Magnetohydrodynamics (MHD) III

Transcription

1 Magnetohydrodynamics (MHD) III Yong-Su Na National Fusion Research Center POSTECH, Korea, 8-10 May, 2006

2 Review II 1. What is Stability? 2. MHD Instability Interchange Mode Flux Tube Instabilities 3. Formulation of MHD Instabilities Fourier Normal Mode (Eigenmode) Analysis The Energy Principle 4. Classification of MHD Instabilities 5. MHD Instabilities in a Tokamak 6. Microinstability (Turbulence)

3 Review II Classification of MHD Instabilities Macro-instability Micro-instability - Ideal MHD Current driven (kink) Pressure driven (ballooning) - Resistive MHD Current driven (tearing) Pressure driven (resistive interchange)

4 Contents 1. Limits in Tokamak Operations 2. Sawtooth 3. Neoclassical Tearing Mode (NTM) 4. Resistive Wall Mode (RWM) 5. Edge Localised Mode (ELM) 6. H-mode 7. Internal Transport Barrier (ITB) 8. Tokamak Operation Scenario

5 Contents 1. Limits in Tokamak Operations 2. Sawtooth 3. Neoclassical Tearing Mode (NTM) 4. Resistive Wall Mode (RWM) 5. Edge Localised Mode (ELM) 6. H-mode 7. Internal Transport Barrier (ITB) 8. Tokamak Operation Scenario

6 Tokamaks and Their Operational Space To obtain the goal of nuclear fusion, tokamaks have to maximise the energy confinement time τ E ( I p or 1/q for fixed B-field) the fuel density n (P fus n 2 σv or (nt) 2 at optimum T of kev) the normalised pressure β = p kin /p mag (P fus p kin2 or β 2 at fixed B-field)

7 Tokamaks and Their Operational Space q, n and β are limited by the occurrence of large scale MHD instabilities (free energy of poloidal field and plasma pressure). MHD instabilities can be ideal (τ A = ~ μs) or resistive (τ R = ~ ms) Examples: Disruptions at low q and high density (current driven islands) Neoclassical Tearing Modes ( pressure driven islands) Resistive wall modes (current and pressure driven ideal kink) Two strategies: Avoid natural tendency, but limits operational space Control needs active tools, but increases op. space

8 Contents 1. Limits in Tokamak Operations 2. Sawtooth 3. Neoclassical Tearing Mode (NTM) 4. Resistive Wall Mode (RWM) 5. Edge Localised Mode (ELM) 6. H-mode 7. Internal Transport Barrier (ITB) 8. Tokamak Operation Scenario

9 Sawtooth ASDEX Upgrade pulse I p (MA) 10 P NBI (MW) P RF (MW) 1 W MHD (MJ) 6 Nel x T i (kev) T e (kev) time (s)

10 Sawtooth ASDEX Upgrade pulse I p (MA) 10 P NBI (MW) P RF (MW) 1 W MHD (MJ) 6 Nel x T i (kev) T e (kev) time (s)

11 Sawtooth 1. T(0) and j(0) rise 2. q(0) falls below 1 kink instability grows 3. Fast reconnection event: T, n flattened inside q=1 surface q(0) rises slightly above 1 kink stable

12 Sawtooth Stabilisation JET with ICRH current drive

13 Sawtooth Stabilisation ASDEX Upgrade with ECCD Experiments with slow B t -ramp, 0.8 MW co-eccd and 5.1 MW NBI: increase of sawtooth period for deposition outside inversion radius decrease of sawtooth period for deposition inside inversion radius Ctr-ECCD shows inverse behaviour

14 Contents 1. Limits in Tokamak Operations 2. Sawtooth 3. Neoclassical Tearing Mode (NTM) 4. Resistive Wall Mode (RWM) 5. Edge Localised Mode (ELM) 6. H-mode 7. Internal Transport Barrier (ITB) 8. Tokamak Operation Scenario

15 Neoclassical Tearing Mode (NTM)

16 Neoclassical Tearing Mode (NTM)

17 Neoclassical Tearing Mode (NTM) p Pressure flattening across magnetic islands due to large transport coefficients along magnetic field lines

18 Neoclassical Tearing Mode (NTM) Pressure gradient drives plasma current by thermo-electric effects (Bootstrap current): j BS p Inside islands p and thus j BS vanish Loss of BS current inside magnetic islands acts as helical perturbation current driving the islands so once seeded, island is sustained by lack of bootstrap current

19 NTM Stabilisation Missing bootstrap current inside island can be replaced by localised external current drive. Complete stabilisation in quantitative agreement with theory!

20 NTM Stabilisation by ECCD

21 NTM Stabilisation by ECCD JT-60U

22 Contents 1. Limits in Tokamak Operations 2. Sawtooth 3. Neoclassical Tearing Mode (NTM) 4. Resistive Wall Mode (RWM) 5. Edge Localised Mode (ELM) 6. H-mode 7. Internal Transport Barrier (ITB) 8. Tokamak Operation Scenario

23 Resistive Wall Mode A. Bondeson et al., PRL 94 Ideal branch Ideal regime: Ideal kink stable if wall is close enough RWM branch RWM regime: RWM is stable when slipping between mode and wall is large enough When ideal kink is wall stabilised, RWM can grow on wall time scale Rotation w.r.t. wall can stabilise the RWM if ω rot >> 1/τ W Balance between wall drag and (rotating) plasma drag on mode

24 Resistive Wall Mode Stabilisation Saddle coils for direct stabilisation Different feedback schemes exist First results look promising New experiments with in-vessel coils under way on DIII-D

25 Contents 1. Limits in Tokamak Operations 2. Sawtooth 3. Neoclassical Tearing Mode (NTM) 4. Resistive Wall Mode (RWM) 5. Edge Localised Mode (ELM) 6. H-mode 7. Internal Transport Barrier (ITB) 8. Tokamak Operation Scenario

26 Edge Localised Mode (ELM) I p (MA) # D α P NBI (MW) 4xl i β N H 98 (y,2) 1.0 H 98 (y,2) <n e >/n GW <n e >/n GW Even n Odd n Time (s)

27 Edge Localised Mode (ELM) Pulse Example of sawteeth and ELMs

28 Edge Localised Mode (ELM) ELM oscillations A: critical pressure gradient in ETB region reached, short unstable phase (ELM event) B. Energy and particle loss has lead to reduced gradients C. Gradients build up during reheat/refuelling phase

29 Model for ELM Cycle ELM: coupled kink and ballooning modes 1. After ELM: pressure gradient builds up faster than edge current 2. Pressure gradient clamped by ballooning stability, edge current grows 3. Kink (peeling) instability: ELM crash, loss of pressure and edge current

30 Type of ELMs Type I: Large ELMs low frequency which rises with input power with significant effect (lowering) of ETB pressure. Type III: Small ELMs high frequency with little or no effect on height of (ETB)

31 Edge Localised Mode (ELM)

32 Contents 1. Limits in Tokamak Operations 2. Sawtooth 3. Neoclassical Tearing Mode (NTM) 4. Resistive Wall Mode (RWM) 5. Edge Localised Mode (ELM) 6. H-mode 7. Internal Transport Barrier (ITB) 8. Tokamak Operation Scenario

33 H-mode 1982 IAEA Wagner et al. (ASDEX) - Transition to H-mode: state with reduced turbulence at the plasma edge - Formation of an edge transport barrier: steep pressure gradient at the edge

34 H-mode Advantage of divertor configuration - First contact with material surface at a distance from plasma boundary - High density maintained by re-ionisation of neutrals near target plate (recycling)

35 H-mode

36 Turbulence Stabilisation E B One reason: Losses of fast ions at the plasma edge sheared radial electric field sheared ExB rotation eddies get tilted and ripped apart cause turbulence suppression! xb

37 Turbulence Stabilisation

38 Contents 1. Limits in Tokamak Operations 2. Sawtooth 3. Neoclassical Tearing Mode (NTM) 4. Resistive Wall Mode (RWM) 5. Edge Localised Mode (ELM) 6. H-mode 7. Internal Transport Barrier (ITB) 8. Tokamak Operation Scenario

39 Internal Transport Barrier (ITB) Turbulence suppression most effective for non-monotonic current profiles Current profile corresponding to conductivity Non-monotonic or flat current profile j(r) j(r) r/a r/a

40 Internal Transport Barrier (ITB) Conventional Tokamak Advanced Tokamak Internal Transport Barrier (ITB) H-Mode ETB

41 Internal Transport Barrier (ITB) Conventional Tokamak Advanced Tokamak

42 Advanced Tokamak Steady State Operation Non-monotonic current profile Turbulence suppression high pressure gradients large bootstrap current

43 Contents 1. Limits in Tokamak Operations 2. Sawtooth 3. Neoclassical Tearing Mode (NTM) 4. Resistive Wall Mode (RWM) 5. Edge Localised Mode (ELM) 6. H-mode 7. Internal Transport Barrier (ITB) 8. Tokamak Operation Scenario

44 Tokamak Operation Scenario

45 Tokamak Operation Scenario plasma pressure plasma pressure 0 ITB ITB H-mode a H-mode strong Reversed shear weak q-profiles plasma pressure 0 W Hybrid hybrid W core W ped plasma radius a 0 Good confinement Poor stability Only weak RS plasmas are stable but they require a delicate active control a 1 Hybrid ELMy H-mode r/a Good confinement together with high stability w/o active control

46 Reversed Shear Scenario q 95 ~ 5 Technique used since mid 1990 s I p II: Create ITB III: Performance at stable q(r) I: Reverse q(r) time I: Heat during current rise, external current drive (reverse q). II: Increase heating power to stabilise turbulence (ITB). Improve plasma confinement, try to increase pressure (β N ) III: Keep going: ITER non-inductive regime: H H 1.6; β N 3.0 (9MA, 50% external current drive (73MW), 50% bootstrap fraction)

47 Hybrid Scenario q 95 = I p II: Timing, heating, MHD III: Perf. at stable q(r) I: Form q(r) time I: Obtain low magnetic shear in the centre q 0 > 1 II: Timing and amount of the heating are important. MHD behaviour: (no sawteeth, but fishbones and/or small NTMs). H-mode, but no confinement transients (ITBs). III: Mild MHD events to obtain stable q(r). Ultimate goal: H 89 β N > 6 stationary, ~50% non-inductive drive.

48 Status of Fusion Research Todays tokamak plasmas are close to breakeven, The next step (ITER) will ignite ot at least operate at high Q ( 10), and thereby prove the scientific and technological feasibility of fusion energy. 45

49 International Thermonuclear Experimental Reactor International project: Europe, Japan, Russia, and the USA (before 1998). Outline Design in 1999, Final Report due July m R [m] 6.2 a [m] 2.0 k 1.7 d 0.35 I p [MA] 15.1 B [T] 5.3 T puls [s] 400 P fusion [MW]

50 Summary Fluid description of Plasmas MHD Equations MHD Equilibrium MHD Stability MHD Instabilities in Tokamaks