Current drive by using lower hybrid fast wave in VEST

An efficient central or off-axis current drive is necessary for the steady-state operation of tokamak fusion reactors. The fast wave branch in the frequency range above two times the lower hybrid resonance frequency at high density, the so-called lower hybrid fast wave (LHFW), could be such an efficient current drive scheme in high density and high temperature of reactor-grade tokamak plasmas. This is because it has a higher parallel wave electric field for efficient Landau damping, compared to the fast wave branches in other frequency ranges, and it can more deeply penetrate high density plasmas than the slow wave in the same frequency range. An experimental study has been carried out to confirm the feasibility, in collaboration with Korea Atomic Energy Research Institute, Seoul National University, KwangWoon University, and Korea Accelerator and Plasma Research Association, in VEST. The results show that plasma current can be driven by the fast electrons generated by the LHFW. The details are reported including the theoretical background and RF system as well as the experiment results.


Introduction
The non-inductive current drive is a key issue in achieving steady-state operation of tokamaks.Much attention has been paid to a current drive method from the early 1980s, the socalled Lower Hybrid Current Drive (LHCD), that uses the slow wave in the lower hybrid resonance frequency range (ω ⩾ 2ω lh ), because it had shown superior current drive efficiency in several experiments as predicted by theory and simulation [1][2][3][4][5][6][7][8].However, it has not appeared to remain efficient in 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.high-density plasmas [9,10], although some advances have been made recently [11][12][13].Meanwhile, fast waves have been steadily suggested as an alternative current drive scheme to overcome the density limit in reactor-grade high density and high temperature plasmas.The fast wave near the lower hybrid resonance frequency range (ω ci ≪ ω < ω lh ) was firstly proposed in the 1980s since it can satisfy the accessibility condition with low N ∥ , and has good penetration and moderate electron absorption properties even at high density [14][15][16].In addition, it was considered to be more viable from an engineering perspective, being implemented with a high-power RF source and launcher.However, in several experiments, a density limit similar to LHCD was observed, or the current drive efficiency was too low to confirm the effect clearly [17][18][19].The cause was speculated to be due to parasitic coupling to slow waves at the edge region or the parametric decay of the slow wave mode-converted from the launched fast wave [20,21].In 1995, high harmonic fast wave (ω ci < ω ≪ ω lh ) was suggested for heating and current drive (H & CD) in a high beta, low aspect ratio tokamak [22], since strong local single pass absorption and resultant current profile control were predicted in such tokamak conditions.It was determined that the current drive was feasible, however, the efficiency was not as high as LHCD, and was limited to the core region only [23,24].Recently, a fast wave very close to the lower hybrid resonance (ω ⩽ ω lh ), the so-called helicon wave, has been suggested as an off-axis current drive and is currently being intensively researched in KSTAR and DIII-D with Mega Watt RF power levels, despite the multipactoring issue [25][26][27].RF current drive schemes that have been explored so far using LHCD or fast waves below the lower hybrid resonance frequency have exhibited weaknesses in terms of density limit or low efficiency.However, the fast wave in the same frequency range as LHCD, the so-called lower hybrid fast wave (LHFW), might provide a high efficiency current drive with relatively good penetration in high density plasma [28].First, it has a relatively large perpendicular group velocity compared to the lower hybrid slow wave (LHSW) which is used for LHCD.This means that it can propagate into a higher density central region than LHSW, so the density limit problem can be addressed.Second, it has a higher electric field parallel to the magnetic field, which is favorable to an efficient current drive due to Landau damping (LD), compared to the fast wave branches in other frequency ranges.Third, the parasitic coupling to slow waves can work as LHCD free from parametric instability or ion heating in the frequency range.The LHFW is plotted with other wave branches suggested for the current drive of the tokamak on the CMA diagram as a reference, in figure 1, where ion cyclotron range of frequency fast wave is included and n means a harmonic number of ion cyclotron resonance.Though the usefulness of LHFW has been rarely considered, some studies have shown that at those lower hybrid frequencies the fast wave current drive (FWCD) can be significant.Theoretically, it has been shown that efficient current drive is possible through self-consistent quasi-linear theory calculations considering scattering and shear effects in a straight cylinder geometry [29], and a fast wave branch can also be applied to ITER in the LHCD by using a ray tracing-Fokker Planck coupled simulation [30].Experimentally, it was observed that a fast wave can be launched and current drive can occur only above a specific density by using a slottedwaveguide fast wave coupler at ω ≈ 6ω lh , although it was conjectured that the mode-converted slow wave plays a role in the current drive and some parametric decay instability (PDI) study was carried out at a lower frequency [31,32].However, neither a more detailed theoretical study nor further experimental research have yet been conducted to confirm the LHFW current drive scheme including the confirmation of the launching and mode-conversion(confluence layer) boundaries, the coupling ratio of the slow and fast wave branch regarding to the launcher polarization, and so on.An experimental feasibility study was initiated to confirm the current drive scheme through a collaboration between Korea Atomic Energy Research Institute, KwangWoon University (KWU), Seoul National University, and Korea Accelerator and Plasma Research Association (KAPRA).A 10 kW Klystron was prepared by refurbishing an old ultra high frequency (UHF) broad casting system.A comb-line type traveling wave antenna was newly developed for the LHFW launcher.The RF power and the launcher were installed in VEST to conduct the H & CD experiments.The theoretical background, including the dispersion relation and absorption, is provided in section 2, along with ray tracing and coupling simulations on VEST.The experimental setup of the RF system and diagnostics is given in section 3. The experimental results are analyzed and discussed in section 4. Finally, conclusions are given in section 5.

Dispersion and propagation
A fast or slow wave branch can be deduced using a general cold plasma dispersion relation, as in equation ( 1), where A, B, and C are the functions of the Stix parameters S, D, P, R and L, and a parallel refractive index N ∥ [33].Then, the two wave branches in the lower hybrid resonance frequency range ω ∼ ω lh , LHSW and LHFW, can be obtained by keeping the dominant terms in the frequency range from equation (1), From P = 0 and N 2 ∥ = R in equation ( 2), the lower propagation boundaries of the wave branches can be found, as follows, respectively.
for LHSW Meanwhile, an upper propagation boundary can be found when the determinant of the quadratic equation ( 1) is zero and a so-called confluence takes place.At the condition, physically, the two wave branches become mode-converted to each other and reflected so they cannot propagate above the density of the determinant-zero.The approximate confluence density can be represented as equation ( 4) [34], The confluence density can be increased by increasing the parallel refractive index N ∥ .It is, in essence, the same as the Stix-Golant accessibility condition [33].The propagation boundaries of LHFW are depicted with real perpendicular wave number in log scale on the CMA diagam in figure 2.
Even if the upper propagation boundary of the LHWs (LHSW and LHFW) are identical, the dynamic behaviors in continuously varying plasma media are very different from each other depending on the dispersion relation.In addition, unlike a vacuum wave, since the direction of the group velocity is different from the phase velocity, it is necessary to investigate the group velocity throughout the magnetic fields and plasma parameters.The ratio of perpendicular to parallel group velocity is represented by equation ( 5) [35], Inserting the perpendicular wave numbers in equation ( 1) and retaining only leading terms, equation ( 5) may be approximated to equation (6), For LHSW, at most plasma parameters except P ∼ 0 in the lower propagation boundary region, the perpendicular group velocity is much smaller than the parallel group velocity.This means that the LHSW is rapidly aligned to the magnetic field as the density increases, and it cannot penetrate high density bulk plasma after being launched in the edge low density plasma.In contrast, the ratio of LHFW is on the order of unity near the lower boundary (N 2 ∥ ∼ R) and it remains up as long as the plasma frequency does not exceed ∼ √ ωω ce .This means that LHFW can propagate into an even higher density region, though it does not propagate toward central region directly across the magnetic field.

Absorption
The absorption of LHFW can be understood through the imaginary part of the refractive index given in equation ( 7) [36].It can be obtained from the plasma dispersion with hot dielectric tensor and the series of approximations given in appendix, for LHFW (7) where N ⊥,S , N ⊥,F , ω ce , ω pe are the perpendicular wave numbers of equation ( 2), electron cyclotron frequency, electron plasma frequency, respectively, and η are the ratio of parallel phase velocity of the wave to electron thermal velocity.The fast wave has the same efficient LD term as the slow wave but it depends crucially on the plasma density in addition to the real perpendicular wave number.When the density is as low as the the launching density of LHFW in equation ( 3), the denominator becomes as large as m i /m e .This means that LHFW can propagate into the bulk plasma region without considerable damping in the edge plasma.But, if the plasma density increases as the LHFW propagates into the central region, the denominator decreases and so effective damping becomes possible.In the derivation in equation ( 7), the damping term by electron magnetic pumping (MP) is neglected.This makes it necessary to justify the assumption that MP is weaker than LD for LHFW because it has a considerable E y field, which is responsible for the MP, although it decreases in high density.
The power absorption, in general, can be obtained from the following equation ( 8), where ϵ A is the anti-Hermitian part of the hot dielectric tensor equation (A.1), defined by 1 2i (ϵ − ϵ † ), and the terms responsible for the MP and LD of the electrons are ϵ A yy |E y | 2 and , respectively, with n = 0 of harmonic number.Using the electric field polarization of equation ( 9) for LHFW and the dispersion relation in equation ( 2), the power absorption of LHFW for electrons by MP and LD can be obtained.
The electric field polarization and power absorption of the LHFW are plotted on the CMA diagram assuming a parallel refractive index of 4 and electron temperature of 3 keV in figures 3 and 4, respectively.One can see LD is stronger than MP in the lower hybrid resonance frequency range, as shown in the sign(LD-MP) of figure 4(bottom).Therefore, neglecting of MP can be justified.

Ray tracing simulation on VEST
A ray tracing simulation was carried out to confirm the theoretical analysis in the previous subsections and to determine the N ∥ for a LHFW launcher.It was performed using GENRAY code [37] with a VEST EFIT equilibrium g-EQDSK file [38].
The parameters for the simulation are summarized in table 1.
The RF frequency was 500 MHz and the parallel refractive index N ∥ ranged from 3.5 to 4.5.The frequency was selected to be about four times higher than the lower hybrid resonance frequency for VEST parameters.This ensures a high enough E z field for LD as shown in figures 3 and 4, though the density coupling window becomes slightly narrower.The density and temperature profile follow the relation of equation (10), The ray tracing simulation result is shown in figure 5.When N ∥ is 3.5, the two wave branches cannot propagate into the bulk high density region by reflection due to the low N ∥ .As the N ∥ increases, the LHWs can propagate into the higher density region and the LHFW propagates more deeply into the central region than the LHSW.The plot of electric field along the

Coupling of LHFW
Coupling is an important issue in LHFW like the other FWCD schemes, since the launching density of LHFW is much higher than that of LHSW by the factor (N 2 ∥ − 1)ωω ce as given in equation ( 3).Although the polarization of the electric field of the launcher is more suitable for LHFW since the E y field perpendicular to the magnetic field is dominant, some power can be coupled to the LHSW because it still has an E y field component even though it is much smaller than the E z field, as shown in figure 3.In addition, since the evanescent layer thickness in front of the launcher can be much shorter than that of LHFW, depending on the density profile, the coupling power to LHSW can be more significant than expected.A coupling simulation with a one dimensional full wave code was carried out to determine the characteristics [36].The coupling efficiency and coupled power ratio are shown in figure 6 for a magnetic field of 0.15 T and N ∥ = 4 near antenna.If the pedestal-top bulk plasma density is so low that it is less than the launching density of the LHFW, which is about 3 × 10 17 m −3 , all the power is coupled only to the LHSW.However, once the density becomes greater than the launching density of the LHFW, the coupling efficiency increases drastically and most power is coupled to the LHFW, although some amount of power is still coupled to the LHSW.

RF system
A RF system was prepared and developed for the LHFW current drive experiment on VEST.The overall RF system schematic is depicted in figure 7. It consists of a RF power system, a LHFW launcher, and sub-components to deliver the  RF power to the launcher [36].The main component of the RF power system is a Klystron which can amplify the input RF power from a solid state amplifier up to 10 kW in CW or pulse mode depending on the input.The launcher is a combline traveling wave antenna which was newly developed suitable for the LHFW experiment, with N ∥ = 4 and VSWR < 2. Preparation of the Klystron and launcher, and the integration test result are as following: (i) RF Power: The Klystron was prepared by refurbishing an old UHF broadcasting system provided by KAPRA.Most of the parts including the Klystron tube, HV source, and magnet were reused after testing and attaching a control and monitoring system.The refurbished and integrated RF power system is shown in figure 8(a).The final beam perveance was measured to be 1.6 µ after intensive tuning.(ii) Launcher: The LHFW launcher was developed in collaboration with KWU in a type of traveling wave antenna as shown in figure 8(b) [39].The coupling and propagation of the LHFW were confirmed via the launcher-plasma coupled electromagnetic wave simulation.The calculated peak N ∥ spectrum was about 4 at 500 MHz in proportion to the operating frequency.(iii) RF system integration: all the RF system components except the vacuum feed-through and direct current break were assembled and integrated as shown in figure 8(c).The maximal achieved operating power was 10 kW at the input power of 27 dBm after intensive tuning at the modulating voltage of 13 kV and emission current of 20 A.

Diagnostics
The diagnostics for the experiment are a triple Langmuir probe (LP), two magnetic probes (MPs), and two Hard X Ray (HXR) systems.The triple LP was located at R = 0.745 m on the equatorial plane and 130 degrees away from the antenna center.It was used to measure the edge density and temperature and find suitable shots for LHFW coupling.The MPs were used to measure the parallel and perpendicular wave numbers and ensure that the wave branch propagating is LHFW.The MP1 and MP2 were located below input port 1, and 105 degrees away from the antenna, respectively.The vertical position of the MPs was about 35 cm below the equatorial plane.
The position configuration of the LP and MPs is shown in figure 9 [40].The HXR measurement systems are two kinds.
The first is a conventional gamma-ray detector originally used for nuclear data measurement that was used during the initial 0.1 T phase of the experiment.The second is a newly developed one dedicated to the detection of fast electrons generated by LD in the LHFW and runaway electrons emerging during the plasma current ramp down phase or disruption [41].
The former is referred to as HXR1 and the latter as HXR2 to distinguish.

Vacuum conditioning
Before the RF power injection for VEST plasma, intensive vacuum conditioning was carried out.In the initial phase, the out-gassing was severe and the amount was random at the same dissipation power.It, however, gradually decreased with the conditioning progress and showed a regular pattern decreasing rapidly shot by shot [43].The transmitted RF power to dummy load was achieved up to 10 kW after the successful vacuum conditioning as shown in figure 10.

Experimental results and discussion
4.1.Power coupling experiment at 0.1 T 4.1.1.RF power coupling for a 30 kA shot.RF power injection was conducted for a target plasma with a current of about 30 kA, with an edge density suitable for the LHFW coupling.The RF powers of #20845 and the density and temperature evolutions with and without the RF power are shown in figure 11.The plasma parameters were measured with a triple LP mentioned in the section 3.2.The target shot #20841 without RF started at 470 ms by injecting 2.45 GHz ECH power for pre-ionization.The edge density was in the order of 10 16 m −3 , and the temperature was around 15 eV.The Ohmic swing started at 495 ms accompanying a 5 eV temperature increase.The plasma density jumped and the temperature dropped as a closed flux surface emerged around 502 ms, and the plasma current started to increase rapidly.The closed flux surface retained its configuration until 514 ms and then shrank drastically after that as shown in figure 12(a).The power coupling appeared to be very low before the Ohmic swing start, except for the initial power injection of ECH as shown in figure 11(a).It increased gradually after the Ohmic swing and then saturated or decreased slightly around 497 ms.It increased dramatically around 502 ms as the closed flux surface emerged and the density approached the launching density of the LHFW which is about 1.2 × 10 17 m −3 at N ∥ = 4.The coupling jump characteristic regarding the density coincides qualitatively with the coupling simulation in figure 6.
The coupled waves were confirmed to be LHFW by the measured wave numbers, as shown in figure 13.The perpendicular wave number regarding to the parallel wave number agrees with that of the LHFW in the dispersion relation of equation (2).To be like the LHSW, the perpendicular numbers should be greater than the measured wavenumbers.Therefore, it can be concluded that the propagating wave is LHFW.
When the LHFW was coupled, a slight increase in plasma current and shot-length extension were observed, as shown in figures 11 and 12, respectively.In addition, a peak count around several tens keV energy was detected with the HXR1 system, unlike the shot without RF power, as shown in figure 14.This implies that high-energy electrons were generated by the LD of LHFW.

Power coupling at a plasma current of 100 kA.
One interesting thing in the experiment for the 30 kA shot was the up-shift in the parallel refractive index N ∥ as shown in figure 13(a).The N ∥ near the antenna measured with MP1 was about 4 as designed, but it was measured to be 8 by MP2 which was 130 degrees away from the launcher.Since the N ∥ up-shift during propagation enables the LHFW scheme in the much higher density regime, intensive study on  the characteristics of the up-shift was carried out by measuring several wave characteristics such as pumping wave power, spectral broadening, and the wave numbers.The analysis showed that the mechanism can be attributed to wave scattering [44][45][46] rather than PDI [8,47] or the geometrical effect [48-51], because there is no threshold power as would be expected for PDI and the geometrical effect is not sufficient to explain the 100% increase of N ∥ as shown in figure 5(c).
In order to confirm the possibility of coupling in even higher densities than the initial confluence density at the launching N ∥ , a coupling experiment was conducted for 100 kA shots where the overall density including central and edge density is much higher than 30 kA shots [40].An example of the shots is shown in figure 15.The attained coupling efficiency was more than 90%, which is much higher than the coupling efficiency of about 50% for the 30 kA shot shown in figure 11.At first, this appeared to explain an N ∥ upshift, because the confluence density can increase to about 8 × 10 17 m −3 if the N ∥ increases to 8.5 by the wave scattering mechanism.However, it was found that there are efficient coupling peaks during the ramp-up and ramp-down phases where the edge density agrees roughly with that of the coupling window at the launching N ∥ of the antenna.This means that some N ∥ up-shift does not take place at the time.Another plausible explanation might be inferred from the following two points.The first is that more efficient LHSW can take part in the coupling, particularly in the high current shots with one hundred kA because the poloidal magnetic field emerges as large as the toroidal magnetic field.As shown in figure 6,  the coupling of LHSW is still present even in the case of E y excitation for LHFW launching, and it dominates over that of LHFW in the case of E z excitation for LHSW launching.The second is that the confluence can localize the LHWs in a thin layer that propagate only very close to the antenna if the N ∥ upshift does not occur sufficiently to avoid the accessibility limit.The two points suggest that the RF power of the launcher can be efficiently coupled and absorbed in the thin layer in front of the antenna instead of being transmitted to the dummy load.This hypothesis seems to be supported by the wave measurement.Interestingly, the wave signal was not detected at all, even at MP1 as well as MP2, unlike the normal LHFW coupling case of a 30 kA shot.If the wave is only confined to a very thin layer in front of the antenna, it is not surprising that one cannot detect a signal even at MP1 which is just below the antenna.(iv) A N ∥ up-shift from 4 to 8 was observed during propagation.And it seems to be attributed to wave scattering by the density fluctuation.(v) Improved coupling was observed for an 100 kA shot which exceeds the confluence density for N ∥ = 4 .But this is speculated to be due to the localization of the power coupling and absorption within a very thin layer in front of the antenna, rather than thanks to the power coupling to the bulk plasma by the large increase in parallel refractive index during the propagation.It implies that misalignment between Faraday shield enabling perpendicular electric field polarization of the launcher and tokamak magnetic field can be crucial in the LHFW coupling and launching.The 0.1 T experiment demonstrated the possibility that LHFW can propagate, generate fast electrons, and contribute to an increase in plasma current and shot length extension, accompanying an increase in parallel refractive index, in spite of a very narrow coupling density window at the initial coupling stage.However, the change in plasma density or increase in electron temperature were not obvious.In addition, it was impossible to inject RF power of more than 2 − 3 kW due to breakdown and large reflection.Therefore, it was difficult to conclude that LHFW plays a definitive role in the shot extension and current increase in the experiment.
The breakdown at higher power seems due to the very narrow coupling density window at the coupling stage, although the propagative density range is even expanded during propagation by the N ∥ up-shift caused by wave scattering, PDI, and/or the geometrical effect.The density profile region for LHFW coupling and propagation at 0.1 T is depicted in figure 16(a).Since the coupling window is very narrow, during a shot the accessibility condition can be easily broken and then the RF power can be localized only near the antenna.This will not be a problem if the wave energy density in the local region is below a certain level.But once it goes above the critical level due to higher power injection, excessively heated electrons in the localized layer might cause a breakdown, interacting with the antenna surface or cavity box.To resolve this problem in the initial coupling stage, it is necessary to expand the coupling window by increasing the toroidal magnetic field.As shown in figure 16(b), one can see that the density profile for the LHFW coupling at 0.2 T is more expanded.In this case, the accessibility condition will not be easily broken and then it will enable higher power injection and coupling without breakdown, unlike the 0.1 T case.It is important to note that the coupling window problem only appears in the low toroidal magnetic field devices.For example, for a 2 T tokamak, the upper limit by confluence can be 100 times larger than that of a 0.2 T machine if the same N ∥ is assumed.Therefore, the upper coupling limit is not of interest for conventional medium-size or reactor-grade tokamaks with higher magnetic fields.

Power coupling experiment at 0.15 T [42]
4.2.1.RF power coupling and current drive experiment.A power coupling and current drive experiment was conducted at 0.15 T to confirm the characteristics of 0.1 T after upgrading the toroidal magnetic field up to 0.2 T. The plasma densities and temperatures of the two reference shots (#22644 and #22647) are shown in figure 17.Plotting the launching and confluence density on the electron density of figure 17(a), one can expect effective power coupling and resultant H & CD in the time zone of green.The edge electron temperature was less than 10 eV.
The RF powers and the change in plasma parameters are shown in figure 18.The RF power was injected six times in pulsed mode for the reference target shot.The pulse length was 2 msec, and the repetition period was 3 msec.Efficient power coupling occured in pulse numbers 2 and 5, as expected from figure 17(a).In contrast, the power coupling in pulse numbers 1 and 6 was relatively weak due to the low density and long gap distance between the antenna and the launching density region of LHFW.The coupling in pulse numbers 3 and 4 was very unstable, and the coupled power appeared very spiky, although it was time-averaged sufficiently.
The change in plasma parameters corresponding to the coupled power is shown in figure 18(b).To see the reproducibility, two RF shots (#22645 and #22646) were conducted between two reference shots.An evident increase in plasma temperature appeared for pulse numbers 1, 2, 5, and 6.The large increase in electron temperature in pulses 1 and 6 compared to that in pulses 2 and 5 seems due to their relative low density.It was difficult to discern the change in plasma parameters in pulse numbers 3 and 4.
The effect of RF power on the change of plasma current is shown in figure 18(b)(bottom).It is not easy to discern directly the increase of the plasma current of RF shots from that of reference shots as shown in figure 18(a)(bottom) because the Ohmic power is more than ten times that of RF power.But plotting the difference of plasma current between shots with and without RF power as shown in figure 18(b)(bottom), the plasma current increase appears obviously in accordance with coupled RF power.Strong current increases appeared in pulse numbers 2 and 5 in agreement with the more coupled power, while a weak increase occured in pulse number 1.No current  increase was found in pulse number 6 in spite of the considerable increase of temperature.It seems that the plasma current was so low that the last closed flux surface was far from the antenna during the pulse 6 period.In that case, the majority of the power can be dissipated in SOL plasma and cannot contribute significantly to the plasma current.The density pumping out in pulse number 6 might be concerned with this power coupling to the SOL plasma.
To confirm the acceleration of electrons by LHFW, HXR measurement was carried out with the newly developed HXR2 system.The plasma current and HXR of the target shot is shown in figure 19(a).The HXR appeared typically after the main tokamak plasma during a shot when the plasma density was so low that runaway electrons developed easily.But it was suppressed during the tokamak plasma period.Figure 19(b) shows the HXR time-evolution when the RF power of figure 19(d) was applied to the reference target plasma.Interestingly, 40 keV HXR developed instantly after RF injection, and the plasma current increased up to two times that of the shot without RF power.Since the resonant electron energy of the LHFW is about 16 keV when no parallel wave number change is assumed, one can expect that the high energy comes from electrons accelerated by LD of the LHFW.Meanwhile, since the RF power is only 2 kW and the RF injection time is short and discontinuous, the continuous increase in the HXR at 40 keV could be explained by Ohmic power, even though the seed is generated by LHFW power.So, the shot (#34991) could be regarded as an RF-assisted (or triggered) Ohmic current drive shot.The instant and peaky increase in HXR counts near 516 ms in accordance with short RF power coupling confirms fast electron generation again.The integrated HXR spectrum during the tokamak plasma periods of with and without RF power in figure 19(c) shows more evident generation of high electron tail.Summarizing the experimental results at 0.15 T, (i) By increasing the magnetic field, it was possible to inject RF power up to 8 kW and the coupled power reached 6 kW.(ii) It was confirmed that LHFW propagates into the bulk plasma within the coupling density window in agreement with the dispersion relation of LHFW.(iii) An electron temperature was increased with the coupled RF power and it ranged two to three times that of the reference shot depending on the plasma density.(iv) An obvious current drive by LHFW appeared, in accordance with RF power injection and adequate coupling to plasma inside the LCFS.(v) A considerable HXR increase was measured, significantly in the 40 keV channel, which is close to the Landau resonance.
The experimental results at 0.15 T confirm that LHFW can propagate into plasma when the proper density condition is satisfied, and can play a role in the H & CD of tokamak plasma by generating high-energy electrons through LD.

Conclusions
A feasibility study of LHFW current drive was conducted in VEST to confirm the possibility of an alternative current drive scheme for future tokamak reactors.It was confirmed that the plasma current can be driven by the LHFW through the modulated RF power injection and measurement of the plasma parameters, wavenumbers, corresponding high-energy electrons generated.It was revealed that the power coupling depends crucially on the launching density at the launched N ∥ value through a series of 0.1 T and 0.15 T experiments, though the N ∥ can become up-shifted during propagation and contribute to the propagation in higher density.The superior coupling for 100 kA shot implies the possibility of considerable LHSW launching unintended and the importance of launcher alignment with tokamak magnetic field.If the LHFW current drive scheme is confirmed to have a good efficiency, addressing several issues including coupling in the higher field tokamaks, it might become a key external current drive scheme for tokamak reactors in the future.

Appendix. Imaginary refractive index of LHWs
The general hot dielectric tensor for Maxwellian distribution function is as follows [33,35], where For brevity, remaining the order of real and imaginary terms for the dielectric tensor of equation (A.1) and subsequently keeping the lowest order in the FLR (Finite Larmor Radius) approximation, the dielectric tensor can be reduced to equation (A.(A.4) It is necessary to note that the MP related term is neglected by remaining only zeroth order terms.S I and D I are terms related to fundamental cyclotron resonance damping and are meaningful only in the cyclotron damping layer, | ω−Ωcs k ∥ v th,s | ⩽ 1.The higher order terms disregarded by the FLR approximation can be of importance near harmonics layers | ω−nΩcs k ∥ v th,s | ⩽ 1 when the FLR is broken by high energy charged particles such as fusion-born alpha particles.However, it appeared that the alpha particle absorption can be minimized at high frequencies near the lower hybrid resonance in reactor-grade density and temperature plasmas [16,29].Therefore, S I and D I might be approximated further to zero.From the determinant of the Maxwell operator with the dielectric tensor in equation (A.2), for uniform plasmas in the Stix frame, the dispersion relation can be obtained as follows,

Figure 4 .
Figure 4. Power absorption channels of MP, LD, and sign of the difference between the two channels.

Figure 6 .
Figure 6.Coupling efficiency (top) and Coupled power ratio (bottom) with respect to bulk plasma density for LHFW launching case (a) by Ey excitation and LHSW launching case (b) by Ez excitation (reprinted from [36], Copyright (2016), with permission from Elsevier).

Figure 7 .
Figure 7.The schematic of the RF system for LHFW CD study on VEST.

Figure 8 .
Figure 8.Refurbished RF power Klystron and its perveance curve (a), fabricated antenna and plasma coupling simulation (b), assembly and integration test result (c).Reprinted from[42], with the permission of AIP Publishing.

Figure 9 .
Figure 9.The position of LP, MPs on Toroidal and Poloidal section (reprinted from [40], with the permission of AIP Publishing).

Figure 10 .
Figure 10.Transmitted power after successful vacuum conditioning.

Figure 11 .
Figure 11.RF powers (a), and plasma parameters & current with and without the RF power (b).

Figure 12 .
Figure 12.Time evolution of plasma equilibrium of shots without RF power (a) and with RF power (b).

Figure 13 .
Figure 13.Parallel and perpendicular wave numbers measured with MP1 and MP2 (reprinted from [40], with the permission of AIP Publishing).

Figure 14 .
Figure 14.Time-integrated HXR spectra during plasma current evolving 497-517 ms with and without RF power; wide range spectrum (a), narrow range spectrum around several tens keV for detail view (b).

4. 1 . 3 .
Discussion of RF power coupling at 0.1 T.Summarizing the main results of the 0.1 T experiment, (i) It was confirmed that LHFW can propagate into the bulk plasma of a 30 kA target shot, by measuring the RF power within the coupling density window, and the wave number in agreement with the LHFW dispersion relation.(ii) At about 1 kW coupled power, the shot length was extended 1 − 2 msec, and the plasma current peak increased slightly.But, it was difficult to discern the change in electron density and temperature at the coupled RF power.(iii) A HXR count increase was observed near several tens keV, which is close to the resonant electron energy for the antenna parallel refractive index of 4.

Figure 15 .
Figure 15.RF powers for a shot of 100 kA plasma current.The coupling peak appears around 504 ms and 515 ms (marked by red ellipse) when the density is roughly in agreement with the LHFW launching density at the launched N ∥ value.

Figure 16 .
Figure 16.Density profile for LHFW propagation at B 0 = 0.1 T (a) and 0.2 T (b) in the initial coupling stage without N ∥ up-shift in front of the antenna.

Figure 17 .
Figure 17.Time evolution of electron density (a) and temperature (b) of target shots.Reprinted from [42], with the permission of AIP Publishing.

Figure 18 .
Figure 18.The RF powers plasma current (a), change of plasma parameters and plasma current (b); each number in a circle means pulse number, the plasma currents for four shots(#22644-#22647) (a) (bottom), the difference of plasma currents between with RF shots (#22645, #22646) and without RF shots (#22644, #22647) (b) (bottom).Reprinted from [42], with the permission of AIP Publishing.

AN 4 ⊥ − BN 2 ⊥ 6 )
+ C = 0 (A.5)where A, B, C are functions of S, D, P, R ≡ S + D, L ≡ S − D, and N || in the same form as equation (1).The two separate solutions of equation (A.3) in the lower hybrid frequency range areNeglecting the imaginary of S and D and noting that the imaginary terms are smaller than the real terms in equation (A.4), the imaginary perpendicular wave number of the two wave branches can be approximated to equation (A.5) through some algebraic operations considering the lower hybrid resonance frequency range, .Kim  https://orcid.org/0000-0003-3661-615XJ.G. Jo  https://orcid.org/0000-0002-2783-6276

Table 1 .
Parameters for ray tracing simulation on VEST.The calculated current drive by the LHFW and LHSW for N ∥ = 4.5 is shown in figure5(d).The peak position of the current drive of LHFW is more centered than LHSW and the efficiency is comparable to LHSW.The simulation results for wave propagation and absorption are in good agreement with the theory in sections 2.1 and 2.2.