Solenoid-free current drive via ECRH in EXL-50 spherical torus plasmas

As a new spherical tokamak (ST) designed to simplify engineering requirements of a possible future fusion power source, the EXL-50 experiment features a low aspect ratio (A) vacuum vessel (VV), encircling a central post assembly containing the toroidal field coil conductors without a central solenoid. Multiple electron cyclotron resonance heating (ECRH) resonances are located within the VV to improve current drive effectiveness. Copious energetic electrons are produced and measured with hard X-ray detectors, carry the bulk of the plasma current ranging from 50kA to 150kA, which is maintained for more than 1s duration. It is observed that over one Ampere current can be maintained per Watt of ECRH power issued from the 28-GHz gyrotrons. The plasma current reaches Ip>80kA for high density (>5e18me-2) discharge with 150kW ECHR heating. An analysis was carried out combining reconstructed multi-fluid equilibrium, guiding-center orbits of energetic electrons, and resonant heating mechanisms. It is verified that in EXL-50 a broadly distributed current of energetic electrons creates smaller closed magnetic-flux surfaces of low aspect ratio that in turn confine the thermal plasma electrons and ions and participate in maintaining the equilibrium force-balance.

. The tokamak has been the most investigated and furthest advanced configuration among the magnetic confinement fusion systems. More recently, the spherical tokamak (ST) concept of aspect ratios around 1.5 [3,4] has been experimentally (START [5], NSTX [6], MAST [7], and Globus-M [8]) tested to realize a substantially higher plasma beta compared to the tokamak of aspect ratios around 3, and is an attractive candidate for realizing a relatively compact fusion reactor. In this article, the special torus (ST) indicates the spherical tokamak.
The tokamak plasma current is required to insure a high plasma confinement capability to restrain transport losses from the core to the edge. The start-up and ramp-up of this current have been commonly driven by a toroidal electric field induced by current changes in a centre solenoid (CS) magnet. This however causes engineering difficulties for the ST due to the limited space available within a narrow centre column. Furthermore, a CS magnet is capable of sustaining the plasma current over limited time period, which is to be augmented by non-inductive methods in a future fusion reactor. To develop a solenoid-free current drive capability therefore has been an important research endeavour for the STs. On the positive side, removing the CS allows additional space to increase the toroidal field (TF), further improving compactness and economy.
The original physics concept and principle of the ENN Spherical Torus with a major radius 58 cm (EXL-50) in Energy iNNovation (ENN) Science and Technology Development Co. were recently proposed by Peng [9]. One of the key EXL-50 experimental goals is to test the effectiveness of electron cyclotron resonance heating (ECRH) and current drive in the absence of an CS magnet.
CS-free ECRH and current drive have been tested in several earlier ST devices (CDX-U [10], LATE [11][12][13][14][15], TST-2 [16][17], MAST [18][19], and QUEST [20][21][22][23][24][25][26]). A toroidal current of 1.05 kA was generated using about 8 kW of ECRH power on CDX-U [9], proving the possibility of current start-up by ECRH alone. Later, a 7kA plasma current was generated by about 30kW ECRH in LATE [11][12]. A current flattop with closed flux surface (CFS) plasma was sustained for 60ms in LATE, proving the potential for steady-state ECRH and current drive of the ST plasmas. In MAST, a plasma current of 73kA was produced by 60kW ECRH power with the help of the unique grooved mirror-polarizer installed on the central rod [18]. In QUEST, a plasma current of 90kA was obtained with about 200kW ECRH power through combined first and second harmonic resonances [24].
In this paper, we present the latest ECRH experimental results from EXL-50. Not only are the operational parameters of CS-free current drive by ECRH significantly expanded, but also observed are some remarkable plasma behaviours. Discharges with plasma currents substantially above 100kA are routinely obtained in EXL-50, with the current flat-top sustained for up to or beyond 2 seconds. Data of current drive efficiency higher than 1A current per Watt of ECRH power issued from the gyrotrons, averaged over hundreds of discharges, have been accumulated.
This paper is organized as follows: an introduction to the experiment setup in EXL-50 is given in section 2. The high efficiency current drive experimental results are described in section 3. Section 4 gives the discussion of energetic electrons and current drive mechanisms. High density current drive experiments are presented in section 5. Conclusions and future plans are summarized in section 6.

Experimental setup
The EXL-50 device is a medium-sized ST with a cylindrical vacuum vessel (see, Fig. 1). An important characteristic of EXL-50 is that it does not have a central solenoid. Six poloidal field (PF) coils are located outside the vacuum vessel and the TF coil conductors. Inner limiters on the center column and outer limiters on the vessel wall have leading edges at 0.186m and 1.512m in major radius, respectively. The design of the large space of EXL-50's vacuum vessel is mainly for the confinement and accommodation of energetic electrons whose spatial distribution area is larger than that of thermal plasmas. Two microwave frequencies have been utilized so far, 28-GHz from high power gyrotrons for higher toroidal field discharges and 2.45-GHz from low power magnetrons for lower toroidal field discharges and wall cleaning. Fig.1 shows the poloidal cross section of the EXL-50 device. Two sets of 28GHz gyrotrons (50kW source power for ECRH1 and 400kW for ECRH2) are available to inject power through two outboard ports above the mid-plane.
Another 400kW 28GHz gyrotron (ECRH3) and two sets of 2.45GHz magnetrons (30kW source power each) are available to inject power through the mid-plane ports. The toroidal injection angles of the ECRH systems can be adjusted over limited ranges (as shown in Fig.1b). Both the 2.45-GHz and the 28-GHz systems are arranged to inject primarily ordinary-mode (O-mode) wave in recent experiments on the EXL-50. When the electric current of a 12-turn TF coils per turn was set to about 100kA, the fundamental and higher ECR layers (up to five resonances) coexist within the EXL-50 vacuum region (as shown in Fig.1a). The electron density is measured by single-chord tangential microwave interferometer [27]. Two CdTe detectors with energy resolution are applied to observe the forward and backward bremsstrahlung hard x-ray (HX) emission [28].

High efficiency current drive experimental results in EXL-50
Here, a simplified current drive effectiveness / is defined as follows and utilized: where IP is the plasma current, PECRH is the ECRH power issued from the gyrotrons.  fig.2, respectively. The PECRH in this paper is the power measured at the matching optical unit (MOU) which is close to the exit power of the gyrotrons. The power delivered from the antenna inside the vacuum vessel is unknown at present due to the lack of monitoring equipment. A directional coupler in the miter bend will be installed to obtain the waveform of the injected power in future experiments. The duration of high current (IP >100kA) for the higher ECRH power plasma in Fig.2 is longer than 2s. The total pulse length for 28GHz ECR heating plasma is less than 6s limited by temperature rise at the top joints of the TF coils at 100kA current. One notable phenomenon shown in Fig.2 is the density jump when the ECRH power is turned off, indicating possibly a cessation of density pump-out by ECH [29] or confinement transition, which is not addressed in this paper.  Fig.4b. It can be found that the Ip increases with the external vertical magnetic field Bv in the appropriate PECRH range. Fig.4b also demonstrates that both Bv and PECRH are the essential elements for increasing the plasma current. Bv is not a plasma current driving source, but it will affect the maximum plasma current driven by ECRH. So much potential for raising A/W through optimizing and matching of PF coil current and power of ECRH remains unexplored at present, which will be explored and improved in future experiment in EXL-50. In the first experiment campaign in EXL-50, the main target are to start-up and maintain plasma current. The density is operated in a narrow range (0.5~210 18 m -2 ) for the shots in fig.3. Fig.4c shows the relation between the plasma current and the density in flattop phase for the same shots in fig.3 and fig.4b. It can be seen that too low density is not conducive to the increase of plasma current. The favorite density for high Ip increases with PECRH.

Energetic electrons and current drive mechanisms
The Pfirsch-Schluter (PS) current is a dominant component during the initial start-up phase, and drastically decreases with increasing Bv following the formation of CFS. The boot-strap current drive by the pressure gradient is at present estimated to be less than several percent for these EXL-50 plasmas. The conventional electron cyclotron current drive (ECCD) via Fisch-Boozer mechanism [30] or Ohkawa mechanism [31] can also contribute to the non-inductive current.
However, such ECCD effects, being sensitive to the ECRH injection angle, have not been confirmed in EXL-50 experiments. Fig.5 shows the waveforms of two shots with the same PECRH in EXL-50. Although the toroidal angle for the ECRH antenna was set at -16 0 for count-current drive in shot 7448 and 17 0 for co-current drive in shot 7449, the plasma current remained largely unchanged. The single pass absorption of electron cyclotron wave (ECW) is very weak in the present low temperature EXL-50 plasmas. The angle and mode of ECW are randomized during the multiple wall reflections, so that the conventional ECCD mechanism may contribute a negligible fraction to the total plasma current. QUEST and LATE experiments have proven that the energetic electrons play a primary role for the CS-free current drive. EXL-50 experimental results confirm that the plasma current is mainly carried by such energetic electrons. The shot shown in Fig.6 is a very stable and wellcontrolled discharge, showing a nearly stationary plasma current, electron density, as well as a zero loop voltage from 1.5s to 4.5s. During the entire discharge, the plasma current, and hard xray intensity and its photon temperature (the average energy of energetic electrons) vary conjointly in magnitude. It is seen that both the number and the energy of energetic electrons contribute directly to the increase of plasma current.
It should be noted that the role of induction in the CS-free ECRH driven current remains unresolved. That is, does the toroidal electric field induced by changes in the PF coils and plasma currents accelerate the already decoupled energetic electrons to even higher energies and carry a significant fraction of plasma current during a discharge? Experiments dedicated to resolving this question were carried out. As indicated in Fig. 6a  In addition, the velocity distribution of energetic electrons driven by ECRH is different from that of runaway electrons induced by a toroidal electric field. In the former case, the energetic electrons possess similar magnitudes of parallel and perpendicular velocities, while in the latter, the parallel velocities dominate. Fig.6c shows the hard x-ray intensity and energy spectrum in forward (countcurrent) direction and backword (co-current) direction, indicating relatively moderate differences.
The three-temperature Maxwellian distribution model (3T model) [32,33] can be applied for the anisotropic distribution of runaway electrons or energetic electrons in RF heating plasmas. The detail for the HX spectrum simulation is presented in appendix I. The simulated HX spectrum based on 3T model is shown in Fig.6d. For the runaway distribution case (T//F=10T =10T//B, blue line in Fig.6d), the simulated backward HX intensity at 100keV is around 1/20 that of forward HX intensity. The backward photon temperature of HX is only as 2/3 as that of forward HX in the runaway cases. Compared to the runaway simulation cases, the simulated HX spectrum based on the distribution of equal parallel forward and perpendicular temperature (red line in Fig.6d) is much more approximateto the experimental data in Fig.6c. On the other hand, the energetic electrons can be strongly accelerated in the parallel direction by the relative high loop voltage during current ramp-down after the ECRH is turned off. These experimental observations indicate that the inductive and runaway-like current drive mechanisms are not significant in the CS-free ECRH plasmas.  Fig.7 shows the orbit confinement analysis for energetic electrons in velocity space. A three-fluid equilibrium of a 50kA EXL-50 plasma was obtained via the multi-fluid equilibrium model [33] for the computation of the guiding-center orbits [34]. A strongly asymmetric distribution in the parallel direction of the contained orbits in the v||, v, and energy space, is obtained, and shown to be accentuated as the electron energy increases toward the limiting energy of orbit containment. The asymmetric structure of the confined energetic electron orbits as shown in fig.7 is determined by the PF coil currents, not the ECRH injected angle. The population of energetic electrons is mainly related to the density and power of ECRH. As mentioned above, the conventional ECCD mechanisms provide a minor contribution to the total plasma current in EXL-50. Although the ECRH injection angles are quite different in the shots in fig.5, the plasma currents are quite similar because the other main parameters such as the PF setting, density and ECRH power are the same. Further, the design of EXL-50 (as shown in Fig.1a) permits the coexistence of five ECR layers within the vacuum vessel. Considering the effect of relativistic Doppler shift [23], the resonance layers for energetic electrons broaden in major radius direction. Fig.8a shows the radial dependence of the characteristic resonant energies for the fundamental and harmonic ECW for EXL-50. For electrons of energy above 100keV, the width of a resonance upshifts to overlap with the downshifted resonance of the next higher harmonic. It can be seen that the individual resonance widths for the energetic electrons fill the entire space inside EXL-50's vacuum vessel. The single-pass absorption of ECW is estimated to be relatively low in EXL-50 for the present range of plasma densities and temperatures. The smooth stainless steel vacuum vessel walls and limiters, including those on the center column, assist in ensuring multiple reflecting paths of the injected ECW back to the plasma. Wall-reflection further helps by converting O-mode wave to the X-mode and vice versa, thus taking advantage of the higher efficiency of X-modes by energetic electrons [26]. Another notable feature of EXL-50 plasma is that the cross section of the plasma current carried by the energetic electrons is much bigger than that of CFS during the flattop phase of plasma current. Fig.8b and c show 2D contour plot of plasma current, last close flux surface (LCFS), and the profiles of thermal plasma and current for a 120kA discharge shown in Fig.2, computed via the multi-fluid equilibrium model [30]. A significant fraction of the plasma current (52% in this case) is flowing outside the LCFS. The phenomenon that the energetic electrons play a substantial role in the formation of closed flux surface and carry a dominant fraction of the plasma current that extends over the open field line region in the solenoid-free ECRH sustained ST plasmas has been confirmed in LATE [11,12]. Similar analysis has also been conducted in EXL-50. As a first approximation, a multi-fluid equilibrium model that includes a high-energy electron component in addition to the low-energy electron and ion components was applied to describe the equilibrium characteristics of EXL-50. The simulation results were in good agreement with the available experimental data [33]. Some special experiments have been performed in EXL-50 to indicate the considerable population of energetic electrons outside the LCSF [35]. Moreover, a removable limiter will be installed in future machine upgrade plan. The space for high harmonic ECH resonance layer and gap between LCFS and limiter will be actively controlled to systematically investigate their effects on plasma current in EXL-50.

Current drive in high density plasmas in EXL-50
High density ECRH discharges are also obtained in EXL-50. The electron Bernstein wave (EBW) can be excited and played key role to heat plasma and drive current for the over-dense (i.e. the density is higher than the cut-off density of electron cyclotron wave ) ECRH plasmas. Such overdense plasma has been achieved in the low toroidal field (TF=20kA) operation mode in EXL-50. The 2.45Ghz microwave system is applied for the ECRH heating when the current of TF coil reduce to 20kA. There are still two resonance layers coexist for the 2.45GHz ECRH in low TF situation. The major radius for the three resonance layers are 0.55 m and 1.1 m for the 1 st and 2 nd harmonic, respectively. The typical discharge waveforms of over-dense plasma with 2.45GH ECRH heating are shown in fig.9a. The line averaged density can be as higher as three times of the ordinary mode (O-mode) cut-off density in the 2.45GHz ECH discharges.
High density plasma is obtained with multi-pulse gas puffing in 28GHz ECRH discharges. The nozzle for gas puffing is located at the middle of the central stack (Z=0 in fig.1a). It can be seen in fig.10 that the density increase rapidly at round 3s. The plasma density keeps high level (>510 18 m -2 ) status from 3s to 4s. At the same time, the plasma current is higher than 80kA during high density phase. The density profile for core plasma is unavailable in EXL-50 at present. The core density maybe exceeds the cut-off density of 28GHz ECW in the high density plasma. It is surmised that the electron Bernstein wave (EBW) has been excited to drive current for such high density discharges.
The general current drive efficiency CD=neRIp/PECRH for non-inductive current is estimated for the high density ECRH experiments in EXL-50. For the 2.45GHz ECRH high density discharge in fig.9, CD=neRIp/PECRH = 0.01310 19 0.533kA/20kW is around 0.01110 19    Only the electron-ion bremsstrahlung radiation is considered for the hard x-ray simulation. The electron-electron bremsstrahlung and recombination radiation can be neglected compare to the electron-ion bremsstrahlung [32]. The x-ray is the line integrated measurement. The radial profile of ion density, energetic electron density and temperatures in 3T model are the key parameters to determine the shape of HX spectrum. For the simulation of HX spectrum in EXL-50, the energetic electron density is assumed as constant in thermal plasma region. The profiles of the ion density and energetic electron temperatures are assumed as parabolic distribution. T /T||F andT||B /T||F are 0.1 and 0.1for runaway case, 1 and 0.75 and for ECRH case, respectively. The ratio of T /T||F and T||B /T||F is fixed and not change with radius. Under the above assumption, the best fitting of forward HX spectrum for 7841 in Fig.6 can be obtained when the peak value of T||F is setting as 220keV for runaway case and 180keV for ECRH case.