1 EX/P8-12

Stabilization of the Helically TrappedEnergetic Ions driven Resistive Interchange

Mode by on-axisElectron-Cyclotron-Heating in a Helical

Plasma

X.D. Du1, S. Ohdachi1,2, M. Osakabe1,2, R. Seki1,2, T. Ozaki1, K. Fujii3, M. Goto1, K.Nagaoka1, K.Y. Watanabe1,2, K. Tanaka2, K. Ogawa1,2, M. Isobe1,2, S. Sakakibara1,2, S.Nishimura4, T. Ido1, T. Nicolas1, Y. Suzuki1,2 and LHD experiment Group1

1National Institute for Fusion Science, 509-5292 Toki, Japan2Department of Fusion Science, The Graduate University for Advanced Studies, 509-5292Toki, Japan3Graduate School of Engineering, Kyoto University, Kyoto 606-8501, Japan4Kobe City College of Technology, Kobe 651-2194, Japan

Corresponding Author: duxiaodi@nifs.ac.jp

Abstract:

A bursting resistive interchange mode destabilized by the resonant interaction with thehelically trapped energetic ions (EPs), known as ‘EIC’, has been identified in Large HelicalDevice. It can induce the significant loss of the EPs in plasma peripheral region. It isfound that when the power of electron-cyclotron-heating (ECH) near the magnetic axisexceeds a certain threshold, the EIC locating in the plasma peripheral region can be fullystabilized. The finite orbit width effect is thought to play an important role on the observedstabilization of the EIC in LHD.

1 Introduction

To realize the future magnetic-confined fusion reactors based on the types of tokamak orstellarator/helical devices, sustaining the burning plasma by α-particle heating is crucial.Therefore, mitigation or fully suppression of various energetic particle (EPs) driven mag-netohydrodynamics (MHD) instabilities [1, 2] by experimental tools is an urgent task toreduce the large amount loss of energetic particles (EPs). Such efforts have recently beenintensively made in Fusion community. Several successful trials are achieved. For exam-ple, in a shearless stellarator, the energetic particle modes and global Alfven eigenmodesare stabilized by electron-cyclotron-current-drive, possibly due to the increase of mode

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damping through enhancement of the local magnetic shear [5, 6]. It is also shown thatthe reversed-shear Alfven eigenmodes can be suppressed by the localised deposition ofelectron-cyclotron-heating (ECH) power at the minimum of the magnetic safety factor inDIII-D tokamak [3, 4]. Moreover, it is shown that by using the static magnetic perturba-tion, the fast ion drive can be reduced and meanwhile, a temporary transition of burstingAlfven modes into a saturated continuous mode with reduced magnitude is observed [7].

In the Large Helical Device (LHD), a bursting resistive interchange mode, known asthe helically trapped energetic-ion-driven resistive interchange modes or ‘EIC’, is reportedand it induces significant losses of helically trapped energetic ions [8, 9]. Contrary toother eigenmodes that can resonate with EPs such as internal/external kink modes orAlfven eigenmodes, the resistive interchange mode (RIC) destabilized in the unfavourableaverage curvature region, is usually localized at the mode rational surface with narrowradial width δw. The δw can be restricted by experimental tools such as ECH to the sizecomparable with or less than the orbit size of helically trapped energetic ions produced bythe hydrogen neutral beam injection nearly perpendicular to the magnetic axis (PERP-NBI). In this proceeding, the result of the control of the EIC locating in plasma peripheralregion with on-axis ECH by tailoring the radial width of the eignemode are presented.

2 Observation of EIC suppression by ECH

Figure 1(a) shows that the magnetic fluctuations bθ measured by the magnetic probesexhibits the strong bursting behaviors in the low frequency range, when PERP-NBI isapplied after 4.0 s. The bursts are identified as the EIC in the previous work [8, 9]. Theelectron-cyclotron-wave of ∼ 77 GHz is launched radially to the plasma with magneticfield strength of Bt ∼ −2.85 T at the magnetic axis from 4.25 s to 5.25 s to control theEIC. That is, the ECH power using a staircase function up to 5 MW is deposited near themagnetic axis. As seen from Fig. 1(b), a clear change of the EIC behavior is observed.The major difference is that a continuous oscillatory component, which is considered tobe an enhanced pressure-driven RIC, starts to be destabilized. In addition, the EIC issuppressed. This oscillatory mode becomes even weaker when the ECH power increasesstep by step. Specifically, the amplitudes of the RIC (continuous oscillation mode) showsa stair-like decay. It should be noted that in each step it takes about ∼ 40 ms with agood reproducibility for the magnetic fluctuation to decrease after the increase in ECHpower. The time is comparable with that needed for electron temperature measured byelectron cyclotron emission (ECE) to reach the thermal equilibrium after the ECH powerincreases. All of the modes are stabilized when the ECH power exceeds 4 MW and therecurrence of the EIC does not take place until the ECH power decreases back to 2 MW.

3 Physical mechanism of EIC suppression with ECH

In this experiment, about 92% of the total ECH power is absorbed in the plasma core ofr/a < 0.5 and no ECH power is absorbed in the plasma peripheral region of r/a > 0.8,

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estimated by TRAVIS code [11]. In that the ECH power is highly localized in plasmacore, the possibility of the stabilizing effects on the EIC and RIC locating in plasmaperipheral region from the modified rotational transform, radial electric field and effectiveelectron collisionality are eliminated. Instead, the dominant effect at the mode rationalsurface is simply increased electron temperature there, shown in Fig 1(c). The on-axisECH increases the electron temperature even at ι = 1 surface near the edge by a factor ofthree, shown in Fig. 1(c). The electron density is almost not changed from 4.25 s to 4.6 s.Therefore, the dynamical friction of beam ions by the background electrons is reducedand the friction by the background ions is not altered. That is, the suppression of the EICis not due to the decreased helically trapped EP content in plasma. This consideration isfurther supported in the experiment by rising electron density from 4.7 s. The increaseof the electron density may relate with the release of the He from the wall. The increaseof ne exponentially decreases the shine-through rate ηST of the neutral beam followingthe relation ηST = exp(−σeffneL), where σeff is the effective cross section for ionisationby bulk plasma and L is NB flight path [13]. As seen from Fig. 1(c), a clear increase ofthe trapped EP content is reflected on the volume-averaged beam beta perpendicular tomagnetic field line βEP due to the increase of birth density of the PERP-NBI. Here, βEP isestimated as βEP = βd− βb, where the diamagnetic beta βd is obtained by a diamagneticloop and the bulk plasma beta βb is derived from Thomson scattering diagnostics and

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charge exchange spectroscopy.The possibility of the suppression of the EIC due to the increased mode damping is also

investigated. This is considered to be implausible. The main change of the damping of theinterchange mode induced by the ECH is the modified perpendicular thermal conductivity.This change is concluded to be negligible based on the simulation result [20].

The theory of trapped EP-driven resistive interchange-ballooning mode [19] suggeststhe strong dependence of the threshold of the EIC excitation on the radial width ofeigenmode, i.e., the RIC. The theory claims that for the excitation of the EIC, ‘the EPneeds to be incorporated inside the resistive layer’. The threshold of the EIC excitationcan be efficiently modified by altering the mode width by a factor of,

fow ∼ (ρi/δw) ln(ρi/δw), (1)

where ρi is orbit width of EPs. This is indeed similar with the well-known effect that thegrowth rate of EP-driven high-n TAE strongly depends on the mode number due to finiteorbit width effect in tokamak as γ ∝ m−2 [16, 17], as well as in stellarator as γ ∝ m−1

[18]. These stabilisation effects are often called ‘finite larger radius effect’ or ‘finite orbitwidth effect’. Since the width of the RIC in LHD has a highly localised nature and it canbe even as narrow as orbit width of EP produced by PERP-NBI. The attention is paidto study the change of radial eigenmode structure by injecting the ECH.

3.1 Expansion of the mode width before onset of the EIC with-out the ECH

First, we analyse a weakly oscillatory mode of ∼ 4 kHz in phase I before the EIC withoutthe ECH. As seen from Fig. 2, the electron temperature fluctuation δTe shows an evenfunction strongly localised around ι = 1 mode rational surface. The trough and the crestof δTe appear in phase and synchronise with the magnetic probe signal. The observedradial fluctuation structure is similar with the typical mode structure of the RIC.

Second, the eigenfunction in phase II just before entering the EIC phase has a similarcharacter of that in phase I, but extends radially inwards, have a much broader modewidth. The magnetic fluctuation amplitude bθ derived from the time integration of theprobe signal is enhanced almost double amplitude is significantly enlarged. This phe-nomenon of radial expansion of the radial width of the RIC is commonly observed justbefore the onset of the EIC, suggesting a certain threshold of δw of the RIC exists for theEIC destabilisation.

3.2 Reduction of mode width of the RIC with the ECH

It is also found that the application of the ECH can effectively control the width of the RICin experiment. In Fig. 3, the radial profiles of the coherence of the magnetic fluctuationand δTe induced by the RIC without ECH and with the ECH of 5MW are compared, aswell as the phase difference. In this shot, EICs are stabilized by the injection of the ECHpower of 5MW without multi-step power scan. The reduction of the δw of the coherence

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FIG. 2: (color) Time evolutions of magnetic probe signal with one typical EIC (a), andthat of the electron temperature fluctuation profile (b).

FIG. 3: (color online) Radial profiles of the coherences and phase differences of themagnetic fluctuation and electron temperature fluctuations induced by the RIC without theECH (solid dots and line) and with the ECH of 5MW (circles and dashed line) withoutpower scan in shot 129647.

profile by ∼ 50%, preserving the typical interchange-type phase difference, is recognizedduring the ECH of 5 MW. Similarly, the continuous change of the measured width of thecontinuous oscillatory mode is also found in the multi-step power scan experiment, shownas solid squares in Fig. 4.

Note that, the gyroradius ρL of the energetic ions trapped in the helical-ripple wellaround the mode rational surface in LHD is constant. In this experiment, it is estimatedto be ∼ 1.5 cm for the local magnetic field strength at 1.8 T and initial beam energyat 34 keV. That is ∼ 2.3% of the normalised minor radius. Moreover, the finite orbitwidth of helically trapped EP is ∼ 5% of the normalised minor radius calculated for

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the vacuum field by a Lorentz orbit simulation code. The values are of the same orderof magnitude as the observed δw. According to the dispersion relation given in theory[19], the change of the threshold of the EIC excitation is expected. Simple calculationshows that, for example if using ρi/a = 4.6%, the reduction of δw/a from ∼ 5% to ∼ 2%observed in experiment will give a rise of threshold for the EIC destabilisation by oneorder of magnitude of fow ∼ 20, as seen from Fig. 4(b).

FIG. 4: (color online) the derived δw of the RIC and oscillatory mode derived fromthe coherence profiles (circles) and inferred from the measured plasma paramter change(dashed line), and the varied thresholds for the EIC excitation fow (b).

4 Discussion and Summary

If considering the the linear theory, it is not surprising that ECH can modify RIC widththrough the modification of the background plasma. The bulk plasma parameter depen-dence of radial width of the resistive interchange linear eigenfunction is given by [15],

δw ∝ S−1/3β1/6L−1/6p , where S is the local lundquist number, β is the equilibrium pressure

normalised by the magnetic pressure, Lp is the scale length of the pressure gradient. Theapplied ECH brings about the large increase in S by the rise of electron temperature atthe mode rational surface, as shown in Fig. 1(c). This will contribute to the reduction ofthe mode width, following the relation S−1/3. On the other hand, the increased electronpressure at the mode rational surface will expand the δw, following the relation of β1/6. Asexpected, the pressure scale length Lp will not noticeably altered, because no change ofthe shape of profile is observed. Therefore, the radial width of linear eigenfunction of theRIC , shown with the dashed curve in Fig. 4, can be crudely estimated from the relativechange of measured bulk plasma parameters along with the measured δw before injectionof the ECH as the reference, obtained from the measured profile from the coherence of theelectron temperature fluctuation and magnetic fluctuation before the ECH injection. Thecalculation result shows that the reduction of the mode width of the RIC due to the ECH-modified Te and pe will be as large as ∼ 20%, shown in Fig. 4. Even though this value islower than the directly measured change of δw, it can induce an increase of threshold of

7 EX/P8-12

the EIC excitation by a factor of 3. This increase of the threshold is sufficient to suppressthe EIC in LHD, obviously because the power of the PERP-NBI is not enough to providethe free energy to destabilise the mode. It should be noted that the mode is suppressedin this case without necessarily relaxing any EP pressure gradient in plasma. Thus, theECH is considered to be a very powerful tool to control the EIC mode and to suppress theloss of the helically trapped energetic ions in stellarator/helical devices. Apparently, thecausality about the necessary of radial extension of the RIC to destabilize the EICs canalso be explained by the finite orbit width effect. That is the radial expansion of the RICjust before the onset of the EIC will abruptly lower the threshold for the EIC excitation.

In summary, the EIC, locating in the plasma peripheral region, is successfully sup-pressed when the power of the on-axis ECH exceeds a certain threshold. The suppressionof the EIC is achieved from tailoring the radial width of the eigenmodes, i.e., RIC. Dueto the highly localised nature of the RIC, this study, for the first time, offers a rare ex-perimental glimpse on finite orbit width effect on the excitation of EP-driven mode.Thedata presented here also demonstrates the ECH will be a powerful tool in the futurestellarator-based fusion device for the purpose of the control of the EP-driven mode andthe suppression of the associated loss of the EPs.

Acknowledgement

The author (X.D. Du) would like to thank L. Chen for fruitful discussions. This work is inpart supported by NIFS budget code ULPP021and ULPP028, the Ministry of Education,Science, Sports and Culture Grant-in-Aid for Scientific Research 24360386 and 26249144,and the JSPS-NRF-NSFC A3 Foresight Program (NSFC: No.11261140328, NRF: No.2012K2A2A6000443).

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