# Generation of shear flows induced by AE / EPM in LHD plasma

J. Varela, C. Hidalgo, T. Tokuzawa, K. Nagaoka, K. Tanaka, K. Nagasaki, S.

Ohdachi, K. Ida, X. Du, A. Cappa, et al.

► To cite this version:

J. Varela, C. Hidalgo, T. Tokuzawa, K. Nagaoka, K. Tanaka, et al. Generation of shear flows induced by AE / EPM in LHD plasma. Nuclear Fusion, 2024, 65 (2), pp.026002. 10.1088/1741-4326/ad9ab6. hal-05468254

HAL Id: hal-05468254

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# Generation of shear flows induced by AE / EPM in LHD plasma

## J. Varela

E-mail: jvrodrig@fis.uc3m.es

Institute for Fusion Studies, Department of Physics, University of Texas at Austin, Austin, Texas 78712, USA

National Institute for Fusion Science, National Institute of Natural Science, Toki, 509-5292, Japan

## C. Hidalgo

Laboratorio Nacional de Fusion—CIEMAT, Madrid, Spain

## T. Tokuzawa

National Institute for Fusion Science, National Institute of Natural Science, Toki, 509-5292, Japan

## K. Nagaoka

National Institute for Fusion Science, National Institute of Natural Science, Toki, 509-5292, Japan

## K. Tanaka

National Institute for Fusion Science, National Institute of Natural Science, Toki, 509-5292, Japan

## K. Nagasaki

Institute of Advanced Energy, Kyoto University, Uji, Kyoto, Japan

## S. Ohdachi

National Institute for Fusion Science, National Institute of Natural Science, Toki, 509-5292, Japan

## K. Ida

National Institute for Fusion Science, National Institute of Natural Science, Toki, 509-5292, Japan

## X. Du

General Atomics, P.O. Box 85608, San Diego, California 92186-5608, USA

## A. Cappa
Laboratorio Nacional de Fusion—CIEMAT, Madrid, Spain

S. Sharapov

UKAEA, Culham Science Centre, Abingdon, Oxfordshire OX14 3DB, UK

D. Zarzoso

Aix-Marseille Université, CNRS, Centrale Marseille, M2P2 UMR 7340,
Marseille, France

D. A. Spong

Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-8071, USA

L. Garcia

Universidad Carlos III de Madrid, 28911 Leganes, Madrid, Spain

Y. Ghai

Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-8071, USA

J. Ortiz

Universidad Carlos III de Madrid, 28911 Leganes, Madrid, Spain

**Abstract.** The generation of shear flows (SF) by Alfven Eigenmodes (AE) and energetic particle modes (EPM) have important effects on the operation of future nuclear fusion reactors, because SF regulate the saturation of the AE / EPM, the transport of EPs and thermal plasma as well as the formation of transport barriers between other consequences. The aim of this study is the analysis of shear flows generation during the saturation phase of Alfven Eigenmodes (AE) and energetic particle modes (EPM) in LHD plasma. Experiments performed in the 23rd and 24th LHD experimental campaigns are dedicated to explore the destabilization of AE / EPM in discharges with different heating patterns, thermal plasma and magnetic field configurations. In particular, the shots 176490 and 179697 show the destabilization of MHD bursts and energetic-ion-driven resistive interchange modes (EIC), respectively. Charge exchange spectroscopy (CXS) measurements in both discharges indicate the generation of shear flows by AE / EPM uncorrelated with the perturbation induced by the NBI. Nonlinear simulations performed using the gyro-fluid code FAR3d show the generation of zonal structures, specially shear flows, induced during the saturation phase of Toroidal Alfven Eigenmodes (TAE) triggered in the MHD burst as well as by the 1/1 EIC in the bursting phase. The simulations indicate shear flows are caused by the radial electric fields powered by energy transfers from the unstable AE / EPM towards the thermal plasma. The strongest shear flows are measured during the EIC bursting phase once the 1/1 EPM overlaps with nearby resonances at the plasma periphery. Likewise, the largest shear flows during the MHD burst are observed once TAEs radially overlap in the inner-middle plasma region.

PACS numbers: 52.35.Py, 52.55.Hc, 52.55.Tn, 52.65.Kj

Keywords: Stellarator, LHD, MHD, AE, pressure gradient driven modes
# 1. Introduction

The energetic particles (EP) generated by neutral beam injectors (NBI) in Large Helical Device (LHD) can induce instabilities [1, 2, 3, 4, 5, 6, 7]. EP driven modes enhance the EP transport and losses before thermalization, reducing the device performance and leading to an inefficient plasma heating [8, 9, 10, 11, 12, 13, 14, 15, 16, 17].

EP driven instabilities can be triggered if the EP drift, bounce or transit frequencies resonate with the shear Alfvén waves [18]. Alfvén eigenmodes (AE) are destabilized in the gaps of the shear Alfvén continua [19, 20], in particular the toroidicity induced AEs (TAE) are caused by the coupling between $m$ with $m + 1$ shear Alfvén waves of the same toroidal mode family ($n$ is the index of the toroidal mode and $m$ the index poloidal mode number) [21, 22]. In addition, energetic particle modes (EPM) are triggered inside the continuum if the EP driving effect is strong enough to exceed the continuum damping [23, 24, 25].

Large Helical Device (LHD) experiments with low plasma density and high thermal ion temperature, strongly heated by perpendicular neutral beam injectors [26], show magnetic fluctuations similar to the fishbone oscillations [27, 28] if the resistive interchange mode (RIC) is unstable at the plasma periphery [10, 29, 30, 31, 32]. The instability is called 1/1 energetic-ion-driven resistive interchange mode (EIC), triggered by the resonance between the precession motion of the helically trapped EP generated by the perpendiculars NBI (around the 10 kHz) and the RIC [27]. The 1/1 EIC belongs to the category of the energetic particle modes (EPM) [33, 34]. Numerical studies reproducing the saturation phase of the 1/1 EIC indicate the bursting behavior and complex radial structure are caused by the overlapping of the 1/1 perturbation with nearby resonances [35].

LHD operation scenarios with low magnetic field and plasma density heated by tangential NBIs show the destabilization of AEs [2, 36]. In addition, if the magnetic axis is displaced inward (inward shifted LHD configurations) bursting MHD activity is observed, induced by multiple TAEs triggered in the inner-middle plasma region in the frequency range of the 40 to 80 kHz [37, 38]. Recent numerical studies suggest the bursting behavior is caused by the overlapping between TAEs induced by different toroidal mode families [39, 40].

Nonlinear simulations performed by several authors indicate shear flows induced during the AEs saturation phase may lead to a reduction of the plasma turbulence level, improving the thermal plasma confinement [41, 42, 43, 44, 45]. The generation of shear flows by AE / EPM is not demonstrated yet, although there are indirect evidences from EAST and JET experiments. For example, the generation of shear flows by reverse shear AEs (RSAE) may explain why the operation requirements for the L-H transition in EAST plasma and formation of electron-internal transport barriers are relaxed if RSAEs are unstable [46]. Also, the generation of shear flows by fishbones could be behind the improved thermal plasma confinement observed in JET plasma [47].

LHD plasma is heated by three tangential NBI lines mainly parallel to the magnetic axis with a beam energy of 180 keV. In addition, two NBIs perpendicular to the magnetic axis are injected in the plasma periphery with a beam energy of 32 keV [48, 49, 50].

Present study is dedicated to analyze the generation of shear flows during the saturation phase of AE / EPM in LHD plasma, comparing experimental data and the output of nonlinear simulations. On that aim, a set of experiments were performed during the 23rd and 24th LHD campaigns, measuring the shear flows induced during the destabilization of EIC and MHD bursts. Next, the shear flows observations are compared with the zonal structures calculated in nonlinear simulations during the saturation phase of 1/1 EIC and TAEs using the gyro-fluid code FAR3d [39].

The FAR3d code solves the reduced nonlinear resistive MHD equations coupled with the moment equations of the energetic ion density and parallel velocity [51, 52, 53]. The Landau damping/growth is included by Landau closure relations, reproducing the linear wave-particle resonance effects on six field variables that evolve from a three dimensional equilibria generated by the VMEC code [54].

This paper is organized as follows. First, there is a description of the experiments and main plasma actuators in section 2. Next, the instabilities induced by the EPs are identified and described using different diagnostics in section 3. Shear flows measurements are discussed in section 4. Experimental and simulations data are compared in section 4.2. Finally, the conclusions of this paper are presented in section 6.
## 2. Experiments description

This section is dedicated to introduce the set of experiments performed to analyze the shear flows induced during MHD and EIC bursts. A subset of experiments is selected to compare discharges with and without bursting activity. The criteria to select the discharges for a detailed analysis is based on the plasma relaxation intensity, taking the cases showing the largest magnetic perturbations and frequency spectrum signal, and the identification of instabilities with clear TAE / EIC patterns by analyzing magnetic probe and BES data. Following simulations predictions, strong AE / EPM activity must lead to intense zonal structures, maximizing the possibilities of measuring shear flows in the experiment.

### 2.1. MHD burst

Experiments in the 23th LHD campaign, shot numbers 176481 to 176500, are dedicated to study shear flows induced during MHD bursts. The working gas is Hydrogen, the toroidal magnetic field strength of 0.8 T in the clockwise direction and the LHD configuration is inwards shifted with the vacuum magnetic axis at 3.6 m. The experiment target is to regulate the magnitude of the MHD burst perturbation, studying the link between shear flows and AE activity level.

MHD bursts are triggered in the frequency range of 40 to 80 kHz corresponding to TAEs destabilized in the inner-middle plasma region [37, 40]. The MHD burst causes an enhancement of the EP fluxes and the Mirnov coils show stronger MHD activity as well as an increment of high energy EP detection around 135 keV. The confinement of passing EP was analyzed using an E//B-type charge exchange tangential neutral particle analyzer (NPA) installed on a tangential port [55].

The intensity of the AE activity in the experiments is controlled modifying the NBI injection power (operating at full or half power) and by means of the variation of the NBI heating pattern (combination of NBIs 1, 2 and 3). Modifying the NBI power and heating pattern, EP population (EP $\beta$) changes between discharges as well as the AE stability. In addition, experiments with low $0.2 \cdot 10^{19} m^{-3}$ and high $1 \cdot 10^{19} m^{-3}$ thermal plasma density are performed. The AE activity also changes with respect to the thermal plasma density because the properties of the EP resonance depends on the thermal ion density, in particular the Alfvén velocity of the plasma. The general trend indicates high density discharges lead to a lower AE activity because the EP resonance is weaker and the EP slowing down time is faster [56].

A sub-set of discharges is selected; the shot 176490 with full NBI power and high thermal plasma density leading to the destabilization of an MHD

burst (figure 1) and the discharge 176492 with half NBI power and high thermal plasma density that shows unstable TAEs although the MHD burst is not triggered (figure 2).

Figure 1 shows the destabilization of an MHD burst between $t = 4.0$ and $4.3$ s. There is a sharp increase of the magnetic probes signal amplitude from $t = 4.0$ s as well as a broad AE activity from 40 to 90 kHz. It should be noted that the maximum frequency broadening of the AE activity is observed while the NBI 1 is injected ($t = 3.8$ to $4.0$ s), getting narrower and decaying until the MHD burst ends. From $t = 4.3$ s only the signal of individual TAEs are observed in the frequency ranges of 45, 50, 60 and 70 kHz. Figure 2 shows the same discharge configuration although reducing the EP drive by decreasing the NBI 2 and 3 power injection to half of the available power. Here, the NBI 1 operates at full power from $t = 3.8$ to $4.8$ s, leading to the destabilization of several TAEs in the frequency range of 45 to 90 kHz, although the TAE activity is much weaker compared to the discharge 176490 and the overlapping between the frequency range of TAEs signal is rather small, that is to say, the MHD burst is not triggered. Once the NBI 1 is turn off, NBI 2 and 3 cannot sustain an EP population large enough to destabilize TAEs, except for a TAE signal observed in the frequency range of 75 kHz. It should be noted that the magnetic probes signal is similar in both discharges because low frequency modes activity, identified as pressure gradient driven modes (PGDM), is almost the same (plasma averaged diamagnetic $\beta$ is comparable). The PGDM measured in the experiments are instabilities destabilized by low toroidal mode families, reason why these perturbations can be categorized as interchange modes.

In summary, the sub-set of discharges analyzed shows the NBI operational regime can be adapted to control the MHD burst destabilization threshold and perturbation magnitude. The onset of the MHD burst depends on the TAEs magnitude, that is to say, the radial overlapping level between different resonances.

### 2.2. EIC burst

Experiments in the 24th LHD campaign, shot numbers 179678 to 179697, are dedicated to study shear flows induced during EIC bursts. The working gas is Deuterium, the magnetic fields tested are 2.75 T and 1.375 T (half field configuration) in the clockwise direction with the vacuum magnetic axis at 3.6 m. Again, the experiment target is the destabilization of EIC burst in different operation scenarios modifying the relaxation intensity and studying the link between shear flows and EIC activity.

1/1 EIC shows different phases during the saturation phase [57]. 1/1 EIC bursting phase begins
<figure><img src="image_2.png" /><figcaption>**Figure 1.** Discharge 176490. Time evolution of the (a) NBI heating pattern, (b) averaged electron thermal density (black line) and plasma internal energy (red line), (c) thermal electron (green line) and ion (blue line) temperature, (d) magnetic perturbation measured by the magnetic probes, (e) frequency spectrum between 100 – 500 kHz and (f) below 100 kHz. The light cyan dashed vertical lines indicate the MHD burst during the discharge.</figcaption></figure>

<figure><img src="image_3.png" /><figcaption>**Figure 2.** Discharge 176492. Time evolution of the (a) NBI heating pattern, (b) averaged electron thermal density (black line) and plasma internal energy (red line), (c) thermal electron (green line) and ion (blue line) temperature, (d) magnetic perturbation measured by the magnetic probes, (e) frequency spectrum between 100 – 500 kHz and (f) below 100 kHz.</figcaption></figure>

with a sudden increase of the mode frequency to 9 kHz and an inwards extension of the perturbation from the plasma periphery towards the middle plasma region showing a complex eigenfunction structure, probably caused by the overlapping of the 1/1 EIC with nearby resonances [35].

The control of the EIC burst intensity in the experiments is more subtle compared to the MHD

burst case. The perpendicular NBIs power injection and heating pattern are fixed, the EIC activity is controlled by modifying the thermal plasma density and magnetic field intensity. The general trend indicates discharges with high density and high magnetic field show a lower EIC activity because the EP resonance is weaker [34]. On top of that, different heating patterns are tested with respect to the input
power of tangential NBIs, electron and ion cyclotron
resonance heating, because an increment of the thermal
plasma temperature at the plasma periphery improves
the 1/1 EIC stability [58, 34]. In addition, there is a
stabilizing effect of the passing EPs on the 1/1 EIC
[34]. It should be noted that the perpendicular NBI
4 operates using a pulsing pattern, requirement of the
charge exchange diagnostic (CXS).

A sub-set of discharges is selected; the shot 179697
is a configuration with half magnetic field strength
leading to unstable 1/1 EIC (figure 3) and the shot
179685 is a full magnetic field strength configuration
showing only unstable PGDM ( figure 4).

Figure 3 indicates the destabilization of 1/1 EIC bursts while the perpendicular NBI is injected from $t = 3.3$ to $5.3$ s. The magnetic probes signal is 35% larger compared to the discharge 176490 during the MHD burst, showing a broad EPM activity between 5 to 15 kHz. On the other hand, figure 4 indicates the destabilization of discrete PGDM at several frequencies below 20 kHz and a lower MHD activity, less than 20% compared to the discharge with 1/1 EIC bursts. It should be noted that the tangential NBI 1 during the discharge 179697 stops at $t = 3.9$ s, reason why the analysis is performed from $t = 4.0$ s to avoid the pollution of the plasma perturbations caused by EPMs.

In short, 1/1 EIC stability threshold and the
intensity of the 1/1 EIC relaxation can be controlled
by modifying the strength of the magnetic field in the
discharges, leading to an enhancement of the trapped
EP resonance in operation scenarios with half field
compared to full field discharges.

**3. Instability identification**

This section is dedicated to analyze the instabilities
observed in the reference discharges. In addition,
the plasma perturbations caused directly by the
NBI injection or by EP driven instabilities are
distinguished.

3.1. TAE destabilization in the MHD burst

The plasma perturbations caused by the NBI injection
and EP driven instabilities can be detached analyzing
the Broadband Radio-frequency Spectrometer (RF)
data. RF diagnostic measures the oscillating electric
field in the radiofrequency wave range (from 10 MHz to
3 GHz), providing information of high frequency waves
generated in the plasma by external actuators or EPs.
Figure 5a shows the correlation between RF signal
maxima in the range of 230 MHz and the injection of
the tangential NBI (pink arrow). On the other hand,
RF signal in the range of 600 MHz (fig. 5b) shows
perturbations uncorrelated with the NBI injection and
originated inside the plasma. That means the RF

data in this frequency range partially filtered out the
perturbation induced by the NBI injection and can be
used to identify plasma perturbations induced by EPs.

Figure 6 compares the local maxima of RF signal and magnetic field perturbation variation rate ($B'_{\theta}$) measured by the magnetic probes from 4.0 to 4.3 s. There is a correlation between the local maxima of RF and $B'_{\theta}$ (red arrows) indicating the presence of instabilities in the plasma. Such instabilities are not directly caused by the NBI injections at 4.0, 4.1 and 4.2 s. The sharp increase of the MHD activity highlighted by the orange arrow indicates the onset of the MHD burst at $t = 4.04$ s.

Figure 7 shows the coherence analysis between
the Beam Emission Spectroscopy (BES) and magnetic
probes (MP) data, dedicated to analyze the interrela-
tion between turbulence and magnetic perturbations.
BES can measure the macroscopic turbulence level and
zonal flow generation [59, 60, 61] while the magnetic
proves indicate the MHD activity in the plasma. The
analysis indicates unstable AEs in the frequency range
between 45-60 kHz once the MHD burst is triggered
at $t = 4.04$ s, consistent with previous experiments
[37, 38]. From $t = 4.04$ to $4.2$ s there is an en-
hancement of the AE activity around 60 kHz as well
as the destabilization of multiple AEs between 35-85
kHz. Previous numerical studies indicate these modes
are TAEs destabilized by different toroidal mode fam-
ilies [39]. These TAEs could be radially overlapped in
the inner-middle plasma region, leading to a transition
from the soft to the hard MHD limit and the triggering
of the MHD burst [40]. During the saturation phase of
the TAEs, the energy from the AEs is transferred to-
wards the thermal plasma generating zonal structures
as shear flows [43]. Consequently, there is an enhance-
ment of the macroscopic plasma turbulence linked to
a re-adjustment of the plasma flows during the MHD
burst. From $t = 4.2$ s the MHD activity above 50
kHz weakens as the TAEs saturate, thus AEs no longer
overlap as the radial width and amplitude of the per-
turbations decrease, reason why fig. 1 shows detached
and faded TAE signals after the MHD burst.

Summarizing, the analysis of the Broadband
Radio-frequency Spectrometer and magnetic probes
data shows the destabilization of instabilities driven
by EPs, uncorrelated with the perturbations directly
induced by the beams. Also, the coherence analysis
between Beam Emission Spectroscopy and magnetic
probes data indicates the destabilization of multiple
TAEs in the frequency range of 35-85 kHz that may
indicate the MHD burst is triggered by the radial
overlapping of the TAEs, leading to a transition from
the soft to hard MHD regime, an enhancement of
the plasma macroscopic turbulence as well as the
generation of shear flows.
<figure><img src="image_4.png" /><figcaption>**Figure 3.** Discharge 179697. Time evolution of the (a) NBI and ECH heating pattern, (b) averaged electron thermal density (black line) and plasma internal energy (red line), (c) thermal electron (green line) and ion (blue line) temperature, (d) magnetic perturbation measured by the magnetic probes, (e) frequency spectrum between 100 – 500 kHz and (f) below 100 kHz.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>**Figure 4.** Discharge 179685. Time evolution of the (a) NBI and ECH heating pattern, (b) averaged electron thermal density (black line) and plasma internal energy (red line), (c) thermal electron (green line) and ion (blue line) temperature, (d) magnetic perturbation measured by the magnetic probes, (e) frequency spectrum between 100 – 500 kHz and (f) below 100 kHz.</figcaption></figure>

## 3.2. EPM destabilization in the EIC burst

The EIC bursts are analyzed using the same method than the previous section. Nevertheless, the energy of the EPs injected by the perpendicular NBIs is almost 5 times lower compared to the tangential beam, deposited close to the plasma periphery. That involves the RF data in the range of 600 kHz can captures both the plasma perturbation directly induced by the perpendicular NBI injection as well as the instabilities

driven by the EPs, reason why RF data in the range of 230 kHz is not shown.

Figure 8 shows the RF data in the discharges 179685 (only PGDM activity) and 179697 (EIC burst). Panel a indicates largest perturbations in the discharge 179685 during the injection of the perpendicular NBIs (pink arrows), that is to say the perturbations induced by unstable PGDM are filtered out. Panel b shows large perturbation uncorrelated with the injection of
<figure><img src="image_6.png" /><figcaption>**Figure 5.** Discharge 176490. Broadband Radio-frequency Spectrometer data at (a) 230 and (b) 600 MHz. Bold pink arrows and vertical pink dashed lines indicate the tangential NBI injection times. Dashed light cyan vertical lines indicate the MHD burst during the discharge.</figcaption></figure>

the perpendicular NBIs (bold green arrows) or during failures of the perpendicular NBI 5 (cyan arrow). The magnitude of the uncorrelated perturbations is as large as the perturbations induced by the perpendicular NBI and could be linked to the destabilization of EIC bursts.

Figure 9 shows the RF and magnetic probe data in the shot 179697 during the discharge time highlighted in fig. 8b with a bold orange arrow. This EIC event is selected because the data is not polluted by the failure of the perpendicular NBI 5 at $t = 4.0$ s and it is clearly uncorrelated with respect to the injection of the perpendicular and tangential NBIs. The study is performed from $t = 4.92$ to 4.94 s. The data shows several correlated $B'_\theta$ and RF maxima (orange arrows). The magnetic probes data shows a sudden increase of $B'_\theta$ followed by a chain of rather large fluctuations, similar to the magnetic field perturbations identified by other authors during the EIC bursting phase [27, 56].

In shot, the discharge 179697 shows the destabilization of large MHD perturbations uncorrelated with the injection of tangential and perpendicular NBIs. Local maxima in RF and magnetic probe data indicate

<figure><img src="image_7.png" /><figcaption>**Figure 6.** Discharge 176490. Broadband Radio-frequency Spectrometer data at 600 MHz between (a) 4.0-4.1 s, (c) 4.1-4.2 s and (e) 4.2-4.3 s. Magnetic field perturbation variation rate measured by the magnetic probes between (b) 4.0-4.1 s, (d) 4.1-4.2 s and (f) 4.2-4.3 s. Red arrows indicate the local maxima of the magnetic probe signal. Orange arrow indicates the plasma perturbation linked to the MHD burst onset.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>**Figure 7.** Discharge 176490. Coherence analysis between the Bean Emission Spectroscopy and magnetic probes data. Vertical pink dashed lines and arrows indicate the tangential NBI injection. Dashed orange vertical line and arrow indicate the onset of the MHD burst.</figcaption></figure>
<figure><img src="image_9.png" /><figcaption>**Figure 8.** Broadband Radio-frequency Spectrometer data at 600 MHz. Discharge (a) 179685 and (b) 179697. Pink arrows indicate the injection of the perpendicular NBIs. Cyan arrows indicate plasma oscillation linked to a failure of the perpendicular NBI 5. Green bold arrows show plasma perturbation uncorrelated with the injection of the perpendicular NBIs. Orange bold arrows indicate the EIC event studied in fig. 9.</figcaption></figure>

plasma perturbations identified as EIC bursts. On the other hand, the discharge 179685 only shows plasma perturbations correlated with the injection of the perpendicular NBIs as well as a lower MHD activity compared to the shot 179697, mainly linked to the destabilization of PGDM.

## 4. Shear flows measurements

This section is dedicated to analyze the shear flows generated during MHD and EIC bursts measured by the charge exchange spectroscopy (CXS) diagnostic. CXS data provide information of the poloidal/toroidal rotation velocities using the charge exchange collisions between the neutral beam and impurities [62, 63]. On that aim, NBI 4 is injected using a modulated pattern (10 Hz with 80 ms beam-on 20 ms beam-off) to subtract the background emission.

<figure><img src="image_10.png" /><figcaption>**Figure 9.** (a) Broadband Radio-frequency Spectrometer (600 MHz) and (b) Minor coils data in the discharge 179697 for the EIC events highlighted in fig. 8 between $t = 4.92-4.94$ s. Orange bold arrows indicate individual bust events.</figcaption></figure>

### 4.1. Shear flows measured during MHD and EIC bursts

Figure 10a shows the CXS data in the discharge 176490. There are radial electric fields ($E_r$) larger than 30 kV/m in the inner-middle plasma region ($R < 4.2$ m), reaching the maximum value at $t \approx 4.1$ s during the injection of the tangential NBIs (indicated by the pink dashed vertical lines). In addition, there is another radial electric field maximum at the plasma periphery ($R > 4.5$ m), around 30 kV/m, generated by the perpendicular NBI 4. The radial electric field leads to the generation of shear flows ($\vec{V}_{\theta,\zeta} = \vec{E}_r \times \vec{B}$ with $\vec{V}_{\theta}$ the poloidal thermal plasma velocity and $V_{\zeta}$ the toroidal thermal plasma velocity) as can be observed in panels b and c. In particular, the local maximum of $E_r$ at the inner-middle plasma region is linked to an enhancement of $V_{\zeta}$, consistent with the plasma perturbation induced by the tangential NBIs. Likewise, the local maxima of $E_r$ at the plasma edge is correlated with an enhancement of $V_{\theta}$ as would be expected for the plasma perturbation induced by the perpendicular NBIs. The analysis of the shear flows
during the MHD burst is performed doing a zoom in of the CXS data in the plasma region where the AE activity is observed, the inner-middle plasma region, while the event is observed, $t = 4.0-4.3$ (panels d to f). Panel d shows at $t = 4.1$ s two local maxima of $E_r$ around $R = 3.75$ m and $3.85$ m. $E_r$ maximum at $R = 3.75$ m is larger than -40 kV/m and it is correlated with a local maximum of $V_ζ > 15$ km/s (panel f). On the other hand, $E_r$ maximum at $R = 3.85$ m ($\approx -30$ kV/m) shows a much weaker correlation with $V_ζ \approx -5$ km/s although larger with respect to $V_θ$, up to $\Delta|V_θ| = 12$ km/s between $R = 3.85$ and $4.0$ m (panel e). The poloidal component of the thermal plasma velocity enhances after the TAEs are destabilized at $t = 4.02$ s (orange solid vertical line), before the NBI injection at $t = 4.1$ s that causes a further enhancement of the flows. That means, CXS data may indicate the generation of shear flows in the inner-middle plasma region during the MHD burst.

Figure 11a indicates for the discharge 179697 several $E_r$ maxima nearby the magnetic axis and plasma edge correlated in time. This is caused by the perpendicular NBI injection (pink dashed vertical lines), inducing plasma perturbations that reach the inner plasma region. The consequence is the generation of shear flows in the inner plasma and the edge (panel b), although slightly weaker in the middle plasma region. It should be noted that the largest $V_ζ$ values are observed nearby the magnetic axis induced by the tangential NBI after the NBI 1 stops (panel c), because NBI 1 and 2 injection directions are opposite reason why $V_ζ$ was balanced before $t = 3.9$ s). To analyze the shear flows generated during the EIC burst, CXS data is zoom in between the middle-outer plasma region ($R = 4.2-4.55$ m) from $t = 4.5$ to $5.0$ s. The EIC is triggered nearby the 1/1 rational surface located around $R = 4.4-4.5$ m. There are several $E_r$ local maxima uncorrelated with the injection of the perpendicular NBIs (panel d) linked to EIC bursts (green dashed vertical lines). EIC bursts also lead to an enhancement of $V_θ$ although a rather weak variation of $V_ζ$. That means the destabilization and saturation of the EICs may generate shear flows with $\Delta|V_θ| \approx 5-10$ km/s, particularly around $R = 4.45$ m. In addition, the EIC perturbation extends towards the middle plasma region and secondary maxima of $E_r$ and $V_θ$ appear from $R = 4.45$ to $4.30$ m.

In summary, CXS data may indicate MHD and EIC burst induce shear flows in the inner-middle and middle-outer plasma regions, respectively. The measured local maxima of $V_θ$ correlate with the radial location of unstable TAEs and 1/1 EIC, induced during the saturation phase of the AE / EPM.

## 4.2. Experimental observation versus nonlinear simulations

This section is dedicated to compare the output of nonlinear simulations performed using the code FAR3d and experimental data during the MHD and EIC bursts, particularly the generation of shear flows. FAR3d code solves a reduced set of equations for high-aspect ratio configurations and moderate $\beta$-values (of the order of the inverse aspect ratio) [64, 65, 66, 67], retaining the toroidal angle dependency in an exact three-dimensional VMEC equilibrium [54]. The EP perturbation is added by moments of the gyro-kinetic equation, the EP density ($n_f$) and the EP velocity parallel to the magnetic field lines ($v_{||f}$). The model requires performing gyro-kinetic simulations to obtain the Landau closure coefficients in the gyro-fluids simulations, matching the analytic TAE growth rates of the two-pole approximation of the plasma dispersion function with a Lorentzian energy distribution function for the energetic particles. The model equations can be found in the reference [68].

FAR3d code participated in bench-marking studies showing similar results compared to gyro-kinetic and hybrid codes [69]. FAR3d code was validated comparing simulation results and experimental data in studies dedicated to explore the linear [33, 34, 35, 39, 40] and nonlinear [70, 71, 72, 73] MHD stability in LHD plasma.

Fixed boundary equilibria were calculated using the VMEC code after the destabilization of an EIC burst in the discharge 116190 and an MHD burst in the shot 47645. The detailed description of FAR3d code simulations reproducing MHD and EIC bursts are found in the references [35, 40].

Figure 12 compares the measured radial electric field and thermal plasma poloidal velocity between the discharge 176490 and the output of the nonlinear simulations performed to reproduce the MHD burst in the discharge 47645. Panel a shows an increment of the electrostatic potential in the simulations during the MHD burst phase (red line) compared to the pre-burst phase (green line), increasing from $\Delta\Phi = 0.2$ keV to 1.3 keV in the inner-middle plasma region ($R = 3.75$ to $4.05$ m). The radial electric field in the simulation, panel b, also increases from $\Delta E_r = 5$ kV/m in the pre-burst phase to $16$ kV/m in the burst phase. The radial electric field measured by the CXS diagnostic in the discharge 176490 at $t = 4.01$ s (before the MHD burst, cyan line) is smaller with respect to $t = 4.11$ s (during the MHD burst, blue line), $\Delta E_r = 12$ and $38$ kV/m respectively. Consequently, the trends in simulations and experimental data are consistent. Panel c shows an increase of the thermal plasma poloidal velocity from $\Delta V_θ = 6$ km/s to $26$ km/s comparing pre-burst and burst phases in the simulation. The measured
<figure><img src="image_11.png" /><figcaption>**Figure 10.** Discharge 176490 CXS data. (a) Radial electric field, (b) poloidal plasma velocity and (c) toroidal plasma velocity. Zoom in CXS data during the MHD burst ($t = 4.0-4.3$ s) at the inner-middle plasma region ($R = 3.6-4.2$ m) of the (d) radial electric field, (e) poloidal plasma velocity and (f) toroidal plasma velocity</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>**Figure 11.** Discharge 179697 CXS data. (a) Radial electric field, (b) poloidal plasma velocity and (c) toroidal plasma velocity. Zoom in CXS data during the EIC burst ($t = 4.5-5.0$ s) at the middle-outer plasma region ($R = 4.2-4.8$ m) of the (d) radial electric field, (e) poloidal plasma velocity and (f) toroidal plasma velocity</figcaption></figure>

thermal plasma poloidal velocity is $\Delta V_{\theta} = 4$ km/s at $t = 4.01$ s and $\Delta V_{\theta} = 16$ km/s at $t = 4.11$ s. Again, simulations and experimental data tendencies are similar. It should be noted that the radial electric field and thermal plasma poloidal velocity in the simulations are smaller compared to the CXS data, discrepancy that may indicate the MHD burst simulation reproduces a weaker plasma relaxation compared to 176490 experiment.

Figure 13, panels a and b, show the correlation between local maximum of the $n/m = 0/0$ component

of the time averaged electric field and the poloidal thermal plasma velocity once the MHD burst is triggered in the simulation. That means, the saturation of the TAEs triggered in the inner-middle plasma leads to the generation of radial electric fields powered by the energy transfer from the AEs towards the thermal plasma. At the same time, the radial electric field induces shear flows, particularly large in the plasma region where the MHD burst is triggered in agreement with CXS measurements.

Figure 14 compares the measured radial electric
<figure><img src="image_13.png" /><figcaption>**Figure 12.** Time averaged (a) electrostatic potential, (b) radial electric field and (c) thermal plasma poloidal velocity. The red line represents the simulation burst phase, the green line the simulation pre-burst phase, the cyan line the measured data at $t = 4.01$ s and the blue line the measured data at $t = 4.11$ s in the discharge 176490. The experimental uncertainty, vertical blue / cyan lines are included in the graphs.</figcaption></figure>

field and thermal plasma poloidal velocity at the plasma periphery ($R = 4.2$ to $4.55$ m) between the discharge 179697 at $t = 4.93$ s and the output of the nonlinear simulations performed to reproduce the EIC burst in the discharge 116190. It should be noted that there is a difference of $0.05$ m comparing the magnetic axis location of the experiments and the intensity of the EIC triggered in the 116190 discharge is stronger, although a qualitative comparison between experiment and simulations can be performed. Panel a indicates the electrostatic potential obtained in the simulations is two times larger in the burst phase (red line) compared to the pre-burst phase (green line), increasing from $\Delta\Phi = 0.2$ keV to $0.4$ keV. The local maximum of the radial electric field in both pre-burst and bursting phases is located at $R = 4.4-4.45$ m,

<figure><img src="image_14.png" /><figcaption>**Figure 13.** Time averaged poloidal contour of (a) the radial electric field and (b) the logarithm of the poloidal component of the thermal plasma velocity during the MHD burst in the simulation.</figcaption></figure>

the radial location of the 1/1 EIC (panel b), two times larger in the simulation bursting phase with respect to the pre-burst phase, $\Delta E_r = 110$ and $50$ kV/m respectively. It should be noted that during the simulation bursting phase there are secondary maxima of the electric field at $R \approx 4.32$ and $4.25$ that correspond to the destabilization of $3/4$ and $2/3$ EPMs with $\Delta E_r = 50$ and $15$ kV/m, respectively. CXS data of the discharge 179697 at $t = 4.93$ s (blue line) also shows three local maxima of the electric field at the plasma periphery that could be also explained by the destabilization of other EPMs beside the 1/1 EIC, although the measurement uncertainty is rather large thus no clear conclusions can be done. The largest $\Delta E_r = 20$ kV/m is observed at $R = 4.4-4.5$ m linked to the 1/1 EIC. The other local maxima at $R \approx 4.35$ and $4.22$ m with $\Delta E_r = 15$ and $10$ kV/m respectively, could be triggered by unstable EPMs, consistent with the nonlinear simulations. The radial electric field is five times larger in the simulations compared to the CXS data. Likewise, the thermal plasma poloidal velocity in the simulation bursting phase is $\Delta V_\theta = 30$ km/s although CXS data shows $\Delta V_\theta = 7$ km/s, $4$ times smaller. The plasma radial electric field and thermal plasma poloidal velocity of the modeled EIC burst in the 116190 discharge are larger compared to the CXS measurements in the 179697 discharge, difference explained by the stronger plasma relaxation measured in the 116190 shot compared to the 179697 discharge. Nevertheless, the simulated values are close to the experimental observations in other discharges, for example the shot 109190, showing an electrostatic potential above $10$ kV and radial electric fields around $75$ kV/m measured with the heavy ion beam probe
(HIBP) [27]. On the other hand, an excess on the energy transfer from the EIC to the thermal plasma and the lack of neoclassical effects in the model leading to an extra damping of the poloidal flows, can also partially explain the simulation overestimation.

<figure><img src="image_15.png" /><figcaption>**Figure 14.** Time averaged (a) electrostatic potential, (b) radial electric field and (c) thermal plasma poloidal velocity. Red line represents the simulation burst phase, the green line the simulation pre-burst phase and the blue line the measured data in the discharge 179697 at *t* = 4.93 s. The experimental uncertainty, vertical blue lines are included in the graphs.</figcaption></figure>

Figure 15, panels a and b, indicates the correlation of the *n/m* = 0/0 component of the time averaged electric field and the poloidal thermal plasma velocity in the plasma regions where the 1/1 EIC is triggered. EIC energy is transferred towards the thermal plasma inducing radial electric fields and shear flows during the modes saturation phase, following the same trends than the CXS measurements.

In short, there is a reasonable agreement between CXS measurements and nonlinear simulation with respect to the radial location of the EIC and MHD

<figure><img src="image_16.png" /><figcaption>**Figure 15.** Time averaged poloidal contour of (a) the radial electric field and (b) the logarithm of the poloidal component of the thermal plasma velocity during the EIC burst in the simulation.</figcaption></figure>

burst. In addition, similar trends are obtained in the analysis of the simulation and CXS data. Experimental and numerical results may suggest the generation of shear flows by AE / EPM in nuclear fusion plasma, particularly during bursting events.

## 5. Discussion

A set of experiments in the 23th and 24th LHD campaigns is dedicated to analyze the generation of shear flows by AE / EPM during bursting events, in particular for MHD and 1/1 EIC bursts. The first part of the study is dedicated to identify the most appropriate actuators to control the bursts destabilization threshold and intensity. Next, a subset of experiments is selected to analyze and compare the MHD activity in discharges with and without bursts. Finally, shear flows are measured using the CXS diagnostic during the MHD bursts triggered in the shot 176490 and 1/1 EIC bursts in the shot 179697.

MHD burst destabilization threshold can be controlled modifying the NBI injection pattern, regulating the TAEs amplitude and radial overlapping. A higher NBI injection intensity leads to a larger population of passing EP in the plasma, more unstable TAEs and virulent MHD bursts. On the other hand, 1/1 EIC bursts are more violent and show a higher recurrence if the magnetic field strength of the operation scenario is reduced, because trapped EP resonance is enhanced in LHD configurations with half field compared to full field discharges.

The analysis of discharges with MHD burst (shot 176490) and without bursting activity (shot 176492) indicates MHD bursts are triggered above a given
threshold of the AE activity, that is to say the AEs perturbation is wide enough to induce the radial overlapping of TAEs and cause the transition from the soft to the hard MHD limit. The study of the coherence between Beam Emission Spectroscopy and magnetic probes data in the discharge 176490 at the time the MHD burst is triggered may suggest the plasma is in the hard MHD regime, showing the destabilization of multiple TAEs in the frequency range of 35-85 kHz. These observation are consistent with previous numerical studies concluding that MHD bursts are triggered due to the overlapping of TAEs induced by different toroidal mode families [40].

Another transition from the soft to the hard MHD limit leading to the destabilization of 1/1 EIC bursts is observed in the half field discharge 179697, unlike the full field discharge 179685 that only shows unstable PGDM. Reduce the strength of the LHD magnetic field causes an enhancement of the trapped EP resonance, hence a stronger and wider 1/1 EPM perturbation at the plasma periphery [34]. The consequence is the inwards propagation of the perturbation [57] and the radial overlapping of the 1/1 EPM with nearby resonances, as it is observed in the CXS measurement of the discharge 179697. These results are consistent with nonlinear simulation that suggest the 1/1 EIC bursts are triggered once the 1/1 EIC is radially overlapped with 3/4 and 2/3 EPMs [35].

Verify the generation of zonal structures by AE / EPM requires measuring shear flows uncorrelated with the perturbations induced during the NBIs injection, that is to say, shear flows must be generated by plasma born instabilities due to the EP drive. Broadband radio-frequency spectrometer and magnetic probes data indicate the destabilization of plasma perturbations uncorrelated with the injection of parallel and perpendicular NBIs in the discharges 176490 and 179697. The analysis of the CXS data indicates shear flows in the inner-middle plasma are generated during the MHD burst and at the plasma periphery during the 1/1 EIC bursts. The local maximum of the poloidal component of the thermal plasma velocity is correlated with the radial location of the unstable AEs / EPMs.

The accuracy of the CXS data decreases in the inner plasma, particularly nearby the magnetic axis, although improves at the middle-outer plasma region. Specifically, the uncertainty of the electric field and poloidal velocity is in the range of 25–50% with respect to the measured value at different radial locations. The analysis of the CXS data considering the uncertainty indicates the measurements have the required accuracy to identify the generation of zonal structures although it is not enough to provide a good estimation of the intensity of the flows and radial electric fields. New

diagnostics must be applied in future experiments to better constrain the intensity of the shear flows and radial electric fields.

CXS measurements and nonlinear simulations reproducing MHD and 1/1 EIC bursts are compared, showing a reasonable agreement with respect to the radial location of the zonal structures [35, 40]. The analysis of the nonlinear simulations suggests there is an energy transfer from the AE / EPM towards the thermal plasma during the modes saturation phase, leading to the generation of radial electric field and shear flows. It should be noted that the 1/1 EIC burst simulation predicts stronger shear flows compared to the experiment at the plasma periphery. Nevertheless, the electrostatic potential and radial electric field obtained in the simulation are close to the values measured in other discharges as the shot 109190, indicating that the simulation reproduces a stronger plasma relaxation than the EIC activity observed in the discharge 179697.

Comparing simulation results and experimental data must be done considering the model limitations. FAR3d uses Maxwellian EP distribution functions, thus the resonance induced by slowing down distribution functions are approximated by performing parametric studies using multiple Maxwellian distributions, fitted to the EP populations and encompassing the key resonances in the experiment. In addition, the trapped EP model used in the EIC simulations should be considered a first order step in the analysis of resonances induced by toroidal and helically trapped EP, approximating the resonance caused by particles with different pitch angles by adapting the bounce distance and frequency of the trapped EP in the model. It must be also mentioned that neoclassical effects are not included in the model leading to a possible overestimation of the shear flow intensity in the simulations, although the vorticity equation includes a diffusivity term which acts effectively like a viscosity and the time scales of the viscosity effects are larger compared to the total simulation time, thus a possible shear flow overestimation should be small. Nevertheless, the nonlinear simulations can still reproduce several of the MHD and EIC burst features observed in the experiments.

The generation of shear flows could be beneficial for the thermal plasma confinement in future nuclear fusion reactors, reducing the turbulence transport and the device operation requirements for the L-H transition [46, 47, 74, 75, 76, 77]. This is the case for shear flows induced by AE / EPM [46, 47, 78, 79] and kinetic ballooning modes [80] although it is unclear for other instabilities as interchange modes [72, 81] and tearing modes [82]. Thus, further analysis are required to confirm if shear flows induced by AE / EPM in LHD plasma leads to an improved thermal
plasma confinement and a reduction of the turbulent transport. Preliminary observational studies of the plasma turbulence may indicate EIC bursts lead to decrease of the plasma turbulence level [56]. Moreover, it is essential to distinguish the effect of the shear flows generated by AE / EPM on the thermal plasma confinement for plasmas in the soft and hard MHD regimes, that is to say, avoiding the device operation in the hard MHD limit might be mandatory to gain an improved device operation. It should be noted that several authors already discussed an enhancement of fluids turbulence in the presence of shear flows [83, 84, 85, 86], particularly if there are instabilities that lead to torn flux surfaces, the case of bursting events in nuclear fusion plasma [35, 40, 43, 45, 73]. Consequently, shear flows generation by AE / EPM and the effect on the thermal plasma confinement should be considered as a key topic in future nuclear fusion reactors. In the short term, it is mandatory analyzing the shear flows in ITER and JT60SA plasmas because several numerical models predict the destabilization of AE / EPM [87, 88, 89, 90, 91, 92, 93], thus the saturation of AE / EPM may have an influence on their performance. Future analysis will be dedicated to explore the effect of the AE shear flows on turbulence and thermal plasma confinement.

## 6. Conclusions

The key actuators to control MHD and EIC bursts destabilization threshold and intensity are the NBI injection intensity and magnetic field strength, respectively. Stronger NBI injection leads to more intense MHD burst and low magnetic field induces more recurrent and intense EIC burst.

CXS measurement identify zonal structures induced during the MHD burst in the inner-middle plasma and by the 1/1 EIC bursts at the plasma periphery. Data accuracy is now the adequate to study the flows intensity although enough to identify the presence of shear flows.

Experimental data and nonlinear simulations show a reasonable agreement with respect to the radial location of the shear flows. The simulations predict stronger flows compared to the experiment for the EIC case, overestimation that could be linked to the effect of the neoclassical viscosity not included in the model.

Shear flows induced by saturating AE / EPM linked to the destabilizing effect of alpha particles could have a beneficial effect on the thermal plasma confinement for future fusion reactors. Further studies are required to confirm this possibility.

## Acknowledgments

The authors would like to thank the LHD technical staff for their contributions in the operation and maintenance of LHD. This work was supported by US DOE under grant DE-FG02-04ER54742, the Comunidad de Madrid under the project 2019-T1/AMB-13648 and NIFS07KLPH004. The data supporting the findings of this study are available in the LHD experiment data repository at https://doi.org/10.57451/lhd.analyzed-data.

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