M. NAGATA et al. [Left hand page running head is author’s name in Times New Roman 8 point bold capitals, centred. For more than two authors, write

AUTHOR et al.]

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EXPERIMENTAL STUDIES OF PLASMOID RECONNECTION FOR CLOSED FLUX CURRENT GENERATED BY COAXIAL HELICITY INJECTION ON HIST

M. NAGATA, A. FUJITA, Y. IBARAKI, Y. KIKUCHI and N. FUKUMOTO

Graduate School of Engineering, University of Hyogo Himeji, Hyogo 671-2280, Japan Email of corresponding author: nagata@eng.u-hyogo.ac.jp T. KANKI Japan Coast Guard Academy Kure, Hiroshima 737-8512, Japan

Abstract

Plasmoid reconnection for the flux closure has been demonstrated by transient-coaxial helicity injection (T-CHI) in the Helicity Injected Spherical Torus (HIST) device. The intensive measurement of internal magnetic structures indicates that two or three plasmoids are generated in an elongated Sweet-Parker current sheet during the T-CHI. Here, we report that in the T-CHI start-up plasmas, (i) the observed regular oscillations of magnetic field, electron density and ion flow indicate repetitive generation of small-size plasmoids due to the magnetic reconnection, (ii) one of plasmoids grows up to a large-size, and a doublet-type ST configurations is formed as a result. Consequently, the plasmoid reconnection could be the leading mechanism for the formation of multiple X-point, i.e., the fast flux closure in the T-CHI discharge. From the comparison of CHI discharges with H2 and He gas, we have found that doublet-type closed flux surfaces have been more easily formed in the He discharge due to the slower reconnection speed.

1. INTRODUCTION

The Spherical Tokamak (ST) is a leading candidate for an advanced fusion reactor due to its compact size. If the central solenoid coil could be eliminated, the ST design would be allowed access to lower aspect ratio configurations. The CHI-based non-inductive plasma current drive method is necessary for the viability of the ST concept without the central solenoid coil. Transient CHI (T-CHI) is one of CHI schemes, and it is used to generate and ramp-up the plasma current at the initial phase of a discharge. The T-CHI method has been successfully applied to NSTX for the start-up followed by inductive ramp-up [1]. Recently, the T-CHI with a new CHI electrode configuration has been successfully demonstrated on QUEST at Kyushu University [2]. One of the most important issues in T-CHI is whether it can establish a plasma current sufficient for succeeding current drive and heating. In order to generate the sufficient closed plasma current, the fast magnetic reconnection at the X-point is required in the short CHI start-up time. Understanding the fast reconnection mechanism for the flux closure is the primary purpose of the T-CHI experiment on HIST [3].

It is well known that the Sweet-Parker (S-P) steady-state reconnection model [4], which is characterized by the long current sheet, cannot account for fast events with the high Lundquist number S such as the solar corona and sawtooth crashes in tokamaks. A similar difficulty appears for the T-CHI plasma with the high S in the presence of the high toroidal (guide) field in achieving the closed flux formation within a start-up period. As a result from lots of theoretical and computational studies within the resistive MHD mode framework, it has been recognized that the plasmoid instability [5] realizes a reconnection rate larger than the S-P rate as well as mechanism based on Hall effects and electromagnetic turbulence. The recent MHD simulation on T-CHI predicts the formation and breakup of an elongated S-P current sheet and a transition to plasmoid-driven reconnection during T-CHI [6]. According to this simulation, the reconnection rate based on the plasmoid instability is faster than that by the S-P model and becomes nearly independent of the Lundquist number S. However, the multiple small-scale plasmoids have not experimentally identified in any fusion devices. In this experiment, we have found two or three plasmoids in the elongated current sheet which is very similar to that demonstrated in the MHD simulation. In this paper, we report the details of plasmoid reconnection observed during the T-CHI by the internal magnetic field measurements to form the single or doublet-type ST magnetic configuration.

2. EXPERIMENTAL SETUP

2.1. HIST device

IAEA-CN-123/45 [Right hand page running head is the paper number in Times New Roman 8 point bold capitals, centred]

FIG. 1 Schematic diagram of the HIST device and internal diagnostics.

FIG.2 Time evolution of the derivative of axial magnetic field dBz/dt (a), the electron density ne (b), the ion flow Vr, V, and Vz (c) in an H2 discharge.

The HIST device (major radius R = 0.3 m, minor radius a = 0.24 m, aspect ratio A = 1.25), shown in Fig. 1, produces the ST plasmas (high-q: q > 1 and low-q including spheromaks: q < 1) and is characterized by utilizing the variation of the external toroidal field (TF) coil current Itf = 0~219 kA. The TF coil current ITF = 160 kA produces the vacuum toroidal field Bt.v = 0.13 T at R = 0.25 m. Details of the HIST are provided in the reference [7]. The T-CHI capacitor bank for start-up discharges has a maximum charging voltage of Vmax =10 kV and a capacitance of C = 2.9 mF. The bias magnetic flux (bias < 2.5 mWb) is applied by the bias solenoid coils installed in the outer electrode. The peak gun current is about 75 kA with a charging voltage of 5 kV. The discharge is consisted of three phases; injection phase, partially and fully decaying phase. The plasma starts to decay due to its resistivity from t = 0.25 ms. The maximum toroidal current driven by T-CHI is about 40-120 kA and lasts for 0.4 ms.

2.2. Diagnostics

The toroidal plasma current It is measured by a 16-channel surface poloidal pick-up coils. The electron temperature and density are measured by two double electrostatic probes. For one of them, a probe current is measured by applying a triangular sweep voltage of up to 32 V with a maximum frequency of 100 kHz. The radial profile of the Doppler ion temperature Ti.D has been measured by Ion Doppler Spectrometer (IDS). To study internal magnetic field structures of T-CHI produced plasmas, we use a set of 2D magnetic probe arrays which is comprised of 85 x Bz and 85 x Bt pick-up coils with ΔR = 0.02 m or 0.05 m and ΔZ = 0.148m or 0.074 m on the R-Z poloidal plane, as shown in Fig.1. Here, Bz and Bt are the axial and toroidal (azimuthal) components of the magnetic fields, respectively. Then we can obtain the poloidal flux p contours by assuming axisymmetric magnetic configurations. Also, we have calculated 2D profile of the toroidal current density (current sheet) jt by the equation of Ampere’s law (Br/Z-Bz/R)/0, where Br=–(1/2R) p/Z.

3. EXPERIMENTAL RESULTS

3.1. Plasmoid reconnection dynamics

Figure 2 shows the time evolution of the derivative of poloidal magnetic field dBz/dt measured at each radial location on the midplane (Z=0 m) in the flux conserver (FC), the electron density ne, and the ion flows (Vr, V, and Vz) measured by Mach probe at R=0.35 m and Z=0 m. The regular fluctuations with the frequency of 165 kHz can be seen in all signals between t=0.178-0.22 ms and between R=0.3-0.4 m. The electron density ne =2-3x1019 m-3 is measured at R=0.35 m and Z=0 m The density fluctuation δne~1x1019 m-3 is well correlated with the Bz fluctuation. These observations obtained in H2 discharges indicate that a small-size plasmoid is repeatedly generated by the reconnection and moves toward the right side (-Z direction) as the out flow. The velocity of the accelerated plasmoid in an oscillation cycle is δVz=3-5 km/s that superposed on the background poloidal flow.

M. NAGATA et al. [Left hand page running head is author’s name in Times New Roman 8 point bold capitals, centred. For more than two authors, write

AUTHOR et al.]

3

FIG.3 Time evolution of the derivative of axial magnetic field dBz/dt (a), the electron density ne (b), the ion flow Vr, V, and Vz (c).

FIG.5 p contours in He discharges. Three small-scale plasmoids can be seen at t=0.16 ms (b). Doublet type closed flux surfaces are formed at t=0.19 ms (c)

FIG.4 Comparison of the toroidal current density Jt and the poloidal flux p contours between H2 (a) and He discharge (b).

Figure 3 shows the oppositely directed poloidal fields measured at R=0.3 m and R=0.35 m which together to be reconnected show the oscillating waveform with an out-phase that synchronizes with the fluctuations of density δne and the out flow δVz. Reconnection electric field Et.rec calculated by dp

/dt, where p is the reconnecting poloidal flux, shows small-size plasmoid dynamics. The plasmoid behaviour is almost axisymmetric manner on the background n=1 dynamo current drive. Et.rec < 0 indicates the merging of two plasmoids and then Et.rec > 0 a separation of the merged plasmoid.

3.2. Comparison between H2 and He discharges

Figure 4 shows comparison of the Jt contours plotted on the p contours between H2 and He discharges under the high toroidal field of ITF=160 kA. The current path in the H2 discharge surrounds widely around the reconnection point on the mid-plane during the current rise phase. The reconnection occurs as the reconnection current sheet length L increases and the current sheet full width becomes enough thin. The two or three plasmoids (islands) are generated as the reconnection occurs in the elongated current sheet. The is estimated to be < 5 cm from the Jt contour plot. The small-size plasmoids grow up to the large closed flux volume during the decay phase.

IAEA-CN-123/45 [Right hand page running head is the paper number in Times New Roman 8 point bold capitals, centred]

FIG.6 Comparison between H2 and He discharges of toroidal current It (a), total poloidal magnetic energy Wm.pol (b), self-generated toroidal energy Wm.tor (c),p contours with the toroidal electric field Et color contours at t=0.15 ms (d) and t=0.168 ms (e).

Figure 5 shows the poloidal flux p contours of a He discharge in the whole FC region. It can be seen that two or three small-size plasmoids (R with a radial width <0.1 m) are generated during the rise phase of It as well as in H2 discharges. The reconnection speed in the He discharge is relatively slower compared to the H2 discharge so that the oscillation is not observed. As the reconnection proceeds, the plasmoid with the closed current in the right side grows up, leading to a double-type configuration as shown by Fig.5 (c).

Figure 6 shows that the time evolution of the poloidal and self-generated toroidal magnetic energy Wm.pol, Wm.tor and the toroidal electric field Et=-dp/dt contours around the X-point. The toroidal current It and the poloidal magnetic energy Wm.pol in the He discharge remain much lower than those in the H2 discharge, butWm.tor increases rapidly after t=0.17 ms. This indicates that the poloidal current flowing in the open flux region is transported to the two closed flux columns and the reconnection proceeds in the current decaying phase. The radial flow driven by ExB~EtxBz drift is directed toward the X point (see Fig. 6 (d)) and then the reconnection continues to occur slowly by t=0.19 ms, resulting in the formation of two large-scale plasmoids (see Fig, 5 (c)). These results indicate that the detailed process in H2 and He discharges are quite different even though the existence of plasmoids are the same.

4. SUMMARYS

The fast reconnection driven by plasmoids for the flux closure has been demonstrated by T-CHI in the HIST device. The intensive measurement of internal magnetic structures indicates that two or three plasmoids are generated due to the reconnection as an elongated Sweet-Parker current sheet becomes unstable in the tearing mode during the T-CHI. The experimental findings are as follows; (1) The observation of the regular oscillations of Bz, ne and Vz in the elongated current sheet provides a strong evidence of the plasmoid reconnection. (2) In the He discharges, the two discrete closed flux surfaces have been established after the mini-plasmoid develops to the large-size plasmoid by the ongoing reconnection with a slower rate as compared to H2 discharges. Consequently, the plasmoid reconnection could be the leading mechanism for the formation of multiple X-point, i.e., the fast flux closure in the T-CHI discharge on HIST.

REFERENCES

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[2] Kuroda, K et al., Plasma Fusion Research RC, 12, (2016) 1202020.

[3] Nagata, M, et al., the 26th IAEA-Fusion Energy Conference, Kyoto, EX/P5-21, (2016).

[4] Parker, E. N., J. Geophys. Res. 62, (1957) 509.

[5] Loureiro, N. F. et al., Phys. Plasmas, 14, (2007) 100703.

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[7] Nagata, M., et al., Phys. Plasmas 10, (2003) 2932.