1. MHD Behaviour of Low-Aspect-Ratio RFP Plasmas in RELAX S.Masamune, T.Onchi, A.Sanpei, R.Ikezoe, K.Oki, T.Yamashita, H.Shimazu, N.Nishino 1), R.Paccagnella 2) Kyoto Institute of technology, Kyoto, Japan 1) Hiroshima University, Higashi-hiroshima, Japan 2) Consorzio RFX, Padova, Italy 13th IEA/RFP Workshop Oct.9-11, 2008 (Stockholm)

2. Lowering the aspect ratio of RFP may lead to new regime Increased separation of mode rational surfaces => influence on nonlinear MHD Reduced nonlinear interaction of the tearing modes Reduced saturated island width => Easy access to QSH and new dynamo mechanism Enhanced neoclassical effect => current sustainment Increase in trapped particle fraction => Increase in bootstrap current fraction due to neoclassical viscosity Bootstrap current fraction of 94% possible with  >60% Construction of low-A RFP machine RELAX with A=2 （ R/a=0.5m/0.25m ）

3. Motivation for lowering A (I) - larger separation of mode rational surfaces - Internally nonresonant modes → RWM Internally resonant tearing modes - RFP dynamo - Magnetic chaos - Locked modes Externally nonresonant modes → RWM m=1/n >0 Lowering A  Increased separation of mode rational surfaces

4. Motivation for lowering A (II) - increase in bootstrap current fraction - Low-aspect-ratio RFP machine “RELAX” (REversed field pinch of Low Aspect ratio eXperiment) R/a=0.51m/0.25m, A=2 (world’s lowest) (Shiina et al., 2005) increase in trapped particle fraction by lowering A increase in bootstrap current due to neoclassical viscosity theoretical prediction of an equilibrium with bootstrap fraction of >90% in reactor- regime parameters Simple MHD mode dynamics?

5. Low aspect ratio RFP machine “RELAX” (REversed field pinch of Low Aspect ratio eXperiment) Vacuum vessel - R/a=0.51m/0.25m - SS, 4mmt A=2 (world’s lowest) Toroidal field system: - Number of coils ： 16 - 16 x 4 = 64 turns Poloidal field system: -Primary winding ： 16 turn coils coaxial with vacuum vessel

6. Typical discharge with flat-topped plasma current => I p starts decreasing Br (m=1/n=2) measured on the outer surface of the vacuum vessel Growth rate vs. na/R of external kink modes for α-Θ 0 model profiles

7. Quasi-periodic growth of a single helical mode (m=1/n=4) in shallow-reversal or high-current (Ip ＞ 60kA) discharges Spectral index N s Characteristic of the QSH RFP state with a lower mode number (mostly n = 4) than in other RFPs.

8. Estimate of bootstrap current fraction with equilibrium reconstruction code “RELAXFit” For present RELAX plasmas: Bootstrap current fraction < 5 % T e (0)=300eV, n e (0)=4.0x10 19 /m 3 (target parameters) For improved plasma parameters: Requirement:  p ~30% at I p ~100kA

9. Estimate of nonlinear coupling of m=1 tearing modes Results of bispectral analysis in MST(A=3): b 2 (1,1,2)= 0.35 (S. Assadi et al., Phys. Rev. Lett. 69, 281 (1992)) bicoherence b 2 (k 1,k 2,k 3 ) => Indication of three-wave coupling Results of bispectral analysis in RELAX(A=2) b 2 (1,1,2) < 0.1 → nonlinear coupling of m=1 modes less important in RELAX (A=2)

10. A large-scale magnetic field profile change in shallow-F discharge - Possibility of rotating Ohmic Helical Equilibrium state - Quasi-periodic oscillation between reversed and non-reversed states Similar large-scale oscillatory behavior in B r and B  B  (mT) Ip (kA)

11. Comparison with Ohmic Helical Equilibrium solution R. Paccagnella, IEA / RFP Workshop 2000 Numerical solution of Helically symmetric RFP equilibrium : Low-frequency (f<2kHz) component Theory Experiments Excellent agreement may be an indication of rotating Helical Ohmic Equilibrium state 0.44 brbr bzbz bb Flux surfaces recovered! Radial profiles (0.6<r/a<1.0) :

12. Upgrade of RELAX machine Replacing the iron core and TF coils ⇒ Larger iron core for OH current drive ⇒ Larger TF coils with increased number ⇒ reduced toroidal ripple, improved accessibility for diagnostics -- Discharge optimization in progress --

13. A 60-kA discharge with loop voltage of ~40V m=1/n=4 mode behaviour:  Slow rotation and periodic growth in current rise phase  Rapid rotation in flat-topped phase

14. Behavior of m=1/n=4 mode in shallow reversal case:  Moderate rotation throughout the discharge  Quasi-periodic growth  Lower N s than deep reversal case 60kA shallow-reversal discharge with Vloop ~ 50V – comparison of MHD with deep reversal case –

15. A 100-kA discharge with loop voltage of ~30V m=1/n=4 mode behaviour:  Slow rotation and periodic growth in current-rise phase  Slow rotation and growth with shorter periods

16. Summary In shallow-reversal discharges with high I p, quasi-periodic growth of a single helical mode has been observed. The toroidal mode spectrum near the maximum amplitude looks like QSH state. A simple helical structure observed with fast camera may be an indication of simple MHD dynamics in RELAX.  next presentation by Ohchi Bispectral analysis has shown that nonlinear coupling of m=1 tearing modes in RELAX is not so strong as in other RFPs with higher A. One of the possible reasons is relatively large separation of mode rational surfaces in low-A RELAX. More comparative studies are required. Bootstrap current fraction in the present RELAX plasmas is lower than 5%. Improvement of  p to ~30% will result in bootstrap current fraction of ~25%, which may be detectable. A large-scale change in magnetic field profiles observed in self-reversal discharges may be an indication of rotating Helical Ohmic Equilibrium state. Discharge resistance has been reduced dramatically in upgraded RELAX machine. Further discharge optimization is in progress.

17. Simple filament structure observed with fast camera Filament structure indicates simple structure of plasma parameters → effect of low A? t Simulated helix with m=1/n=4 (80,000 frames/s) Nonresonant modes