1. Contribution of KIT to LHD Topics from collaboration research on MHD phenomena in LHD S. Masamune, K.Y. Watanabe 1), S. Sakakibara 1), Y. Takemura, KIT group, LHD experimental group 1),2) Kyoto Institute of Technology 1) National Institiute for Fusion Science 2) Kyoto University

2. Motivation Comparative studies on MHD phenomena associated with current-driven and pressure- driven global instabilities in high-beta plasmas in current-free LHD and Ohmically-heated RFP Accumulation of data set for pressure-driven global MHD instabilities for active control of low-order MHD modes in LHD plasmas

3. Mag. Well Hill Low order rational surface m<=3 Magnetic hill exists in the finite beta gradients region => MHD instabilities (interchange/ pressure driven) would appear in high beta regime. Characteristics MHD equilibrium related to stability A p =6.2, p~(1-  2 )(1-  8 ) (%)  dia > m/n=3/2 m/n=2/1, 3/2,1/1(,2/2,3/3), 3/4,2/3 3/4 1/1(,2/2,3/3) 2/1 2/3

4. Study on MHD instabilities in LHD I Objectives: - Avoidance of confinement degradation caused by global MHD instabilities in Heliotron plasmas - Development of control scheme of the MHD instabilities # Understanding the excitation mechanism of the mode excitation Identification of the condition of mode appearance and mechanism of the mode axand mechanism of the excitatio => Experimental identification of the conditions for mode appearance and comparison with predictions from linear and nonlinear theories # Quantitative estimate of the effects of MHD instabilities on plasma confinement and understanding the mechanism of confinement degradation => Experimental identification of the relationship between confinement degradation and MHD modes, including the relationship between the mode structure and edge magnetic fluctuations. Comparison of the experimental results with predictions by nonlinear theories. # Development of active control methods of MHD instabilities to avoid confinement degradation => Use of the resonant magnetic field, control of plasma flow, etc.

5. # Core resonant MHD instabilities ⇒ - causing local flattening of the pressure profile. - stable in high-beta region. # MHD instabilities resonant in the peripheral region ･ rotating modes ⇒ - dominant modes in high-beta region. - appearing when D I ≾ 0.2, D R >0 - magnetic fluctuation amplitudes increase with increase in beta and magnetic Reynolds number ・ non-rotating modes ⇒ - appearing in low magnetic shear configuration with relatively low beta - appearing when D I >0.2, D R >0 - accompanying generation of magnetic island, with confinement degradation (decrease in beta by ~50%) MHD instabilities in LHD II magnetic fluctuation behavior Magnetic Reynolds Number, S % rotating (%) 0.01 10 -3 10 -4 10 -5 1.2 1.0 0.8 0.6  a -  0 non-rotating (%) 0.06 0.04 0.02 0.0 What have been known for pressure-driven modes ・ Effect of rotating MHD modes on plasma confinement ・ Growth (decay) and saturation of non-rotating MHD modes New Findings:

6. Effects of rotating MHD modes on confinement I Analysis of internal mode structure and change in Te profile associated with apperance of the modes have relealed the effects of MHD modes on plasma confinement. Experiments have been performed under marginal stability condition to rotating MHD modes resonant in the peripheral region where ~1%. 1.8s 5% Coh in b 1.9s f~1.8kHz line integral No phase change (or inversion) => No magnetic island => linear ideal/resistive interchange characteristic instability disappeared at t=1.9s fitting =>  /a p ~5% Major radial profile in SXR emission at t=1.8s plasma displacement

7. Effects of rotating MHD modes on confinement II 1.8s 5% 1.9s Normalized difference from Te at t=1.9s (just after the disappearance of fluctuation ) 1.8s 1.83 1.87 TeTe  T e /T e 1.9s Global confinement properties have been improved by 10% when the mode having normalized width of 5% with edge magnetic fluctuation level of 0.01% disappeared.

8. Growth and saturation of the rotating MHD modes 磁場揺動 の相関 sx15, 14, 13, 12, 11 sx18, 17, 16 SXR fluctuation profile line integrated (t=1.8s) - No positional dependence in the initial grow phase. -Slower grow at further location from resonant surface in the second stage. Two-step growth of rotating MHD modes Initial phase: growth time ~0.6ms Second phase: growth time ~1.7ms x1~x10 of linear growth time

9. Growth (decay) and saturation of the non-rotating MHD modes  t~30ms Prediction Linear growth rate (FAR3D)  ~1/(100  s) Non-rotating MHD instability; often observed in low shear, high hill configurations # growth time of tild-b :50~100ms (similar to  decay time) # linear theory prediction (  g ):~100  s inconsistent No localized rapid decay phenomena? Prior to global decay, intermittent small-scale Te0 decay is observed with time scale of linear theory prediction. relation with linear theory? relation with global decay? ~100  s growth time; 50~100ms Further study Decay profile in Te: similar to structure of linear ideal interchange

10. Summary I 1-(1) Rotating MHD mode (m=1/n=1) has caused confinement degradation. Quantitative estimates have shown that he mode having mode width of 5% with edge magnetic fluctuation of 0.01% has caused 10% degradation of global confinement. 1-(2) The rotating MHD mode (m=1/n=1) grows with two steps. The growth time in the initial phase is consistent with linear theory prediction, while the growth time in the second phase is order-of-magnitude longer than linear theory prediction. Future work: - Data accumulation on relationship between mode widths and edge magnetic fluctuation amplitudes, on mode widths and confinement degradation. - Nonlinear saturation mechanism of the mode through detailed comparison with linear and nonlinear theories of ideal and resistive interchange modes.

11. Summary II 2. Growth (or decay) time of non-rotating MHD mode (m=1/n=1) is 50-100 ms, two- or three-order-of-magnitude longer than the linear theory prediction. Prior to the global decay of beta, intermittent small-scale decay in electron temperature occurs with time scale consistent with linear theory prediction. Future work: - Internal mode structure of the intermittent temperature decay. - Relation between the intermittent phenomena and succeeding global decay -Nonlinear saturation mechanism of the mode through comparison with theories.