 scientists. Activities to date  Integration : collation of fusion energy capabilities, ITER workshop proponent.  Presentations: DEST, DITR, DEH, AIE, ANSTO, EU commission representatives, members of parliament  Submissions : parliamentary enquiry on non-fossil fuels, NCRIS  Media : Various newspapers, ABC radio… Australasian Science Australian ITER Forum

65. The University of Sydney AUSTRALIA FLINDERS UNIVERSITY ADELAIDE  AUSTRALIA THE AUSTRALIAN NATIONAL UNIVERSITY UNIVERSITY OF CANBERRA Australian Nuclear Science &Tec. Org. Australian Ins. of Nuclear Science & Eng. H-1 National Facility Theory program High beta physics Quasi-toroidal pulsed cathodic arc Plasma theory/ diagnostics plasma fuelling, soft x-ray imaging Computational MHD modelling High heat flux alloys MAX alloys are one promising route Manages OPAL research reactor ~1000 staff Consortium of all Australasian nuclear research institutes Australian ITER Forum

66. 5.10 Next Step Challenges for Fusion Theory (1) Burning Plasma science :  Fusion plasmas are not thermalized, but are energy pumped in a steady-state  Produces new challenges to description of steady-state, and magnetic field  Multiple energetic resorvoirs can drive different mode activity, which may degrade confinement  Burning plasmas are high beta environments, (2) Improved understanding of 3D magnetic confinement:  stellarators  tokamaks, through error fields (which can lead to disruption) (3) Continued advance in understanding turbulence, dynamics, and effect on confinement

67. 6.0 Conclusions (1) Described magnetic confinement fusion, and progress to date (2) Provided an overview of some ANU plasma and fluid theory research, motivation, and international linkages: focus on  Understanding magnetic perturbations  Advances in plasma modelling  Observation-lead theory development  Exploring the dynamics of turbulence  Frustrated Taylor relaxation  Burning Plasma Physics (3) Introduced the next step for fusion science: ITER (4) Highlighted some theoretical challenges for the future.

68. Very Cool Kermit!