Jiayuan ZHANG(张家源),Jinping QIAN(钱金平),Xianzu GONG(龚先祖),Bin ZHANG (张斌),Muquan WU (吴木泉),Miaohui LI (李妙辉),Jiale CHEN (陈佳乐),Qing ZANG (臧庆),Shiyao LIN (林士耀),Yan CHAO (晁燕),Hailin ZHAO (赵海林),Ruirong LIANG (梁瑞荣),Tianqi JIA (贾天琦) and Yunchan HU (胡云禅)

1 Institute of Plasma Physics,Hefei Institutes of Physical Science,Chinese Academy of Sciences,Hefei 230031,People’s Republic of China

2 University of Science and Technology of China,Hefei 230026,People’s Republic of China

3 Advanced Energy Research Center,Shenzhen University,Shenzhen 518060,People’s Republic of China

Abstract In recent EAST experiments,current profile broadening characterized by reduced internal inductance has been achieved by utilizing radio-frequency current drives(RFCD).In contrast to previous density scan experiments,which showed an outward shift of the current density profile of lower hybrid current drive (LHCD) in higher plasma density,the core electron temperature(Te(0)) is found to affect the LHCD current profile as well.According to equilibrium reconstruction,a significant increase in on-axis safety factor (q0) from 2.05 to 3.41 is observed by careful arrangement of RFCD.Simulations using ray-tracing code GENRAY and Fokker-Planck code CQL3D have been performed to thoroughly analyze the LHCD current profile,revealing the sensitivity of the LHCD current profile to Te(0).The LHCD current density tends to accumulate in the plasma core with higher current drive efficiency benefiting from higher Te(0).With a lower Te(0),the LHCD current profile broadens due to off-axis deposition of power density.The sensitivity of the power deposition and current profile of LHCD to Te(0)provides a promising way to effectively optimize current profile via control of the core electron temperature.

Keywords: current profile broadening,equilibrium reconstruction,core electron temperature,lower hybrid wave

1.Introduction

The advanced tokamak (AT) is widely considered to be one of the most promising approaches to tackle challenges regarding future fusion reactors,where inductive current drive is replaced by external current drive and bootstrap current drive[1].Current profile tailoring is of great significance for AT operation since a proper current profile shape is capable of avoiding MHD activities and forming internal transport barriers (ITB),which would enhance plasma performance to a large extent.There have been a number of research projects on the active control of current profile in dominant machines worldwide.DIII-D proposed feedback control of on-axis or minimum value of q using electron cyclotron wave heating (ECH) and neutral beam injection(NBI) to modify plasma conductivity so as to slow down the inward penetration of Ohmic current during the current ramp-up phase [2].An elevated minimum q (qmin)～1.4 has also been obtained using off-axis NBI after redirecting up to 5 MW of NBI from on-to off-axis in DIII-D,reaching a high value of βN～3.5 free of tearing modes owing to high qmin[3].However,improved confinement was not obtained in JET using the same strategy,albeit a similar q profile was demonstrated,an alternative with a faster current ramp-up rate and current overshoot was chosen to reach the target of high plasma confinement with broad current profile[4].Besides,a sustained ITB for 3.7 s with low/negative magnetic shear remaining off-axis has also been obtained by continuing the coupling of LHCD power during the main heating phase in JET [5],where the lower hybrid wave spectral broadening induced by parametric instability(PI)[6,7]is considered to play an important role.ASDEX Upgrade[8]discovered different plasma confinements with early heating during the current rampup phase and late heating during the flattop phase,where the former generated a transient reversed q profile.Real-time control of qminhas been achieved in JT-60U [9]using off-axis LHCD which could raise on-axis q under a proper setup;this process was completed through the control of the injected power of LHCD,hence its current drive.

In EAST,LHCD [10,11]has been used as the main actuator to control the current profile because of its widely recognized high current drive efficiency.Different shapes of safety factor profiles have been demonstrated in past EAST campaigns under careful LHCD arrangements [12-16].It is,however,not easy to establish weak or reversed magnetic shear due to high-Z impurity accumulation in the core region,which is believed to improve confinement significantly,especially when EAST has upgraded both upper and lower divertor to ITER-like tungsten divertors in 2021.Therefore,to explore current profile broadening in the hope of shear reversal establishment,a series of current profile control experiments have been conducted in EAST.In this work,broad current profiles characterized by reduced internal inductance operation have been achieved using different heating and current drive (H&CD) schemes of radiofrequency (RF) waves.By examining the current profile characteristics in the process,it is found that the Te(0) plays a key role in the current profile broadening.According to both experiments and simulation analysis,current profiles and power density profiles of LHCD are found to be sensitive to the Te(0)where higher Te(0) leads to peak LHCD current profile while lower Te(0) helps broaden the LHCD current profile.

In the following sections,a summary of recent EAST experiments is given in section 2 with a detailed demonstration of current profile broadening experiments with different RF arrangements.The sensitivity of LHCD current profiles and power density profiles to the core electron temperature is discussed in section 3 in detail.Finally,a summary is given in section 4.

2.Broadening of current profiles through RF adjustment

It is desirable to obtain broad current profiles since ITB formation is heavily associated with the weak or reversed shear and hence broad or even hollow current profiles[17].EAST is equipped with very flexible radio-frequency heating and current drive systems which are in use at present to tailor the current profile,two ECH gyrotron systems capable of producing a maximum power of 2 MW in total at a frequency of 140 GHz,and two LHCD systems at frequencies of 2.45 GHz and 4.6 GHz,respectively.It should be noted that the 4.6 GHz LHCD is preferred to the 2.45 GHz LHCD in EAST to fulfill the role of current drive and current profile control,considering the avoidance of parametric instability (PI) [10]which would influence the coupling of the lower hybrid wave into plasmas and hence the current drive efficiency at lower frequency [18,19]and the topology analysis of the propagation domain [20].

Figure 1 summarizes recent current profile control experiments with the same Ip= 0.4 MA in EAST,showing the correlation of the internal inductance between plasma density and Te(0),whererevealing the shape of the current profile (i.e.,decreasinglirepresents current profile broadening and vice versa).As shown in previous experiments[12],higher plasma density is beneficial to the current profile broadening because the LHCD current profile is likely to shift outward under higher plasma density as the LHCD is the dominant current drive in EAST.The correlation betweenliand neshown in figure 1(a) also demonstrates the same tendency,implying the effect of plasma density on current density profiles.On the other hand,the correlation betweenliand Te(0)makes it more obvious that higher Te(0)leads to a peak current profile as shown in figure 1(b),indicating that current density profiles may be more sensitive to Te(0).

Figure 1.Summary of recent current profile control experiments in EAST,where (a) demonstrates the correlation between the internal inductance and plasma density and (b) shows the correlation between li and Te(0).

Figure 2.Time traces of several plasma parameters of EAST shots with different RF H&CD schemes including (a) plasma current in MA,(b) line-averaged density,(c) internal inductance,(d) power of ECH in MW and (e) power of LHCD in MW.

The sensitivity of Te(0)to current profile is also observed in detailed experiments.Broad current profiles characterized by reducedliwith Ip= 0.4 MA and line-averaged density〈ne〉～4.5 × 1019m−3have been achieved using different RF injection schemes as shown in figure 2.As can be seen from figure 2(d),the difference in RF H&CD lies mainly in the ECH power.In the discharge of #85327,an ECH power of 0.9 MW is applied,whereas no ECH power is applied in shot #85389.The power of LHCD is only slightly lower in the discharge of #85389,as shown in figure 2(e) at about 2.7 MW compared to 3 MW in shot #85327.Note that the first power stage in figure 2(e) indicates the injection of 2.45 GHz LHCD while the second indicates the injection of 4.6 GHz LHCD.The difference in the input power results in a significant decrease ofli,as is clearly shown in figure 2(c).In shot #85327,theliduring the flattop phase is about 0.88 while that in #85389 is about 0.74,representing obvious current profile broadening with LHCD only.

Equilibrium reconstruction [21,22]has been carried out with the verification of the soft x-ray(SXR)emissivity profile based on the theory that iso-emissivity surfaces of SXR are able to represent surfaces of poloidal flux when assuming that electron density,impurity density and electron temperature are all constant on a magnetic surface [23].It should be pointed out that the reconstruction process has been constrained by the internal measurement of the polarimeterinterferometer (POINT) [24].The SXR iso-emissivity surfaces are used to verify the reconstruction results as a double check,as shown in figure 3(b).The equilibrium reconstruction results are deemed reasonable considering two factors.First,fluxes of both poloidal flux and SXR emissivity share the same peak location at R = 1.9 m,indicating the same magnetic axis in both profiles.Second,the rectangle in black illustrates four points along the profiles,showing the same value of poloidal flux at the same SXR emissivity with a tolerable error of 0.7% between F1and F2.As shown in figure 3(a),q0is 2.05 in #85327 with the H&CD of both LHCD and ECH while increased q0～3.41 is obtained in#85389 with LHCD only,confirming that the current profile is significantly broadened in#85389 with LHCD as the only actuator.The distinct difference in q profiles is also in line with that inl.i

3.The impact of core electron temperature on current profile

In order to understand the mechanism of current profile broadening through RF H&CD arrangement,an investigation into the influence of Te(0) on the current profile has been carried out.The main difference for the cases discussed above is the RF actuator which serves as the electron-heating source.Therefore,the difference in RF power input would straightforwardly influence the electron temperature.On the other hand,the deposition location of ECH is in the plasma core with the toroidal and poloidal angles of 200° and 77°,respectively,in shot#85327,which would consequently lead to the difference in Te(0).Based on these facts,Te(0) is assumed to play a key role in the current profile broadening process.

Figure 4 illustrates time traces of ECE signals,liand RF power input from 1 to 4 s,covering phases of the initiation and the maintenance of theliseparation.ECE signals shown in figure 4(a)represent the Te(0)variation[25]with RF power injection,as in figures 4(c)and(d),clearly distinguishing the gap in Te(0)between shots#85327 and#85389.To examine the current profile behavior of LHCD when thelistarts to separate,hard x-ray (HXR) analysis has been carried out at t = 2.4 s,as the magenta dashed line shows in figure 4.The comparison between HXR radiation profiles in different forms is demonstrated in figure 5 where the shaded area represents the plasma core region near chord number 12.Figure 5(a) illustrates the relative intensity comparison of HXR profiles where higher intensity is observed for shot#85327 compared to shot #85389.It has been widely recognized that the measurement of LHCD performance can be examined by fast electron population generated through electron Landau damping[26,27],which can be observed by HXR diagnostics by receiving the bremsstrahlung emission in the spectrum range of the HXR.Hence,the higher HXR intensity shown in shot #85327 indicates that much more power is deposited in the plasma core,implying a higher LHCD efficiency for shot #85327 with higher Te(0) with ECH.On the other hand,the LHCD current profile broadening could be inferred by normalized HXR profiles given in figure 5(b) where the normalization is performed through normalizing the intensity of HXR in each chord to the value of chord 12,which could reveal the shape of the LHCD current profile.Compared to the normalized HXR profile for shot#85327,shot#85389 shows multiple peaks at chords of 11,13 and 15,indicating a much broader LHCD current profile with lower Te(0).Therefore,combined with the differences in both LHCD efficiency and power deposition location shift indicated by different forms of HXR profiles in figure 5,it is reasonable to conclude that a higher Te(0) with the H&CD scheme of both LHCD and ECH leads to a peak LHCD current profile and provides evidence of the sensitivity of the LHCD current profile to Te(0).

Figure 3.(a)Safety factor profiles at t = 3.8 s during flattop phase with error bar in the light shaded area,(b)magnetic flux profile obtained in equilibrium reconstruction in blue versus emissivity profile obtained from SXR reconstruction in red at Z = 0,both of which are normalized to its own maximum value.The black rectangle marks four points on profiles,where E1 and E2 are on the emissivity profile,F1 and F2 are on the flux profile.

Figure 4.Time histories from 1 to 4 s of several plasma parameters including(a)ECE signal signifying Te(0),(b)internal inductance,(c)power of ECH in MW and(d)power of LHCD in MW.The magenta dashed line indicates t = 2.4 s shortly after li separation while the green dashed line indicates t = 3.8 s when a large gap of li separation is maintained.

Figure 5.HXR profiles for shot#85327 in red and shot#85389 in blue at t = 2.4 s.(a)HXR relative intensity profiles with error bars and(b) normalized HXR profiles.

Figure 6.(a) Temperature profiles,(b) density profiles,(c) LHCD current profiles and (d) power deposition profiles of LHCD.The shaded area is the error bar region for each profile.

Figure 7.Comparison of (a) measured HXR profiles and (b) HXR profiles came from CQL3D.

More evidence could be found intuitively in the phase when a larger difference in Te(0) between shots #85327 and#85389 is maintained.A detailed simulation analysis of the LHCD current profile has been carried out during this phase at t = 3.8 s,as shown in figure 6,along with temperature profiles which came from Thomson scattering (TS) diagnostics and density profiles obtained by POINT and reflectometry.The difference in Te(0)shown in Teprofiles is in line with ECE signals,showing consistency of the measurement between TS and ECE.Density profiles in figure 6(b) only show slight differences,thus excluding the role of density in the current profile broadening process.

Current density profiles and power deposition profiles of LHCD are calculated using ray-tracing code GENRAY and Fokker-Planck code CQL3D,as shown in figures 6(c) and(d).Note that errors may exist in Wentzel-Kramers-Brillouin(WKB) approximation in the ray-tracing code [28,29],nevertheless results are consistent with experimental observations.As can be seen,LHCD current profiles vary with temperature profiles.In the case of higher Te(0),the LHCD current profile peaks near the plasma core region with higher

peak value.From the power deposition profile,one can also find that a large amount of power is deposited near the plasma core,which is in line with the current profile.Clear broadening of the LHCD current profile could be observed in shot#85389 with lower Te(0) by the generation of a second current peak near ρ～0.7.The peak value close to the core also decreases owing to lower LHCD efficiency.Likewise,the broadening of the LHCD current profile also reflects in the power deposition profile,whose shape remains flat in the radius of ρ＜0.7.

Measured HXR profiles in figure 7(a) show that the current drive efficiency drops with decreasing Te(0),indicated by decreased intensity in the core,which serves as another factor in current profile broadening.Simulated HXR profiles obtained in CQL3D code are also given in figure 7(b).In a comparison of simulated HXR profiles with measured ones,calculated LHCD current profiles using GENRAY-CQL3D could be verified.Despite spikes in measured HXR profiles which came from diagnostics,the shape and tendency are quite similar in the core region,showing a good match of LHCD current profiles between experiments and modelling.

By summarizing results of both experimental observation and simulations,it is not difficult to conclude the sensitivity of the LHCD current profile to the Te(0).Based on the HXR profile analysis shortly afterlistarts to separate,the peak LHCD current profile could be found in the higher Te(0)case while the broadened current profile could be inferred from different forms of HXR profiles with lower Te(0).More intuitively,LHCD current profiles broaden as the LHCD deposition location shifts outward in the lower Te(0) case when theliseparation is maintained at t = 3.8 s compared to the higher Te(0) case.The formation of the peaked current profile is a result of the combined action of on-axis LHCD deposition and higher current drive efficiency in higher Te(0).

4.Summary

In this work,the clear broadening of a current profile characterized by lowerliis achieved by using LHCD as the only actuator compared with the case with H&CD of both LHCD and ECH.In the absence of ECH power,the Te(0) becomes lower compared to the case with both LHCD and ECH,which results in the outward shift of both the current profile and the power density profile of LHCD.The equilibrium reconstruction also confirms the current profile broadening behavior with q0increased to 3.41 in lower Te(0) from 2.05 in higher Te(0).More intuitively,the sensitivity of the LHCD current profile to Te(0) is carefully evaluated by HXR analysis and detailed simulations of LHCD current profiles using GENRAY and CQL3D,both of which confirm that higher Te(0) leads to the peaking of LHCD current profiles,while lower Te(0) is beneficial in the broadening of the LHCD current profile.

As mentioned before,similar current profile broadening behavior has been observed in EAST density scan experiments.However,it is the difference in plasma density that accounts mainly for the LHCD current profile broadening,thus leading to the overall current density profile broadening.In fact,the temperature profile also varies in density scan experiments,albeit to a smaller degree.The summary in figure 1 points out the dependence of current profile broadening on plasma density,as well as on Te(0).The tendency found in the correlation betweenliand Te(0)is more obvious compared to density,which indicates that the current profile may be more easily affected by temperature.According to the sensitivity of the LHCD current profile to Te(0) demonstrated in this work,the profile control of temperature may be more effective in tailoring the current density profile in EAST,which provides promising approaches to establishing weak or reversed shear in future experiments.

Acknowledgments

This work is supported by the National MCF Energy R&D Program of China (No.2019YFE0304000),National Natural Science Foundation of China (Nos.12005262 and 11975274),the Anhui Provincial Natural Science Foundation(No.2108085J06),the Users with Excellence Program of Hefei Science Center CAS (Nos.2021HSC-UE018 and 2020HSC-UE011),the External Cooperation Program of Chinese Academy of Sciences (No.116134KYSB20180035)and the Science Foundation of Institute of Plasma Physics,Chinese Academy of Sciences (No.DSJJ-2021-04).