Flow damping due to stochastization of the magnetic field

ARTICLE Received 9 Jun 2014 | Accepted 11 Nov 2014 | Published 8 Jan 2015 DOI: 10.1038/ncomms6816 OPEN Flow damping due to stochastization of the magnetic field K. Ida1, M. Yoshinuma1, H. Tsuchiya1, T. Kobayashi1, C. Suzuki1, M. Yokoyama1, A. Shimizu1, K. Nagaoka1, S. Inagaki2, K. Itoh1 & the LHD Experiment Group* The driving and damping mechanism of plasma flow is an important issue because flow shear has a significant impact on turbulence in a plasma, which determines the transport in the magnetized plasma. Here we report clear evidence of the flow damping due to stochastization of the magnetic field. Abrupt damping of the toroidal flow associated with a transition from a nested magnetic flux surface to a stochastic magnetic field is observed when the magnetic shear at the rational surface decreases to 0.5 in the large helical device. This flow damping and resulting profile flattening are much stronger than expected from the Rechester–Rosenbluth model. The toroidal flow shear shows a linear decay, while the ion temperature gradient shows an exponential decay. This observation suggests that the flow damping is due to the change in the non-diffusive term of momentum transport. 1 National Institute for Fusion Science, Toki, Gifu 509-5292, Japan. 2 Research Institute for Applied Mechanics, Kyushu University, Kasuga 816-8580, Japan. Correspondence and requests for materials should be addressed to K.I. (email: ). *List of participants and their affiliations appear at the end of the paper. NATURE COMMUNICATIONS | 6:5816 | DOI: 10.1038/ncomms6816 | www.nature.com/naturecommunications & 2015 Macmillan Publishers Limited. All rights reserved. 1 ARTICLE S Vφ (km s–1) 100 Observation of flow damping. Figure 1 shows the time evolution of toroidal flow, angular momentum, rotational transform, magnetic shear, and inverse of the electron and ion thermal diffusivity in the discharge, where the direction of the NB injection (NBI) is switched from co-injection to counter-injection (parallel to anti-parallel to the equivalent plasma current, which gives the poloidal field produced by the external coil current) at t ¼ 5.3 s. The vacuum magnetic axis is 3.6 m and the magnetic field strength is 2.75 T. The edge rotational transform decreases due to the NB current drive (NBCD) and the central rotational transform increases due to the inductive current; the magnetic shear at the i/2p ¼ 0.5 rational surface starts to decrease and reaches the steady-state value of 0.5 at t ¼ 5.8 s after the switch of the NBI. This decrease of magnetic shear increases the magnetic island width and finally causes stochastization due to the overlapping of magnetic islands with higher modes9,10. The toroidal flow velocity changes its sign from positive (co-rotation) to negative (counter-rotation) and becomes steady state at a central 2 6 Nested 6.25 s 6.73 s 6 Stochastic 4 region Magnetic 4 island 2 2 2 0 0 0 50 0.5 reff /a99 1 0 0 1 0 0.5 reff /a99 1 0.5 reff/a99 0 reff /a99 =0.25 M (N ms) –50 Stochastization reff /a99 =0 0.01 reff /a99<0.5 0.00 –0.01 Stochastization 0.69 0.57 0.5 0.47 0.31 0.0 reff /a99 Stochastization 1.0 S Stochastization 0.5 Counter-NBI Counter-NBI 1/e 1/i (m–2 s) Results Experimental set-up. The large helical device (LHD) is a heliotron-type device for magnetic confinement of high-temperature plasmas. The LHD has three tangential neutral beams (NBs); two beams are used to change the direction of the plasma current from parallel (co-injection) to anti-parallel (counter-injection) with respect to the equivalent plasma current. The toroidal flow and ion temperature are measured with charge exchange spectroscopy7, while the rotational transform, i/2p, and magnetic shear, s[ ¼ (r/i)qi/qr], at the rational surface (i/2p ¼ 0.5) are measured with motional stark effect spectroscopy (MSE)8 in the LHD. There are three kinds of topology of the magnetic field in the plasma: the first is nested magnetic flux surfaces, the second is a stochastic magnetic field and the third is a magnetic island. The magnetic topology is identified by the characteristics of heat pulse propagation produced by modulated electron cyclotron heating (MECH), measured with electron cyclotron emission9. In the nested magnetic flux surfaces, the heat pulse propagates outwards on the time scale of the heat transport. In contrast, the heat pulse propagation becomes very fast due to the propagation along the magnetic field line in the stochastic region in the plasma. 5.75 s 6 4 reff /a99 =0.5 /(2) tochastization of the magnetic flux surface is expected to be induced when the magnetic islands are overlapped and their width exceeds a threshold in toroidal plasmas. Stochastization of magnetic surfaces has been considered to be important because this mechanism, caused by perturbation fields, has a strong impact on transport and MHD events, such as a major disruption or an edge localized mode crash. The role of stochasticity in electron and ion heat transport has been studied in reverse field pinch (RFP) plasmas (in a reversed field experiment (RFX)1,2 and in the Madison Symmetric Torus (MST)3–5), where magnetic islands overlap and field lines are stochastic. In general, good agreement between the electron thermal diffusivity estimated from power balance and the analytic predictions of the Rechester–Rosenbluth model6 has been reported. However, the role of stochastization of the magnetic field in plasma flow has not been discussed before, in spite of the importance of flow shear in the turbulence in plasma, which determines the transport in toroidal magnetized plasmas, such as in tokamak, helical and RFP plasmas. Here we demonstrate that stochastization of the magnetic field occurs when the magnetic shear at the rational surface decreases in a plasma and the damping of toroidal flow due to the stochastization is stronger than expected by the Rechester– Rosenbluth model. Delay time (ms) NATURE COMMUNICATIONS | DOI: 10.1038/ncomms6816 0.0 Co-NBL 0.10 0.01 i 10 e 102 5.0 5.5 6.0 Time (s) 6.5 7.0 Figure 1 | Time evolution of flow velocity and other plasma parameters. Time evolution of (a) toroidal flow velocity, Vf, (b) angular momentum in the core (reff/a99o1/2), (c) rotational transform, i/2p, (d) magnetic shear, s, at the rational surface (i/2p ¼ 0.5), and (e) inverse of the electron and ion thermal diffusivity, 1/we, 1/wi, at reff/a99 ¼ 0.35 in the discharge where the direction of neutral beam injection (NBI) is switched from co- to counter-injection. Radial profiles of delay time of heat pulse produced by modulated electron cyclotron heating (MECH) at three time slices (t ¼ 5.45, 6.02, 6.72 s) are also plotted. The error bars of the delay times are standard deviations. The error bars of toroidal rotation are derived from the uncertainty of the fitting parameter of the charge exchange line emission to a Gaussian profile. The error bars of rotational transform and magnetic shear are derived from the standard devia (...truncated)