Ion heating characteristics of merging spherical tokamak plasmas for burning high-beta plasma formation

High-power ion heating of merging spherical tokamak (ST) plasma has been investigated using TS-3U, TS-4, and UTST at the University of Tokyo for future direct access to burning high-beta ST plasma without using any additional heating. We developed a two-fluid/kinetic interpretation of the promising scaling of ion heating energy that increases with the square of reconnecting magnetic field B rec ∼ poloidal magnetic field B p. We find that reconnection heating creates interesting high-beta ST plasmas with hollow currents and broad/hollow T i profiles. These high-beta ST plasmas often have reversed-shear or absolute minimum-B profiles, depending on their reconnection heating power and q-values.


Introduction
Since 1986, the high-power reconnection (ion) heating of merging toroidal plasmas has been developed at the University of Tokyo using TS-3 and TS-4 spherical tokamak (ST)/spheromak merging experiments [1][2][3][4][5][6].We found, for the first time, that the reconnection/merging of two spherical torus plasmas significantly heats plasma ions.In 1996, the maximum ion temperatures T i ∼ 250 eV and ∼150 eV were obtained using a reconnecting magnetic field B rec of about 0.05 T for merging spheromaks and merging ST plasmas, respectively [6].The merging ST experiment has also been developed in the START experiment as merging compression, which measures its electron temperature [7,8].We Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
found the B rec 2 -scaling law of reconnection (ion) heating using merging ST plasmas in 2011 [9].This finding leads us to the UK-Japan joint experiment of high magnetic field reconnection heating in MAST, realizing the highest ion temperature T i ∼ 1.2 keV using B rec ∼ 0.15 T [10][11][12][13].It also led us to the development of the reactor-relevant externalcoil merging experiment UTST [11], where two ST formations and mergings were performed using just external PF coils located outside of the vacuum vessel.Recently, PIC simulations started analyzing this reconnection heating physics using the slab model with open outflow and the two merging tokamak models, in agreement with our B rec 2 -scaling of ion heating energy [14][15][16].Cheng et al developed the first analytical kinetic/two-fluid model of reconnection heating [17].The B rec 2 -scaling of the ion heating depends only on the square of the reconnecting magnetic field B rec ∼ poloidal magnetic field B p , but not on the scale size.The series of reconnection heating experiments, simulations, and theory suggest a good possibility to use merging ST for direct access to burning/high-beta ST plasmas, starting with new high-field ST merging experiments TS-6 in the University of Tokyo [18] and UK-Japan collaboration in the ST-40 of Tokamak Energy Inc [19,20].
The main purpose of this paper is to propose merging/reconnection heating as a new type of burning high-beta ST plasma formation primarily using experimental results of ST plasma merging and reconnection.In section 2, we first describe how we can use reconnection heating to start and heat ST plasmas and suggest ST merging operation for direct access to burning plasma.Then, in section 3, we describe three ST merging devices: TS-3U, TS-4, and UTST at the University of Tokyo.In section 4, we explain the mechanism and scaling law of reconnection ion heating in ST merging.In section 5, we describe the high-beta characteristics of ST plasmas formed by the reconnection heating and, finally, conclusions in section 6.

Application methods of reconnection heating to ST startup and heating
As shown in figure 1(a), we merge two ST plasmas in the axial direction, creating an X-point and current sheet at their contacting point.Since the toroidal flux does not reconnect in the merging STs, the magnetic reconnection transforms the private poloidal magnetic fluxes of the two ST plasmas into the common poloidal flux of the new ST plasma.As shown in figure 1(a ′ ), its current sheet tilts due to the Hall current j Hall flowing into the X-point.The high-guide field reconnection drives a bi-directional reconnection outflow, forming two high ion temperature areas in the downstream [9].As depicted in figures 4 and 5, the ST merging spends about half of the poloidal magnetic energy W mp (< toroidal magnetic energy W mt ) on ion heating, realizing 10 MW of ion heating power in the TS-3U ST merging experiment.This ion heating power is large for small-size (major radius: 0.2 m) experiment and is almost comparable to the NBI power of JT-60 tokamak experiment with a major radius of 3 m.We can increase the ion heating power further if we merge two spheromaks with opposing toroidal magnetic field B t , as shown in figure 1(b).This allows us to use about half of the toroidal and poloidal magnetic energy W mp + W mt (W mp ∼ W mt ) for reconnection heating because both poloidal and toroidal magnetic field lines reconnect during the spheromak merging with opposing B t [6].Just like in the conventional reconnection model without a guide field, their X-point area has zero toroidal (guide) magnetic field, as shown in figure 1(b ′ ).In this method, we first produce a field-reversed configuration (FRC) by annihilating the opposing B t of two merging spheromaks and then transform the FRC into a high-beta ST by applying an external B t , as shown in figure 1(b) [1,6].The former method can maintain the merging of toroids more stably than the latter method because ST plasmas have better stability than FRC plasmas especially in the MHD regime [21].However, FRC plasmas have plasma beta roughly about unity, allowing us to produce higher plasma beta of the ST plasmas than the new ST produced by the ST plasma merging.In these methods, reconnection heating enables us to use about half of the reconnecting (poloidal in merging STs) magnetic energy for ion heating within the reconnection time much shorter than the confinement time, increasing the (ion) temperature T, keeping nτ (density times the confinement time) about constant, as shown in figure 2(a).In conventional tokamaks, they utilize ohmic heating power for startup.However, its heating power W OH decreases with (electron) temperature T because the classical (Spitzer) resistivity is proportional to T e −3/2 , as shown in figure 2(b).The alpha heating power W α increases with T but since both W OH and W α are not sufficient in the low keV region, we tend to use additional heating like neutral beam injection (NBI) to bridge the Ohmic heating region to the alpha heating region.In contrast, reconnection heating, whose MHD interpretation is close to the Sweet-Parker model with large anomalous resistivity, has no or very weak temperature dependence, as shown in the red arrow of figure 2(b).The ion heating energy is as high as half of the reconnecting magnetic energy, almost equal to the poloidal magnetic energy.These facts suggest that reconnection heating can transform the produced ST plasma directly into the burning plasma over keV, as shown in figure 2(b).We will check this possibility in figure 4(a).Once we obtain sufficient alpha heating power by ST merging, the alpha-heating power is expected to drive the bootstrap current while maintaining the ST plasma.We also demonstrate intermittent merging operation of ST plasmas in TS-4 for future intermittent reconnection heating [22].

Experimental setups
Figure 3(a) shows the vertical cross-section of the TS-3U ST merging device.The cylindrical vacuum vessel, with a diameter of 0.8 m and axial length 1.2 m, has two poloidal magnetic field (PF) coils for two ST plasma formations [11,18].Their merging speed is controlled by two acceleration coils on both sides of the vessel and by two separation coils at around the midplane.A central toroidal coil with diameter of 0.12 m is inserted along the geometric axis to apply an external toroidal field B t to the merging toroids.A 2D array of magnetic probes is installed on the R-Z plane of the cylindrical vessel to measure 2D profiles of B z and B t magnetic fields.Another 2D array of optical fibers, which are connected to a polychrometer with an ICCD camera, is installed on the surface of the cylindrical vessel to measure the 2D profile of the line-integrated line spectrums [11].The Abel inversion transforms the measured line-integrated spectrums into the 2D profile of local light emission as a function of wavelength for the calculation of the 2D ion temperature T i profile.The 2D electron temperature profile is measured by scanning a 1D electrostatic probe array, but recently by 2D Thomson scattering measurements using multiple reflections of YAG laser light and time of flight of scattered light [23,24].The TS-4 merging device constructed in 2000 has similar cylindrical vacuum vessel and PF coil system, but its size is about 2.5 times larger than that of TS-3U.Two ST plasmas or two spheromaks have major radii of 0.5 m.Figures 3(b) and (c) show photos of TS-3U and TS-4 merging devices after their recent upgrades for high magnetic field experiments, respectively.Figure 3(d) shows the photo of UTST devices.This demonstrates the formation of two STs and merging by external coils outside the vacuum vessel, as shown in figure 3(e).Since fusion reactors do not tolerate any internal coil installation, we developed this reactor-relevant formation called double-null ST formation using UTST.After we obtain 1.2 keV ion temperature just from the reconnection/merging heating in MAST [10], the new high magnetic field merging experiment ST-40 with major radius 0.4 m was constructed at Tokamak Energy Inc. and TS-3 was upgraded to the high field merging experiment TS-3U (TS-6) to solve key physics of reconnection heating using various 2D plasma diagnostics mentioned above.

Mechanism and scaling law of reconnection ion heating
An important question is how the reconnection heating energy, primarily ion heating during ST merging, increases with the reconnecting magnetic field B rec , which is close to the poloidal magnetic field of the two merging ST plasmas.As shown in figures 1(a) and (b), we axially merge two ST plasmas or spheromak plasmas to create a new high-beta ST or the FRC which is transformed into a high-beta ST plasma.We have already found that their heating energy is determined only by the reconnecting magnetic field B rec in both cases.[23,24].We have newly included recent data from TS-3U and TS-4 and their electron densities are controlled within 30% accuracy by the gas filling pressure.All of these experiments roughly agree that the ion temperature increment ∆T i increases with B rec 2 ∼ B p 2 up to 2.3 keV under constant electron density n e ∼ 1.5 × 10 19 m −3 [23,24].As shown in figures 1(a ′ ) and 4(b), our tokamak merging experiments demonstrate high-guide field reconnections whose bulk magnetic Reynolds numbers are much higher than those of conventional laboratory reconnection experiments, but the Xtype current sheet structure does not depend on B rec because the compression of the current sheet to the ion gyroradius increases its local effective resistivity [25].In this scan, the ion gyroradius, determined by B t and T i , stays almost constant.The maximum T i ∼ 2.3 keV was obtained recently in the ST-40 merging experiment with B rec ∼ B p ∼ 0.3 T [23,24].It is noted that we routinely produce keV ST plasmas by merging of two STs with B p ∼ 0.2 T. Those results strongly suggest that we have a good possibility to obtain the reactor-relevant burning ST plasma with T i ∼ 10 keV if we increased B rec ∼ B p over 0.6 T in the future.Our TS-3U experiment found that this scaling is obtained when the current sheet structure is transformed from a simple MHD type current sheet to two-fluid or kinetic type current sheet structures.Figure 4(c) shows R-Z contour of the electrostatic potential, which is measured by scanning a 1D electrostatic probe array.A quadrupole-type electrostatic potential structure is clearly formed around the current sheets of two merging ST plasmas.It is noted that this structure spreads out over the whole merging ST configuration.This twofluid/kinetic energy conversion is not a localized reconnection phenomenon but a global phenomenon.The most probable mechanism is that the reconnection electric field accelerates plasma electrons along the reconnecting magnetic field lines to the downstream.Since electrons move along magnetic field lines much faster than ions, the current sheet always has a radial Hall current j Hall flowing toward the X-point, as shown in figures 1(a ′ ) and 4(b).The current sheet also produces negative and positive potential wells and hills for ion acceleration, as shown in figure 4(b); finally, the ion flow is driven by the electric field provided by the quadrupole electrostatic potential structure.When the current sheet is compressed by external flow, this quadrupole structure appears more clearly and the effective resistivity of the current sheet increases significantly, increasing the reconnection outflow speed to the order of Alfven speed V Alf = B rec / √ µ 0 m i n i of reconnecting (poloidal) magnetic field.Figure 5(b) shows the radial profile of the radial ion flow velocity which is measured by Doppler probes.We observed a bi-directional reconnection outflow ∼40 km s −1 .This sub-Alfvenic outflow with roughly 70% of the poloidal Alfven speed is related to the observed B rec 2 -scaling of the ion heating energy because this flow energy is about half of the reconnecting magnetic field energy.These bi-directional outflows collide with the reconnected field lines, forming two high ion temperature/electron density areas in the downstream.This fast shock-like process and ion viscosity are considered to transform the ion kinetic energy of reconnection outflow into ion thermal energy [9].In the case of merging STs, we found that the reconnection converts about half of the poloidal magnetic energy of the merging ST plasmas mainly to ion thermal/kinetic energy of the new ST plasma.Recently, Cheng et al developed the first analytical model of kinetic/two fluid reconnection heating and suggested that about half of poloidal magnetic energy is converted into ion thermal/kinetic energy [17].Using the Harris sheet without flow and toroidal field, Yamada also explain 50% of magnetic energy flow to ion flow energy [26].
Recent PIC simulations of merging STs and spheromaks at the National Institute of Fusion Science (NIFS) confirmed the quadrupole structure of electrostatic potential wells and hills in the downstream [14][15][16].The current sheet compression to the order of gyroradius turns on micro-instabilities like driftkink mode, increasing the effective resistivity of current sheet [27].Since their geometries are different from our merging tokamak experiments, we need a more detailed comparison to explain our experimental results.However, these works suggest that the large increase in effective resistivity caused by the sheet compression is considered to increase the reconnection speed and the outflow speed, increasing the outflow heating of ions to the amplitude consistent with the B rec 2 -scaling.The PIC simulation results provide our global MHD interpretation of ST merging close to the Sweet-Parker model with anomalous resistivity which is determined by the current sheet compression, not by the electron temperature as mentioned in section 2.

High-beta ST characteristics formed by reconnection heating
The next important question arises as to what type of ST plasma this reconnection heating produces.Figures 5(a)-(d) show the radial profiles of ion temperature T i measured by ion Doppler tomography, radial velocity V r measured by the Doppler probe, electron density n e measured by the electrostatic probe and absolute value of magnetic field |B| measured by magnetic probe array at t = 30 µs (during reconnection) and at t = 40 µs (after merging) in TS-3U ST merging experiment.In figure 5(b), we can confirm the bi-directional reconnection outflow up to V r ∼ 40 km s −1 .These outflows V r are observed to be damped (just like the 'fast shock') at the two downstream positions (R = 0.14 and 0.21 m) where all of T i , n e and |B| peak.
We observed that the broad or hollow profiles of T i and the absolute value of the magnetic field |B| are maintained in the new ST plasmas after the merging is over.We can confirm the hollow T i and |B| profiles at t = 40 µs in figures 5(a) and (d).It is noted that |B| becomes minimum at around magnetic axis.This fact indicates that the high-power reconnection heating produces the absolute minimum-B configuration, when we maximize the reconnection heating power under relatively low-q condition.The 2D contour of ion temperature T i in the 2D PIC simulation reveals the ring-type high T i region in [14,16].This fact suggests that the double peaked T i profile at t = 40 µs in figure 5(a) is a part of the ring-type high T i area.Those experiments and PIC simulations agree that the merging STs are transformed into new high-beta ST plasma with hollow and broad pressure profile.This hollow pressure profile is often equipped with an absolute minimum-B configuration, when we maximize the reconnection heating power.
In the present merging experiments, only TS-3U and TS-4 can measure internal magnetic field profile of the absolute minimum-B configuration, but MAST and ST-40 can measure similar double-peaked or hollow profiles of T i and ion pressure [23,24].
Figure 6(a) shows the 2D contour of the absolute value of the magnetic field |B| of the high-beta ST plasmas produced by type (b) merging in figure 1(b), compared with that of low-beta ST without merging/reconnection heating in figure 6(b).The corresponding poloidal flux contours of highbeta and low-beta ST plasmas are also shown in figures 6(a ′ ) and (b ′ ).The high-beta ST has the wide minimum-B area around the magnetic axis, while the low-beta ST without reconnection heating does not have any B-minimum.It is noted that FRC plasmas have three absolute minimum-B areas because they have null-B points at the magnetic axis and at two geometric axis positions.The high-beta ST has a larger absolute minimum-B area than the FRCs, because its strong toroidal field transforms the inner low magnetic field area of FRC into high magnetic field area.High-beta STs with absolute minimum-B are expected to be stable against all kinds of interchange instabilities, including ballooning modes.
Figure 7 shows radial profiles of the safety factor: q-value and toroidal current density j t of the produced high-beta ST plasma when the reconnection heating is suppressed using slow merging operation in the TS-3U merging experiment.They were measured directly by 2D magnetic probe array in the TS-3U experiment.It is noted that the produced highbeta ST plasma has a hollow current profile as well as a reversed shear profile.These facts indicate that the reconnection heating tends to form a hollow current profile that sustains a broad or hollow thermal pressure profile in the produced high-beta ST plasmas.The broad or hollow pressure is formed because the reconnection outflow heats plasma ions from the peripheral flux surface to the core.The outflow speed becomes maximum in the middle of merging, causing the hollow or broad ion temperature profile of the produced ST plasma.Although we cannot measure the internal magnetic field profiles in MAST or ST-40, we observed similar hollow ion thermal pressure in MAST [23,24] and similar hollow ion temperature profile in ST-40 measured by Doppler spectroscopy.

Conclusions
Three merging experiments at the University of Tokyo have led to the development of high-power reconnection heating techniques using two merging ST and spheromak plasmas.These results confirm the promising B rec 2 -scaling of the ion heating energy under constant density of about n e ∼ 1.5 × 10 −19 m −3 .The reconnection heating converts about the half of the reconnecting magnetic energy into ion thermal/kinetic energy.This fact is consistent with the measured reconnection outflow whose speed is about 70% of poloidal Alfven speed in the TS-3U ST merging experiment.The reconnection outflow is converted in ion thermal energy through ion viscosity and/or fast-shock-line structure in the downstream.The high-power heating is obtained when we compress the current sheet to the order of the ion gyroradius, triggering fast reconnection and fast outflow.Since the conventional Ohmic heating power decreases with temperature (∼T −3/2 ), we conventionally use the additional heating like NBI to turn on the alpha heating.However, reconnection heating with no temperature dependence has a good potential to transform the produced ST plasma directly into the burning plasma without using any additional heating, because the significant ion heating using half of poloidal magnetic energy completes within the reconnection time much shorter than the confinement time.We find interesting characteristics of the high-beta ST plasma produced by the reconnection heating, such as the reversed shear and absolute minimum-B profiles.These high-beta characteristics can be controlled by reconnection heating, but their detailed methods are still under investigation.Since the outflow speed becomes maximum in the middle of reconnection, the produced new ST plasma tends to have hollow and broad ion temperatures T i and thermal pressure profiles, also causing the formation of hollow current.This unique reconnection heating is simple and cost-effective and has sufficient ion heating power to form burning ST plasmas in the alpha-heating region.

Figure 1 .
Figure 1.(a) Two merging ST plasmas to create a high-beta ST, (b) two merging spheromaks to form an FRC and its transformation to a high-beta ST and (a ′ ), (b ′ ) their corresponding reconnection regions with and without guide toroidal field Bt.

Figure 2 .
Figure 2. (a) Trajectory of the reconnection heating to ignition and self-ignition regimes in the space of temperature (T) and density times confinement time (nτ ).(b) Heating power of the conventional fusion plasma heating composed of ohmic heating, alpha heating and additional heating and that of the reconnection heating as a function of temperature.

Figure 4 .
Figure 4. (a) Dependence of ion temperature increment ∆T i on reconnecting magnetic field Brec of two merging STs and spheromaks under ne ∼ 1.5 × 10 19 m −3 in TS-3, TS-3U, TS-4, MAST and ST-40 devices, (b) mechanism for Hall current density j Hall and quadra-pole electrostatic potential ϕ formation and current sheet rotation/ deformation caused by j Hall × Bt force, (c) 2D contour of ϕ (color) measured by electrostatic probe array and poloidal flux (solid lines).

Figure 6 .
Figure 6.2D contours of (a) absolute value of magnetic field |B| and (a ′ ) poloidal flux Ψ of the high-beta ST plasmas (q 0 ∼ 1.5) produced by type (b) merging in figure 1.The corresponding (b) |B| contour and (b ′ ) Ψ contour of low-beta ST without merging.

Figure 7 .
Figure 7. Radial profiles of the q-value and toroidal current density jt on the midplane (z = 0) in the TS-3U ST merging experiment.