Global ion heating/transport during merging spherical tokamak formation

Here we report global ion heating/transport characteristics of magnetic reconnection during merging spherical tokamak formation experiment on TS-6 (TS-3U). Using the 96CH/320CH ultra high resolution ion Doppler tomography diagnostics, the full-2D imaging measurement clearly revealed that magnetic reconnection initially forms localized hot spots in the downstream region of outflow jet with inboard/outboard asymmetry (more deposition in the high field side) but the continuous accumulation of the heating coupled with transport process expands the high temperature region globally and forms characteristic poloidally ring-like structure aligned with field lines. The dynamic ion heating/transport process is also affected by the polarity of toroidal field and poloidally tilted/rotating global structure has experimentally been found both during and after merging. The characteristic poloidal asymmetry gets flipped when toroidal field direction is reversed and it was found that higher temperature appears in the positive potential side, which is opposite to the conventional understanding/prediction of guide field reconnection. Through the parallel acceleration process coupled with global heat transport, poloidally asymmetric non-classical feature has experimentally been found for the first time.


INTRODUCTION
Central solenoid (CS)-free plasma startup is a critical issue in spherical tokamak (ST) research because of the limited amount of solenoid flux due to the small space for the centre conductor [1].ST fusion reactors could potentially support high beta plasma performance which is preferable for commercial plants [2]; however the low aspect ratio (A < 2) machine structure sacrifices the space for the centre stuck, saving the solenoid flux consumption during plasma startup is a crucial problem for practical plasma scenarios for spherical tokamak [3].In the last 3 decades of ST research, various CS-free plasma startup scenarios were proposed such as merging compression (MC) [4], local helicity injection (LHI) [5], electron Bernstein wave (EBW) plasma startup [6] and so on.The former two explores high beta records [7,8,9] and H-mode performance [10] in mega ampere (MA) scale experiments [1,4,11], while the latter explores long pulse steady scenario which has longer duration time than 100ms [1,3].In addition to the initial current formation method, merging plasma startup scheme is known that it also enables the advantage of impulsive MW-GW scale plasma heating during plasma formation through magnetic reconnection process [12].
Magnetic reconnection is a fundamental process which brakes/reconnects magnetic field line configuration and accelerates/heats plasmas through the self-organization [13,14].This process is known as an efficient way of converting magnetic energy into thermal energy of plasmas in proportion to the square of the amplitude of reconnecting magnetic field component (Ti ∝ Brec 2 ) [15].Magnetic reconnection is observed in many fusion, laboratory and astrophysical plasmas such as sawtooth crashes in tokamaks [16], merging compression of two flux tubes [4,15], geomagnetic substorms in the Earth's magnetosphere and solar flares [13,14,17].In the 1990s, the application of reconnection heating was pioneered in TS-3 and START with MW-GW scale significant ion heating during merging compression [1,4,8,11], MAST achieved 1.2keV plasma formation through this process [18] and ST40 is now trying to explore more upgraded heating performance in 1-10keV [19].In the last three decades, heating physics of plasma merging and magnetic reconnection was investigated in a number of experiments: TS-3 [15], MRX [20], SSX [21], VTF [22], TS-4 [23], UTST (TS-5) [24], C-2U [25], MAST [26], TS-3U (TS-6) [27] and ST40 [28].For those experiments, the following common characteristics have been reported: (i) magnetic reconnection heats ions downstream and electrons around the Xpoint where magnetic field lines reconnect [15]; (ii) ions are heated by the thermalization of flow energy of the reconnection outflow jet [29] while electrons gain energy mostly by resistive dissipation of the current sheet [30]; (iii) most of the heating energy goes to ions, and electron heating is small [31] (ions are heated globally but electron heating is localized around the X-point); and (iv) the achieved maximum reconnection heating rate depends on the amplitude of the reconnecting component of the magnetic field: Brec (Bp for tokamak) [15,30].
In addition to those basic characteristics of reconnection heating, formation of fine structure through magnetic reconnection was reported in MAST [26,32], UTST [33] and TS-6 [27] experiments, satellite observations [34] and PIC simulation [35].When high guide field is applied, localized hot spot of electron heating is observed in a smaller scale than ion skin depth c/pi [26,36] and high Ti region also forms fine structure around X-point as well as downstream [37].Ion-electron decoupling around X-point leads to quadrupole potential structure [38] and poloidally tilted heating structure was also reported when mass ratio is high [27] to enhance ion skin depth and gyro radius.Although MAST experiments provided the finest heating profile as a frontier of reconnection heating physics using high resolution Thomson scattering and ion Doppler tomography [39], further detailed investigation with the information of magnetics was not available in MAST due to the absence of proper magnetic diagnostics to visualizes the double-axis configuration of merging flux tubes during reconnection.To explore the new frontier in reconnection heating, we made further diagnostics upgrade in TS-6: 96CH/320CH ion Doppler tomography [27][40] and ~ 200CH magnetic probes [41] for clearer 2D imaging measurement.Here we report our new finding from the full-2D ultra high-resolution imaging measurement of ion heating/transport process during merging/reconnection startup.

MERGING PLASMA STARTUP SCENARIO OF SPHERICAL TOKAMAK IN TS-6 (TS-3U)
Figure 1 illustrates typical plasma scenario in the TS-6 spherical tokamak.TS-6 has a cylindrical vacuum vessel (0.75m × 1.44m), centre stuck with m (slim-CS (30 turns × 2) and TF coil (12 rods)), two pairs of poloidal field (PF1 (4 turns) and PF2 (3 turns)) coils inside the chamber and a couple of equilibrium field coils (EF: 234 turns) at the top and bottom of the device as shown in Fig. 1 (a).PF coils are connected with 40kV capacitor banks (C = 18.75F) and the power supplies starts to discharge from t = 0s as shown in [27,37] (In this paper, only a pair of PF2 was used to drive merging compression to demonstrate MAST/ST40-like scenario [4][28]).Initial plasma rings are formed by the induction of PF2 and the formed plasma rings are pushed toward midplane by the negative half swing of the LC discharge current (T ~ 100s) of PF2 and vertical field supplied by the EF coils (0.15kA/turn).When both upper and lower PF coils are used, two plasma rings are formed and merge together around midplane (assisted by the drag force from coaxial plasma current and the compression force from PF and EF coils); while if only one of the PF2 (lower or upper) is used, CT injection-like single plasma ring is formed at the top or the bottom of the vacuum vessel and is pushed toward midplane as the captured visible light images in Fig. 1 (b).Hydrogen gas is used as a bulk gas species and the characteristic red color mostly from H radiation is captured in the fast camera images as in START experiment [1].The apparent visible image at t = 250s is similar in both merging and CT injection-like (without merging) startup scenarios but the former one has an advantage to have higher ion temperature through magnetic reconnection heating.Time evolution of single code ion temperature is measured on midplane using a high speed ion Doppler spectroscopy system with image intensified CMOS fast camera (Photron/SA-Z: operated in 100kfps with Invisible Vision/UVi P46 intensifier) in Fig. 1(c).Ion thermal energy increases during reconnection with the rate of ~ 10MW/m 3 and then connected to confinement phase after merging.

FIG. 1. Time evolution of high speed camera images and line-average ion temperature during plasma startup in the TS-6 (TS-3U) spherical tokamak. Initial plasma rings at t = 50s are formed by the induction of PF coils as a central solenoid free plasma startup scheme. By forming a pair of initial plasma rings at the top and bottom of the device and then pushing
then toward midplane, plasma merging occurs and ion temperature increases through magnetic reconnection process.
Figure 2 shows the time evolution of 1D and 2D ion temperature profile during the merging plasma startup with contour lines of poloidal flux when Bt ~ 0.15T and Brec ~ 0.03T (Bt/Brec ~ 5).Through the outflow heating mechanism as illustrated in the model in Fig. 2 (a) [15,29], ion temperature typically increases in the downstream region of outflow jet through the dissipation of flow energy to form radially double-peak structure as shown in the 1D plot of ion temperature profile in Fig. 2 (b).In the merging startup geometry, the X-point of magnetic reconnection is located around the midplane as the reference poloidal flux profiles in Fig. 2 (c) and the double axes configuration changes to a single axis one through reconnection process.Time evolution of ion temperature profile around midplane is visualized by 2D ion Doppler tomography (Fig. 2 (d)) [27,42,43].At t = 65s before merging, ion temperature is smaller than 10eV (upstream Ti is also smaller than 10eV as shown in Fig. 1 (c)) around the X-point, then it starts to increase through reconnection heating process.Ion heating starts initially around the diffusion region where magnetic field lines reconnect [37], then the high temperature region propagate radially to form hot spots in the downstream region, and finally characteristic double-peak [15] structure appears after merging to form poloidally hollow which is aligned with the closed flux surface.
Although the characteristic double-peak profile has large ion temperature gradient in the order of ∇Ti ~ 1keV/m at maximum which radially crosses the flux surface, ion heat flux q = - i //∇//Ti - i ⊥∇⊥Ti +  i ⋀(B/|B|) × ∇Ti mostly propagates toward field line direction because the ratio of ion heat conductivity satisfies  i /// i ⊥ ~ 2(ciii) 2 >> 1 and  i /// i ⋀ ~ 0.8ciii >> 1 (especially,  i /// i ⊥ > 1000 in the high field side).As shown in the time evolution of ion temperature profiles, the double-peak structure lasts much longer time scale than merging time in the order of 10 ~ 20s [26,27,32], field-aligned structure becomes clearer in the quasi-steady/confinement phase after merging. 2 >> 1 and the merging startup spherical tokamak sustains the characteristic hollow ion temperature profile after the end of merging.

Full-2D visualization of ion temperature profile during magnetic reconnection
The formation of double-peak/hollow Ti profile itself as in Fig. 2 has been published in many previous papers [15,44] and MAST merging experiment demonstrates its sustainment in millisecond time scale with much higher toroidal guide field Bt > 0.3T [26,39].The relaxation process itself toward hollow flux function is not surprising and here we present more dynamic/complicated heating/transport process during the merging time frames.As reported in [27], the new experiment TS-6 enables flexible diagnostics access for full-2D imaging measurement both for in-situ probes [41] and optical diagnostics [40].Figure 3 shows the highlight of experimentally measured full-2D (r-z) ion temperature profile during plasma merging (Brec ~ 0.02T and Bt ~ 0.1T): (1) reconnection heating/transport model, (2) measured 2D ion temperature profile Ti in 3 major time frames at t = 65s, 75s and 85s (before/during/after merging) with poloidal flux contour lines and (3) 1D vertical profile of radially averaged Ti in 0.10m < r < 0.14m at each z position.At the beginning of reconnection (t = 65s), initial upstream plasmas simply have peaked Ti profile around their magnetic axes; however, magnetic reconnection changes the profile to have hot spots in the outflow region: radially inside (r ~ 0.12m) and outside (r ~ 0.26m) of X-point (RX-point ~ 0.2m).Accumulation of outflow heating continues to increase Ti and the hot spot at r ~ 0.12m grows upto Ti ~ 60eV at t = 80s as shown in the 1D vertical profile in Fig. 3 (right).After merging at t = 85s, the peak Ti starts to be decreased but its thermal energy is transported toward vertical direction and the high temperature region gradually surrounds the closed flux surface to form poloidally ring-like structure as summarized in the schematic model in Fig. 3. Before our full-2D visualization, it was blankly believed that this process completes in microsecond time scale and results from 1D measurement on midplane could be used for full-volume integrated analysis just by simply assuming that Ti immediately becomes flux function without validation [15,30,44].However, our visualization clearly revealed that completion of poloidally symmetric structure formation needs much more delay time as shown in Fig. 2 and 3.Even if the localized hot spot was equilibrated in the order of ion thermal speed v i th ~ 100km/s = 0.1m/s and the equilibration propagates 0.5m in 5s, the contribution of high guide field and toroidal effect extend the actual heat transport paths: the ratio of toroidal/poloidal magnetic field 4 < Bt/Bp < 5 leads to longer orbit including 2rr~0.12m.Then parallel heat conduction propagates less than 0.1m in 5s on the poloidal plane in the high field side and the finite delay time of dynamic 2D heat transport on poloidal plane is clearly detected for the first time in the history of fusion research in the new experiment on TS-3U.

Poloidally asymmetric global structure formation
The result from Fig. 3, the visualization of full-2D imaging of Ti and heat transport on poloidal plane from the impulsively formed hot spots in experiment, is an important milestone to establish the first full-2D imaging without the assumption of poloidal symmetry but the nature of the heat transport process itself is not necessarily surprising from the knowledge of classical characteristic as in the schematic model in Fig. 3 (left).More advanced notable characteristics have experimentally been found by changing the polarity of toroidal magnetic field: poloidally asymmetric global structure formation by reconnection heating/transport.Figure 4 shows the 5 comparison of ion temperature profile at t = 75s and 85s when the polarity of toroidal field is flipped (Bt ~ ± 0.1T).The heating/transport structure completely reversed by changing the polarity of toroidal guide field Bt.
FIG. 4. Poloidally asymmetric global structure formation through heating/transport process of merging/reconnection. Globally rotating characteristic ion temperature profile is formed dependently on the polarity of toroidal guide field

CHARACTERIZATION/INTERPRETATION OF THE POLOIDALLY ASYMMETRIC STRUCTURE
The formation of poloidally asymmetric structure is one of trends/frontiers in reconnection studies.In the last 5 years, the formation mechanism of the poloidally asymmetric structure is mostly discussed from the view of Hall-effect.Ion-electron decoupling around the X-point makes quadrupole potential profile [44] and this process was discussed in many papers with two-fluid approaches and particle in cell (PIC) simulations [45,46,47].
Effective broadening of the in-plane (r-z) component of velocity distribution in PIC simulation shows that apparent ion temperature increases through the potential drop and higher temperature appears in lower potential region of quadrupole potential structure in the collision-less regime [45].However in Fig. 4, the measured heating structure has opposite polarity with the expected one: higher potential side has higher temperature than lower potential region.
To characterize the measured asymmetry, here we discuss the possible sources of particle acceleration and heating: (i) in-plane electric field formed by Hall-effect, (ii) major bulk flow component: E×B drift, and (iii) parallel acceleration by field-aligned electric field E// using Fig. 5.In the experimental geometry, there are toroidal and poloidal electric field Et and Ep.In the first scenario, in-plane electric field could form poloidally tilted structure, but this static acceleration scenario does not explain the measured ion temperature profile.The direct acceleration by this in-plane electric field should form high temperature region in the lower potential region but measured ion temperature is higher in the higher potential region.In the small machine TS-6, the scale effect enhances poloidal electric field in kV/m range, but this electric field works mostly for E×B drift and most of ions just pass through on same potential levels and effective energy gain could not be simply explained by the potential drop.About inboard-outboard asymmetry, E×B drift distribution partially explains the difference as a second scenario: more deposition in the high field side, while convective transport and poloidal rotation after merging are negligibly small (less than 10km/s).The third scenario is one of the most possible one to make the characteristic distribution: acceleration by parallel electric field, especially the contribution of the parallel component of inductive toroidal electric field Et.Here the parallel electric field is calculated as E// = E• B/|B| = (EtBt + EpBp)/|B| = (ErBr + EtBt + EzBz)/|B|.On the experimental condition with positive poloidal flux, the increment of poloidal flux around the X-point spontaneously/inductively forms negative toroidal electric field.
In the toroidal merging geometry, the global parallel electric field at t = 68s accelerates ions toward -B/|B| direction.When toroidal field is negative, this negative parallel electric field accelerates ions as follows: -z direction in the high field side and + z direction in the low field side: same polarity with the detected global ion temperature profile.In the experimental condition with ii < 5s, potentially ions could be accelerated to vi 5s = qE///mp t (1s) < 250km/s, but ions are also affected by E×B drift and pass through the acceleration region quickly (~30km/s = 0.03m/s) and ion temperature increment in tens of eV is a reasonable energy gain through this process.After merging, both parallel electric field and ExB become negligibly small and confinement/ transport process starts to equilibrate the poloidally asymmetric ion temperature profile.Poloidal rotation speed is negligibly small (< 10km/s) and the equilibration process is mostly driven by ion heat flux q.Although perpendicular heat conduction is negligibly small, the third term is not negligibly small in low field side (1 <  i /// i ⋀ < 10) and the profile equilibration proceeds with poloidally gyrating global asymmetry as shown in Fig. 4.

SUMMARY AND CONCLUSION
In this study, global ion heating/transport process of magnetic reconnection during merging plasma startup of spherical tokamak has been investigated using our ultra-high 2D imaging diagnostics such as 96CH/ 320CH ion Doppler tomography in TS-3U (TS-6).In MAST/ST40-like high guide field merging/reconnection experiment, it was found that (i) magnetic reconnection heats ions globally downstream of outflow jet and forms a hollow temperature profile with inboard/outboard asymmetry to have higher temperature in the high field side, (ii) perpendicular heat conduction is strongly suppressed by guide field and becomes negligibly small to enable the connection to quasi-steady sustainment of double-peak profile after merging, (iii) full-2D imaging measurement clearly reveals that downstream ion heating forms poloidally ring-like global structure surrounding the merging flux tubes and (iv) the global heating profile forms poloidally asymmetric structure.The poloidally asymmetric structure depends on the polarity of toroidal guide field and the characteristic structure gets flipped when TF coil current is reversed.This poloidal asymmetry could not be simply explained by Hall-effect and the quadrupole potential structure of guide field reconnection and it was found that higher potential region has higher temperature.The opposite polarity effect of ion heating is originated from the contribution of parallel electric field and the combination of inductive/reconnection electric field with in-plane electric field toward field line direction makes the toroidal field dependent global heating structure.Maximum ion temperature is typically observed in the high field side by higher deposition of heating source and its accumulation through slower parallel heat transport characteristic by toroidal effect in the high field side.Microsecond time scale heat transport from the impulsively formed hot spots has clearly been visualized using our advanced imaging diagnostics and detailed heating/transport characteristic of merging spherical formation has successfully been revealed.

FIG. 3 .
FIG. 3. Time evolution of full-2D ion temperature profile during magnetic reconnection with Brec ~ 0.02T and Bt ~ 0.1T.Through the merging process, initially peaked ion temperature profile on magnetic axes of two plasma rings at r ~ 0.2m are converted to hollow one to have high temperature region around r ~ 0.12m and r ~ 0.27m by outflow heating mechanism of magnetic reconnection.The impulsively formed localized hot spots in the outflow region is then transported mostly on the field line direction to equilibrate the profile on the flux surface as shown in the 1D time evolution of Ti at r ~ 0.12m.

FIG. 5 .
FIG. 5. Confirmation of the origin of the poloidally asymmetric heating structure formation.(i) quadrupole potential profile and the in-plane static electric field does not explain the measured heating structure.(ii) distribution of E×B drift velocityprofile partially explains inboard/outboard asymmetry, but global gyration is not explained.(iii) Parallel acceleration, which includes the contribution of inductive toroidal electric field, explains the measured poloidally asymmetric structure.