Study of the fast electron behavior in electron cyclotron current driven plasma on J-TEXT

Xiaobo ZHANG (張霄波),Wei YAN (嚴(yán)偉),?,Zhongyong CHEN (陳忠勇),?,Jiangang FANG (方建港),Junli ZHANG (張俊利),You LI (李由),Xixuan CHEN (陳曦璇),Yunong WEI (魏禹農(nóng)),Ruihai TONG (佟瑞海),Zhifang LIN(林志芳),Yu ZHONG(鐘昱),Lingke MOU(牟玲可),Feng LI(李峰),Weikang ZHANG(張維康),Lu WANG (王璐),Donghui XIA (夏冬輝),Zhonghe JIANG(江中和),Zhoujun YANG(楊州軍),Nengchao WANG(王能超),Zhipeng CHEN(陳志鵬),Yonghua DING(丁永華),Yunfeng LIANG(梁云峰),4,5,Yan PAN (潘垣) and the J-TEXT Team,6

1 International Joint Research Laboratory of Magnetic Confinement Fusion and Plasma Physics,State Key Laboratory of Advanced Electromagnetic Engineering and Technology,School of Electrical and Electronic Engineering,Huazhong University of Science and Technology,Wuhan 430074,People’s Republic of China

2 Southwestern Institute of Physics,Chengdu 610041,People’s Republic of China

3 School of Electrical Engineering & Automation,Jiangsu Normal University,Xuzhou 221116,People’s Republic of China

4 Institute of Plasma Physics,Chinese Academy of Sciences,Hefei 230031,People’s Republic of China

5 Forschungszentrum Jülich GmbH,Institut für Energie- und Klimaforschung-Plasmaphysik,D-52425 Jülich,Germany

Abstract In J-TEXT tokamak,fast electron bremsstrahlung diagnostic with 9 chords equipped with multichannel analyzer enables detailed studies of the generation and transport of fast electrons.The spatial profiles and energy spectrum of the fast electrons have been measured in two ECCD cases with either on-axis or off-axis injection,and the profiles processed by Abel-inversion are consistent with the calculated power deposition locations.Moreover,it is observed that the energy of fast electrons increases rapidly after turning off the ECCD,which may be attributed to the acceleration by the recovered loop voltage at low electron density.

Keywords: fast electron,tokamak,electron cyclotron current drive,power deposition location

1.Introduction

The goal of the advanced tokamak[1]program is to produce and sustain a plasma with high confinement and high pressure over an extended period of time with well aligned current profile.Electron cyclotron current drive(ECCD)is a viable path towards this goal by driving non-inductive current and the electron cyclotron wave(ECW) can propagate from the launching structure towards the plasma without passing through evanescent layers [2-4].Fast electrons could be generated by ECW through wave-particle interaction when the resonant condition is fulfilled [5].The fast electron distribution is determined by the following factors: the position of resonant layer,the radial diffusion of fast electron and the acceleration by residual toroidal electric field [6].Since the very beginning of ECCD experiments in tokamaks,it has been recognized that fast electron bremsstrahlung(FEB)diagnostic[7]is the most efficient method for investigating ECCD experiments in plasma physics.The FEB diagnostic cannot only characterize the spectrum and spatial profile of fast electrons generated by ECW,but also measure the details of fast electron momentum dynamics and the power deposition location of the ECW.

Powerful FEB diagnostics have been developed in many devices such as TCV [8],FTU [9] and HL-2A [10] to assess the ECCD performance.In FTU,the correlation between FEB intensity and loop voltage drop after ECW injection is verified[11] and the radial diffusion coefficient of fast electrons is estimated by the exponential decay of FEB intensity[12].The FEB diagnostic has been combined with ray-tracing and Fokker-Planck codes to investigate the role of fast electron radial transport in radio-frequency current drive in TCV [13].The comparison of various fast electron transport models suggests a dependency of the radial transport on the ECW power [14].

In 2019,the 105 GHz ECRH/ECCD system [15] was formally put into operation on joint Texas experimental tokamak(J-TEXT) [16,17],which not only expanded the parameter range of J-TEXT plasma,but also put forward the demand for the research of ECRH plasma.A vertical FEB diagnostic system with CdZnTe detectors,dedicated to study the dynamics of fast electron in the energy range of 30-300 keV during ECCD experiments,has been developed on J-TEXT[18].The detectors are arranged radially to obtain the spatial profile of fast electrons.

In this study,the fast electrons generated by ECCD are described in detail and the power deposition location of ECCD is measured by the FEB diagnostic using Abelinversion on J-TEXT.The ECW deposition location obtained by FEB diagnostic is consistent with the result calculated for both on-axis and off-axis cases.

The remainder of this paper is organized as follows.The introduction of experimental setup is presented in section 2.The on-axis and off-axis ECCD experiments are discussed in section 3.The phenomenon after turning off ECCD is discussed in section 4.Lastly,the summary is presented in section 5.

2.Experimental setup

The J-TEXT tokamak is a medium-sized conventional iron core tokamak with operating parameters summarized as follows:major radius R=105 cm,minor radius 25-29 cm which can be modified by a movable titanium-carbide coated graphite limiter,maximum plasma current Ip=220 kA lasting for 600 ms,maximum toroidal magnetic field BT=2.3 T,and central line averaged electron density ne=(1-6) × 1019m-3.The locations of the diagnostics and auxiliary system which have been used in this experiment are shown in figure 1(a).The electron density and current profiles are measured by the three-wave far infrared ray laser polarimeter-interferometer system (POLARIS) [19].The electron temperature profile is measured by a 24-channel heterodyne electron cyclotron emission(ECE)radiometer,covering most of the plasma within the frequency range of 80-125 GHz[20].The hard x-ray radiation(HXR)in the energy range of 0.5-5 MeV resulting from the thick target bremsstrahlung when runaway electrons are lost from the plasma and impinge on the vessel walls is measured by two NaI detectors with collimators.

The FEB diagnostic [18] consists of four CdZnTe detectors and five CdTe detectors in upper window of port 6.The best measurement range of FEB emissions is 30-300 keV,while in higher energy level (＞300 keV) the detection efficiency will be lower than 15%.Nine viewing chords span the entire minor radius of the plasma with a radial resolution of 5 cm on the midplane as shown in figure 1(b).The CdZnTe detectors are placed with chord No.from #5 to #8,and the measured positions of minor radius on the midplane are 0 cm,+5 cm,+10 cm and+15 cm respectively.Five CdTe detectors are placed in other chords,and the detection efficiency is much lower than that of CdZnTe detector,which can only be used in the case of suprathermal discharge.Therefore,only the results of CdZnTe detectors are given in the following part.The data is processed by two methods: one is directly collected after envelope-demodulation,which provides the time evolution ofmaximum energy of fast electrons,and the other provides energy spectrum by using a multi-channel analyzer (MCA).The signal from the demodulator will be specially noted.

The ECRH/ECCD system [15] uses a 105 GHz gyrotron with output power of 500 kW and pulse duration of 1 s to inject ECW with second harmonic of X-mode into plasma.The toroidal injection angle(φEC)and poloidal injection angle(θEC)is adjusted by a plane mirror,with the range of -20°-+20°.There is a polarizer installed at the elbow to change the microwave polarization parameters,which is convenient for the efficient coupling of microwave and plasma.

ECRH/ECCD has the characteristic of localized power deposition.The precise knowledge of the power deposition profile is importance for the control of profile parameters,which aims at controlling magnetohydrodynamic (MHD)modes and plasma profile shaping by heating or current drive.On other tokamaks,the ray-tracing code is generally used to calculate the power deposition of ECW.But such code is not yet available on J-TEXT.ECW with frequency of 50-200 GHz can be absorbed by the plasma in the vicinity of either the fundamental or a higher harmonic electron cyclotron frequency[21].These resonant frequencies are characterized by

where fris the resonant frequency,fceis the electron cyclotron frequency,and n is the number of the harmonic.The electron cyclotron frequency is determined by the magnetic field B,the electron charge e and the electron mass meas follows:

In equation (2),the local magnetic field B is determined by the central toroidal magnetic field B0and the location.As the toroidal field decays with the major radius(R)as 1/R,the absorption region in the plasma is localized at a specific position of the major radius.In J-TEXT,fr～105 GHz,n ～2,so the ECW deposition location is roughly estimated according to the formula

Here,R is the major radius of deposition location.Two shots with different B0are performed,as shown in table 1.The power deposition locations are 0 cm and +5 cm,which are categorized as on-axis and off-axis cases,respectively.

3.Fast electron behavior during ECCD

In TCV,ECCD is more effective for fast electron generation compared with the launch at φEC=0,i.e.perpendicular launch[8].Because ECW with perpendicular launch only increases primarily the perpendicular velocity of the resonant electrons,but if φEC≠0,ECW will increase the parallel momentum of the electrons.So,in this experiment,the θECof ECW is 0° and the φECof ECW is -20° (the minus sign ‘-’ indicates that the injection direction is opposite to the plasma current direction).

3.1.On-axis ECCD

When B0=1.875 T,the ECW absorption area is on-axis according to the calculation.A typical on-axis ECCD experiment with a number of fast electrons is shown in figure 2.In shot#1071241,plasma current is 150 kA,central electron density is kept at about 1×1019m-3.The ECW is injected during 250-350 ms.Figures 2(c) and (g) display a line integrated intensity signal from the central chord of FEB (IFEB),IFEBbegins to rise during the ECCD period and rapidly increases to a higher level after the turning off of ECCD,which will be discussed in section 4.Figure 2(e) displays the ECE signals at 102.5 GHz(yellow line) and 80.5 GHz (black line).The 102.5 GHz ECE measures the signal near the core (+2.56 cm) while 80.5 GHz ECE corresponding to a 2nd harmonic resonance layer outside the plasma (+31.96 cm).The 80.5 GHz ECE is dominated by relativistically downshifted emission by the high-energy tail of the electron distribution function and can thus be employed to diagnose the population of fast electrons [22].The trend of 80.5 GHz ECE signal is consistent with that of FEB signal during ECCD.It can be observed that the loop voltage decreases from 1.34 to 0.84 V after 150 kW ECCD injection (see figure 2(d))and the current driven by ECW can also be roughly estimated to be 56 kA [23].

Figure 1.(a)The locations of the diagnostics and auxiliary system on J-TEXT,(b)optical design of FEB diagnostic on J-TEXT.The CdZnTe detectors are placed on the blue chords to measure the fast electrons generated during ECCD.The CdTe detectors are placed on the red chords to measure the fast electrons during superthermal discharge.

Figure 2.Temporal evolution of typical on-axis ECCD experiment which generated a large number of fast electrons.From the top to bottom,the waveforms are: (a) the plasma current,(b) the central line averaged electron density,(c) FEB signal at the radial position of 0 cm(from demodulator),(d)the loop voltage,(e)ECE signals at the radial position of +2.56 cm and +31.96 cm (out of plasma),(f)ECCD power.About 150 kW ECW power is injected into plasma from 250 to 350 ms and (g) the enlarged FEB signal of dashed box.

Figure 3.FEB spectrum of the central chord in shot#1071241:(a)the intensity of different energies with time,the black line represents the time of injecting ECCD,(b) the energy spectrum before and during ECCD.

Figure 4.Time trace of counts from various energy ranges at FEB central chord.

Figure 5.The upper figure shows the time trace of counts from energy range of 40-50 keV at various FEB chords in shot #1071241.The lower figure shows the decay of fast electron counts (40-50 keV) in the core just after the turning off of ECCD.τd is the radial diffusion time of fast electrons.D0 is the radial diffusion coefficient.

Figure 6.Line-integrated FEB emission radial profile (a) and local FEB emissivity radial profile derived from Abel-inversion (b).

During ECCD,IFEBis considerably higher than that before ECCD at all energies and the maximum energy of photons increases from 150 to 250 keV in the spectrum of FEB central chord as shown in figure 3.The fast electron tail in the electron velocity distribution is obvious in this figure.

The increase of IFEBindicates that ECCD generates fast electrons,and the drop of loop voltage partly indicates that these fast electrons carry non-inductive plasma current [24].

The response of IFEBto ECCD varies as a function of radial position and energy.In figure 4,the counts of 40-90 keV increase rapidly after turning on ECCD and decrease rapidly after turning off ECCD.This shows that the FEB signal has a strong correlation with ECCD.For a fixed FEB chord,the lower energy range has a higher growth rate and counts during ECCD.As an example,the counts of 40-50 keV increase fastest,and the counts are twice those of 80-90 keV.So,the range of 40-50 keV with the highest counts is selected to analyze the signals in different chords.Quasilinear diffusion of the electron distribution function in momentum space is the reasonable explanation for the different response of FEB at different energy ranges during ECCD [14].In addition,the building up in time from lower energy to higher energy may also be one of the reasons.

For a fixed energy range of 40-50 keV,the FEB emissivity at the deposition position is significantly higher than that of the boundary area(figure 5).Moreover,the growth rate of central chord is higher than that of outer channel when ECCD is injected into plasma.With the turning off of ECCD,both of them begin to decrease,and the delay rate of central chord is higher than that of outer channel.This may be caused by the outwards radial diffusion of fast electron.By fitting the time trace using an exponential law,the radial diffusion coefficient D0can be estimated.From the exponent provided by the fit,1/τd,the diffusion coefficient can be deduced,D0～a2/5.8τd[12],yielding D0～3.07 m2s-1,where a is the minor radius of tokamak.The inferred value for D0agrees with the measurements in other tokamaks [25].

The radial profile of IFEBcan be obtained by combining the detector signals of different positions (figure 6(a)).The integral signal cannot accurately reflect the emissivity of the radial position,so it is necessary to use an Able-inversion method to derive the localized emissivity [26].Figure 6(b) displays the inverted radial profile of IFEBwith a maximal at r=0 cm during ECCD,which indicates the experimental deposition position of ECW lies at around 0 cm.This observation is consistent with the calculation results displayed in table 1 for Bt=1.875 T.

Figure 7.Time trace of counts from energy range of 40-50 keV at various FEB chords in shot#1071242.The bottom figure is the time evolution of counts from the detector at+5 cm after ECCD is turned off,τd is the fitted radial diffusion time of fast electrons.

3.2.Off-axis ECCD

If we want to control NTM through ECCD,the ECCD must be deposited at the location of the magnetic island,i.e.to apply off-axis current drive.Therefore,we also studied the off-axis ECCD on J-TEXT.

There are two ways to change the deposition location of ECCD,one is to change the poloidal angle of ECW injection,and the other is to change the toroidal magnetic field.In this experiment,the poloidal angle of ECW injection is still fixed at 0° and the central toroidal magnetic field is changed to 1.96 T.The calculated deposition location is+5 cm of the minor radius,and the other parameters are with the same as the on-axis case.

Figure 7 shows the time evolution of the IFEBat different radial positions in the off-axis ECCD case.It can be seen that the number of counts measured by the detector at +5 cm is the highest,which reflects the strongest radiation of FEB and hence indicates the deposition location.

Figure 8.Line-integrated FEB emission radial profile (a) and local FEB emissivity radial profile derived from Abel-inversion (b).

Figure 9.Temporal evolution of shot #1071242.From the top to bottom,the waveforms are:(a)the plasma current and ECCD power,(b) the central line averaged electron density,(c) FEB signal at the radial position of 0 cm (from demodulator),(d) the loop voltage,(e) ECE signals at the radial position +38 cm (80.5 GHz),out of plasma,(f) the HXR emission intensity.

Figure 10.Time trace of FEB emission intensity in several energy ranges for shot #1071242.The shaded area indicates the time interval in which ECCD is applied.

Figure 11.(a) Time evolution of energy spectrum at 0 cm chord,(b) time evolution of photon temperature Tph profile from FEB emission spectrum.

At the end of ECCD,the signals of all chords increase evidently except the one at the deposition location.The increase of FEB signals will be further analyzed in section 4.Nevertheless,the prompt decrease of FEB counts at 5 cm in the range of 40-50 keV indicates that the diffusive loss dominants the behavior of these ECCD driven fast electrons in this case.The off-axis fast electron diffusion time and diffusion coefficient are calculated as τd～3.95 ms,D0～2.72 m2s-1,respectively.There is little difference compared with that for on-axis case.

The deposition location obtained from the Abel-inverted profile is at minor radius+5 cm as shown in figure 8,which is also consistent with the calculation results from equation (3).The consistency of the deposition positions between the inferred from Abel-inverted profile and calculation results for both onaxis and off-axis cases indicates that the reliability of FEB diagnostic in judging the deposition position of ECW is verified.

4.Fast electron behavior after turning off ECCD

Sometimes,IFEBwill increase rapidly after the turning off of ECCD as shown in figure 7,which has been also observed after turning off LHCD in HT-7 [27].Figure 9 shows the signals of shot #1071242,IFEBincrease rapidly when 150 kW ECCD is turned off at 350 ms.As the enhancement of IFEB,HXR signal also begins to increase,indicating the generation of runaway electrons.The evolution of fast electrons in different energy ranges is shown in figure 10.The fast electrons in the energy range of 40-100 keV are generated during ECCD and the counts continue to increase for a while after ECCD is turned off.Meanwhile,the counts of fast electrons in the energy range of 200-300 keV also begin to increase.The appearance time of fast electrons in the energy range of 400-500 keV lags behind 200-300 keV about 380 ms.Then the counts of 400-500 keV fast electrons increase accompanied by the decreasing counts of 40-100 keV fast electrons.This may be due to the fact that the plasma current is controlled by feedback,so the loop voltage and toroidal electric field E||increase after switching off the ECCD.The E||increases from 0.13 to 0.20 V m-1(E‖～VL/2πR0) and accelerates those fast electrons driven by ECCD to higher energy,even to be runaway electrons.

Figure 12.Correlation of the increase of IFEB,ne and ECCD power.

It is well known that for given plasma conditions there is a threshold electric field for generation of runaway electrons.Below the critical fieldEth=ER≡(e3nelnΛ) /(4ec2)[28],no runaway electrons are produced.Then considering the modifications of the synchrotron radiation losses[29]and magnetic fluctuations [30] to the Eth,for the parameters of this experiment (B0=1.96 T,ne=1.2×1019,Zeff=3,=2×10-5),the threshold electric field is estimated as Eth～0.17 V m-1.This is comparable with the measured electric filed from experiments.After turning off ECCD,the E||is about 0.2 V m-1(＞Eth～0.17 V m-1),so enables the generation of runaway electrons.The fast electron tail is extended from 150 to 300 keV as compared with ECCD period (250-350 ms) as shown in figure 11(a).By a standard least-squares fit,the photon temperature Tphis derived.The time slice of Tphat different chords is shown in figure 11(b).It can be seen that the Tphincreased significantly after 350 ms when ECCD is turned off.The photon temperature Tphindicates the ‘hardening’ of the x-ray spectrum,resulting from the interaction of fast electrons with residual loop voltage.The statistical results in figure 12 show that the increase of IFEBoccurs at low electron density(＜1×1019m-3),and ECW power has little effect on it.This may imply that the decrease in the electron density plays a key role in this phenomenon.

5.Summary

A set of FEB diagnostic system consisted of CdZnTe detectors has been used in the J-TEXT tokamak to measure the hard x-ray which is generated by bremsstrahlung of fast electron bremsstrahlung in the energy range of 30-300 keV.The data of detectors are processed by MCA to obtain the energy spectrum of fast electrons.In the 150 kW ECCD experiments,the emissions of the FEB with energy of 30-250 keV are observed using the FEB diagnostic during ECCD phase,which suggests that the fast electrons with energy of 30-250 keV are generated during ECCD.

The line integral profile of FEB emissivity is obtained and the local emissivity profile is derived using Abel-inversion,which can reflect the deposition location of ECCD.Compared with the deposition location calculated according to the principle of ECW absorption,it is verified that FEB diagnostic can provide quite accurate information about the deposition location of ECCD.The study of deposition location lays the foundation for further ECCD experiments such as tearing mode control,sawtooth instability control and current profile modification.

Furthermore,the process of fast electron acceleration after turning off ECCD is also observed.This may be due to the increase of loop voltage and E||after the switch off of ECCD.The increased E||can then accelerate those fast electrons generated during ECCD phase to higher energy or even runaway.The statistical analysis shows that this phenomenon mostly occurs in the case of low electron density (＜1×1019m-3).

Acknowledgments

This work is supported by the National Key R&D Program of China (Nos.2017YFE0302000,2018YFE0309103,2019YFE030-10004,2017YFE0300501,2018YFE0310300,2018YFE0309100),National Natural Science Foundation of China(Nos.11775089,51821005,11905077 and 11575068)and the China Postdoctoral Science Foundation (No.2019M652615).

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