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SUMMARY:Interaction between energetic-particle-driven MHD mode and drift-w
ave turbulence based on global gyrokinetic simulation
DTSTART;VALUE=DATE-TIME:20210513T064700Z
DTEND;VALUE=DATE-TIME:20210513T070400Z
DTSTAMP;VALUE=DATE-TIME:20210417T025115Z
UID:indico-contribution-17064@conferences.iaea.org
DESCRIPTION:Speakers: Akihiro Ishizawa (Kyoto University)\nIn the study of
burning plasmas it is important to understand multi-scale interactions be
tween energetic-particle-driven MHD mode and drift-wave turbulence for est
ablishing good confinement of both energetic particles and bulk plasmas si
multaneously. We investigate nonlinear multi-scale interactions between TA
E\, which is unstable at low $n$\, and drift-wave turbulence\, which is dr
iven by micro-instabilities at high $n$\, by means of a global gyrokinetic
simulation code (GKNET [A]). We have revealed that TAE suppresses the mos
t unstable drift-wave mode by violating the ballooning structure of the dr
ift-wave mode\, and the TAE transfers the energy from the most unstable dr
ift-wave mode to lower $n$ modes to modulate turbulence\, because the TAE
has a finite $n$ in contrast to zonal flows ($n=0$). This modulation of dr
ift-wave turbulence by TAE leads to an enhancement of both energy flux of
bulk ions and particle flux of energetic ions. Hence\, TAE and drift-wave
turbulence synergistically enhance the transport of both bulk plasma and e
nergetic particles.\n\n**Introduction**: In order to realize good confinem
ent of burning plasmas it is necessary to reduce both energetic particle t
ransport and bulk plasma transport simultaneously. In burning plasmas drif
t-wave turbulence (DWT) and toroidal Alfven eigenmode (TAE) driven by ener
getic particles coexist\, and they interact each other by nonlinear mode c
oupling\, and thus the interaction may result in new transport phenomena\,
for instance\, the transport of energetic particles may be influenced by
turbulence and zonal flows which are active even in finite $\\beta$ plasma
s [B]. Since TAE is an MHD mode and drift-wave turbulence is electromagnet
ic at finite $\\beta$\, magnetic perturbations play an important role in t
he interaction and can increase turbulent transport by intensifying electr
ostatic potential perturbations [C]. In addition\, interactions between TA
E and drift-wave turbulence may excite stable low $n$ modes and increase t
urbulent transport as shown by the study of multi-scale interactions betwe
en magnetic islands and drift-wave turbulence [D].\n\n**Simulation model a
nd linear stability**: We investigate nonlinear interactions between TAE a
nd drift-wave turbulence by means of a global $\\delta$f gyrokinetic simul
ation code (GKNET) [A]. We consider a normal magnetic shear tokamak plasma
which has energetic particle pressure gradient and bulk plasma pressure g
radient with $\\beta=1.28\\%$\, $T_f/T_i=25$\, $m_i/m_e=100$\, and $\\rho_
*=1/100$. Figure 1 (a) shows that this plasma is unstable against a TAE at
low toroidal mode number $n=2$\, which has real frequency in the gap of A
lfven continuum indicated by yellow color. On the other hand\, a drift-wav
e instability (kinetic ballooning mode: KBM) is unstable at high toroidal
mode number $n \\geq 6$. The TAE has global structure (Fig. 1 (b))\, while
the KBM has ballooning structure characterized by micro-scale (Fig. 1 (c)
).\n\n![(a) Linear growth rate $\\gamma$ and real frequency $\\omega$ as a
function of toroidal mode number $n$\, where the gap of Alfven continuum
is indicated by yellow color. Color map of electrostatic potential $\\phi
$ of (b) TAE ($n=2$) and (c) a drift-wave instability (KBM) with $n=12$.][
1]\n\n**Turbulence modulated by TAE**: We have performed a nonlinear simul
ation of the plasma which is unstable against both the TAE and drift-wave
instability (KBM) (referred as "TAE+DWT"). In addition\, we carried out no
nlinear simulations of a plasma with flat energetic particle pressure prof
ile to obtain drift-wave turbulence ("only DWT") and a plasma with flat bu
lk pressure profile to obtain TAE ("only TAE")\, and then we compare them
with "TAE+DWT" to understand the influence of interactions between TAE and
drift-wave turbulence.\n\nIn "TAE+DWT"\, drift-wave turbulence (DWT) with
zonal flows is established at first ($t=12$ and 16 in Fig. 2) because the
growth rate of the drift-wave mode (KBM) is much higher than the TAE as s
hown in Fig. 1 (a). Then\, in this turbulent state\, the TAE ($n=2$) grows
slowly and violates the ballooning structure of the turbulence to reach a
quasi-steady turbulent state ($t=22$ and 36 in Fig. 2). We here compare t
ime evolution of some main toroidal modes of perturbations in "TAE+DWT" an
d "only DWT" in Fig. 3 (a). The most unstable drift-wave mode ($n=12$) get
s saturated by producing zonal flows ($n=0$) at $t=13$ for both "TAE+DWT"
and "only DWT". Then\, at $t=20$\, the TAE ($n=2$) grows in "TAE+DWT"\, wh
ile $n=2$ mode decreases in "only DWT"\, resulting in much higher amplitud
e of $n=2$ mode in "TAE+DWT" as indicated by the red arrow. Following the
growth of TAE ($n=2$) the most unstable drift-wave mode ($n=12$) further d
ecreases in "TAE+DWT" compared to "only DWT" after $t=20$ as indicated by
the blue arrow. Since the TAE has finite toroidal wavenumber in contrast t
o zonal flows ($n=0$)\, this nonlinear mode coupling between the TAE ($n=2
$) and the drift-wave mode ($n=12$) enhances another lower toroidal wavenu
mber mode ($n=12-2=10$) as indicated by the green arrow. Hence\, the TAE s
uppresses the most unstable drift-wave mode but enhances a lower toroidal
wavenumber mode to modulate the drift-wave turbulence. Due to this modulat
ion of turbulence by TAE\, the energy flux of bulk ions $Q_i$ in "TAE+DWT"
is enhanced at middle wavenumbers ($4 \\leq n \\leq 10$)\, and the peak o
f $Q_i$ in "TAE+DWT" is shifted from $n=12$ to $n=10$ compared to "only DW
T" (Fig. 3. (b)). In addition\, the particle flux of energetic ions $\\Gam
ma_f$ is enhanced in "TAE+DWT" compared to "only TAE" (Fig. 3. (c)). Thus\
, the interaction between TAE and drift-wave turbulence enhances the trans
port of both bulk plasma and energetic particles.\n\n![Color map of electr
ostatic potential $\\phi$ for "TAE+DWT" that is the nonlinear simulation o
f the coexistence of TAE and drift-wave turbulence.][2]\n\n![(a) Time evol
ution of electrostatic potential $\\phi_n$ of zonal flow ($n=0$)\, $n=2$\,
and drift-wave modes ($n=10$ and 12) in "TAE+DWT" (TAE and drift-wave tur
bulence) and "only DWT" (DWT without TAE). The red arrow indicates the enh
ancement of $n=2$ mode by the growth of the TAE ($n=2$) in "TAE+DWT". The
blue arrow indicates the suppression of the most unstable drift-wave mode
($n=12$) by the presence of TAE\, and the green arrow indicates the enhanc
ement of a drift-wave mode ($n=10$) caused by the interaction between the
TAE and the most unstable drift-wave mode ($n=12$). Time averaged spectrum
of (b) the energy flux of bulk ions $Q_i$ and (c) the particle flux of en
ergetic ions $\\Gamma_f$. These spectra are averaged over the time period
$t=25-38$.][3]\n\n[A] K. Imadera\, Y. Kishimoto\, K. Obrejan\, T. Kobiki a
nd J. Q. Li\, IAEA-FEC\, TH/P5-8 (2014).\n[B] A. Ishizawa\, K. Imadera\, Y
. Nakamura\, and Y. Kishimoto\, Phys. Plasmas\, 082301 (2019).\n[C] A. Ish
izawa\, D. Urano\, Y. Nakamura\, S. Maeyama\, and T.-H. Watanabe\, Phys. R
ev. Lett.\, 025003 (2019).\n[D] A. Ishizawa\, Y. Kishimoto\, and Y. Nakamu
ra\, Plasma Phys. Control. Fusion\, 054006 (2019).\n\n\n [1]: https://wor
kshop.nifs.ac.jp/fec2020/image/24-Ishizawa-image-fig_1.jpg\n [2]: https:/
/workshop.nifs.ac.jp/fec2020/image/24-Ishizawa-image-fig_2.jpg\n [3]: htt
ps://workshop.nifs.ac.jp/fec2020/image/24-Ishizawa-image-fig_3.jpg\n\nhttp
s://conferences.iaea.org/event/214/contributions/17064/
LOCATION:Virtual Event
URL:https://conferences.iaea.org/event/214/contributions/17064/
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