MHD Equilibrium and Stability of Tokamaks and RFP Systems with 3D Helical Cores

Size: px
Start display at page:

Download "MHD Equilibrium and Stability of Tokamaks and RFP Systems with 3D Helical Cores"

Transcription

1 15th Workshop on MHD Stability Control, Madison, WI, USA, November 15-17, 21 MHD Equilibrium and Stability of Tokamaks and FP Systems with 3D Helical Cores W. A. Cooper Ecole Polytechnique Fédérale de Lausanne, Association EUATOM-Confédération Suisse, Centre de echerches en Physique des Plasmas, CH115 Lausanne, Switzerland. Collaborators EPFL/CPP: J. P. Graves, O. Sauter, A. Pochelon, L. Villard Consorzio FX: D. Terranova, M. Gobbin, P. Martin, L. Marrelli, I. Predebon ONL: S. P. Hirshman Culham Science Centre: I. T. Chapman W. Anthony Cooper, CPP/EPFL 15th Workshop on MHD Stability Control, Madison, WI, USA, November 15-17, 21 1

2 MOTIVATION Manifestation of internal 3D structures in axisymmetric devices: SHAx states in FX-mod. Lorenzini et al., Nature Physics 5 (29) 57 Snakes in JET A. Weller et al., Phys. ev. Lett. 59 (1987) 233 Disappearance of sawteeth but continuous dominantly n = 1 mode in TCV at high elongation and current H. eimerdes et al., Plasma Phys. Control. Fusion 48 (26) 1621 Y. Camenen et al., Nucl. Fusion 47 (27) 586 Change of sawteeth from kink-like to quasi-interchange-like with plasma shaping in DIII-D E. A. Lazarus et al., Plasma Phys. Contr. Fusion 48 (26) L65 Long-lived saturated modes in MAST I. T. Chapman et al., Nucl. Fusion 5 (21) W. Anthony Cooper, CPP/EPFL 15th Workshop on MHD Stability Control, Madison, WI, USA, November 15-17, 21 2

3 THEOY EVIEW Analytic studies of ideal nonlinearly saturated m = 1, n = 1 modes Avinash,.J. Hastie, J.B. Taylor, Phys. ev. Lett. 59 (1987) 2647 M.N. Bussac,. Pellat, Phys. ev. Lett. 59 (1987) 265 F.L. Waelbroeck, Phys. Fluids B 59 (1989) 499 Pellet deposition in magnetic island on q = 1 surface J.A. Wesson, Plasma Phys. Control. Fusion B 37 (1995) A337 Large scale simulations of nonlinearly saturated MHD instability L.A. Charlton et al., Phys. Fluids B 59 (1989) 798 H. Lütjens, J.F. Luciani, J. Comput. Phys. 227 (28) 6944 Bifurcated equilibria due to ballooning modes with the NSTAB code P. Garabedian, Proc. Natl. Acad. Sci. USA 13 (26) FX-mod SHAx MHD equilibria D. Terranova et al., in Plasma Phys. Contr. Fusion 52 (21) Bifurcated tokamak equilibria similar to a saturated internal kink W.A. Cooper et al., Phys. ev. Lett. 15 (21) 353 W. Anthony Cooper, CPP/EPFL 15th Workshop on MHD Stability Control, Madison, WI, USA, November 15-17, 21 3

4 OUTLINE We investigate the proposition that the instability structures observed in the experiments constitute in reality new equilibrium states with 3D character; an axisymmetric boundary is imposed 3D magnetohydrodynamic (MHD) fixed boundary equilibria with imposed nested flux surfaces are investigated with: VMEC2 S. P. Hirshman, O. Betancourt, J. Comput. Phys. 96 (1991) 99 ANIMEC W. A. Cooper et al., Comput. Phys. Commun. 18 (29) 1524 MHD equilibria with 3D internal helical structures computed for TCV, ITE (hybrid scenario), MAST, JET (Snakes) and FX-mod Linear ideal MHD stability computed with TEPSICHOE for FXmod D. V. Anderson et al., Int. J. Supercomp. Appl. 4 (199) 33 W. Anthony Cooper, CPP/EPFL 15th Workshop on MHD Stability Control, Madison, WI, USA, November 15-17, 21 4

5 Magnetohydrodynamic Equilibria 3D Impose nested magnetic surfaces and single magnetic axis Minimise energy of the system W = ( B d 3 2 x + p (s, B) ) 2µ Γ 1 Solve inverse equilibrium problem : = (s, u, v), = (s, u, v). Variation of the energy dw dt = s=1 [ dsdudv F [ dudv t + F (p + B2 2µ )( u t + F λ ] λ t t u )] t W. Anthony Cooper, CPP/EPFL 15th Workshop on MHD Stability Control, Madison, WI, USA, November 15-17, 21 5

6 Magnetohydrodynamic Equilibria 3D The MHD forces are F = F z = u [σ gb u (B )] + v [σ gb v (B )] [ )] (p + B2 + [ )] (p + B2 u s 2µ s u 2µ g ) + [(p + B2 σ 2 (B v ) 2] 2µ u [σ gb u (B )] + v [σ gb v (B )] + [ )] (p + B2 [ )] (p + B2 u s 2µ s u 2µ The λ force equation minimises the spectral width and corresponds to the binormal projection of the momentum balance at the equilibrium state. [ F λ = Φ (σbv ) (s) (σb ] u) u v For isotropic pressure p = p = p and σ = 1/µ. W. Anthony Cooper, CPP/EPFL 15th Workshop on MHD Stability Control, Madison, WI, USA, November 15-17, 21 6

7 Magnetohydrodynamic Equilibria 3D Use Fourier decomposition in the periodic angular variables u and v and a special finite difference scheme for the radial discretisation An accelerated steepest descent method is applied with matrix preconditioning to obtain the equilibrium state The radial force balance is a diagnostic of the accuracy of the equilibrium state in this approach Fs 1 p Φ = (s) Φ σbv ι(s) σbu (s) s B s g s g denotes a flux surface average A = L (2π) 2 2π/L dv 2π du ga(s, u, v) This model is implemented in the ANIMEC code, an anisotropic pressure extension of the VMEC2 code. L is the number of toroidal field periods. W. Anthony Cooper, CPP/EPFL 15th Workshop on MHD Stability Control, Madison, WI, USA, November 15-17, 21 7

8 Boundaries for TCV, ITE, MAST and JET Fixed axisymmetric boundary equilibrium studies are explored. TCV boundary description: b = cos u +.6 cos 2u; b =.48 sin u MAST, JET boundary: b = + a cos(u + δ sin u + τ sin 2u); b = Ea sin u MAST: =.9m, a =.54m, E = 1.744, δ =.3985, τ =.198 JET: = 2.96m, a = 1.25m, E = 1.68, δ =.3, τ = TCV ITE MAST JET W. Anthony Cooper, CPP/EPFL 15th Workshop on MHD Stability Control, Madison, WI, USA, November 15-17, 21 8

9 Bifurcated equilibria in TCV Selection of q-profiles that yield bifurcated equilibria in TCV. Boundary description: b = cos u +.6 cos 2u, b =.48 sin u. q =(.5+s 1.1s 4 ) 1, (.7+.7s s 4 ) 1, (.9+.2s.8s 6 ) 1, (.98.7s 9 ) q = 1/ι s W. Anthony Cooper, CPP/EPFL 15th Workshop on MHD Stability Control, Madison, WI, USA, November 15-17, 21 9

10 CPP TCV toroidal flux contours at various cross sections TCV toroidal magnetic flux contours with prescribed ι =.9+.2s.8s6 profile. Axisymmetric v=π v= v = π/3 v = 2π/3 Helical W. Anthony Cooper, CPP/EPFL 15th Workshop on MHD Stability Control, Madison, WI, USA, November 15-17, 21 1

11 Helical equilibrium structures in TCV Helical axis displacement and energy difference as function of q min. q(s) = [.9 + α 1 s (.6 + α 1 )s 6 ] 1, α 1 = (); 1 () µ (W hel W axi ) x () ; 1 () q min µ (W hel W axi ) q min W. Anthony Cooper, CPP/EPFL 15th Workshop on MHD Stability Control, Madison, WI, USA, November 15-17, 21 11

12 TCV helical structures at finite β Flat core pressure and q-profile with weak shear reversal q(s) = (.9 +.3s s 4 ) 1. p(s) = p ( s s s s s 1 ). p, q-profiles 1 (); 1 () p(s)/p() ; q(s) s 1 () ; 1 () <β> W. Anthony Cooper, CPP/EPFL 15th Workshop on MHD Stability Control, Madison, WI, USA, November 15-17, 21 12

13 ITE equilibrium profiles Prescribe mass profile and toroidal current profile. p(s) M(s)[Φ (s)] Γ Equilibria have toroidal current 13 14MA, B t = 4.6T, β 2.9% q-profile q-profile range for helical states MA q q MA s s W. Anthony Cooper, CPP/EPFL 15th Workshop on MHD Stability Control, Madison, WI, USA, November 15-17, 21 13

14 CPP ITE pressure contours at various cross sections Contours of constant pressure of an ITE hybrid scenario equilibrium with 13.3M A toroidal plasma current v= W. Anthony Cooper, CPP/EPFL v = π/3 v = 2π/3 v=π 15th Workshop on MHD Stability Control, Madison, WI, USA, November 15-17, 21 14

15 Convergence of solutions Define helical excursion parameter δ H = 2 1 (s = ) (s = ) a Convergence of δ H with N r = number of radial grid points δ H /N r x 1 4 W. Anthony Cooper, CPP/EPFL 15th Workshop on MHD Stability Control, Madison, WI, USA, November 15-17, 21 15

16 Helical core ITE equilibria Variation of the helical axis distortion parameter δ H with respect to the toroidal current and corresponding variation with respect to q min. δ H versus current δ H versus q min δ H.2 δ H TOOIDAL CUENT q min W. Anthony Cooper, CPP/EPFL 15th Workshop on MHD Stability Control, Madison, WI, USA, November 15-17, 21 16

17 CPP ITE pressure contours as a function of plasma current Contours of constant pressure at the cross section with toroidal angle v = 2π/3 13.1M A 13.2M A 13.3M A 13.4M A 13.5M A 13.6M A 13.7M A 13.8M A W. Anthony Cooper, CPP/EPFL 15th Workshop on MHD Stability Control, Madison, WI, USA, November 15-17, 21 17

18 Finite β ITE scan The ITE hybrid scenario is projected in the range 12 14MA with B t = 5.3T. With a sharper core concentrated toroidal current at 12M A, the variation of the helical axis distortion parameter δ H with respect to β is computed δ H <β> W. Anthony Cooper, CPP/EPFL 15th Workshop on MHD Stability Control, Madison, WI, USA, November 15-17, 21 18

19 MAST pressure contours at various cross sections Contours of constant pressure of a MAST equilibrium 1.8 v = (a) 1.8 v = π/3 (b) 1.8 v = 2π/3 (c) 1.8 v = π (d) v= v=π/ v=2π/ v=π This serves as a model for long-lived modes in MAST -I.T. Chapman et al., Nucl. Fusion 5 (21) Saturated internal kinks also observed on NSTX -J.E. Menard et al., Nucl. Fusion 45 (25) 539 W. Anthony Cooper, CPP/EPFL 15th Workshop on MHD Stability Control, Madison, WI, USA, November 15-17, 21 19

20 JET snake equilibrium profiles Prescribe mass profile and toroidal current profile. Equilibrium has toroidal current 3.85MA, B t = 3.1T, β 2.3% pressure profile q-profile pressure s q s W. Anthony Cooper, CPP/EPFL 15th Workshop on MHD Stability Control, Madison, WI, USA, November 15-17, 21 2

21 JET pressure, mod-b contours at various cross sections CPP Contours of constant pressure and mod-b of a JET snake equilibrium v= v=π v = π/3 v = 2π/3 2 (b) 2 (c) 2 (d) (a) v= W. Anthony Cooper, CPP/EPFL 2 3 v=π/ v=2π/3 4 2 v=π th Workshop on MHD Stability Control, Madison, WI, USA, November 15-17, 21 21

22 JET snake equilibrium structure Standard view of a snake (with variation with respect to toroidal angle in lieu of time in the simulation). experiment (courtesy of A. Weller) ANIMEC simulation W. Anthony Cooper, CPP/EPFL 15th Workshop on MHD Stability Control, Madison, WI, USA, November 15-17, 21 22

23 FX-mod toroidal flux and j B/B 2 contours Contours of constant toroidal flux (VMEC coordinates) and j B/B 2 (Boozer coordinates) in a FX-mod SHAx equilibrium state.4 v =.4 v = π/21.4 v = 2π/21.4 v = π/ φ=.4 v=π/21.4 v=2π/21.4 v=π/ φ =.4 φ = π/21.4 φ = 2π/21.4 φ = π/ φ=.4 φ=π/21.4 φ=2π/21.4 φ=π/ W. Anthony Cooper, CPP/EPFL 15th Workshop on MHD Stability Control, Madison, WI, USA, November 15-17, 21 23

24 FX-mod toroidal flux and mod-b contours CPP Contours of constant toroidal flux and mod-b in the Boozer coordinate frame for the FX-mod SHAx equilibrium state φ=.4 φ = π/21.4 φ = 2π/ φ= φ= W. Anthony Cooper, CPP/EPFL φ=π/ φ=2π/ φ = π/21 φ = π/ φ = 2π/ φ=π/ φ = π/7 15th Workshop on MHD Stability Control, Madison, WI, USA, November 15-17, 21 24

25 Mod-B 2 Fourier amplitudes in FX-mod Dominant Fourier amplitudes of B 2 in the FX-mod SHAx equilibrium state m/n=/ B 2 mn m/n=1/14.2 m/n=/7 m/n=1/7 m/n=1/ s W. Anthony Cooper, CPP/EPFL 15th Workshop on MHD Stability Control, Madison, WI, USA, November 15-17, 21 25

26 Linear Ideal MHD Stability Internal potential energy δw p = 1 2 d 3 x [C 2 + Γp ξ 2 D ξ s 2] Use Boozer coordinates ξ = gξ s (B s) θ φ + η B 2 + Fourier decomposition in angular variables [ J(s) Φ (s)b 2η µ ] B ξ s (s, θ, φ) = l s q lx l (s)sin(m l θ n l φ + ) η(s, θ, φ) = l Y l (s)cos(m l θ n l φ + ) A hybrid finite element method is applied for the radial discretisation. In the 3D TEPSICHOE stability code, COOL finite elements based on variable order Legendre polynomials have been implemented. The order of the polynomial is labelled with p. W. Anthony Cooper, CPP/EPFL 15th Workshop on MHD Stability Control, Madison, WI, USA, November 15-17, 21 26

27 MHD stability in FX-mod Ideal MHD stability with respect to n = 8 family of modes (w/a = 1.99) λ λ λ q=1/8 q s W. Anthony Cooper, CPP/EPFL 15th Workshop on MHD Stability Control, Madison, WI, USA, November 15-17, 21 27

28 Fourier Amplitudes of ξ s The three leading Fourier amplitudes of the radial component of the displacement vector ξ s mn with w/a = and p = 5 for core q /q < for core q /q >.2.15 core dq/ds < m/n=1/ core dq/ds > m/n=1/8 ξ s mn.1.5 m/n=2/15 m/n=1/ S ξ s mn m/n=1/6.2 m/n=2/ S W. Anthony Cooper, CPP/EPFL 15th Workshop on MHD Stability Control, Madison, WI, USA, November 15-17, 21 28

29 Wall Stabilisation Effects λ for core q /q < for core q /q > p=1 1 2 p= λ λ w/a w/a W. Anthony Cooper, CPP/EPFL 15th Workshop on MHD Stability Control, Madison, WI, USA, November 15-17, 21 29

30 The Instability Driving Terms The magnetohydrodynamic instability driving terms correspond to ballooning/interchange (δw BI ) and kink (δw J ) structures δw BI = δw J = ds 1 1 ds ds ds 2π L s 2π L s 2π L s 2π L s dφ dφ dφ dφ 2π 2π 2π 2π [ gp dθp (s) + ψ (s)j(s) Φ (s)i(s) (s) ] g (ξ s ) 2 s dθp (s) B s B 2ξs ( gb ξ s ) [ gb 2( ) j B dθ s 2 B 2 ( ) j B (ξ s ) 2 B 2 ( j B dθ B 2 B 2 ) h s ξ s ( gb ξ s ) ] + ψ (s)φ (s) Φ (s)ψ (s) W. Anthony Cooper, CPP/EPFL 15th Workshop on MHD Stability Control, Madison, WI, USA, November 15-17, 21 3

31 Perturbed Internal Energy Profiles The kink mode driving energy δw J and the ballooning/interchange driving energy δw BI profiles with core q /q > at different conducting wall positions δw J δw BI δ W J x 1 3 w/a=1.198 ( 1 1 ) w/a=2.976 w/a= S δ W BI x 1 6 w/a=1.198 w/a=2.976 w/a= S W. Anthony Cooper, CPP/EPFL 15th Workshop on MHD Stability Control, Madison, WI, USA, November 15-17, 21 31

32 Structure of δw J The structure of the kink driving energy δw J for core q /q < and w/a = at three cross sections covering half of a field period (1/14th of the torus) W. Anthony Cooper, CPP/EPFL 15th Workshop on MHD Stability Control, Madison, WI, USA, November 15-17, 21 32

33 Summary and Conclusions equilibrium Nominally axisymmetric eversed Field Pinch and Tokamak systems can develop MHD equilibrium bifurcations that lead to the formation of core helical structures. In FX-mod, the development of a SHAx equilibrium state is computed with a seven-fold toroidally periodic structure when q in the core 1/7. In Tokamak devices, reversed magnetic shear (sometimes just very flat extended low shear) with q min 1 can trigger a bifurcated solution with a core helical structure similar to a saturated m = 1, n = 1 internal kink. We have computed these 3D core helical states in TCV, ITE, MAST and JET. The JET snake phenomenon is reproduced with our model. W. Anthony Cooper, CPP/EPFL 15th Workshop on MHD Stability Control, Madison, WI, USA, November 15-17, 21 33

34 Summary and Conclusions MHD stability Brief periods in which the relatively quiescent SHAx state in FXmod relaxes to a turbulent multiple helicity state are observed. Lorenzini et al., Nature Physics 5 (29) 57. We have investigated the ideal MHD stability of SHAx equilibria by examining mode structures that break the m = 1, n = 7 periodicity of the system. Either a drop in q well below 1/8 or the disappearance of core shear reversal triggers ideal MHD modes dominated by m = 1, n = 8 coupled with m = 2, n = 15 components. For w/a > 1.2, global unstable kink mode structures are triggered. These kink modes are driven by the Ohmic current. The drive for ballooning and Pfirsch-Schlüter current modes is very weak. The dominant mode structure is a nonresonant m = 1, n = 6 component and is basically internal with a finite edge amplitude. Coupling with toroidal sidebands constitutes a significant contribution. W. Anthony Cooper, CPP/EPFL 15th Workshop on MHD Stability Control, Madison, WI, USA, November 15-17, 21 34

35 Summary and Conclusions In tokamaks, the issue of MHD stability is complicated by the fact that any mode to be investigated is in principle also a component of the equilibrium state. Possible exceptions: local ballooning/mercier modes, external kink modes, stellarator-symmetry breaking modes. The 3D helical core equilibrium states in nominally axisymmetric systems that have been obtained constitute a paradigm shift for which the tools developed for stellarators in MHD stability, kinetic stability, drift orbits, wave propagation or heating, neoclassical transport, gyrokinetics, etc become applicable and necessary to more accurately evaluate magnetic confinement physics phenomena. The constraint of nested magnetic flux surfaces and absence of X- points in our model preclude the generation of equilibrium states with magnetic islands. Saturated tearing modes could be investigated with SIESTA, PIES, HINT or SPEC. W. Anthony Cooper, CPP/EPFL 15th Workshop on MHD Stability Control, Madison, WI, USA, November 15-17, 21 35

(a) (b) (c) (d) (e) (f) r (minor radius) time. time. Soft X-ray. T_e contours (ECE) r (minor radius) time time

(a) (b) (c) (d) (e) (f) r (minor radius) time. time. Soft X-ray. T_e contours (ECE) r (minor radius) time time Studies of Spherical Tori, Stellarators and Anisotropic Pressure with M3D 1 L.E. Sugiyama 1), W. Park 2), H.R. Strauss 3), S.R. Hudson 2), D. Stutman 4), X-Z. Tang 2) 1) Massachusetts Institute of Technology,

More information

A simple formula for the trapped fraction in tokamaks including the effect of triangularity

A simple formula for the trapped fraction in tokamaks including the effect of triangularity A simple formula for the trapped fraction in tokamaks including the effect of triangularity O. Sauter Centre de Recherches en Physique des plasmas, Ecole Polytechnique Fédérale de Lausanne, CRPP-EPFL,

More information

Effects of stellarator transform on sawtooth oscillations in CTH. Jeffrey Herfindal

Effects of stellarator transform on sawtooth oscillations in CTH. Jeffrey Herfindal Effects of stellarator transform on sawtooth oscillations in CTH Jeffrey Herfindal D.A. Ennis, J.D. Hanson, G.J. Hartwell, E.C. Howell, C.A. Johnson, S.F. Knowlton, X. Ma, D.A. Maurer, M.D. Pandya, N.A.

More information

Simulations of Sawteeth in CTH. Nicholas Roberds August 15, 2015

Simulations of Sawteeth in CTH. Nicholas Roberds August 15, 2015 Simulations of Sawteeth in CTH Nicholas Roberds August 15, 2015 Outline Problem Description Simulations of a small tokamak Simulations of CTH 2 Sawtoothing Sawtoothing is a phenomenon that is seen in all

More information

Control of Sawtooth Oscillation Dynamics using Externally Applied Stellarator Transform. Jeffrey Herfindal

Control of Sawtooth Oscillation Dynamics using Externally Applied Stellarator Transform. Jeffrey Herfindal Control of Sawtooth Oscillation Dynamics using Externally Applied Stellarator Transform Jeffrey Herfindal D.A. Ennis, J.D. Hanson, G.J. Hartwell, S.F. Knowlton, X. Ma, D.A. Maurer, M.D. Pandya, N.A. Roberds,

More information

arxiv: v1 [physics.plasm-ph] 11 Mar 2016

arxiv: v1 [physics.plasm-ph] 11 Mar 2016 1 Effect of magnetic perturbations on the 3D MHD self-organization of shaped tokamak plasmas arxiv:1603.03572v1 [physics.plasm-ph] 11 Mar 2016 D. Bonfiglio 1, S. Cappello 1, M. Veranda 1, L. Chacón 2 and

More information

W.A. HOULBERG Oak Ridge National Lab., Oak Ridge, TN USA. M.C. ZARNSTORFF Princeton Plasma Plasma Physics Lab., Princeton, NJ USA

W.A. HOULBERG Oak Ridge National Lab., Oak Ridge, TN USA. M.C. ZARNSTORFF Princeton Plasma Plasma Physics Lab., Princeton, NJ USA INTRINSICALLY STEADY STATE TOKAMAKS K.C. SHAING, A.Y. AYDEMIR, R.D. HAZELTINE Institute for Fusion Studies, The University of Texas at Austin, Austin TX 78712 USA W.A. HOULBERG Oak Ridge National Lab.,

More information

MHD equilibrium calculations for stellarators. Antoine Cerfon, MIT PSFC with F. Parra, J. Freidberg (MIT NSE)

MHD equilibrium calculations for stellarators. Antoine Cerfon, MIT PSFC with F. Parra, J. Freidberg (MIT NSE) MHD equilibrium calculations for stellarators Antoine Cerfon, MIT PSFC with F. Parra, J. Freidberg (MIT NSE) March 20, 2012 MAGNETIC FIELD LINE HAMILTONIAN Consider a general toroidal coordinate system

More information

Snakes and similar coherent structures in tokamaks

Snakes and similar coherent structures in tokamaks Snakes and similar coherent structures in tokamaks A. Y. Aydemir 1, K. C. Shaing 2, and F. W. Waelbroeck 1 1 Institute for Fusion Studies, The University of Texas at Austin, Austin, TX 78712 2 Plasma and

More information

Formation and Long Term Evolution of an Externally Driven Magnetic Island in Rotating Plasmas )

Formation and Long Term Evolution of an Externally Driven Magnetic Island in Rotating Plasmas ) Formation and Long Term Evolution of an Externally Driven Magnetic Island in Rotating Plasmas ) Yasutomo ISHII and Andrei SMOLYAKOV 1) Japan Atomic Energy Agency, Ibaraki 311-0102, Japan 1) University

More information

Theory for Neoclassical Toroidal Plasma Viscosity in a Toroidally Symmetric Torus. K. C. Shaing

Theory for Neoclassical Toroidal Plasma Viscosity in a Toroidally Symmetric Torus. K. C. Shaing Theory for Neoclassical Toroidal Plasma Viscosity in a Toroidally Symmetric Torus K. C. Shaing Plasma and Space Science Center, and ISAPS, National Cheng Kung University, Tainan, Taiwan 70101, Republic

More information

Performance limits. Ben Dudson. 24 th February Department of Physics, University of York, Heslington, York YO10 5DD, UK

Performance limits. Ben Dudson. 24 th February Department of Physics, University of York, Heslington, York YO10 5DD, UK Performance limits Ben Dudson Department of Physics, University of York, Heslington, York YO10 5DD, UK 24 th February 2014 Ben Dudson Magnetic Confinement Fusion (1 of 24) Previously... In the last few

More information

AC loop voltages and MHD stability in RFP plasmas

AC loop voltages and MHD stability in RFP plasmas AC loop voltages and MHD stability in RFP plasmas K. J. McCollam, D. J. Holly, V. V. Mirnov, J. S. Sar, D. R. Stone UW-Madison 54rd Annual Meeting of the APS-DPP October 29th - November 2nd, 2012 Providence,

More information

RFP helical equilibria reconstruction with V3FIT-VMEC

RFP helical equilibria reconstruction with V3FIT-VMEC RFP helical equilibria reconstruction with V3FIT-VMEC D. Terranova 1 J.D. Hanson 2, S.P. Hirshman 3, L. Marrelli 1 1 Consorzio RFX, Associazione EURATOM-ENEA sulla Fusione, Padova, Italy 2 Auburn University,

More information

Nonlinear 3D MHD physics of the helical reversed-field pinch

Nonlinear 3D MHD physics of the helical reversed-field pinch Nonlinear 3D MHD physics of the helical reversed-field pinch Daniele Bonfiglio* Consorzio RFX, Euratom-ENEA Association, Padova, Italy *In collaboration with: S. Cappello, L. Chacón (Oak Ridge National

More information

Current-driven instabilities

Current-driven instabilities Current-driven instabilities Ben Dudson Department of Physics, University of York, Heslington, York YO10 5DD, UK 21 st February 2014 Ben Dudson Magnetic Confinement Fusion (1 of 23) Previously In the last

More information

Overview of Tokamak Rotation and Momentum Transport Phenomenology and Motivations

Overview of Tokamak Rotation and Momentum Transport Phenomenology and Motivations Overview of Tokamak Rotation and Momentum Transport Phenomenology and Motivations Lecture by: P.H. Diamond Notes by: C.J. Lee March 19, 2014 Abstract Toroidal rotation is a key part of the design of ITER

More information

HOW THE DEMO FUSION REACTOR SHOULD LOOK IF ITER FAILS. Paul Garabedian and Geoffrey McFadden

HOW THE DEMO FUSION REACTOR SHOULD LOOK IF ITER FAILS. Paul Garabedian and Geoffrey McFadden HOW THE DEMO FUSION REACTOR SHOULD LOOK IF ITER FAILS Paul Garabedian and Geoffrey McFadden 1. Summary Runs of the NSTAB equilibrium and stability code show there are many 3D solutions of the advanced

More information

SMR/ Summer College on Plasma Physics. 30 July - 24 August, Introduction to Magnetic Island Theory.

SMR/ Summer College on Plasma Physics. 30 July - 24 August, Introduction to Magnetic Island Theory. SMR/1856-1 2007 Summer College on Plasma Physics 30 July - 24 August, 2007 Introduction to Magnetic Island Theory. R. Fitzpatrick Inst. for Fusion Studies University of Texas at Austin USA Introduction

More information

MHD Linear Stability Analysis Using a Full Wave Code

MHD Linear Stability Analysis Using a Full Wave Code US-Japan JIFT Workshop on Progress of Extended MHD Models NIFS, Toki,Japan 2007/03/27 MHD Linear Stability Analysis Using a Full Wave Code T. Akutsu and A. Fukuyama Department of Nuclear Engineering, Kyoto

More information

Active MHD Control Needs in Helical Configurations

Active MHD Control Needs in Helical Configurations Active MHD Control Needs in Helical Configurations M.C. Zarnstorff 1 Presented by E. Fredrickson 1 With thanks to A. Weller 2, J. Geiger 2, A. Reiman 1, and the W7-AS Team and NBI-Group. 1 Princeton Plasma

More information

Stabilization of sawteeth in tokamaks with toroidal flows

Stabilization of sawteeth in tokamaks with toroidal flows PHYSICS OF PLASMAS VOLUME 9, NUMBER 7 JULY 2002 Stabilization of sawteeth in tokamaks with toroidal flows Robert G. Kleva and Parvez N. Guzdar Institute for Plasma Research, University of Maryland, College

More information

Reversed Field Pinch: basics

Reversed Field Pinch: basics Reversed Field Pinch: basics Piero Martin Consorzio RFX- Associazione Euratom-ENEA sulla fusione, Padova, Italy Department of Physics, University of Padova Notes for the lecture at the European Ph.D. Course

More information

Oscillating-Field Current-Drive Experiment on MST

Oscillating-Field Current-Drive Experiment on MST Oscillating-Field Current-Drive Experiment on MST K. J. McCollam, J. K. Anderson, D. J. Den Hartog, F. Ebrahimi, J. A. Reusch, J. S. Sarff, H. D. Stephens, D. R. Stone University of Wisconsin-Madison D.

More information

BRIEF COMMUNICATION. Near-magnetic-axis Geometry of a Closely Quasi-Isodynamic Stellarator. Greifswald, Wendelsteinstr. 1, Greifswald, Germany

BRIEF COMMUNICATION. Near-magnetic-axis Geometry of a Closely Quasi-Isodynamic Stellarator. Greifswald, Wendelsteinstr. 1, Greifswald, Germany BRIEF COMMUNICATION Near-magnetic-axis Geometry of a Closely Quasi-Isodynamic Stellarator M.I. Mikhailov a, J. Nührenberg b, R. Zille b a Russian Research Centre Kurchatov Institute, Moscow,Russia b Max-Planck-Institut

More information

Electron Bernstein Wave Heating in the TCV Tokamak

Electron Bernstein Wave Heating in the TCV Tokamak Electron Bernstein Wave Heating in the TCV Tokamak A. Mueck 1, Y. Camenen 1, S. Coda 1, L. Curchod 1, T.P. Goodman 1, H.P. Laqua 2, A. Pochelon 1, TCV Team 1 1 Ecole Polytechnique Fédérale de Lausanne

More information

The non-resonant kink modes triggering strong sawtooth-like crashes. in the EAST tokamak. and L. Hu 1

The non-resonant kink modes triggering strong sawtooth-like crashes. in the EAST tokamak. and L. Hu 1 The non-resonant kink modes triggering strong sawtooth-like crashes in the EAST tokamak Erzhong Li 1, V. Igochine 2, O. Dumbrajs 3, L. Xu 1, K. Chen 1, T. Shi 1, and L. Hu 1 1 Institute of Plasma Physics,

More information

Innovative Concepts Workshop Austin, Texas February 13-15, 2006

Innovative Concepts Workshop Austin, Texas February 13-15, 2006 Don Spong Oak Ridge National Laboratory Acknowledgements: Jeff Harris, Hideo Sugama, Shin Nishimura, Andrew Ware, Steve Hirshman, Wayne Houlberg, Jim Lyon Innovative Concepts Workshop Austin, Texas February

More information

Exploration of Configurational Space for Quasi-isodynamic Stellarators with Poloidally Closed Contours of the Magnetic Field Strength

Exploration of Configurational Space for Quasi-isodynamic Stellarators with Poloidally Closed Contours of the Magnetic Field Strength Exploration of Configurational Space for Quasi-isodynamic Stellarators with Poloidally Closed Contours of the Magnetic Field Strength V.R. Bovshuk 1, W.A. Cooper 2, M.I. Mikhailov 1, J. Nührenberg 3, V.D.

More information

From tokamaks to stellarators: understanding the role of 3D shaping

From tokamaks to stellarators: understanding the role of 3D shaping Under consideration for publication in J. Plasma Phys. From tokamaks to stellarators: understanding the role of 3D shaping Samuel A. Lazerson and John C. Schmitt 2 Princeton Plasma Physics Laboratory,

More information

The RFP: Plasma Confinement with a Reversed Twist

The RFP: Plasma Confinement with a Reversed Twist The RFP: Plasma Confinement with a Reversed Twist JOHN SARFF Department of Physics University of Wisconsin-Madison Invited Tutorial 1997 Meeting APS DPP Pittsburgh Nov. 19, 1997 A tutorial on the Reversed

More information

Highlights from (3D) Modeling of Tokamak Disruptions

Highlights from (3D) Modeling of Tokamak Disruptions Highlights from (3D) Modeling of Tokamak Disruptions Presented by V.A. Izzo With major contributions from S.E. Kruger, H.R. Strauss, R. Paccagnella, MHD Control Workshop 2010 Madison, WI ..onset of rapidly

More information

NIMROD FROM THE CUSTOMER S PERSPECTIVE MING CHU. General Atomics. Nimrod Project Review Meeting July 21 22, 1997

NIMROD FROM THE CUSTOMER S PERSPECTIVE MING CHU. General Atomics. Nimrod Project Review Meeting July 21 22, 1997 NIMROD FROM THE CUSTOMER S PERSPECTIVE MING CHU General Atomics Nimrod Project Review Meeting July 21 22, 1997 Work supported by the U.S. Department of Energy under Grant DE-FG03-95ER54309 and Contract

More information

Recent Developments in Theory for W7-X

Recent Developments in Theory for W7-X Recent Developments in Theory for W7-X J. NÜHRENBERG, M. DREVLAK, R. HATZKY, R. KLEIBER, A. KÖNIES, P. MERKEL, D. MONTICELLO +,C.NÜHRENBERG, A. REIMAN +,T.M.TRAN? Max-Planck-Institut für Plasmaphysik,

More information

Electron temperature barriers in the RFX-mod experiment

Electron temperature barriers in the RFX-mod experiment Electron temperature barriers in the RFX-mod experiment A. Scaggion Consorzio RFX, Padova, Italy Tuesday 5 th October 2010 ADVANCED PHYSICS LESSONS 27/09/2010 07/10/2010 IPP GARCHING JOINT EUROPEAN RESEARCH

More information

The Field-Reversed Configuration (FRC) is a high-beta compact toroidal in which the external field is reversed on axis by azimuthal plasma The FRC is

The Field-Reversed Configuration (FRC) is a high-beta compact toroidal in which the external field is reversed on axis by azimuthal plasma The FRC is and Stability of Field-Reversed Equilibrium with Toroidal Field Configurations Atomics General Box 85608, San Diego, California 92186-5608 P.O. APS Annual APS Meeting of the Division of Plasma Physics

More information

Stellarators. Dr Ben Dudson. 6 th February Department of Physics, University of York Heslington, York YO10 5DD, UK

Stellarators. Dr Ben Dudson. 6 th February Department of Physics, University of York Heslington, York YO10 5DD, UK Stellarators Dr Ben Dudson Department of Physics, University of York Heslington, York YO10 5DD, UK 6 th February 2014 Dr Ben Dudson Magnetic Confinement Fusion (1 of 23) Previously... Toroidal devices

More information

INTERACTION OF DRIFT WAVE TURBULENCE AND MAGNETIC ISLANDS

INTERACTION OF DRIFT WAVE TURBULENCE AND MAGNETIC ISLANDS INTERACTION OF DRIFT WAVE TURBULENCE AND MAGNETIC ISLANDS A. Ishizawa and N. Nakajima National Institute for Fusion Science F. L. Waelbroeck, R. Fitzpatrick, W. Horton Institute for Fusion Studies, University

More information

Effect of Resonant and Non-resonant Magnetic Braking on Error Field Tolerance in High Beta Plasmas

Effect of Resonant and Non-resonant Magnetic Braking on Error Field Tolerance in High Beta Plasmas 1 EX/5-3Ra Effect of Resonant and Non-resonant Magnetic Braking on Error Field Tolerance in High Beta Plasmas H. Reimerdes 1), A.M. Garofalo 2), E.J. Strait 2), R.J. Buttery 3), M.S. Chu 2), Y. In 4),

More information

Finite-Orbit-Width Effect and the Radial Electric Field in Neoclassical Transport Phenomena

Finite-Orbit-Width Effect and the Radial Electric Field in Neoclassical Transport Phenomena 1 TH/P2-18 Finite-Orbit-Width Effect and the Radial Electric Field in Neoclassical Transport Phenomena S. Satake 1), M. Okamoto 1), N. Nakajima 1), H. Sugama 1), M. Yokoyama 1), and C. D. Beidler 2) 1)

More information

Exponential Growth and Filamentary Structure of Nonlinear Ballooning Instability 1

Exponential Growth and Filamentary Structure of Nonlinear Ballooning Instability 1 Exponential Growth and Filamentary Structure of Nonlinear Ballooning Instability 1 Ping Zhu in collaboration with C. C. Hegna and C. R. Sovinec University of Wisconsin-Madison Sherwood Conference Denver,

More information

Intrinsic rotation due to non- Maxwellian equilibria in tokamak plasmas. Jungpyo (J.P.) Lee (Part 1) Michael Barnes (Part 2) Felix I.

Intrinsic rotation due to non- Maxwellian equilibria in tokamak plasmas. Jungpyo (J.P.) Lee (Part 1) Michael Barnes (Part 2) Felix I. Intrinsic rotation due to non- Maxwellian equilibria in tokamak plasmas Jungpyo (J.P.) Lee (Part 1) Michael Barnes (Part 2) Felix I. Parra MIT Plasma Science & Fusion Center. 1 Outlines Introduction to

More information

High-m Multiple Tearing Modes in Tokamaks: MHD Turbulence Generation, Interaction with the Internal Kink and Sheared Flows

High-m Multiple Tearing Modes in Tokamaks: MHD Turbulence Generation, Interaction with the Internal Kink and Sheared Flows TH/P3-3 High-m Multiple Tearing Modes in Tokamaks: MHD Turbulence Generation, Interaction with the Internal Kink and Sheared Flows A. Bierwage 1), S. Benkadda 2), M. Wakatani 1), S. Hamaguchi 3), Q. Yu

More information

MHD Simulation of High Wavenumber Ballooning-like Modes in LHD

MHD Simulation of High Wavenumber Ballooning-like Modes in LHD 1 TH/P9-16 MHD Simulation of High Wavenumber Ballooning-like Modes in LHD H. Miura and N. Nakajima National Institute for Fusion Science, 322-6 Oroshi, Toki, Gifu 509-5292, JAPAN e-mail contact of main

More information

Direct drive by cyclotron heating can explain spontaneous rotation in tokamaks

Direct drive by cyclotron heating can explain spontaneous rotation in tokamaks Direct drive by cyclotron heating can explain spontaneous rotation in tokamaks J. W. Van Dam and L.-J. Zheng Institute for Fusion Studies University of Texas at Austin 12th US-EU Transport Task Force Annual

More information

MHD. Jeff Freidberg MIT

MHD. Jeff Freidberg MIT MHD Jeff Freidberg MIT 1 What is MHD MHD stands for magnetohydrodynamics MHD is a simple, self-consistent fluid description of a fusion plasma Its main application involves the macroscopic equilibrium

More information

0 Magnetically Confined Plasma

0 Magnetically Confined Plasma 0 Magnetically Confined Plasma 0.1 Particle Motion in Prescribed Fields The equation of motion for species s (= e, i) is written as d v ( s m s dt = q s E + vs B). The motion in a constant magnetic field

More information

Volume 114 Number 4 July-August Journal of Research of the National Institute of Standards and Technology

Volume 114 Number 4 July-August Journal of Research of the National Institute of Standards and Technology [J. Res. Natl. Inst. Stand. Technol. 114, 229-236 (2009)] Design of the DEMO Fusion Reactor Following ITER Volume 114 Number 4 July-August 2009 Paul R. Garabedian Courant Institute, New York University,

More information

ELM control with RMP: plasma response models and the role of edge peeling response

ELM control with RMP: plasma response models and the role of edge peeling response ELM control with RMP: plasma response models and the role of edge peeling response Yueqiang Liu 1,2,3,*, C.J. Ham 1, A. Kirk 1, Li Li 4,5,6, A. Loarte 7, D.A. Ryan 8,1, Youwen Sun 9, W. Suttrop 10, Xu

More information

Model for humpback relaxation oscillations

Model for humpback relaxation oscillations Model for humpback relaxation oscillations F. Porcelli a,b,c.angioni a,r.behn a,i.furno a,t.goodman a,m.a.henderson a, Z.A. Pietrzyk a,a.pochelon a,h.reimerdes a, E. Rossi c,o.sauter a a Centre de Recherches

More information

INTERACTION OF AN EXTERNAL ROTATING MAGNETIC FIELD WITH THE PLASMA TEARING MODE SURROUNDED BY A RESISTIVE WALL

INTERACTION OF AN EXTERNAL ROTATING MAGNETIC FIELD WITH THE PLASMA TEARING MODE SURROUNDED BY A RESISTIVE WALL INTERACTION OF AN EXTERNAL ROTATING MAGNETIC FIELD WITH THE PLASMA TEARING MODE SURROUNDED BY A RESISTIVE WALL S.C. GUO* and M.S. CHU GENERAL ATOMICS *Permanent Address: Consorzio RFX, Padova, Italy **The

More information

Derivation of dynamo current drive in a closed current volume and stable current sustainment in the HIT SI experiment

Derivation of dynamo current drive in a closed current volume and stable current sustainment in the HIT SI experiment Derivation of dynamo current drive and stable current sustainment in the HIT SI experiment 1 Derivation of dynamo current drive in a closed current volume and stable current sustainment in the HIT SI experiment

More information

Two Fluid Dynamo and Edge-Resonant m=0 Tearing Instability in Reversed Field Pinch

Two Fluid Dynamo and Edge-Resonant m=0 Tearing Instability in Reversed Field Pinch 1 Two Fluid Dynamo and Edge-Resonant m= Tearing Instability in Reversed Field Pinch V.V. Mirnov 1), C.C.Hegna 1), S.C. Prager 1), C.R.Sovinec 1), and H.Tian 1) 1) The University of Wisconsin-Madison, Madison,

More information

Current Profile Control by ac Helicity Injection

Current Profile Control by ac Helicity Injection Current Profile Control by ac Helicity Injection Fatima Ebrahimi and S. C. Prager University of Wisconsin- Madison APS 2003 Motivations Helicity injection is a method to drive current in plasmas in which

More information

Investigation of Intrinsic Rotation Dependencies in Alcator C-Mod

Investigation of Intrinsic Rotation Dependencies in Alcator C-Mod Investigation of Intrinsic Rotation Dependencies in Alcator C-Mod D. Kwak, A. E. White, J. E. Rice, N. T. Howard, C. Gao, M. L. Reinke, M. Greenwald, C. Angioni, R. M. McDermott, and the C-Mod and ASDEX

More information

Measurement of magnetic eld line stochasticity in nonlinearly evolving, Department of Engineering Physics,

Measurement of magnetic eld line stochasticity in nonlinearly evolving, Department of Engineering Physics, Measurement of magnetic eld line stochasticity in nonlinearly evolving, nonequilibrium plasmas Y. Nishimura, J. D. Callen, and C. C. Hegna Department of Engineering Physics, University of Wisconsin-Madison,

More information

Plasma instabilities. Dr Ben Dudson, University of York 1 / 37

Plasma instabilities. Dr Ben Dudson, University of York 1 / 37 Plasma instabilities Dr Ben Dudson, University of York 1 / 37 Previously... Plasma configurations and equilibrium Linear machines, and Stellarators Ideal MHD and the Grad-Shafranov equation Collisional

More information

Shear Flow Generation in Stellarators - Configurational Variations

Shear Flow Generation in Stellarators - Configurational Variations Shear Flow Generation in Stellarators - Configurational Variations D. A. Spong 1), A. S. Ware 2), S. P. Hirshman 1), J. H. Harris 1), L. A. Berry 1) 1) Oak Ridge National Laboratory, Oak Ridge, Tennessee

More information

22.615, MHD Theory of Fusion Systems Prof. Freidberg Lecture 15: Alternate Concepts (with Darren Sarmer)

22.615, MHD Theory of Fusion Systems Prof. Freidberg Lecture 15: Alternate Concepts (with Darren Sarmer) 22.615, MHD Theory of Fusion Systems Prof. Freidberg Lecture 15: Alternate Concepts (with Darren Sarmer) 1. In todays lecture we discuss the basic ideas behind the main alternate concepts to the tokamak.

More information

Configuration Optimization of a Planar-Axis Stellarator with a Reduced Shafranov Shift )

Configuration Optimization of a Planar-Axis Stellarator with a Reduced Shafranov Shift ) Configuration Optimization of a Planar-Axis Stellarator with a Reduced Shafranov Shift ) Shoichi OKAMURA 1,2) 1) National Institute for Fusion Science, Toki 509-5292, Japan 2) Department of Fusion Science,

More information

Momentum transport from magnetic reconnection in laboratory an. plasmas. Fatima Ebrahimi

Momentum transport from magnetic reconnection in laboratory an. plasmas. Fatima Ebrahimi Momentum transport from magnetic reconnection in laboratory and astrophysical plasmas Space Science Center - University of New Hampshire collaborators : V. Mirnov, S. Prager, D. Schnack, C. Sovinec Center

More information

Numerical calculation of the Hamada basis vectors for three-dimensional toroidal magnetic configurations

Numerical calculation of the Hamada basis vectors for three-dimensional toroidal magnetic configurations PHYSICS OF PLASMAS 12, 072513 2005 Numerical calculation of the Hamada basis vectors for three-dimensional toroidal magnetic configurations J. N. Talmadge and S. P. Gerhardt a HSX Plasma Laboratory, University

More information

Intermediate Nonlinear Development of a Line-tied g-mode

Intermediate Nonlinear Development of a Line-tied g-mode Intermediate Nonlinear Development of a Line-tied g-mode Ping Zhu University of Wisconsin-Madison In collaboration with C. C. Hegna and C. R. Sovinec (UW-Madison) A. Bhattacharjee and K. Germaschewski

More information

The Linear Theory of Tearing Modes in periodic, cyindrical plasmas. Cary Forest University of Wisconsin

The Linear Theory of Tearing Modes in periodic, cyindrical plasmas. Cary Forest University of Wisconsin The Linear Theory of Tearing Modes in periodic, cyindrical plasmas Cary Forest University of Wisconsin 1 Resistive MHD E + v B = ηj (no energy principle) Role of resistivity No frozen flux, B can tear

More information

GA A THERMAL ION ORBIT LOSS AND RADIAL ELECTRIC FIELD IN DIII-D by J.S. degrassie, J.A. BOEDO, B.A. GRIERSON, and R.J.

GA A THERMAL ION ORBIT LOSS AND RADIAL ELECTRIC FIELD IN DIII-D by J.S. degrassie, J.A. BOEDO, B.A. GRIERSON, and R.J. GA A27822 THERMAL ION ORBIT LOSS AND RADIAL ELECTRIC FIELD IN DIII-D by J.S. degrassie, J.A. BOEDO, B.A. GRIERSON, and R.J. GROEBNER JUNE 2014 DISCLAIMER This report was prepared as an account of work

More information

Simulation Study of Interaction between Energetic Ions and Alfvén Eigenmodes in LHD

Simulation Study of Interaction between Energetic Ions and Alfvén Eigenmodes in LHD 1 Simulation Study of Interaction between Energetic Ions and Alfvén Eigenmodes in LHD Y. Todo 1), N. Nakajima 1), M. Osakabe 1), S. Yamamoto 2), D. A. Spong 3) 1) National Institute for Fusion Science,

More information

Modeling of ELM Dynamics for ITER

Modeling of ELM Dynamics for ITER Modeling of ELM Dynamics for ITER A.Y. PANKIN 1, G. BATEMAN 1, D.P. BRENNAN 2, A.H. KRITZ 1, S. KRUGER 3, P.B. SNYDER 4 and the NIMROD team 1 Lehigh University, 16 Memorial Drive East, Bethlehem, PA 18015

More information

Heat Transport in a Stochastic Magnetic Field. John Sarff Physics Dept, UW-Madison

Heat Transport in a Stochastic Magnetic Field. John Sarff Physics Dept, UW-Madison Heat Transport in a Stochastic Magnetic Field John Sarff Physics Dept, UW-Madison CMPD & CMSO Winter School UCLA Jan 5-10, 2009 Magnetic perturbations can destroy the nested-surface topology desired for

More information

INITIAL EVALUATION OF COMPUTATIONAL TOOLS FOR STABILITY OF COMPACT STELLARATOR REACTOR DESIGNS

INITIAL EVALUATION OF COMPUTATIONAL TOOLS FOR STABILITY OF COMPACT STELLARATOR REACTOR DESIGNS INITIAL EVALUATION OF COMPUTATIONAL TOOLS FOR STABILITY OF COMPACT STELLARATOR REACTOR DESIGNS A.D. Turnbull and L.L. Lao General Atomics (with contributions from W.A. Cooper and R.G. Storer) Presentation

More information

Edge Momentum Transport by Neutrals

Edge Momentum Transport by Neutrals 1 TH/P3-18 Edge Momentum Transport by Neutrals J.T. Omotani 1, S.L. Newton 1,2, I. Pusztai 1 and T. Fülöp 1 1 Department of Physics, Chalmers University of Technology, 41296 Gothenburg, Sweden 2 CCFE,

More information

Gyrokinetic simulations of magnetic fusion plasmas

Gyrokinetic simulations of magnetic fusion plasmas Gyrokinetic simulations of magnetic fusion plasmas Tutorial 2 Virginie Grandgirard CEA/DSM/IRFM, Association Euratom-CEA, Cadarache, 13108 St Paul-lez-Durance, France. email: virginie.grandgirard@cea.fr

More information

GA A26247 EFFECT OF RESONANT AND NONRESONANT MAGNETIC BRAKING ON ERROR FIELD TOLERANCE IN HIGH BETA PLASMAS

GA A26247 EFFECT OF RESONANT AND NONRESONANT MAGNETIC BRAKING ON ERROR FIELD TOLERANCE IN HIGH BETA PLASMAS GA A26247 EFFECT OF RESONANT AND NONRESONANT MAGNETIC BRAKING ON ERROR FIELD TOLERANCE IN HIGH BETA PLASMAS by H. REIMERDES, A.M. GAROFALO, E.J. STRAIT, R.J. BUTTERY, M.S. CHU, Y. In, G.L. JACKSON, R.J.

More information

New Schemes for Confinement of Fusion Products in Stellarators

New Schemes for Confinement of Fusion Products in Stellarators New Schemes for Confinement of Fusion Products in Stellarators W.A. Cooper ), M.Yu. Isaev 1), M.F. Heyn 5), V.N. Kalyuzhnyj 3), S.V. Kasilov 3), W. Kernbichler 5), A.Yu. Kuyanov 1), M.I. Mikhailov 1),

More information

- Effect of Stochastic Field and Resonant Magnetic Perturbation on Global MHD Fluctuation -

- Effect of Stochastic Field and Resonant Magnetic Perturbation on Global MHD Fluctuation - 15TH WORKSHOP ON MHD STABILITY CONTROL: "US-Japan Workshop on 3D Magnetic Field Effects in MHD Control" U. Wisconsin, Madison, Nov 15-17, 17, 2010 LHD experiments relevant to Tokamak MHD control - Effect

More information

ArbiTER studies of filamentary structures in the SOL of spherical tokamaks

ArbiTER studies of filamentary structures in the SOL of spherical tokamaks ArbiTER studies of filamentary structures in the SOL of spherical tokamaks D. A. Baver, J. R. Myra, Research Corporation F. Scotti, Lawrence Livermore National Laboratory S. J. Zweben, Princeton Plasma

More information

Physics Considerations in the Design of NCSX *

Physics Considerations in the Design of NCSX * 1 IAEA-CN-94/IC-1 Physics Considerations in the Design of NCSX * G. H. Neilson 1, M. C. Zarnstorff 1, L. P. Ku 1, E. A. Lazarus 2, P. K. Mioduszewski 2, W. A. Cooper 3, M. Fenstermacher 4, E. Fredrickson

More information

Computer Physics Communications

Computer Physics Communications Computer Physics Communications 180 (2009) 1524 1533 Contents lists available at ScienceDirect Computer Physics Communications www.elsevier.com/locate/cpc Three-dimensional anisotropic pressure free boundary

More information

Drift Mode Calculations for the Large Helical Device

Drift Mode Calculations for the Large Helical Device PPPL-3451 UC-7 PPPL-3451 Drift Mode Calculations for the Large Helical Device by G. Rewoldt, L.-P. Ku, W.M. Tang, H. Sugama, N. Nakajima, K.Y. Watanabe, S. Murakami, H. Yamada, and W.A. Cooper June PPPL

More information

ELM Suppression in DIII-D Hybrid Plasmas Using n=3 Resonant Magnetic Perturbations

ELM Suppression in DIII-D Hybrid Plasmas Using n=3 Resonant Magnetic Perturbations 1 EXC/P5-02 ELM Suppression in DIII-D Hybrid Plasmas Using n=3 Resonant Magnetic Perturbations B. Hudson 1, T.E. Evans 2, T.H. Osborne 2, C.C. Petty 2, and P.B. Snyder 2 1 Oak Ridge Institute for Science

More information

Fundamentals of Magnetic Island Theory in Tokamaks

Fundamentals of Magnetic Island Theory in Tokamaks Fundamentals of Magnetic Island Theory in Tokamaks Richard Fitzpatrick Institute for Fusion Studies University of Texas at Austin Austin, TX, USA Talk available at http://farside.ph.utexas.edu/talks/talks.html

More information

Chapter 1. Introduction to Nonlinear Space Plasma Physics

Chapter 1. Introduction to Nonlinear Space Plasma Physics Chapter 1. Introduction to Nonlinear Space Plasma Physics The goal of this course, Nonlinear Space Plasma Physics, is to explore the formation, evolution, propagation, and characteristics of the large

More information

A New Resistive Response to 3-D Fields in Low Rotation H-modes

A New Resistive Response to 3-D Fields in Low Rotation H-modes in Low Rotation H-modes by Richard Buttery 1 with Rob La Haye 1, Yueqiang Liu 2, Bob Pinsker 1, Jong-kyu Park 3, Holger Reimerdes 4, Ted Strait 1, and the DIII-D research team. 1 General Atomics, USA 2

More information

Blob motion and control. simple magnetized plasmas

Blob motion and control. simple magnetized plasmas Blob motion and control in simple magnetized plasmas Christian Theiler A. Fasoli, I. Furno, D. Iraji, B. Labit, P. Ricci, M. Spolaore 1, N. Vianello 1 Centre de Recherches en Physique des Plasmas (CRPP)

More information

Effect of local E B flow shear on the stability of magnetic islands in tokamak plasmas

Effect of local E B flow shear on the stability of magnetic islands in tokamak plasmas Effect of local E B flow shear on the stability of magnetic islands in tokamak plasmas R. Fitzpatrick and F. L. Waelbroeck Citation: Physics of Plasmas (1994-present) 16, 052502 (2009); doi: 10.1063/1.3126964

More information

Evaluation of CT injection to RFP for performance improvement and reconnection studies

Evaluation of CT injection to RFP for performance improvement and reconnection studies Evaluation of CT injection to RFP for performance improvement and reconnection studies S. Masamune A. Sanpei, T. Nagano, S. Nakanobo, R. Tsuboi, S. Kunita, M. Emori, H. Makizawa, H. Himura, N. Mizuguchi

More information

RESISTIVE BALLOONING MODES AND THE SECOND REGION OF STABILITY

RESISTIVE BALLOONING MODES AND THE SECOND REGION OF STABILITY Plasma Physics and Controlled Fusion, Vol. 29, No. 6, pp. 719 to 121, 1987 Printed in Great Britain 0741-3335/87$3.00+.OO 1OP Publishing Ltd. and Pergamon Journals Ltd. RESISTIVE BALLOONING MODES AND THE

More information

GA A27444 PROBING RESISTIVE WALL MODE STABILITY USING OFF-AXIS NBI

GA A27444 PROBING RESISTIVE WALL MODE STABILITY USING OFF-AXIS NBI GA A27444 PROBING RESISTIVE WALL MODE STABILITY USING OFF-AXIS NBI by J.M. HANSON, F. TURCO M.J. LANCTOT, J. BERKERY, I.T. CHAPMAN, R.J. LA HAYE, G.A. NAVRATIL, M. OKABAYASHI, H. REIMERDES, S.A. SABBAGH,

More information

TRANSPORT PROGRAM C-MOD 5 YEAR REVIEW MAY, 2003 PRESENTED BY MARTIN GREENWALD MIT PLASMA SCIENCE & FUSION CENTER

TRANSPORT PROGRAM C-MOD 5 YEAR REVIEW MAY, 2003 PRESENTED BY MARTIN GREENWALD MIT PLASMA SCIENCE & FUSION CENTER TRANSPORT PROGRAM C-Mod C-MOD 5 YEAR REVIEW MAY, 2003 PRESENTED BY MARTIN GREENWALD MIT PLASMA SCIENCE & FUSION CENTER C-MOD - OPPORTUNITIES AND CHALLENGES Prediction and control are the ultimate goals

More information

Issues in Neoclassical Tearing Mode Theory

Issues in Neoclassical Tearing Mode Theory Issues in Neoclassical Tearing Mode Theory Richard Fitzpatrick Institute for Fusion Studies University of Texas at Austin Austin, TX Tearing Mode Stability in Tokamaks According to standard (single-fluid)

More information

SUMMARY OF EXPERIMENTAL CORE TURBULENCE CHARACTERISTICS IN OH AND ECRH T-10 TOKAMAK PLASMAS

SUMMARY OF EXPERIMENTAL CORE TURBULENCE CHARACTERISTICS IN OH AND ECRH T-10 TOKAMAK PLASMAS SUMMARY OF EXPERIMENTAL CORE TURBULENCE CHARACTERISTICS IN OH AND ECRH T-1 TOKAMAK PLASMAS V. Vershkov, L.G. Eliseev, S.A. Grashin. A.V. Melnikov, D.A. Shelukhin, S.V. Soldatov, A.O. Urazbaev and T-1 team

More information

Control of Neo-classical tearing mode (NTM) in advanced scenarios

Control of Neo-classical tearing mode (NTM) in advanced scenarios FIRST CHENGDU THEORY FESTIVAL Control of Neo-classical tearing mode (NTM) in advanced scenarios Zheng-Xiong Wang Dalian University of Technology (DLUT) Dalian, China Chengdu, China, 28 Aug, 2018 Outline

More information

Bursty Transport in Tokamaks with Internal Transport Barriers

Bursty Transport in Tokamaks with Internal Transport Barriers Bursty Transport in Tokamaks with Internal Transport Barriers S. Benkadda 1), O. Agullo 1), P. Beyer 1), N. Bian 1), P. H. Diamond 3), C. Figarella 1), X. Garbet 2), P. Ghendrih 2), V. Grandgirard 1),

More information

GA A26785 GIANT SAWTEETH IN DIII-D AND THE QUASI-INTERCHANGE MODE

GA A26785 GIANT SAWTEETH IN DIII-D AND THE QUASI-INTERCHANGE MODE GA A26785 GIANT SAWTEETH IN DIII-D AND THE QUASI-INTERCHANGE MODE by A.D. TURNBULL, M. CHOI, and L.L. LAO NOVEMBER 2010 DISCLAIMER This report was prepared as an account of work sponsored by an agency

More information

On the physics of shear flows in 3D geometry

On the physics of shear flows in 3D geometry On the physics of shear flows in 3D geometry C. Hidalgo and M.A. Pedrosa Laboratorio Nacional de Fusión, EURATOM-CIEMAT, Madrid, Spain Recent experiments have shown the importance of multi-scale (long-range)

More information

Microturbulence in optimised stellarators

Microturbulence in optimised stellarators Q Josefine H. E. Proll, Benjamin J. Faber, Per Helander, Samuel A. Lazerson, Harry Mynick, and Pavlos Xanthopoulos Many thanks to: T. M. Bird, J. W. Connor, T. Go rler, W. Guttenfelder, G.W. Hammett, F.

More information

Comparison of Plasma Flows and Currents in HSX to Neoclassical Theory

Comparison of Plasma Flows and Currents in HSX to Neoclassical Theory 1 EX/P3-30 Comparison of Plasma Flows and Currents in HSX to Neoclassical Theory D.T. Anderson 1, A.R. Briesemeister 1, J.C. Schmitt 2, F.S.B. Anderson 1, K.M. Likin 1, J.N. Talmadge 1, G.M. Weir 1, K.

More information

Confinement of toroidal non-neutral plasma in Proto-RT

Confinement of toroidal non-neutral plasma in Proto-RT Workshop on Physics with Ultra Slow Antiproton Beams, RIKEN, March 15, 2005 Confinement of toroidal non-neutral plasma in Proto-RT H. Saitoh, Z. Yoshida, and S. Watanabe Graduate School of Frontier Sciences,

More information

New bootstrap current formula valid for steep edge pedestal, and its implication to pedestal stability

New bootstrap current formula valid for steep edge pedestal, and its implication to pedestal stability 1 TH/P4-12 New bootstrap current formula valid for steep edge pedestal, and its implication to pedestal stability C.S. Chang 1,2, Sehoon Koh 2,*, T. Osborne 3, R. Maingi 4, J. Menard 1, S. Ku 1, Scott

More information

Confinement of toroidal non-neutral plasma in Proto-RT

Confinement of toroidal non-neutral plasma in Proto-RT Workshop on Physics with Ultra Slow Antiproton Beams, RIKEN, March 15, 2005 Confinement of toroidal non-neutral plasma in Proto-RT H. Saitoh, Z. Yoshida, and S. Watanabe Graduate School of Frontier Sciences,

More information

Magnetohydrodynamics (MHD) II

Magnetohydrodynamics (MHD) II Magnetohydrodynamics (MHD) II Yong-Su Na National Fusion Research Center POSTECH, Korea, 8-10 May, 2006 Review I 1. What is confinement? Why is single particle motion approach required? 2. Fluid description

More information