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Effects of Three-Dimensional Magnetic Field Structure On Effects of 3D Magnetic Field Structure to MHD Equilibrium and Stability - aspects from Stellarator/Heliotron Researches Yasuhiro Suzuki for the LHD team National Institute for Fusion Science The Graduate University for Advanced Studies SOKENDAI Toki, Japan [email protected] Special thanks to S.Sakakibara, K.Y.Watanabe, S.Ohdachi, K.Ida, N.Mizuguchi, Y.Todo, H. Yamada 4th International ITER Summer School Austin 31 May - 4 June, 2010 Outline 1.What is Stellarator? 2.The Large Helical Device – LHD - 3.MHD Equilibrium in 3D Field 4.Interaction of the instability and 3D Field 5.Application of 3D tools to Tokamak 6.Summary 2010/6/4 4th International ITER Summer School 2 1. What is Stellarator? Another candidate for Fusion Reactor 2010/6/4 4th International ITER Summer School 3 Why is the rotational transform necessary? For simple torus… Charge separation appears by grad-B drift. Electric field is driven. Disruption! To cancel the charge separation, the connection between up and down of the plasma is necessary. => twist the field lines. http://www.scidacreview.org/0801/html/fusion1.html 2010/6/4 4th International ITER Summer School 4 Classification of the rotational transform creating C.Mercier, “Lectures in Plasma Physics” •Toroidal current along the axis => tokamaks •Torsion of the axis => 8-figure stellarator •Modulation of flux surfaces Model A stellarator, 1951, Princeton L.Spizter Jr. 2010/6/4 4th International ITER Summer School 5 Classification of the rotational transform creating C.Mercier, “Lectures in Plasma Physics” •Toroidal current along the axis •Torsion of the axis •Modulation of flux surfaces Stellarators create the rotational transform by 3D shaping. Advantages: 1. Steady-state operation without current drive 2. No disruptin 2010/6/4 4th International ITER Summer School 6 Classification of the rotational transform creating C.Mercier, “Lectures in Plasma Physics” •Toroidal current along the axis •Torsion of the axis •Modulation of flux surfaces Stellarators create the rotational transform by 3D shaping. Disadvantages: 1. Engineering problems 2. Degradation of the confinement by helical ripples 2010/6/4 4th International ITER Summer School 7 Model C Stellarator “Race Track” Courtesy to PPPL 2010/6/4 4th International ITER Summer School 8 Helical-axis Stellarator “Asperator” Y.Funato, et al., Japanese Journal of Applied Physics 22 (1983) 1188 Y.Funato, et al., Japanese Journal of Applied Physics 27 (1988) 821 2010/6/4 4th International ITER Summer School 9 LHD has worked very well for 10 years Courtesy to H.Yamada SOFT2008 Construction completed within the eight-year plan (FY1990-1997) Operation for 10 years engineering base of a large-scale superconducting and cryogenic system for a fusion reactor < LHD basic dimension > OV coil • Outer diameter 13.5 m • Cold mass 820 ton • Total weight 1500 ton • Magnetic field 3 T • Magnetic energy 0.77 GJ Several-month-long operation, 11 times since 1998 • Operational time of He compressor : 51,654 hours Duty = 99.3 % • Coil excitation number : 1,168 times • Plasma discharges Helical coil : 84,869 shots 2010/6/4 4th International ITER Summer School 10 Stellarators have “vacuum flux surfaces” Vacuum flux surfaces in a heliotron configuration Stellarator field has toroidal periodicity. 2010/6/4 4th International ITER Summer School 11 Flux surfaces are changed due to the “plasma response” 3D MHD equilibrium analysis of an LHD plasma vacuum b~3% However, the plasma response strongly depend on the vacuum configuration! 2010/6/4 4th International ITER Summer School 12 Stellarator is not disruptive Collapsed events are observed but not disruptive! Limit 2nd 3rd 1st Plasma recovered after events! 2010/6/4 4th International ITER Summer School 13 What is the contribution from the stellarator research to ITER? In tokamaks, the magnetic field to confine the plasma is produced by the plasma itself! Btotal = Btor,vac + Bpol,plasma + Bresponse In stellarators, the magnetic field to confine the plasma is produced by external coils for the vacuum. Btotal = Btor,vac + Bpol,vac + Bresponse Bresponse = Btotal - Btor,vac - Bpol,vac Stellarators are platforms to explorer 3D physics! 2010/6/4 4th International ITER Summer School 14 2. The Large Helical Device (LHD) 2010/6/4 4th International ITER Summer School 15 Present View! Large Helical Device (LHD) External diameter 13.5 m World largest superconducting coil system Plasma major radius 3.9 m Magnetic energy 1 GJ Plasma minor radius 0.6 m Cryogenic mass (-269 degree C) 850 t 3 Plasma volume 30 m Tolerance < 2mm Magnetic field 3 T Total weight 1,500 t ECR 84 – 168 GHz Local Island Divertor (LID) ICRF 25-100 MHz NBI NBI 2010/6/4 4th International ITER Summer School 16 2010/6/4 4th International ITER Summer School 17 LHD has large flexibility of magnetic configuration Plasma HC HC HC H - - - - M O M I Poloidal field coil Position of magnetic axis Control of current center of helical coil Elongation Aspect ratio Rotational transform Local Island Divertor coil Generates m/n=1/1 Resonant Magnetic Perturbation (RMP) Magnetic island 2010/6/4 4th International ITER Summer School 18 Typical Iota profile and well/Hill boundary magnetic hill Low beta • In LHD, pressure gradient driven modes are important; stability m/n = 2/3 depends on magnetic 1/q well depth. • With increase of beta, the well region m/n = 1/1 expands. Edge • Unstable region remains in the edge m/n = 2/1 region. • Resistive interchange Core mode always observed in the edge. (slightly increase transports) magnetic well magnetic hill High beta 2010/6/4 4th International ITER Summer School 19 Magnetic well is created due to the Shafranov shift 2010/6/4 4th International ITER Summer School 20 Subjects of MHD studies in Heliotron MHD equilibrium, stability and transport are key issues for production of high-beta plasmas: MHD Equilibrium: Change of magnetic topology and relationship with beta-limit - Stochastization of peripheral magnetic field lines MHD Stability: Effect of pressure-driven mode (Interchange and Ballooning modes) - Magnetic hill in the periphery <b> ~ 0 % Transport: transport related with finite-b effects (magnetic topology, beta and so on) <b> ~ 4 % - Particle loss due to an increment of helical ripple, turbulence caused by steep p 2010/6/4 4th International ITER Summer School 21 3 . 3D MHD Equilibrium studies 3.1 Stochastization due to plasma response 2010/6/4 4th International ITER Summer School 22 High-beta Steady State Discharge <b>max ~ 4.8 %, b0 ~ 9.6 %, HISS95 ~ 1.1 Rax = 3.6 m, Bt = -0.425 T Plasma was maintained for 85tE Shafranov shift D/aeff ~ 0.25 Peripheral MHD modes are dominantly observed. 2010/6/4 4th International ITER Summer School 23 High-beta Discharge – Pellet Injection – Perpendicular-NBI was applied after Rax = 3.6 m, Bt = -0.425 T several pellets were injected and tangential NBI is turned off which leads to reduction P-NBI of Shafranov shift. MHD activity is not enhanced in high- beta regime with more than 4 % 0.5 19 -3 ne (10 m ) 0.4 4 0.3 0.2 2 Te (keV) 0.1 0 0 0 0.2 0.4 0.6 aeff (m) 2010/6/4 4th International ITER Summer School 24 Achievement of the High beta plasma in LHD Sustainment of the high-beta plasma is not a serious problem in helical system(tduration/tE > 100). Limited only by the heating source. Question: How far is from the beta limit? 2010/6/4 4th International ITER Summer School 25 How about is the magnetic surface topology? Degradation of flux surfaces due to increasing b In the peripheral region, magnetic field lines become stochastic as b increases. The volume inside LCFS shrinks drastically. 2010/6/4 4th International ITER Summer School 26 Control Coil Variation Changes Flux Surface Topology ICC/IM = 0 ICC/IM = 0.15 b = 1.8% b = 2.0% VMEC boundary • PIES equilibrium analysis using fixed ICC/IM = 0.15 pressure profile from equilibrium fit b = 2.7% (not yet including current profile). • Calculation: at ~ fixed b, ICC/IM=0.15 gives better flux surfaces • At experimental maximum b values -- 1.8% for ICC/IM =0 -- 2.7% for ICC/IM = 0.15 calculate similar flux surface degradation Courtesy to M.C.Zarnstorff and A.H. Reiman 2010/6/4 4th International ITER Summer School 27 Edge Te does not respond to Pinj 300 400 Pinj=1.3 MW Pinj=1.7 MW Pinj=3.3 MW Pinj=3.4 MW 300 200 200 (eV) e T Te Te (eV) 100 ivac = 0.445 ivac = 0.575 <B> = 1.0 T 100 <B> = 1.25 T ICC/IM=0.15 ICC/IM=0.14 20 -3 20 -3 ne = 2.4 x 10 m ne = 1.7 x 10 m 0 0 1.7 1.8 1.9 2.0 2.1 2.2 1.7 1.8 1.9 2 2.1 2.2 Major Radius (m) Major Radius (m) • Edge Te and Te does not change with increasing Pinj !! Radial transport degrading as power increases • Fixed density, and constant ne profile. Increase in b due to core Te increase • Edge Te lower for i = 0.575 higher radial transport. Courtesy to M.C.Zarnstorff and A.H. Reiman 2010/6/4 4th International ITER Summer School 28 Results from HINT well describes deformation of magnetic surfaces 3-D equilibrium consistent with experimental observation, i.e., Shafranov shift, pressure profile, etc. Significant pressure (Te ) gradient exists in the edge stochastic area Hypothesis 1) Plasma heals flux surfaces 2) Profile is consistent with characteristics of stochastic field 3) Somewhere between 1) & 2) LC-TB : connection length between the torus-top and - bottom LC >> LC-TB Pfirsch-Schlüter current is effective Secure MHD equilibrium LC >> MFP (even under a reactor condition) Plasma is collisional enough to secure isotropic pressure 2010/6/4 4th International ITER Summer School 29 How large is the stochasticity? Degradation of surface quality due to b <b>dia~3% •Two arrows indicate the position of well-defined LCFS on the equatorial plane.
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