Non-disruptive MHD Dynamics in Inward-shifted LHD Configurations

Transcription

1 Non-disrutive MHD Dynamics in Inward-shifted LHD Configurations.Introduction.MHD simulation 3.DNS of full 3D MHD 4. Summary MIUA H. ICHIGUCHI K. NAKAJIMA N. HAYASHI T. (National Institute for Fusion Science) CAEAS.A. (Oak idge National Laboratory)

2 Purose: aiming to Intension to understand lasma behaviors in LHD LHD exeriments ax3.6m (So called Inward-shifted configuration ) linear unstable configuration relatively good confinement Why is the lasma confined under linear unstable state? Investigation by numerical simulation of MHD on ax3.6m config. Three-field MHD simulation and Direct Numerical Simulation (DNS) of full 3D comressible MHD [MHD] suitable for studying various situations Proosition of stabilizing mechanism based on the 3-field MHD simulation [DNS of full 3D MHD] ALL-in-ONE nature No aroximation to the original MHD fully 3D geometry oflhd Elements of MHD dynamics not included in the 3-field MHD comressibility toroidal flows local curvature of magnetic field line They may also influence the good confinement.

3 3-field MHD simulation ( ) Ψ Ψ Φ Φ ζ Ω ζ ψ ζ ζ ζ π Ω ε ν ζ Ω ε β Φ ψ ζ π ζ ζ * // * ˆ t ) ( ) ( d t U ˆ t t J U dt d Z Z P P P P J U J S eq eq Described in the flux coordinate system. Fourier exansion in toroidal (n) and azimuthal (m) direction. Discretized by finite-difference scheme in the radial direction. A lasma stabilization scenario: The ressure rofile can be self-organized so that the LHD lasma should achieve high beta regime along a stable ath. (Presented in IAEA FEC Lyon)

4 Disrutive/non-disrutive behaviors Plasma evolutions often lead to bursting activities when their marching start from ressure rofiles such as ( r) ( ρ )( ρ ) 8 Non-disrutive results by rearing initial ressure as P ( ρ) ap ( ρ) sat Non-disrutive beta achievement u to.5% (confirmed)

5 Key oints of stabilizing mechanism roosed from MHD Time evolution of the interchange mode : low beta the modes with different helicity do not interact directly. high beta the modes interact each other directly through overlaing of vortices leading to bursting activity The bursting activity can be suressed if the saturated ressure rofile is succeeded in the increase of beta. The scenario roosed in the revious IAEA FEC is valid for higher beta (.% and.5%).

6 DNS of full 3D comressible and nonlinear MHD equations ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) η t 3 4 γ t 3 µ t t j ω j j µ η ρ ρ ρ ρ ρ Described in the helical-toroidal coordinate system. ectangular grid finite difference unge-kutta-gill scheme Feature of DNS: Precise MHD dynamics under full 3D geometry of LHD Toroidal flow/ Comressibility/ Local magnetic curvature/ Free boundary Linear analysis. Comressibility (dilatation) reduces the growth rates.. Toroidal flows can become main art of fluid motions when 3D comressible erturbations grow.

7 Disrutive/non-disrutive runs :D stream lines and deformation of the ressure Lines : stream lines which are drawn only by the oloidal comonents of the velocity vector Contours: Pressure un non-disrutive Initial condition β 4 % ax 3.6m ( ρ) ρ (i)hint equilibrium m/n5/ erturbation(re-calc.) run (non-disrutive FEC Lyon) (ii)hint equilibrium white noise run (disrutive) ( ) un disrutive

8 Fourier-mode decomosition in oozer coodinate (run ) Non-disrutive Disrutive Fourier ower sectra of the ressure P m n (t)

9 Generation of toroidal flows Substantial generation of toroidal flow Initial stage is D-like. (MHD aroximation may holds here.) KtK-K > K K total kinetic energy Koloidal contributions to K

10 3D stream lines and deformation of the ressure Non-disrutive Disrutive Toroidal flow and large (ositive or negative) dilatation are generated at the same lace same time. (oth in run and.)

11 Mean rofiles of the ressure and toroidal flow Non-disrutive Disrutive ery rough observation about toroidal flow and ressure deformation: Plasma core and eriheral region or flattened/stee regions) toroidal flows in the oosite direction Strong toroidal flow is generated whether the run is disrutive or nondisrutive.

12 Seculation about effects of comressibility and toroidal flows in LHD D system : v 3D system : u v General consideration: Suose that the kinetic energy is comarable for D and 3D. Then the stream is strong in D than in 3D. D u 3D D 3D ( tobe recise v (v (u v v u v v v ) u v 3 ) u u u 3 u...toroidalcomonent(large) u u u ) D aroximation may overestimate the fluid motions in oloidal section (which cause mushroomlike deformation of the ressure) and 3D simulation can be more stable. A simle numerical test: γ cut off the toroidal and comressibility effects Strong flow generation (Test is not comleted yet.)

13 Simulations with arallel heat conduction ( ) ( ) ( ) ( ) ( ) ( ) 4 // 6 // γ t ρ ρ ρ ω j ω j µ η µ Including effects of arallel thermal conduction the growth rate of unstable modes are reduced and ressure deformation is suressed. (Disrutive run in this run may become non-disrutive by. We must examine carefully how large we can take the arallel conductivity with numerical reliability (undergoing) //

14 Summary Two kinds of simulation: MHD and DNS oth in MHD and DNS Growth of ressure-driven unstable modes and formation of mushroom-like structures of the ressure. MHD alidity of the stabilization scenario in LHD is confirmed for higher beta. Avoiding vortex-vortex interactions between unstable modes with different helicity is considered a key art for the stabilization. Simulations are continued for higher beta values. DNS MHD aroximation can be held in the early stage of linear growth. Substantial toroidal flow generation is observed. The generation of toroidal flow and comressibility are exected to suress deformation of the ressure and make the system more non-disrutive.

15 Momentum reservation/generation t ρd j d ( ρ) d d j d µ ( ) ( ρ) ds ds j d µ ( ) - d 3 ( ) d ds 3 ds Origin of the toroidal momentum is the magnetic field. d

16 Fourier-mode decomositions in detail Fourier ower sectra of the ressure P m n (t)

17 Eigenfunction in disrutive and nondisrutive runs P m n

18 Non-disrutive behaviors Non-disrutive results by rearing initial ressure as P ( ρ) apsat ( ρ) Searated evolutions of unstable modes at resonant surfaces