# Measurement of zero-frequency fluctuations generated by coupling between
Alfvén modes in the JET tokamak

J. Ruiz Ruiz<EMAIL_ADDRESS>Rudolf Peierls Centre for Theoretical
Physics, University of Oxford, OX1 3NP, UK  J. Garcia  CEA, IRFM, F-13108
Saint-Paul-lez-Durance, France  M. Barnes  Rudolf Peierls Centre for
Theoretical Physics, University of Oxford, OX1 3NP, UK  University College,
Oxford OX1 4BH, UK  M. Dreval  National Science Center Kharkiv Institute of
Physics and Technology, 1 Akademichna Str., Kharkiv 61108, Ukraine  C. Giroud
UKAEA (United Kingdom Atomic Energy Authority), Culham Campus, Abingdon,
Oxfordshire, OX14 3DB, UK  V. H. Hall-Chen  Institute of High Performance
Computing, A*STAR, Singapore 138632, Singapore  M. R. Hardman  Tokamak Energy
Ltd, 173 Brook Drive, Milton Park, Abingdon, OX14 4SD, United Kingdom  J. C.
Hillesheim  Commonwealth Fusion Systems, Devens, MA, USA  Y. Kazakov
Laboratory for Plasma Physics, ERM/KMS, TEC Partner, 1000 Brussels, Belgium
S. Mazzi  CEA, IRFM, F-13108 Saint-Paul-lez-Durance, France  F. I. Parra
Princeton Plasma Physics Laboratory, Princeton, New Jersey 08543, USA  B. S.
Patel  UKAEA (United Kingdom Atomic Energy Authority), Culham Campus,
Abingdon, Oxfordshire, OX14 3DB, UK  A. A. Schekochihin  Rudolf Peierls Centre
for Theoretical Physics, University of Oxford, OX1 3NP, UK  Merton College,
Oxford OX1 4JD, UK  Z. Stancar  UKAEA (United Kingdom Atomic Energy
Authority), Culham Campus, Abingdon, Oxfordshire, OX14 3DB, UK  the JET
contributors  See the author list of “Overview of T and D-T results in JET
with ITER-like wall” by CF Maggi et al. to be published in Nuclear Fusion
Special Issue: Overview and Summary Papers from the 29th Fusion Energy
Conference (London, UK, 16-21 October 2023).  the EUROfusion Tokamak
Exploitation Team  See the author list of “Overview of the EUROfusion Tokamak
Exploitation programme in support of ITER and DEMO” by E. Joffrin Nuclear
Fusion 2024 10.1088/1741-4326/ad2be4

###### Abstract

We report the first experimental detection of a zero-frequency fluctuation
that is pumped by an Alfvén mode in a magnetically confined plasma. Core-
localized bidirectional Alfvén modes of frequency inside the toroidicity-
induced gap (and its harmonics) exhibit three-wave coupling interactions with
a zero-frequency fluctuation. The observation of the zero-frequency
fluctuation is consistent with theoretical and numerical predictions of zonal
modes pumped by Alfvén modes, and is correlated with an increase in the deep
core ion temperature, temperature gradient, and confinement factor $H_{89,P}$.
Despite the energetic particle transport induced by the Alfvén eigenmodes, the
generation of a zero-frequency fluctuation that can suppress the turbulence
leads to an overall improvement of confinement.

††preprint: APS/123-QED

Achieving net energy gain from magnetically confined thermonuclear fusion is
primarily hindered by the turbulent transport of heat and particles across the
confining magnetic field. Turbulent transport determines the background plasma
profiles, and, as a result, the overall fusion power-balance in a reactor. In
a burning plasma, fusion reactions between deuterium and tritium (DT) will
generate supra-thermal alpha particles of energy $E=3.5$ MeV, more than two
orders of magnitude higher than the temperature of the thermal plasma,
typically $T\approx 10-15$ keV. Fusion-born alpha particles are expected to
have characteristic velocities larger than the Alfvén speed
$v_{A}=B/(\mu_{0}\sum_{i}m_{i}n_{i})^{1/2}$, where $B$ is the background
magnetic field, $\mu_{0}$ is the vacuum magnetic permeability and the sum is
taken over the thermal ion species of mass $m_{i}$ and density $n_{i}$. Such a
super-Alfvénic population is capable of triggering magnetohydrodynamic (MHD)
Alfvén instabilities, which have been predicted [1] and observed in a wide
range of magnetic-confinement devices [2, 3, 4, 5, 6, 7]. For many years, the
presence of fast-ion-driven Alfvén instabilities has been thought to be
detrimental to the overall plasma confinement, since they are detrimental for
the confinement of the energetic particles themselves [8, 9, 10]. Recently,
however, numerical simulations of the turbulence have shown that fast-ion-
driven Alfvénic activity can have a positive effect on the confinement of the
_thermal_ plasma [11, 12, 13, 14, 15]. The current leading hypothesis
explaining this effect is the pumping by the Alfvén eigenmode of a zonal-flow
component, which could interact with, and suppress, the turbulence. This seems
to be in agreement with analytical predictions of zonal-flow excitation by
Alfvén eigenmodes [16, 17, 18, 19] and with numerical simulations [20, 21, 22,
23, 24]. Zonal modes are zero-frequency perturbations that are constant within
a magnetic-flux surface. In the traditional zonal-flow paradigm, a zonal flow
generated by the turbulence fluctuations can produce stabilization [25, 26,
27, 28, 29]. The zonal-flow generation by Alfvén eigenmodes, however, has so
far lacked direct experimental confirmation. In this article, we report the
first experimental detection of a zero-frequency fluctuation that is pumped by
Alfvén eigenmodes.

The Joint European Torus (JET [30]) is the magnetic-confinement facility that
has come the closest to approaching the physics regimes of a burning plasma
[31, 32, 33, 34]. The JET discharge 97090 was an L-mode characterized by a
plasma current of $I_{p}=2.4$ MA, toroidal magnetic field $B_{0}=3.2$ T, line-
integrated density $\int n_{e}\text{d}l=7.5\times 10^{19}$ m-2, Greenwald
fraction of $f_{GW}=0.36$ [35] and $q_{95}=3.75$, all of which remained
constant within uncertainties throughout the discharge. The central electron
density was $n_{e}\approx 4\times 10^{19}$ m-3. The plasma was ion-cyclotron-
resonance heated (ICRH) using the three-ion scheme [36, 37, 38] (main ions
were composed of $80\%$ hydrogen and $20\%$ deuterium). A first Ohmic phase
was followed by phases of increasing ICRH power of $P_{\text{ICRH}}=$ 2 MW
(low), 4 MW (medium) and 7 MW (high, see black curve in figure 1.(a). A trace
population of 3He ions absorbed $\gtrsim 90\%$ of the ICRH power and was
accelerated to energies of 4-5 MeV, as predicted by TRANSP [39] and TORIC [40]
(consistent with $\gamma$-ray measurements in similar discharges [41]). In the
absence of tritium, MeV-range 3He can mimic the effect of fusion-born alpha
particles in a burning plasma (although the anisotropic ICRH fast-ion
distribution function is qualitatively different from the isotropic alpha-
particle fusion source, and can result in differences in the Alfvénic-
instability drive [42]). The fast 3He ions deposited $\approx 90\%$ of their
energy on the thermal electrons by collisionally slowing down. The remainder
of the ICRH power is predicted to be absorbed directly by electrons, with less
than $1\%$ of the power predicted to be absorbed directly by the thermal ions.
Thus, $\gtrsim 90\%$ of the heating power was predicted to be ultimately
deposited on the electrons. As we will see, this is at odds with the increase
in the deep-core ion temperature observed in this plasma.

Figure 1: (a) Magnetic spectrogram from the MHD magnetic-coil diagnostic in
JET, along with the total ICRH power $P_{\text{ICRH}}$. (b) Electron
temperature from the ECE diagnostic on axis (black) and at $\rho\approx 0.3$
(red). Also shown are $\tau_{ei}/\tau_{E}$ (cyan), the electron-ion collision
time divided by the energy confinement time (TRANSP), and, the L-mode
confinement factor $H_{89,P}$ (blue). Vertical dashed lines indicate times for
which DBS measurements are shown in figures 3, 4 and 5.

The plasma exhibits internal sawtooth oscillations [43] with an inversion
radius at $\rho\approx 0.3$ (consistent with the safety factor $q=1$), where
$\rho$ is the magnetic-flux-surface label defined at the square root of the
normalized toroidal magnetic flux ($\rho=0$ corresponds to the magnetic axis,
while $\rho=1$ is the location of the edge separatrix). The sawtooth period
increases with $P_{\text{ICRH}}$, as shown by the electron temperature $T_{e}$
in figure 1.(b) (from the electron-cyclotron-emission diagnostic, ECE), and
consistent with the stabilization of sawteeth by fast ions [44]. This gives
rise to the so-called monster sawteeth during the medium- and
high-$P_{\text{ICRH}}$ phases. Following a sawtooth event, the on-axis
electron temperature of $T_{e}\approx 5$ keV is shown to drop down to $\approx
2$ keV. The impact of the sawtooth crash is very weakly present near the
inversion radius. In this manuscript, we analyze the plasma during time
windows when the profiles have fully recovered after a sawtooth crash (dashed
lines in figure 1.(b).

After recovery of the profiles from a sawtooth crash, the trapped 3He
population at MeV energies was observed to destabilize a range of Alfvén
eigenmodes during the medium- and high-$P_{\text{ICRH}}$ phases. Both
phenomena are often simultaneously observed in tokamak experiments [45, 46,
47]. Figure 1.(a) shows the magnetic spectrogram of fluctuations from the MHD
magnetic-coil diagnostic. During the medium-$P_{\text{ICRH}}$ phase, magnetic
fluctuations associated with Alfvén modes are observed around $300$ kHz.
During the high-$P_{\text{ICRH}}$ phase, separate branches are observed to
sweep down in frequency in the range $300\rightarrow 280$ kHz, consistent with
the expected temporal evolution of the central safety factor following a
sawtooth crash [48, 49]. This behavior has already been observed in many major
tokamaks, e.g., JT-60U [50, 48, 51, 49, 52], TFTR [53], and JET [54, 55, 47].
The modes are spatially localized around the $q=1$ surface with very low
magnetic shear, as suggested by Doppler-backscattering measurements, pressure-
constrained EFIT (including fast-ion pressure), and ECE.

The unstable Alfvén eigenmodes in figure 1.(a) have toroidal mode numbers in
the range $n=3-6$. The toroidicity-induced gap frequency associated with the
toroidal Alfvén eigenmode (TAE [56]) for large-aspect-ratio tokamaks is
$f_{A}\approx v_{A}/4\pi qR_{0}$, where $R_{0}$ the major radius of the flux-
surface centre. The numerical values for the density, $q=1$ and $R_{0}\approx
2.9$ m lead to $f_{A}\approx 270$ kHz. This is consistent with the magnetic
fluctuations seen in figure 1.(a), which suggests that these modes live in the
TAE gap, and could be identified as tornado TAEs [49]. Note that the plasma
beta in this discharge is low ($\beta_{e}\lesssim 0.004$ for electrons), which
is consistent with the conditions to excite shear Alfvén modes such as TAEs.

Figure 2: (a) Profiles of the main-ion temperature $T_{D}$ at low, medium, and
high $P_{\text{ICRH}}$. (b) Normalized temperature-gradient scale length
$a/L_{TD}$. Both $T_{D}$ and $a/L_{TD}$ increase inside $\rho\approx 0.4$ with
increasing $P_{\text{ICRH}}$, despite negligible main-ion heating.

The dominant electron heating in this discharge increases the electron
temperature at the inner radii from 2 keV (Ohmic) to 5 keV (high
$P_{\text{ICRH}}$). The main-ion temperature in the deep core also increases
(figure 2.(a) and approaches the electron temperature at medium and high
$P_{\text{ICRH}}$. The measurements are made with main-ion charge-exchange
recombination spectroscopy [57] during $10$ ms neutral-beam-injection (NBI)
blips (performed every second), which allow the temperature to be measured
without affecting the overall plasma. The increase in the main-ion temperature
shows that it is not clamped at a specific value, as in recent experiments of
pure electron-cyclotron-resonance heating [58, 59]. This is a very positive
result for fusion, since burning plasmas will have dominant electron heating
from the slowing down of 3.5 MeV alpha particles, but will require high main-
ion temperatures for fusion reactions to occur. The main ions here also
exhibit an increase in the normalized temperature gradient
$a/L_{TD}=-\text{d}\log T_{D}/\text{d}\rho$ inside $\rho\approx 0.4$ ($a$ is
the plasma minor radius). The increase in $a/L_{TD}$ starts outside the
sawtooth inversion radius at $\rho\approx 0.3$, and suggests that fast-ion-
driven modes may be improving the energy confinement of the main ions.

The increase in the main-ion temperature is a striking finding. The main ions
experience negligible direct heating from ICRH, and their collisional coupling
to the electrons decreases as the temperature increases. This is demonstrated
in figure 1.(b), where the electron-ion collision time $\tau_{ei}$ divided by
the total energy-confinement time $\tau_{E}$ is shown to increase (as modeled
by TRANSP). Linear Landau damping of the TAE on the main ions is also expected
to be very weak due to low ion beta [60, 61], as is nonlinear Landau damping
[62, 63, 64, 65] (here $\beta_{i}\lesssim 0.003$). This suggests that a
different mechanism must explain the ion-temperature increase. The total
energy-confinement factor for the L-mode is shown to be $H_{89,P}<1$ in the
low-$P_{\text{ICRH}}$ case, but increases to $H_{89,P}>1$ with increasing
$P_{\text{ICRH}}$ (figure 1.(b)). We conjecture that the improved confinement
and ion-temperature increase observed here are due to the suppression of
turbulent transport by zero-frequency zonal modes pumped by Alfvén eigenmodes
[66, 12, 11, 14]. Below, we provide direct experimental evidence for the
presence of such a mechanism. We stress that this situation is very different
from NBI-heated discharges that use lower-energy fast ions, where most of the
heating is absorbed by the thermal ions, external torque drives flow-shear
suppression of the turbulence, and Alfvén modes are more difficult to
destabilize. Similar experiments in JET with MeV-range ions have exhibited an
improvement in the confinement of the thermal plasma [41, 67, 12].

To confirm that the Alfvén modes shown in figure 1 play a crucical role in the
overall confinement, we performed turbulence measurements at $\rho\approx
0.25-0.35$ using the Doppler-backscattering system (DBS) in JET, which detects
fluctuations of the electron density. In the Doppler-backscattering technique
[68, 69, 70, 71, 72, 73, 74], a beam of microwaves is launched into the core
plasma until it encounters a cutoff surface. The detector receives
backscattered radiation from turbulent fluctuations with characteristic
wavenumber $k_{\perp}$ that are local to the vicinity of the cutoff [75], as
predicted by beam-tracing numerical simulations of the microwave beam [76]. We
normalize the scattered turbulence wavenumber $k_{\perp}$ by the local ion
sound gyroradius $\rho_{s}=c_{s}/\Omega_{D}$, where $c_{s}=\sqrt{T_{e}/m_{D}}$
is the sound speed, $m_{D}$ is the deuterium mass,
$\Omega_{D}=q_{D}B_{0}/m_{D}c$ its gyro-frequency, $q_{D}$ its charge, and $c$
the speed of light. The DBS measurements presented here are sensitive to
density fluctuations at wavenumbers $k_{\perp}\rho_{s}\approx 2-4$. Dedicated
analysis of the scattering trajectory using the beam-tracing code Scotty [76,
75] shows that $k_{\perp}$ has a small toroidal component that overlaps with
$n=3-6$ of the unstable Alfvén modes in figure 1.(a). This suggests that DBS
measurements can be sensitive to Alfvén modes in these conditions.

Figures 3, 4 and 5 show the power spectrum $P_{s}(f)$ and the bicoherence
$B_{s}(f_{1},f_{2})$ of the electron-density fluctuations for the low-,
medium- and high-$P_{\text{ICRH}}$ phases, respectively. The measurements are
taken at specific times that are shown by the colored vertical dashed lines in
figure 1.(b). The backscattered power is calculated from the Fourier-
transformed backscattered complex signal amplitude $\hat{A}_{j}$ as
$P_{s}(f)=\langle|\hat{A}_{j}|^{2}\rangle_{T}$, where the
$\langle.\rangle_{T}$ denotes an ensemble average and the $f=0$ component of
$\hat{A}_{j}$ is removed ($j$ denotes the sample realization). The period of
each time window is $T=0.5-1$ ms, which is much longer than the turbulence
correlation time, which scales as $a/c_{s}\sim 10^{-5}-10^{-6}$ s. The
bicoherence [77] associated with the ensemble of realization signals
$\\{A_{j}\\}$ is

$\displaystyle
B_{s}(f_{1},f_{2})=\frac{\langle\hat{A}_{j}(f_{1})\hat{A}_{j}(f_{2})\hat{A}_{j}(f_{1}+f_{2})^{*}\rangle_{T}}{\langle|\hat{A}_{j}(f_{1})\hat{A}_{j}(f_{2})|^{2}\rangle_{T}^{\frac{1}{2}}\langle|\hat{A}_{j}(f_{1}+f_{2})|^{2}\rangle_{T}^{\frac{1}{2}}}.$
(1)

The modulus of the bicoherence $|B_{s}(f_{1},f_{2})|$ in equation (1) is high
when the frequency $f_{1}$ has a phase-matched relationship with the frequency
$f_{2}$ to generate a third frequency at $f_{1}\pm f_{2}$. The ensemble
averaging $\langle.\rangle_{T}$ is critical to eliminate independent modes at
the frequencies $f_{1}\pm f_{2}$. The bicoherence is a measure of three-wave
nonlinear coupling between fluctuations of frequency $f_{1}$ and $f_{2}$.

Figure 3 shows the modulus of the bicoherence $|B_{s}(f_{1},f_{2})|$ and the
power spectrum $P_{s}(f)$ at low $P_{\text{ICRH}}$. The bicoherence is
calculated for $255$ windows of period $T=1$ ms that are half-overlapping. The
DBS beam reaches the cutoff surface at $\rho=0.247$ (where $q\approx 1$),
corresponding to the scattered wavenumber $k_{\perp}\rho_{s}=2.58$. The power
spectrum $P_{s}(f)$ is broadband for fluctuations in the range $f\lesssim 200$
kHz characteristic of ion-temperature-gradient-driven turbulence (ITG). A peak
at zero frequency is observed, consistent with many previous DBS measurements.
The bicoherence displays broadband phase-matched relationships between
frequencies in the range $f_{1},f_{2}<100$ kHz, as expected from nonlinear
interactions between turbulent eddies characteristic of drift-wave turbulence.
The amplitude, however, remains low at $\approx 0.2$, and this suggests that
nonlinear interactions between low-frequency drift-wave fluctuations are
broadband and modest in the low-$P_{\text{ICRH}}$ phase.

Figure 3: (Left) Bicoherence spectrum at low $P_{\text{ICRH}}$. (Right) Power
spectrum $P_{s}(f)$. Both are characteristic of broadband drift-wave
turbulence.

Figure 4 shows the modulus of the bicoherence and the power spectrum at medium
$P_{\text{ICRH}}$, calculated for a total of $63$ half-overlapping windows of
period $T=0.5$ ms. The DBS beam reaches the cutoff surface at $\rho=0.355$
($q\approx 1$), corresponding to the scattered wavenumber
$k_{\perp}\rho_{s}=2.07$. The power spectrum $P_{s}(f)$ is broader than in the
low-$P_{\text{ICRH}}$ phase, featuring fluctuations in the range $f\lesssim
800$ kHz, as well as spectral peaks at the local Alfvén gap frequency
$f_{A}\approx 290$ kHz and a harmonic at $2f_{A}$. The spectral peaks appear
for positive and negative frequencies, suggesting the presence of
bidirectional Alfvénic activity. Careful analysis of the DBS microwave beam,
pressure-constrained EFIT, and the $q=1$ constraint from ECE shows that the
modes observed in figure 4 are well localized around $q=1$. This is consistent
with previous observations of core-localized TAEs in TFTR [78, 79, 80] and
tornado modes in JT-60U [49]. Such modes were predicted to exist at low shear
[81], consistent with the low shear value in this JET experiment
($\hat{s}\lesssim 0.1$). The bicoherence in figure 4 displays broadband phase-
matched relationships for multiples of the local Alfvén gap frequency $f_{A}$,
the strongest of which are $(f_{1},f_{2})=\\{(\pm f_{A},\pm f_{A})\\}$
(amplitude $\approx 0.6$), which correspond to co-propagating TAEs that couple
to generate a perturbation of frequency $\pm 2f_{A}$, as well as
$(f_{1},f_{2})=\\{(2f_{A},-f_{A}),(-f_{A},2f_{A})\\}$, which correspond to
perturbations of frequency $2f_{A}$ coupling to a counter-propagating
perturbation at frequency $f_{A}$ that generates a co-propagating perturbation
at $f_{A}$. The bicoherence also clearly exhibits phase-matched relationships
between perturbations at multiples of $f_{A}$ and a zero-frequency
fluctuation. To our knowledge, this is the first experimental demonstration in
a magnetically confined plasma that Alfvén modes living inside the fundamental
toroidicity-induced frequency gap (and higher-frequency gaps) beat with
counter-propagating perturbations to generate a zero-frequency fluctuation.
The zero-frequency fluctuations observed here can naturally be interpreted as
zonal modes driven by Alfvén eigenmodes, which have been predicted
analytically [16, 17, 18, 19] and numerically [20, 22, 23, 24, 12, 11, 14].
Such zonal modes can suppress ITG-driven turbulence, which would explain the
increase of the ion temperature and its gradient (figure 2).

Figure 4: The same as figure 3, but at medium $P_{\text{ICRH}}$. (Left) The
bicoherence displays phase-matched relationships for multiples of $f_{A}$
(vertical dashed lines). The strongest interactions are between frequencies
$\pm f_{A}$ and $\pm 2f_{A}$. A weaker phase-matched relationship is observed
between fluctuations at multiples of $f_{A}$ and a zero-frequency fluctuation.
(Right) The power spectrum $P_{s}(f)$ displays spectral peaks at $\pm f_{A}$
and $\pm 2f_{A}$.

Figure 5 shows the modulus of the bicoherence and the power spectrum at high
$P_{\text{ICRH}}$, calculated for a total of $127$ half-overlapping windows of
period $T=1$ ms. The DBS beam reaches the cutoff surface at $\rho=0.251$
($q\approx 0.92$) for $k_{\perp}\rho_{s}=3.78$. The power spectrum is
broadband for fluctuations in the range $f\lesssim 600$ kHz, but also displays
spectral peaks at the local Alfvén gap frequency $f_{A}\approx 290$ kHz and
its multiples. Similarly to figure 4, the bicoherence displays broadband
phase-matched relationships for multiples of $f_{A}$. Importantly, the
highest-amplitude phase matching is now for the frequency pairs
$(f_{1},f_{2})=\\{(2f_{A},0),(2f_{A},-2f_{A}),(3f_{A},0),(3f_{A},-3f_{A})\\}$
(amplitude $\approx 0.5$), i.e., the pairs that involve a zero-frequency
fluctuation. This is different from the medium-$P_{\text{ICRH}}$ phase, in
which the phase-matched relationships involving the zero-frequency fluctuation
were subdominant to other mode-mode interactions. Interestingly, the modes at
the fundamental Alfvén gap frequency $f_{A}$ display a weaker phase-matched
relationship with the zero-frequency fluctuation. Higher multiples of the
Alfvén frequency show weaker phase-matched relationships, resulting in a
peculiar grid structure.

Figure 5: (Left) The bicoherence spectrum at high-$P_{\text{ICRH}}$ displays
phase-matched relationships for multiples of the local Alfvén gap frequency
$f_{A}$. The strongest phase matching is for frequency pairs involving a zero-
frequency fluctuation: $(f_{1},f_{2})=\\{(\pm 2f_{A},0),(\pm 3f_{A},0)\\}$.
(Centre) Zoom into the left pannel. (Right) The power spectrum $P_{s}(f)$
displays spectral peaks at $f_{A}$ and its multiples.

Figures 4 and 5 confirm that Alfvén modes living inside the toroidicity-
induced Alfvén-frequency gap (and higher-frequency gaps) beat with counter-
propagating Alfvén modes to generate a strong zero-frequency fluctuation that
is consistent with a zonal mode. When this behavior is observed, the total
energy-confinement factor increases ($H_{89,P}>1$), as do the main-ion
temperature and its gradient in the deep core, despite negligible direct ion
heating. This shows the strong beneficial effect that Alfvén eigenmodes can
have on the confinement of the thermal plasma. This is to be constrasted with
the stable-Alfvén-mode case (low $P_{\text{ICRH}}$), which exhibited low ion
temperature and temperature gradient, and $H_{89,P}<1$. This is the first
experimental confirmation in a magnetically confined plasma of a zero-
frequency fluctuation that is pumped by Alfvén modes, and is correlated with
hotter-than-expected main ions. It suggests that zonal modes driven by Alfvén
modes can suppress the turbulence and lead to an overall improvement of energy
confinement in the plasma.

Admittedly, the presence of unstable Alfvén eigenmodes is not always
correlated with improved confinement. It is also responsible for strong
energetic-particle transport, which is not studied here, and is highly
detrimental to energy confinement. The balance between this and the improved
confinement for the thermal plasma observed here is still an open problem. It
seems plausible that if this balance is quantitatively understood, unstable
Alfvén modes could be tailored to improve the overall confinement in the
burning plasmas expected to be achieved in the imminent future.

This work has been supported by the Engineering and Physical Sciences Research
Council (EPSRC) [EP/W026341/1]. The work of M.B. and A.A.S. was supported in
part by the EPSRC grant EP/R034737/1. The work of A.A.S. was also supported in
part by the STFC grant STW000903/1 and by the Simons Foundation via a Simons
Investigator Award. V. H. Hall-Chen was partly funded by an A*STAR Green Seed
Fund, C231718014, and a YIRG, M23M7c0127. This work was supported by the U.S.
Department of Energy under contract number DE-AC02-09CH11466. The United
States Government retains a non-exclusive, paid-up, irrevocable, world-wide
license to publish or reproduce the published form of this manuscript, or
allow others to do so, for United States Government purposes. This work has
been carried out within the framework of the EUROfusion Consortium, funded by
the European Union via the Euratom Research and Training Programme (Grant
Agreement No 101052200 — EUROfusion). Views and opinions expressed are however
those of the author(s) only and do not necessarily reflect those of the
European Union or the European Commission. Neither the European Union nor the
European Commission can be held responsible for them.

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