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22EA-3

Light scattering on atmospheric ice particles for lidar applications
Alexander Konoshonkin, V.E. Zuev Institute of Atmospheric Optics SB RAS
RIAM Adviser: Hajime Okamoto, RIAM, Kyushu University

Abstract
Poor knowledge of the microphysical and radiative parameters of cirrus clouds (i.e. sizes,
shapes and spatial orientation of ice crystals of the clouds and their scattering cross-sections andphase functions) is one of the main sources of uncertainties in the modern numerical models forlong-term weather forecasting and the global climate change. Therefore a number ofinternational projects and space missions were focused on such studies. Cloud radar and lidar
instruments are powerful and perspective tools for these investigations. However, interpretationof the cloud radar and lidar signals reflected from cirrus clouds is a difficult problem not solved
decisively yet.
Last years the RIAM team of the project demonstrated (Okamoto et al., 2019-2021) thatsynergy use of the cloud profiling radar (CPR) of CloudSat and space lidar CALIPSO provides
more accurate retrievals of cloud properties than the single use of CPR or lidar. The products andalgorithms for the analysis of cloud microphysics have been developed. Here the problem of
non-spherical scatterings in CPR observables was numerically solved by means of the discrete
dipole approximation (DDA) and FDTD approximations (Okamoto 2002, Ishimoto 2008).
These algorithms were generalized for application to EarthCARE mission with its CPR andlidar ATLID. The treatment of non-spherical scatterings in ATLID observables is crucial for the
retrieval of cloud microphysics and we used the physical-optics approximation developed by the
IAO team of the project (Borovoi, Konoshonkin et al., 2017-2021). During the joint research by
IAO team and RIAM team we have modified and checked jointly the algorithms based on thesynergy use of CPR, lidar ATLID, and multi-spectral radiometer of EarthCARE.
PurposeAim of the joint research was to modify and check jointly the algorithms for retrieval of
microphysical properties of cirrus clouds based on the synergy use of CPR, lidar ATLID, andmulti-spectral radiometer of EarthCARE. While these algorithms have been developed by the
RIAM team earlier as far as the cloud radar signals also were calculated by the reliable
numerical methods, the main obstacle was to calculate the light scattering by the ice crystals of
cirrus clouds for the lidar ATLID.
MethodFor the ATLID lidar (λ = 0.355 μm), the light backscattering matrices for nonspherical ice
particles were calculated within the framework the physical optics method. The refractive index
of ice was taken as 1.3249 + 0i. For the 94-GHz CPR radar (λ = 3189 μm), the backscatteringmatrices of microwave radiation were calculated within the discrete dipole approximation
developed by M. Yurkin; in this case, the refractive index of ice was taken as 1.7864 + 0.0032i.
The following shapes of randomly oriented particles were modeled: hexagonal columns
and plates, bullets, droxtals, aggregates, bullet-rosettes, particles of an arbitrary shape, andspherical particles. When modeling by the discrete dipole method, the particles were represented
by a set from 4000 to 20000 dipoles depending on the particle size.
It is accepted to define dimensions of large nonspherical cirrus cloud particles by theirmaximum size (the distance between the most remote points of the particle) Dmax, but we foundthat the equivalent radius (Req) is more relevant property. In our calculations, it varied within the

range from about 10 to 1000 μm. Thus, the typical crystal size significantly exceeds the
wavelength of the lidar but is less than the wavelength of the cloud radar.
Results
We have obtained the solution of the light scattering problem for the ATLID lidar in termsof Muller matrixes and presented it as a database. As an illustration, Fig. 1a shows the S11
element of the Mueller matrix as a function of the equivalent radius Req of the particle.

a)b)
Fig.1. The S11 element of the Mueller matrix (a), the ratio of the cloud radar to the lidar signal(b)
After we could solve the problem of scattering by cirrus cloud ice particles as applied to
the ATLID and CPR, we could calculate the ratio of the cloud radar signal to the lidar signal.
Figure 1b shows the ratio of the cloud radar signal to the lidar signal. The ratio was calculated by
the equationF

E radar
E lidarcV radarcV lidar

radar
S11
lidar
S11

(1)

Discussion
Equation (1) involves the following assumptions: the cloud radar and the lidar observe thesame ensemble of ice crystals (although the fields of view of the instruments are different) andthe cloud is homogeneous both in the orientation of the crystals and in their size.
Within the scope of this work, we do not consider the question of how such assumptions
are allowable; therefore, special attention should be paid to this when interpreting theexperimental data. Besides, ice crystals in cirrus clouds are not monodisperse but are distributedby sizes. Since the question of choosing the law of crystal size distribution is still underdiscussion, we chose as a preliminary estimate the gamma distribution.
The main conclusion of the research is that it is the cloud radar–lidar ratio that is the mostinformative for retrieve the size of crystals after specifying their shape. The obtained results wereused for modified and check jointly the algorithms based on the synergy use of CPR, lidar
ATLID, and multi-spectral radiometer of EarthCARE.
Publications
1. Shishko V.A., Timofeev D.N., Konoshonkin A.V., Kustova N.V., Kan N., Tkachev I.V.,
Masuda K., Ishimoto H., Okamoto H., Borovoi A.G. Backscattering characteristics of opticaland electromagnetic waves in joint sensing of cirrus clouds by a polarizing lidar (0.355 μm) anda 94-Ghz radar// Atmospheric and Oceanic Optics, 2022, V. 35. No. 06. pp. 775–781. DOI:
10.1134/S1024856022060239
2. Konoshonkin A.V., Tkachev I.V., Kustova N.V., Timofeev D.N., Borovoi A.G. Updated
databank of backscattering Mueller matrices of cirrus clouds’ ice crystals for lidar applications //International Laser Radar Conference, June 26 – July 1, 2022. [S03_P05].
3. Konoshonkin A.V., Kustova N.V., Shishko V.A., Timofeev D.N., Tkachev I.V.,
Salnikov K.S. Light scattering database for interpretation of lidar sounding of cirrus clouds //Proc. SPIE 12265, Remote Sensing of Clouds and the Atmosphere XXVII, 122650D (2022).
DOI: 10.1117/12.2636363

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Plasma start-up and sustainment in spherical tokamak configuration by RF
TAKASE Yuichi(Tokamak Energy Ltd., United Kingdom)
An on-site and on-line hybrid workshop on “Plasma start-up and sustainment in sphericaltokamak configuration by RF” was held on 2nd and 3rd February at Advance Fusion
Research Center in Research Institute for Applied Mechanics, Kyushu University. Lively
discussions were held following each presentation.
Agendand

2 February
10:00 Ǧ10:10
Yuichi Takase / Kazuaki Hanada
WS purpose and agenda
10:10 - 10:30
Kazuaki Hanada
Dependence of wall saturation time on wall temperature in QUEST
10:30 - 11:10
Takumi Onchi
Report on the ECH experiment in QUEST 2022 campaign
11:10 - 11:50
Ryuya Ikezoe
Probing of fast electrons and corresponding kinetic modes on QUEST
11:50 - 13:30 Lunch
13:30- 14:10
Kengoh Kuroda
Development of transient CHI startup using a new electrode configuration
on QUEST
14:10 - 14:50
Shin Kubo
Study on the electron Bernstein wave detection using HCN laser
scattering on QUEST
14:50 - 15:30
Hitoshi Tanaka
Present Status of LATE Experiment (Remote)15:30 – 15:50 Coffee Break15:50 - 16:20
Atsushi Fukuyama
Modeling of O-X-B mode conversion on QUEST
16:20 - 17:00
Yuichi Takase
Achievements and Future Plans at Tokamak Energy
17:00 - 17:40
A. Köhn-Seemann
Simulation of the O-X mode conversion in MAST Upgrade (Remote)17:40 – Group Photo

3rd February
10:00 - 10:40
Naoto Tsuji
Studies of RF start-up on the TST-2 spherical tokamak
10:40 Ǧ 11:20
Masayuki Ono
X-I mode for efficient solenoid-free ECCD plasma current start-up andramp-up for fusion reactor
11:20 Ǧ 12:00
Luis F. Delgado-Aparicio
Off-axis seed and growth of runaway electrons in MST tokamak plasmas
12:00 - 13:00 Lunch
13:00 Ǧ 13:40
Luis F. Delgado-Aparicio
X-ray imaging crystal spectrometer US-Japan collaboration for JT60SA
13:40 Ǧ 14:20
Syunichi Shiraiwa
Integration of RF sheath BC to a large electro-magnetic wave simulation
14:20 Ǧ 15:00
Nicola Bertelli
ICRH simulations of ITER antenna and a comparison with different RFsolvers15:00 Ǧ 15:10
Coffee Break
15:10 Ǧ 16:00
Discussion on future plan in AFRC (QUEST)
All suggested focus and output for this joint drafting session
16:00 ǦDrafting of proposals for experiments, diagnosis, and analysis
17:00 ǦSummary
Presentation Summary
Kazuaki Hanada
Introduction of Japanese stratagem for ST reactor development and the present
standpoint of QUEST were explained. Steady State operation of high-performance
plasma is still one of the most important subjects on the stratagem in the view ofworldwide data base for long pulse operation of high-performance plasma. The QUEST
project has successfully achieved 6 h discharge that is the world record of pulse duration
for tokamak-type plasma and is staying at the turning point to go up the performance. To
obtain high-performance plasma, it is well known that lowering fuel particle recycling isa key. QUEST has been equipped with capability for wall temperature regulation since2015. Consequently, 6h discharges could be achieved at the wall temperature, TW<473K
under the cooling down condition of center-stack cover panels (CSPs) made of SS-316L.
It can be explained by storing hydrogen into the SS-316L material at low temperature
TW<423K. The time for reaching wall saturation, WWS has been investigated, collecting
longer than 30 min. Higher TW reduces WWS, but TW control can assist to make fuelrecycling lower than unity and the pulse duration extended up to more than 3 h from 40
min even TW ~ 623K that is relevant to future fusion reactors.
Takumi Onchi
䞉 For the QUEST spherical tokamak experiment, Medium scale maintenance of 28
GHz-GYT system was completed in 2022.
䞉 Avoiding RF power absorption into energetic electrons, bulk electrons tend toincrease temperature.
䞉 Electron temperature exceeds 1 keV in the small Tokamak-like configuration withretarding electric field.
䞉 ECH + OH realized the density higher than the cut-off density for 8. 56 GHz
Ryuya Ikezoe
Energetic Particle Probe (EPP) was completed, and various information about fastelectrons, which had not been observed before, became available. The first experimentshowed that it can be used in the following three ways;
1. Fast hard X-ray monitor (Hard X-rays from entire plasma regions)Compared to the existing CdTe detectors, the number of counts is very large and fastphenomena can be measured, leading to the world's first observation of highfrequency fluctuations of fast electrons. Experimental evidence for the interaction of
fast electrons and high frequencies modes.
2. Local hard X-ray measurement
At R <1.3 m, braking X-rays from fast electrons colliding with the probe head are
massively measured, which can give the spatial distribution of fast electron flux in
SOL. Unlike general lost-particle detectors mounted on the wall, it can measureparticles that are not in loss trajectories.
3. Local pitch angle & energy (E, θ) spectrum measurement
Ultimately, electron velocity distribution is evaluated.
Kengoh Kuroda
Transient CHI current start-up by using newly designed simple electrode has been
examined in QUEST.
ʀ The result of LFS and HFS CHI on the initial test system suggested that the HFS CHI
was suitable in QUEST configuration.
ʀ In the remodeled HFS CHI system, sufficient injector flux can be formed in theinjector region by PF5-1 coil close to the region, the breakdown mainly occurs in theinjector region by the NSTX type gas manifold, the space between the electrode andouter vessel wall prevents the absorber arc, and the profile of the injector current isestimated by a number of magnetic sensors of Bt’ on the vessel wall.
ʀ In the initial test on the remodeled system, higher toroidal current was repeatedly
achieved under higher injector flux condition. However, flux sufficiently expanded
only under high vertical field (high PF26 coil current) condition because as the PF26
coil current decreased, the injector current flowing out to the absorber region
increased, in which the formation of the closed flux surfaces was not achieved.
In Dec. 2022 CHI exp, we tried to improve the CHI discharge, in which the ceramic
cover was installed on outer parts of the electrode to prevent the injector current fromflowing out to absorber region, the capacitor bank power supply was modified to apply
higher voltage with shorter pulse, and each PF5-1 and PF5-2 coils was individuallycontrolled for forming the injector flux.
ʀ By applying higher voltage (-1925V) with less amount of injected gas (5.5torr*L),
the flux evolved largely under the condition of lower PF26 coil current (0.85kA).
ʀ In fast camera images, the formation of the closed flux surfaces was observed, inwhich the closed flux surfaces shrunk at the center with the decay of the toroidal
current, and very high multiplication (100-200) of the toroidal current suggested thatthe current was no longer the current driven by the injector current, but the confinedcurrent in the closed flux surfaces.
ʀ On the discharge of CHI+OH, the confined current persisted with the closed flux
surfaces for longer time. If lower density CHI plasma is able to be started-up, thecurrent is expected to be ramped-up by OH.
Shin Kubo
The main purpose of this project is a direct detection of the excited electron Bernstein
wave (EBW) near the core region of QUEST. Documentation of the behavior of EBW isimportant for optimizing EBW heating/current drive. Original plan was to use sub-THz

gyrotron (400 GHz) on loan from Fukui Univ. Due to the expiration of the loan term, andmoreover, higher frequency has an advantage in detecting higher wavenumber, we havedecided to utilize HCN laser (890 GHz) as a scattering source. The original design of thescattering geometry is based on the quasi-optical grating plate on the center post of the
QUEST. This configuration is scalable to the 890 GHz. The detection system is to apply
sub-harmonic (× 1/2) mixer and harmonic (×10) generator prepared for 400 GHz. Present
plan is to extend this sub-harmonic mixer to use as 1/5 and configure narrow band highly
sensitive radiometer to cover f0=890 GHz range. Relying on the stability and sharp
frequency spectra of the HCN laser as well as that of EBW f H = 8.5 GHz, by modulating
the local frequency between f 0 /50 and (f 0± f H)/50.
Hitoshi Tanaka
ʀ The LATE device was disassembled in 2021 for repair work of the experimentbuilding. Now Re-assembling of the LATE device has completed and preparation forstarting the discharge is in progress.
ʀ Background magnetic field around the setting position of LATE was measured andfound that there is about 10 times the Earth's magnetic field coming around from thesole plate of WT-3. Correction coils are designed.
ʀ Soft X-ray CT system is developing to investigate the intermittent plasma ejection
phenomena. During the plasma ejection phase, there appear a strong emission fromthe center post at z = 10 ~ 20 cm, near the cross point of LCFS with the center post.
It may be emitted from the high energy electrons lost along the LCFS. A Mo rod
limiter was set behind the center post out of the sight of the CT cameras.
Atsushi Fukuyama
y Kinetic full wave analysis using the integral form of dielectric tensor was applied tothe analysis of the O-X-B mode conversion of electron cyclotron waves in QUEST.
y Some of the power of EBW is absorbed near the ECR, but small amount of collisionleads to significant collisional absorption of EBW.
y Two-dimensional analysis on mid plane in tokamak configura- tion (slab model) has
shown the spatial structure of O-mode, X-mode, and electron Bernstein wave. It was
confirmed that O-mode is efficiently converted to EBW near the optimum injec- tion
angle.
Remaining issues
t Better formulation of absorbed power density
t Mid-plane analysis in toroidal configurationt Poloidal cross section analysis including nonuniform B along B
Yuichi Takaseʀ ST40, a compact high field ST with copper coils at Tokamak Energy (typicalparameters of R0 = 0.4-0.5 m, A = 1.6-1.8, Bt = 1.5-2.2 T, and Ip = 0.4-0.8 MA) has
achieved fusion-relevant ion temperatures of greater than 100 million degrees K (8.6
keV). Plasmas with Ip = 0.3-0.4 MA are formed quickly by merging-compression,
followed by a slower ramp up to higher Ip using the solenoid. Ti was increased

gradually from < 1 keV in June 2021 to nearly 10 keV in February 2022 throughvarious optimisations, including boronisation and between-shot He GDC whichenabled operation in the hot-ion mode, discharge optimization (avoidance of sawteeth,
detachment from the inboard wall, optimization of NBI timing, etc.), improvement of
NBI performance, operation with D NBI into D plasma, and increase of Bt. A 55 kV
NBI (which preferentially heats electrons) was injected from the beginning ofdischarge, and a 24 kV NBI (which preferentially heats ions) was injected later in the
discharge. Ti and Te were measured using the X-ray crystal spectrometer viewing the
He-like Ar line emission. The profiles of density and temperature were inferred byintegrated modelling, and the central Ti was confirmed by an independentmeasurement using the charge exchange recombination spectroscopy. TRANSP
analysis indicated that the deuterium temperature is only slightly lower than themeasured Ar and C temperatures.
ʀ ST80-HTS, a higher field device using high-temperature superconducting ciols (withnominal parameters R0 ~ 0.8 m, A ~ 2, Bt ~ 4-5 T) is being designed. This device will
demonstrate successful integration of critical engineering technology building blocks,
and demonstrate long pulse operation with high duty cycle, at high plasma
performance using D fuel.
A. Köhn-Seemann
The spherical tokamak MAST Upgrade is, among other things, considered as avalidation or test- bed for non-inductive current drive methods to be used in STEP, theSpherical Tokamak for Energy Production, which aims on demonstrating net electricity
production in the 2040s. MAST Upgrade will be equipped with two dual-frequency
gyrotrons, operating at 28 and 34.8 GHz, with a power output in total of 1.8 MW. This
microwave heating system will be used to study the current drive capabilities of the EBW
at the MW power range. In this project, we performed a full-wave analysis of the coupling
to the EBW, where 5 different codes have been used. Scenarios with high conversion
efficiencies slightly above 90 % were identified. The deteriorating effect of plasma
density fluctuations, based on MAST parameters, was investigated: it was found that onlya small reduction of the conversion efficiency on the order of 5 % is expected. MAST
Upgrade is thus ideally suited to study and explore heating and current drive by EBWs.
Naoto Tsujii
Non-inductive start-up using lower-hybrid (LH) waves has been studied on the TST-2
spherical tokamak. Plasma current start-up up to 26 kA has been achieved using the top
launch antenna which is about a quarter of a typical Ohmically driven discharge. The top
launch scenario showed strong thick-target x-ray radiation that indicated substantial LH
wave driven fast electron losses that may be limiting the achievable plasma current. To
overcome this limitation, the outer-off-midplane launch antenna was newly developedand installed in TST-2. Stronger core absorption and smaller fast electron losses are
expected for the new scenario.
Masayuki Ono
The elimination of OH solenoid maybe the most impactful design driver for an
economical compact fusion tokamak reactor system. To address this challenge, anefficient solenoid-free start-up and ramp-up scenario utilizing the X-mode at Z = Ωe (X-I) was investigated to drive ~ 10 MA of plasma current for a compact Sustained HighPower Density tokamak facility with a modest ECH power of ~ 10 MW utilizing the 170
GHz gyrotrons. The high ECCD efficiency is due to the strong wave-particle interactions
at the Doppler broadened Z = Ωe resonance, together with the accessibility constrained
absorption on uni-directional passing electrons. The efficiency of the well localized
current drive remains high for a broad range of launched parallel index of refraction
suggesting that a relatively simple waveguide launcher placed outboard could be used.
As a next step, a time dependent model of the X-I solenoid-free start-up and ramp-up has
been developed. Interestingly, the X-I current ramp-up process appears to possess apositive feed-back of key parameters, ECCD, Ip, L-mode confinement time, and Te, where
increase in any one of the parameters results in corresponding increases in otherparameters resulting in a virtuous cycle of continuous current ramp-up even with aconstant applied power. A typical ramp-up time is 200-300 sec. If shorter ramp-up timeis desired, it would be prudent to have some Te0 control tools such as impurity injection
to increase the plasma resistivity and radiation with sufficient ECH power to overdrive
ECCD well above 10 MA during the ramp-up. Because SHPD is a high field device, theplasma normalized beta stays well below 1 so the discharge is expected to be MHD stable.
As long as Te0 stays below 25 keV, the synchrotron radiation is also negligible < 1 MW.
The present NI X-I ECH start-up and ramp-up can be tested in any tokamaks/STs with
sufficient toroidal magnetic field strength to have the fundamental electron cyclotron
resonance within the plasma.
Luis F. Delgado-Aparicio1) The formation of an off-axis RE population with a linear growth has been resolvedfor photon energies ‫(׽‬20-200)×Te0
2) Emergence of the seed population in the periphery instead of the core is consistentqualitatively and quantitatively with a lower ne and ED as well as hollow E‫צ‬/ED
ratios and streaming parameters, all in agreement with theory and numericalsimulations.
3) Exponential growths have been spatially resolved for the first time and areconsistent with enhanced diffusivity, convective transport of ‫ذ‬VWARE andE~103×Te0.
4) Calculations with BMC successfully resolved the space- and time- dependent
dynamic scenarios including RMP suppression @ the edge with large E‫צ‬/ED.
5) More experiments @ MST and simulations with BMC and KORC
6) Development of RT diagnostic techniques with Si and CdTe sensors
Shinichi Shiraiwa
The radio-frequency (RF)-induced sheath is the rectification of an RF electric field ina sheath layer, which is formed between a plasma and plasma facing components (PFCs).
The resultant DC potential accelerates ions to the PFSs, which potentially causes animpurity in-flux during the ICRF operation. A new formulation to describe the RF sheath
physics is proposed, in order to incorporate it into a global 3D full wave simulation. This
new formulation is characterized by the non-linear iteration scheme that connects physics
variables in a unique order. The new formulation was extensively verified using thevarious 2D simulations in the literature. The model is applied to the WEST ICRF antennaside limiters, predicting the sheath voltage in 100-200V using a realistic density profile

in front of the antenna. Future direction includes acceleration of non-linear sheathcalculation using AI/ML was also discussed.
Nicola Bertelli
The ion cyclotron resonance hearing (ICRH) system in ITER consists of two identical
ICRH antennas to deliver 20 MW to the plasma (baseline, upgradable to 40 MW). ICRH
will play a crucial role in the ignition and sustainment of burning plasmas in ITER and ahigh-fidelity modeling is a very important aspect as well. Better understanding theinteraction of the IC waves with the scrape-off layer (SOL) plasma is required for the
ICRH ITER antenna operation. In this work, we present a series of Petra-M [1,2]simulations for ITER ICRH antenna model. Petra-M code is an electromagnetic
simulation tool for modeling RF wave propagation based on MFEM [http://mfem.org].
Numerical results for different absorption profiles are presented and discussed together
with a comparison of the wave field propagation obtained both for FEM order 2 and order
3. Furthermore, a benchmark between the well tested antenna codes TOPICA [3,4],
RAPLICASOL [5,6], which is based on COMSOL [www.comsol.com], and the Petra-M
code is also presented. Excellent agreement is found among codes comparing S- and Zmatrices, wave electric field in front of the antenna and the coupled power. Finally, initial
Petra-M simulations for the second ITER ICRH antenna model with 8 ports are alsopresented. Results presented in this work will be published in the AIP Conference
proceeding in 2023 [7].
References[1] 5. S. Shiraiwa and et al, EPJ Web of Conference 157, 03048 (2017).
[2]. S. Shiraiwa and et al, “Towards integrated RF actuator modeling: whole device scale
RF fullwave simulation including hot core and 3D sol/antenna regions, [TH/7/2],”
aper presented at the 28th IAEA Int. Conf. on Fusion Energy (Virtual Event) (2021).
[3] D. Lancellotti and et al, Nucl. Fusion 46, S476 (2006).
[4] D. Milanesio and et al, Nucl. Fusion 49, 115019 (2009).
[5] J. Jacquot and et al, AIP Conference Proceedings 1689, 050008 (2015).
[6] W. Tierens and et al, Nucl. Fusion 59, 046001 (2019).
[7] N. Bertelli et al, Accepted for publication in AIP Conf. Proc. (2023).

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㧗ᐦᗘഃࡢἼືఏᦙᇦࢆ᥈ᰝࡋࠊ㟁Ꮚࣂ࣮ࣥࢩࣗࢱ࢖ࣥἼ࡬ࡢ࣮ࣔࢻኚ᥮ࠊ㟁Ꮚࢧ࢖ࢡࣟࢺࣟࣥඹ㬆྾཰ࢆゎᯒࡋࡓࠋࡲࡓࠊPetra-M 䛻䜘䜛᭷㝈せ⣲䝅䝭䝳䝺䞊䝅䝵䞁䜒ᐇ᪋䛥䜜䚸ᅜ㝿䝽䞊䜽䝅䝵䝑䝥䛻䛶ሗ࿌䛥䜜䛯䚹

Numerical simulation of EC and EBW in QUESTBERTELLI Nicola(Princeton University, U.S.A)
Electron Bernstein wave heating and current drive (EBWHCD) scenario in the lowfield side injection is considered for non-inductive radio-frequency plasma ramp-up in
the QUEST. In this scenario, the incident O-mode wave with a specific optimized
refractive index parallel to the magnetic field N//,opt can convert to the slow X-mode wave
at the cut-off layers. The P-cutoff (at ω =ω pe) for the O-mode wave coincides to the Lcutoff (at N//,opt 2 =L) for the slow X-mode wave, where ω and ω pe are wave and plasma
frequencies. Here the parameter L is a Stix’s notation describing with ω, ω pe and theelectron cyclotron frequency ω ce. Figure 1 shows dependencies of squared refractive
index perpendicular to the magnetic field  2 on ω pe2/ω 2 for propagations with N//,opt
and N//,opt+/-0.1. The O-mode wave with N//,opt can
propagate to the high-density (over-dense) side
after the mode conversion to the X-mode wave
at the coincided cutoff layer. There areevanescent layers with  2 <0 for the O-mode

 






 







 



  



waves without N//,opt as the two cutoff layers do
not coincide. Figure 2 (a) shows ray trajectories,
which are analyzed by the TASK/WR code, of
the O-mode wave with N//,opt and N//,opt+/-0.1. In    ependencies of squared refractive
index perpendicular to the magnetic field 2 on ω pe2/ω 2 for propagations with
N//,opt and N//,opt+/-0.1.

the ray tracing approach, the incident O-mode
waves without N//,opt are reflected to the outsideat the cutoff layers. The O-mode wave without
N//,opt should also propagate to the over-denseside through the tunneling, if the evanescentlayer thickness is not larger than the wavelength
well. Figure 2(b) shows the ray trajectories of
the O-mode wave with N//,opt and N//,opt+/-0.1
when taking the tunneling into consideration.
The restart positions after the tunneling (at 2=0) beyond the evanescent layer are searchedalong the density-gradient directions from the



(a)













cutoff positions. The transmitted efficiencies at thetunneling are evaluated from an analytical formula[1]. The converted X-mode waves propagate to the

low-density side and convert to the electrostatic
Bernstein wave (EBW) again at the upper hybrid



(b)

















resonance (UHR) layer. Since the X-mode
wavelength becomes short at the UHR layer, theX-mode can convert to the short-wavelength
electrostatic EBW. Figure 3 shows the normalized
ray powers along the propagations with N//,opt andN//,opt+/-0.1. The transmitted ray powers are dropped
at the tunneling for the propagations with
N//,opt+/-0.1, depending on the incident refractive
indexes at the cutoff layers. The converted EBWs
are absorbed in the up-shift electron cyclotron
resonance area. In the figures, the EBW rays areRay trajectories of the O-mode

traced until the ray powers become 0.1% for thewave with N//,opt and N//,opt+/-0.1 (a): withincident powers. Further investigations are will beand (b): tunneling.

conducted to evaluate deposition and drivencurrent profiles in the EBWHCD scenario by using
multiple rays.
Full 3D NSTX-U device geometry including
realistic antenna geometry and 3D scrape-off-layer(SOL) plasma is also modeled to simulate NSTXUpgrade plasmas using Petra-M finite-elementmethod (FEM) [2]. Petra-M code is a state-of-theart generic electromagnetic simulation tool formodelling radio-frequency wave propagation  
Fig.3. Normalized ray powers along the     propagations with N//,opt and N//,opt+/-0.1.

based on MFEM [https://mfem.org], open-source
scalable C++ finite element method library. This subject was presented at a workshop
entitled “Plasma start-up and sustainment in spherical tokamak configuration by RF”
which was held under a different international RIAM collaboration framework.
[1] E. Mj lhus, J. Plasma Phys. 31, 7 (1984).
[2]N. Bertelli, S. Shiraiwa, and M. Ono, Nucl. Fusion 62, 126046 (2022).

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 "     )%;%D)" ;E' "2"  0  %> E$     )    " "  " %) E$       ) %    )      " )        F       $" %2   " ,   $      )            ) )    $  "            5(.6%
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LX 6?`2MFKT
AMbiBimi2 Q7 S?vbB+b- lMBp2`bBiv Q7 :`2B7brH/- 62HBt@>mb/Q`z@ai`Xe- Rd93N :`2B7brH/- :2`KMv

AX "ah_*hq2 rBHH /2b+`B#2 i?2 [mbB@+Q?2`2Mi KQ/2b BM SLh #v bmT2`biiBbiB+b (R)X h?2 i?2Q`v Q7 i?2 bmT2`biiBbiB+b/2+`B#2b i?2 TT2`M+2 Q7 MQM@:mbbBM biiBbiB+b r?2M irQ /Bz2`2Mi iBK2 b+H2b `2 T`2b2MiX lbmHHv irQ iBK2 b+H2b
`2 BKTQ`iMi 7Q` i?2 TT2`M+2 Q7 i?2 [mbB@+Q?2`2Mi KQ/2-  7bi M/  bHQr iBK2 b+H2X h?2 bHQr iBK2 b+H2 rBHH
#2 B/2MiB}2/ b i?2 iBK2 b+H2 r?2`2 i?2 bB;MH b?Qrb  #2?pBQ` +HQb2 iQ :mbbBM biiBbiB+bX h?2 biiBbiB+H MHvbBb+M #2 /QM2 rBi? KQbi Q7 i?2 /B;MQbiB+b BM SLh- #mi 7Q` KQ/2 B/2MiB}+iBQM  T`Q#2 ?2/ HBF2 BM (k) Bb mb2/X 6Q`
i?2 7mim`2 HbQ i?2 iQKQ;`T?B+ bvbi2K (j) rQmH/ #2 p2`v ?2HT7mHX
AAX"*E:_PlL.

AM iQFKF #b2/ K;M2iBx2/ +QM}M2/ 7mbBQM `2+2MiHv 2/;2@HQ+HBx2/@KQ/2@7`22 +QM}M2K2Mi `2;BK2b ?p2 #2+QK2 Q7
KDQ` BMi2`2biX  KBM 72im`2 Q7 1GJ@7`22 `2;BK2b Bb i?2 TT2`M+2 Q7 [mbB@+Q?2`2Mi KQ/2b H2/BM; iQ +QMiBMmQmbi`MbTQ`iX U1tKTH2b `2 i?2 q*J BM A@KQ/2 M/ Z*J BM 1.@>@KQ/2XV AMi2`2bi BM i?Bb iQTB+ 7`QK i?2 7mbBQM
bB/2 Bb `i?2` bBM+2  b?Q`i iBK2X ZmbB@+Q?2`2Mi KQ/2b ?p2 HQM; #22M Q#b2`p2/ BM SLh M/ bBKBH` HBM2` THbK
/2pB+2bX 1tKTH2b BM SLh `2 i?2 bi`2K2` M/ i?2 bQHBi`v rp2 (9)X ZmbB +Q?2`2Mi KQ/2b i2M/ iQ #2?p2
BMi2`KBii2Mi BM iQFKFb (8) M/ HbQ BM SLh (e)X h?2`2 ?b MQi #22M  +QKT`BbQM Q7 [mbB@+Q?2`2Mi KQ/2b BM
iQFKFb M/ HBM2` /2pB+2b bQ 7`X h?Bb +QHH#Q`iBQM rBi? _AJ HHQrb mb iQ bim/v i?2 T?vbB+b Q7 [mbB@+Q?2`2Mi
KQ/2b BM /2iBH BM HBM2` K;M2iBx2/ H#Q`iQ`v THbKb b Bi Bb BM SLhX 6BM/BM;b +M i?2M #2 TTHB2/ iQ i?2 2/;2Q7 K;M2iB+HHv +QM}M2/ 7mbBQM 2tT2`BK2MibXh`MbTQ`i +Q/2b mb2 2Bi?2`  /BzmbBp2- +QMp2+iBp2 Q`  +QK#BMiBQMH Mbix Q7 #Qi? iQ /2b+`B#2 i?2 i`MbTQ`iX
GBF2rBb2- 2tT2`BK2MiH /i `2 BMi2`T`2i2/ BM i?Bb rvX AM T`iB+mH` BM i?2 b+`T2@Qz Hv2`- im`#mH2Mi i`MbTQ`i/Q2b MQi 7QHHQr :mbbBM biiBbiB+b M/ 7m`i?2`KQ`2 +MMQi #2 /2+QKTQb2/ BMiQ M 2z2+iBp2 /BzmbBpBiv M/ +QMp2+iBp2
p2HQ+Biv (dĜN)- Bi Bb Q7i2M /2bB`#H2 iQ /2b+`B#2 i?2 i`MbTQ`i BM i?Bb /2+QKTQbBiBQMX
h?2 /2+QKTQbBiBQM BMiQ  /BzmbBp2 M/  +QMp2+iBp2 T`i Kv /2T2M/ QM i?2 iBK2 b+H2 i?2 i`MbTQ`i Bb +QMbB/2`2/(Ry)X >2`2 r2 rMi iQ /2KQMbi`i2 i?i i?Bb Bb i?2 +b2X
AAAX

1sS1_AJ1LhG J1h>P.
X .i [mBbBiBQM

6Q` i?Bb Tm`TQb2 i?2 T`Q#2 ?2/ HBF2 BM _27X (k) Bb mb2/ iQ `2+Q`/  #Bb2/ bim`iBQM +m``2Mi bB;MH Isat M/ irQ
bB;MHb Q7 i?2 THbK ~QiBM; TQi2MiBH Φf l X h?2 ~QiBM; TBMb `2 TQbBiBQM2/ i QTTQbBi2 bB/2b Q7 i?2 #Bb2/ TBM M/
HH i?`22 TBMb `2 HB;M2/ T2`T2M/B+mH` iQ i?2 tBb Q7 i?2 KBM +?K#2`X hQ 2biBKi2 i?2 /2MbBiv ;`/B2Mi HbQ 
T`Q#2 ``v K2bm`BM; i?2 T`Q}H2 bBKmHiM2QmbHv Bb mb2/X
SHbK b?Qib `2 T2`7Q`K2/ rBi?  iQiH H2M;i? Q7 t = 600 KbX  iBK27`K2 Bb +?Qb2M r?2`2 i?2 THbK Bb #mBH/ mT
7mHHv M/ bi#H2 bB;MHb `2 +[mB`2/X h?Bb Bb ivTB+HHv i?2 7mHH iBK2 BMi2`pH #2ir22M t1 = 250 Kb M/ t2 = 500 KbX
h?2 2tT2`BK2Mi rb T2`7Q`K2/ i  K;M2iB+ }2H/ bi`2M;i? Q7 B = 1300 :-  #b2 ;b T`2bbm`2 Q7 p = 0.5 S M/ 
_6@?2iBM; TQr2` Q7 P = 3 FqX h?2 T`Q#2 ?2/ rb HQ+i2/ i  `/BH TQbBiBQM Q7 r = 40 KK BM M tBH /BbiM+2
Q7 `QmM/ k K2i2`b iQ i?2 THbK@bQm`+2X
h?2 Z*J /Q2b Q++m` +HQb2 iQ B = 900 :- i?mb i HQr2` K;M2iB+ }2H/ bi`2M;i? i?M i?2 +b2 +QMbB/2`2/ ?2`2X>Qr2p2`- iQ BMi2`T`2i i?2 `2bmHib- r2 }`bi rMi2/ iQ HQQF i  +b2 rBi?Qmi Z*JX
"X

*QMp2+iBp2 Q` /BzmbBp2 i`MbTQ`iq2 rBHH 2biBKi2 i?2 im`#mH2Mi i`MbTQ`i Γτ = ũr ñτ p2`;2/ 7Q` /Bz2`2Mi bm#rBM/Qr bBx2b τ - rBi? ũr b~m+imiBQMb Q7 i?2 `/BH E × B p2HQ+Biv M/ ñ b /2MbBiv ~m+imiBQMbX AM i?2 mb2/ 2tT2`BK2MiH b2imT Q7 SLh b
 HBM2` K;M2iBx2/ THbK /2pB+2 ũr = −∂y Φ̃f l /B M/ ñ ∝ I˜sat X qBi? Φ̃f l b ~m+imiBQMb Q7 i?2 ~QiBM; TQi2MiBHkM/ I˜sat b ~m+imiBQMb Q7 i?2 bim`iBQM +m``2Mi Q7 i?2 THbKX 1+? QM2 Q7 i?2 M22/2/ p`B#H2b Bb +H+mHi2/ 7Q`
2p2`v bm#rBM/Qr /2}M2/ #v  }t2/ bm#rBM/Qr bBx2 τ iQ +H+mHi2 BM/BpB/mH ΓX am#b2[m2MiHv i?2v `2 p2`;2/ Qp2`
HH bm#rBM/Qrb 7Q`  }t2/ τ iQ Q#iBM Γτ X
h?Bb +H+mHi2/ i`MbTQ`i Bb /2+QKTQb2/ BMiQ +QMp2+iBp2 M/ /BzmbBp2 +QKTQM2Mib, dn+ U nτ .
URVΓτ = −Ddr τh?Bb +M #2 #2bi b?QrM b− dn τΓτ
= D dr + U.
nτ
nτ

UkV

h?Bb HBM2` `2HiBQMb?BT b?Qrb i?2 /BzmbBp2 T`i b i?2 bHQT2 M/ i?2 +QMp2+iBp2 T`i b i?2 Qzb2i Q7 i?2 HBM2` 7mM+iBQMX
q2 2biBKi2 HbQ i?2 +Q2{+B2Mi Q7 /2i2`KBMiBQM R2 7Q` 2+? τ X h?Bb T`QpB/2b  K2bm`2 Q7 ?Qr r2HH i?2 i`MbTQ`i Bb/2b+`B#2/ #v i?2 bbmKTiBQM i?i i?2 i`MbTQ`i +M #2 /2+QKTQb2/ BMiQ +QMp2+iBp2 M/ /BzmbBp2 +QKTQM2MibX
GBF2Hv i?2 i`MbTQ`i b?QmH/ #2 KQ`2 +QMp2+iBp2 i bKHH τ M/ KQ`2 /BzmbBp2 7Q` H`;2 τ (Ry)X*X amT2`biiBbiB+b

b /BzmbBp2 i`MbTQ`i Bb bbQ+Bi2/ iQ :mbbBM biiBbiB+bX q2 2ti`+i  HQM; iBK2 b+H2 τSS 7QHHQrBM; i?2 TT`Q+?
t−τ
Q7 i?2 bmT2`biiBbiB+ (R)X h?2 iBK2 b2`B2b Bb /BpB/2/ BM bm#rBM/Qrb Q7 bBx2 τ X "v BMi2;`iBM; i?2 HQ+H ~iM2bb 0 max dt
 t+τ
Qp2` i?2 bm#rBM/Qrb ·t,τ = t dt́ M/ p2`;BM; Qp2` i?2 2Mb2K#H2 Q7 bm#rBM/Qrb
κ(τ ) =

 tmax −τ

1tmax − τ0dt¯ 4 t,τ(ñ − ñ)¯ 2 2t,τ(ñ − ñ)UjV iBK2 b+H2 7mHH }HBM; i?2 +QM/BiBQM
κ(τSS ) = 3

U9V+M #2 7QmM/X *H2`Hv i?Bb +QM/BiBQM bBKTHv BKTHB2b i?i r2 `2 HQQFBM; 7Q` i?2 bBKTH2bi aa-  bmT2`TQbBiBQM Q7 HQ+H:mbbBMb- r?B+? ?p2 HQ+H ~iM2bb j Q`  Fm`iQbBb Q7 x2`Q- `2bT2+iBp2Hv (R)X h?Bb iBK2 b+H2 +M #2 +QKT`2/ iQ
i?2 }M/BM;b #Qp2X AM _27bX (dĜN) QM2 b22b i?i i?2 Q++m``2M+2 Q7 b?Q`i HBpBM; ~m+imiBQMb H2/b iQ /2pBiBQMb 7`QK
HBM2` #2?pBQ` rBi? `2bT2+i iQ 1[X UkVX aBM+2 /BzmbBp2 i`MbTQ`i Bb /2b+`B#2/ rBi? :mbbBM biiBbiB+b- i?Bb b?QmH/+Q``2bTQM/ iQ i?2 +b2 Q7  Fm`iQbBb Q7 x2`QX h?2`27Q`2- QM2 +QmH/ 2tT2+i i?i i?2 i`MbTQ`i +M #2 2tTHBM2/ r2HH #v/BzmbBp2 i`MbTQ`i M/ i?2 }i rBi? i?2 ?2HT Q7 1[X UkV vB2H/b ;QQ/ `2bmHib 7Q` i?Bb T`iB+mH` iBK2 b+H2X

j
AoX 1sS1_AJ1LhG _1alGhah?2 aa K2i?Q/ rQ`FbX "v /2}MBiBQM- κ Bb bKHH 7Q` bKHH τ X aBM+2 7Q` H`;2 τ - κ BM+`2b2b #Qp2 i?`22 U6B;X RV- r2+M /2i2`KBM2 τSS X h?Bb Bb TT`QtBKi2Hv τSS ≈ 1.5 KbX h?2 pHm2 Bb #Qmi r?2`2 QM2 rQmH/ BMimBiBp2Hv ;m2bb i?2
2[mBHB#`BmK iBK2 Q7 bm+? /Bb+?`;2b iQ #2X

6A:X R, oHm2b Q7 +H+mHi2/ κ 7`QK UjV 7Q`  ?B;? p`BiBQM Q7 iBK2rBM/Qr@bBx2b τ X J`F2/ BM `2/ `2 9 `#Bi``BHv+?Qb2M pHm2b iQ #2 +QKT`2/X h?2 2t+i pHm2b +M #2 7QmM/ BM 6B;X kUV κ = 2.4 M/ τ = 0.352 Kb

U#V κ = 3.1 M/ τ = 1.656 Kb

U+V κ = 3.3 M/ τ = 4.902 Kb

U/V κ = 3.5 M/ τ = 22.727 Kb

6A:X k, SHQib BM `272`2M+2 iQ UkV 7Q` /Bz2`2Mi τ M/ κ dn τdr τ
AM i?2 M2ti bi2T- ++Q`/BM; iQ 1[X UkV r2 b?Qr Γnτ ;BMbi nτ X h?2 bHQT2 b?Qrb i?2 /BzmbBQM +Q2{+2Mi- i?2
Qzb2i i?2 +QMp2+iBQM +Q2{+B2Mi M/ i?2 b+ii2` b?Qrb ?Qr r2HH i?2 /2b+`BTiBQM TTHB2bX q2 b?Qr i?Bb BM 6B;X k 7Q`/Bz2`2Mi κ pHm2b Uκ ∈ [2.4, 3.1, 3.3, 3.5]VX 6Q` FTT pHm2b +HQb2 iQ i?`22- r2 2tT2+i #2ii2` ;`22K2MiX h?2 K2bm`BM;
TQBMib b?Qr mT b +HQm/b- /BbiBM+i bi`m+im`2b +MMQi #2 `2+Q;MBx2/ ?2`2X h?2 /i `2 MQi r2HH /2b+`B##H2 pB i?Bb
/BzmbBp2@+QMp2+iBp2 TT`Q+?X

9

6A:X j, oHm2b Q7 +H+mHi2/ κ 7`QK UjV 7Q`  ?B;? p`BiBQM Q7 iBK2rBM/Qr@bBx2b τ X J`F2/ BM `2/ `2 8 iBK2rBM/Qrb
rBi?  κ = 3.00 ± 0.01
Xh?2 /2i2`KBMiBQM Q7 /BzmbBQM +Q2{+B2Mib Bb HbQ K#B;mQmbX h?2`2 `2 /Bz2`2Mi iBK2 rBM/Qr rB/i?b r?B+? HH`2bmHi BM κ = 3X h?2b2 `2 τSS ∈ [1.645, 1.534, 1.524, 1.506, 1.374] Kb b b?QrM BM 6B;X jX A7 r2 p2`;2 i?2K Qp2` i?2b2
rBM/Qr rB/i?b- r2 ;2i +QKTH2i2Hv /Bz2`2Mi bHQT2b M/ i?mb +QKTH2i2Hv /Bz2`2Mi /BzmbBQM +Q2{+B2Mib U6B;X 9VX h?2b2
2p2M b?Qr BMr`/ Q` Qmir`/ i`MbTQ`i- bQ r2 +MǶi 2p2M `2HB#Hv /2i2`KBM2 i?2 /B`2+iBQM Q7 i`MbTQ`iX

UV τ = 1.645 Kb

U#V τ = 1.534 Kb

U/V τ = 1.506 Kb

U+V τ = 1.524 Kb

U2V τ = 1.374 Kb

6A:X 9, GBM2` }ib Q7 i?2 8 iBK2rBM/Qr@bBx2b τ K`F2/ BM 6B;X j
L2p2`i?2H2bb- r2 /B/ i?Bb Qmi Q7 BMi2`2biX 6B;m`2 8 b?Qrb i?2 /BzmbBQM M/ +QMp2+iBQM +Q2{+B2Mib b  7mM+iBQM Q7
i?2 bm# rBM/Qr rB/i? τ BM  HQ;`Bi?KB+ `2T`2b2MiiBQMX h?2 /BzmbBQM +Q2{+B2Mi D `M;2b 7`QK −0.1 iQ 0.4 K2 fb/2T2M/BM; QM i?2 imX h?2 +QMp2+iBQM +Q2{+B2Mi 7`QK +20 iQ −50 KfbX oHm2b #2HQr κ < 3 i2M/ iQ /BzmbBp2 BMr`/i`MbTQ`i rBi?  +H2` +QMp2+iBp2 +QKTQM2Mi iQ i?2 QmibB/2X oHm2b `QmM/ κ = 3 ?p2 HQr /BzmbBQM M/ +QMp2+iBQM+Q2{+B2MibX AM i?2 `M;2 lg(τ ) #2ir22M −2 M/ −1.5 i?2`2 Bb bi`QM; Qmir`/ /BzmbBQM- r?B+? Bb +QKT2Mbi2/ rBi? 
HBM2` BMr`/ TBM+?X Ai Bb i?2 Qi?2` rv `QmM/- b 7Q` bKHH iBK2 b+H2bX 6Q` i?2 H`;2bi iBK2 b+H2b- i?2 +Q2{+B2Mib `2;BM +HQb2 iQ x2`QX >2`2 i?2 2Mb2K#H2 MmK#2` Bb p2`v HQr- i?2 `2bmHib ?2`2 `2 T`Q##Hv MQi biiBbiB+HHv bB;MB}+Mi i

8i?2 HQM;2bi iBK2 b+H2X AM +QM+HmbBQM- i?2 BMi2`T`2iiBQM /2T2M/b iQiHHv QM i?2 iBK2 b+H2 rBi? r?B+? Bi Bb +QMbB/2`2/X
h?2 +Q2{+B2Mi Q7 /2i2`KBMiBQM R2 BM+`2b2b rBi? i?2 bm# rBM/Qr bBx2 τ U6B;X eVX "mi Q7 +Qm`b2 i?Bb Bb QMHv /m2 iQ
i?2 7+i i?i 72r2` K2bm`BM; TQBMib `2 pBH#H2X  +H2` HQ+H KtBKmK Bb MQi b22M ?2`2X

UV .BzmbBp2 T`i- D- Q7 i?2 HBM2` }i 7`QK UkV
Qp2` H;Uτ V

U#V *QMp2+iBp2 T`i- U - Q7 i?2 HBM2` }i 7`QK UkV
Qp2` H;Uτ V

6A:X 8, h?2 /BzmbBp2 M/ i?2 +QMp2+iBp2 T`i- D M/ U - Q7 i?2 HBM2` }i 7`QK UkV 7Q` 2p2`v iBK2rBM/Qr@bBx2 τ QM 
HQ;`Bi?KB+ b+H2X J`F2/ BM `2/ `2 i?2 8 iBK2rBM/Qrb rBi?  κ = 3.00 ± 0.01 7`QK 6B;X j

UV H;UR2 V Qp2` κ

U#V H;UR2 V Qp2` τ

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and IGVP in FY2022: The MQIV FADIS diplexer for ITER with
automatic tuning at QST
Mr. Dr. Carsten Lechte
Introduction: The MQIV diplexer developed at IGVP is a fast switch, power combiner, and mode
filter for megawatt power 170 GHz millimeter waves using a Fabry-Perot resonator in a compact box
design that is vacuum capable and can be directly interfaced with the 63.5 mm ITER ECRH
waveguides which are available at QST. The device has 2 input and 2 output ports, which areconnected as shown in Fig. 1. Our technical partners at TNO in the Netherlands have designed andbuilt a fast mechanical tuning control unit for the device that is also vacuum-compatible.

DN

DR
IN

Fig 1: Diplexer integration into the gyrotron test stand at QST. DN and DR are the dummy loads at
the non-resonant and the resonant channel, respectively, and IN is the input waveguide.
The highpower tests have demonstrated the switching capability of the device, but also highlighted
problems with arcing and stray radiation. Both were addressed in 2022.
Since no travel to Japan was possible in 2022, the work was either of theoretical nature (design
and analysis), or parts sent to IGVP for remanufacturing.
Arc mitigation: It was found in 2020 after electropolishing of the problematic mirror surfaces, thatthe material defects in the surfaces were not just irregularities in shape, but there could also be cavities
which outgas material that is then causing the arc. After careful analysis of the video footage fromsome arcing events, it was decided to return the mirrors to IGVP, where a galvanically deposited“known-good” copper layer will be put down, and the 4 surfaces of the main resonator, which see thegreatest incident power, will be re-machined.

Fig.2: Three of the four mirrors after galvanic treatment, before final machining.
Stray radiation mitigation: IGVP has expertise in designing and fabricating resonant ceramic
absorber coatings. Six absorber plates covering the six internal surfaces of the device were designed
and are being fabricated at the IGVP workshop and at our collaborating partner IFKB at Stuttgart
University.
The absorber consists of 8 mm aluminium plates with coutouts for all the mirrors, waveguide ports,
and observation ports that will be press-fit into the diplexer box (see Fig. 3). The absorbing coatingof aluminium and titanium oxide is applied by an atmorpheric plasma spraying process to a thicknessof approximately 100 μm. It has a high (>70%) single pass absorption at 170 GHz from all but theshallowest angles. Cooling is achieved by radiation and contact with the box structure. Since only afraction of the input power should end up as stray radiation, the absorbers should be able to cool down
between shots if a duty cycle of 1:20 of power on to power off is adhered to. This duty cycle is also
the maximum for the main mirrors.

Fig. 3: CAD drawing of the absorber plates.

ᅜ㝿໬᥎㐍ඹྠ◊✲ᴫせ㻌
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࡟㛵㐃ࡋ࡚࠸ࡿྍ⬟ᛶࡀ࠶ࡾࡲࡍࠋ, ࣮ࣔࢻࡢࣂ࣮ࢫࢺࡣࠊᏙ❧ࡋࡓἼᙧࢆ♧ࡋࡲࡍࠋࡲࡓࠊ, ࣮ࣔࢻ㛢ࡌ㎸ࡵࡣ㟁Ꮚᗘࡢᙉ࠸໙㓄࡟ࡼࡗ࡚≉ᚩ௜ࡅࡽࢀࡲࡍࠋᚑࡗ࡚ࠊ

3$17$ ᐇ㦂⿦⨨࡟࠾ࡅࡿᏙ❧ࢻࣜࣇࢺἼ࡟ᑐࡍࡿ㟁Ꮚᗘ໙㓄ࡢᙳ㡪ࢆヲ⣽࡟ㄪ࡭࡚ࠊ

ࢺ࣐࢝ࢡࡢ , ࣮ࣔࢻ㛢ࡌ㎸ࡵయไࡢ⤖ᯝ࡜ẚ㍑ࡍࡿࡇ࡜ࡀᮏ◊✲ࡢ┠ⓗ࡛ࡍࠋTemperature gradient driven self-steepening of solitary drift-waves (No.12 _ 22NU-9)

Peter Manz , Institute of Physics, University of Greifswald, Germany

Aim : The solitary drift-wave has been extensively studied in PANTA and similar devices [1-5]. A
formation mechanism of steep wave fronts in magnetized plasmas has been proposed in [6]. In a
simple non-linear electrostatic drift-wave model [7] including both density and temperature
gradients, the presence of a gradient in the electron temperature gradient give rise to nonlinearity
similar to the nonlinearity appearing in the Korteweg–de-Vries (KdV) and Burgers equations. Such anonlinearity could be relevant for density bursts in the I-mode confinement regimes of tokamaks [8].
The bursts in the I-mode exhibit a solitary waveform. The I-mode confinement regime ischaracterized by strong gradients in the electron temperature. It would be interesting to study the
impact of the electron temperature gradient on the solitary drift-wave in the PANTA device andcompare to results from the I-mode
confiement regime in the tokamak.
Background - observations in the Imode of ASDEX Upgrade Tokamak:
Figure 1 shows the amplitude ofturbulent fluctuations in L-mode andI-mode in ASDEX Upgrade. In Lmode the fluctuation level is higher,in I-mode it decreases. However,there are density bursts that occur
irregularly and carry the transport.
The transport in the I-mode is
Figure 2Turbulent amplitudes measured with Doppler
therefore strongly intermittent. The bursts
reflectometry in L-mode and I-mode in ASDEX Upgrade. Figure
occur as solitary modes. In the conditionaltaken from P. Manz et al. Nuclear Fusion 57, 086022 (2017)average (Figure 2), the waveform appears
as a solitary pulse modulated at a lower frequency. In addition, the envelope is asymmetric in time.
Figure 1 Conditional average of density
bursts in I-mode. Figure takenIn from P.
Manz et al. Nuclear Fusion 57, 086022(2017)

experimental method: Experiments have been carried out in the linear magnetized plasma
experiment PANTA at RIAM (Kyushu University). The experiments were led by Prof. Dr. Chanho
Moon, he was also our first contact. We would like to thank him again for the experiments. PANTA
exhibits a length of 4.05 m and a diameter of 45 cm. A homogeneous axial magnetic field up to 150
mT can be generated by a set of Helmholtz coils. The plasma is heated by a double loop heliconsource with a diameter of 10 cm at one end of the device. The typical cylindrical plasma radius is 5

cm. At the other end the plasma terminates at a stainless steel end-plate. In PANTA, at higher heating

power the electron temperature gradient steepens up [9]. Therefore, it is possible to study the
impact of the electron tempertaure gradient on the solitary drift-wave at the same magnetic fieldstrength. Measurements were performed at 3kW, 4.5 kW and 6 kW at the highest possible magent
field of 150 mT. Argon has been used as the gas at a pressure of 0.5 Pa. Using radially movable
Langmuir probes array, profiles of plasma density and temperature were recorded. In addition,
fluctuations in the ion saturation current were measured. These are considered as density
fluctuations.
Experimental results:

Figure 3 Radial profile of electron density and tempertaure measured in PANTA at B=150 mT, neutral
gas pressure 0.5 Pa and heating power P=3, 4.5, 6 kW

The density and temperature profiles are shown here above in Figure 3. The profiles are generallysmooth, monotonously falling. These are good measurements. There is a cant at 4 cm in density
where the 64ch probe array sits. Unfortunately, this seems to interfere with measurements at higher
powers. But this is not so bad right now, we will come back to this later. The plasma densities areslightly lower (factor 2 to 3) than the values usually observed in PANTA. This may not seem so criticalat first glance, but it has systematic implications. With increasing heating power, the density in thecenter increases, the temperature in the center remains rather constant. This is generally the typicalbehavior for low-temperature plasmas. In the partial balance, ionization (as source) and transport via
the sheath (sink) have to balance each other. With more power, more ionization can occur and theplasma density increases with power. In the power balance, heating power and ionization (now assink) are in balance. In the first order, the temperature is determined by the ionization energy andthe plasma volume, which do not change here. Indeed, the temperature in the center does notchange much. Helicon plasmas are different, they are characterized by efficient ionization. We would
expect that in the center of the discharge, the plasma is almost completely ionized already at 3 kW.
This usually seems to be the case, but for some reason we did not reach such high densities this time.
Once the plasma is fully ionized, additional heating power cannot be applied for ionization, but theplasma is heated and the temperature rises. The behavior of the profiles with heating power
indicates that the plasma densities really were that low.
Nevertheless, we see that in the outer region (r=3.5-4. 5 cm) the temperature gradient becomessteeper with increasing power. Ion-saturation current fluctuations are taken at r=4cm. We substract
the mean and devide the data by the standard deviation. The fluctuation are shown as amplitudes tocompare with Fig.1.

Figure 4. turbulent amplitudes as measured in PANTA at r=4cm, at different heating powers,
varying the electron temperture gradient.
Figure 4 shows the turbulent amplitude in PANTA at different heating powers. The base fluctuationlevels stays similar. This is different from the I-mode. With increasing heating power, rare strong
events become more rare and stronger in amplitude.
We can examine as at r=4 cm whether the waveform becomes more soliton-like. Since we want toinvestigate rare high amplitude events, we use the conditional averaging technique. For this we
define a trigger tau=0, whenever the signal exceeds 2.5 times the standard deviation of the signal
and is on the rising edge. Then we cut out subwindows with a half-width of 250 μs from the signal
and average over them.

Figure 5. Conditional average of density bursts withvarying heating power or electron temperature
gradient

The result is shown here on the left
hand side. We see a steeper risingedge, and the rising edge also
becomes steeper from the power, so
the temperature gradient increases.
One can already see secondary
minima and maxima at 3 kW, butthese become more pronounced as
the power increases. At 6 kW, mainly
the secondary minima and maxima
are noticeable. The secondary
maxima also move closer to the skinmaximum with increasing power.
This is remarkable if we look again at
the case of the I-mode in ASDEX
Upgrade (Figure 2).

Summary and Conclusion: Measurements in PANTA at different electron gradients have been
performed. Unfortunately, the densities for helicon discharges were very low. This indicates a bad
conditioning of the wall of the experiment. It is necessary to repeat the measurements to confirm
the reproducibility of the experiments. With better conditioning, clearer results can be expected. We
have made a preliminary analysis. There are similarities to the I-mode turbulence. These results arevery promising. Elaborating on these would underscore the importance of smaller laboratory
experiments as PANTA to understand turbulence in reactor-relevant regimes of confined fusion
plasmas.

References[1] H. Arakawa et al., Plasma Physics Control. Fus. 53, 115009 (2011)[2] T. Kobayashi et al., Plasma Fus. Res. 6, 2401082 (2011)[3] S. Oldenbürger et al. ,Plasma Physics Control. Fus. 54, 055002 (2012)[4] T. Kobayashi et al. , Physis Plasmas 22, 112301 (2015)[5] T. Kobayashi et al., Plasma Fus. Res. 12, 1401019 (2017)[6] M. Sasaki et al., Physis Plasmas 22, 032315 (2015)[7] H. Tasso, Phys. Lett. 24A, 618 (1967)[8] T. Happel et al, Nucl. Fus. 56, 064004 (2016)[9] Y. Kawachi et al., Plasma Fus. Res. 16, 120281 (2021)ᅜ㝿໬᥎㐍ඹྠ◊✲ᴫせ㻌
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㟁ὶศᕸࡢィࡢᚲせᛶࡀ♧ࡉࢀ࡚࠸ࡿࡢ࡛ࠊᮏඹྠ◊✲࡛ᚓࡓ▱ぢࢆࡶ࡜࡟᳨ウࢆ㐍ࡵࡿࡇ࡜࡜ࡋ࡚࠸ࡿࠋ

 11RESEARCH REPORT

Date Feb.

Visiting scientist: (name)(position)

Jinping Qian
Professor(university / institute) Institute of Plasma Physics,
Chinese Academy of Sciences

Host scientist: (name)(position)(university / institute)

Research period: (from)K.

HanadaProfessor
Kyushu(to)

University

13

2023

 11

Research subject: Develop and improve EFIT code of the plasma equilibrium
reconstruction for SSO operation and advanced physical study on QUESTDue to COVID-19 pandemicthis year we worked remotely. We analyzed characteristics
of current density profile in EAST high poloidal beta scenario. The experimental results are
summarized in figure 1, showing the correlation between βp and internal inductance li,
revealing the shape of current profile (i.e., decreasing li represents current profile broadening
and vice versa.). From this figure, one can find that the current profile becomes broader
indicated by lower li at higher βp. On the other hand, figure 1(b) presents the dependence of
βp on plasma density, showing elevated βp achieved in higher plasma density. Note that thecollected data in figure 1 includes high βp discharges with the heating schemes of both pureRF and NBI plus RF. The current profile broadening with increasing βp can in part attributeto higher bootstrap current considering the proportional relationship between βp andbootstrap fraction.

Figure 1. Summary of EAST high βp experiments. (a) correlation between βp and internal
inductance and (b) correlation between βp and line-averaged density. Discharges collected in theblue rectangle are driven by both RF and NBI H&CD.

The current profile broadening has been explored by increasing the poloidal beta forhigher bootstrap current fraction and changing the LHCD deposition at high density. Figure
2 shows time histories of several parameters for three representative high beta discharges inthe development of lower li scenario. Same parameters of Ip=400kA and Bt=2.4T are appliedin three discharges while the line-averaged density is set to be 3.0, 3.8 and 4.7 × 1019m-3,
respectively. The internal inductance drops from 1.17 to 0.91 and βp increases from 1.27 to
1.81 with increasing density, indicating that current profiles broaden with increase of both
plasma density and βp. Note that even though the ion-cyclotron radio-frequency (ICRF)
heating power is applied in three discharges at different time as shown in the shaded area in 11

figure 2(d), there is no effective heating or current drive as no variation is observed in βp andli. The bad coupling of ICRF power may result from limitations of arcing in the ICRF antenna
and transmission lines by reflected power.

Figure 2. Time histories for EAST shots of #77801, #89790, #90615 with (a) different line averaged
density, leading to (b) different βp and (c) internal inductance. Injected power of both LHCD and
ICRF in MW is shown in (d), where little effect is observed after application of ICRF in the shaded
area; the same flattop power ~ 0.9MW of EC is shown in (e).

Kinetic equilibrium reconstructions constrained by polarimeter-interferometer (POINT)
internal measurement and kinetic pressure have been performed, where kinetic pressure
consists of density profiles obtained by POINT along with both Thomson scattering (TS)diagnostics and reflectometry, temperature profiles of both electron and ion obtained by TS
and X-ray crystal spectrometer (XCS). Note that the ion density is obtained from quasineutrality condition and Zeff measurement when there is no direct measurement of ion density
diagnostics. The equilibrium reconstruction results are shown in figure 3 combined withdensity profiles and electron temperature profiles, presenting that the current density profile
broadens with increasing density indicated by both safety factor profiles and total current 11

density profiles. However, unlike previous results obtained in L-mode plasmas, where thesafety factor profile could grow to be strongly reversed in higher densities, only slightdifferences are observed in safety factor near core region in H-mode high βp plasmas.

Figure 3. (a) density profiles and (b) electron temperature profiles for discharges #77801, #89790,#90615, note that the scatter points in Te profiles are raw data points came from TS diagnostics.
Equilibrium reconstruction results of (c) safety factor profiles and (d) total current density profiles

To understand the current profile broadening in the high βp plasma, fractions of current
density are calculated using multiple modelling codes. The results are shown in figure 4. In
the simulation, current density profiles and power density profiles of LHCD are obtained
from ray tracing code GENRAY and Fokker-Plank code CQL3D with peak N// = 2.26,
ECCD profiles are simulated by both TORAY code and CQL3D code with toroidal andpoloidal angles of EC wave at 200° and 77° respectively, the fraction of bootstrap current isobtained using Sauter model. Note that the radial diffusion of the fast electrons has been
considered in CQL3D process for both LHCD and ECCD calculation, where the radialtransport diffusion coefficient Dr = 0.9 m2s-1 is applied for LHCD after a list of value scan
and Dr = 6 m2s-1 for ECCD when abnormally high value of current drive in the core wasobtained using TORAY only. From the results, one can find that the LH current profiles shift
outward gradually with increasing density accompanied by decreasing magnitude of current
in the core region. Similar trend could be found in LH power density profiles shown in figure4(b) as well. It is worth noting that the LHCD profile at the highest density case has already 11

shown tendency of off-axis peaking, which is desirable for achieving reverse shear.

Figure 4. Results of different fractions of current density profiles. (a) current density and (b)deposition power density profiles of LH calculated by GENRAY-CQL3D; (c) current density
profiles of EC calculated by TORAY-CQL3D and (d) bootstrap current density profiles by Sautermodel.

The characteristics of current density profile in EAST high poloidal beta operation have been
demonstrated. By summarizing results of high βp experiments, it is found that parameters of
βp, the internal inductance and plasma density are correlated with each other. Higher βpoperation is usually achieved with higher density, which would lead to the decrease of li,
indicating current density profile broadening. Later analyses in pure RF H&CD discharges
with different plasma density confirm that elevated bootstrap current fraction obtained inhigh βp operation broadens current density profile. Current profile and power density profile
of LHCD shifts outward gradually with increasing density, serving as another factor of
current profile broadening process.

 11

(Signature)(Name in print)

J. Qian
Jinping Qianᅜ㝿໬᥎㐍ඹྠ◊✲ᴫせ㻌
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RIAM JOINT RESEARCH REPORT SUMMARY (English Form)

1. Research ID: No.14_22NU-11

2. Research Title: Joint study of long pulse high beta discharges and related edge turbulence transport insteady state operation (SSO) plasmas on QUEST and EAST
3. Category: International
4. Applicant
Affiliation: Institute of Plasma Physics, Chinese Academy of Sciences

Name: GAO xiang

5. RIAM Attendant: Prof.HANADA Kazuaki

6. Summary (150~200 words in Japanese or 100~150 words in English):This year, given the situation of COVID-19, the joint research was still done remotely.
Steady state operation (SSO) of tokamak plasma is one of the basic requirements for future
fusion reactors. Long pulse high beta operation is one of important missions for ITER.
Joint study long pulse high beta discharges in SSO plasma research field on QUEST and
EAST is strongly supporting ITER experiment from both experience and theory. In 2022,
the collaboration research continue focused on the power balance in SSO high performance
discharge and coupling of injected energy and plasma during discharge, which is benefit
for the SSO high beta discharges of EAST and QUEST. A steady-state plasma with aworld-record pulse length of 1056 s was obtained, where the density and the divertor peakheat flux were well controlled, with no core impurity accumulation, and a new highconfinement and self-organising regime (Super I-mode = I-mode + e-ITB) was discoveredand demonstrated.
*) Submit either one of Japanese or English forms.

Introduction
This year, given the situation of COVID-19, the joint research was still done remotely.
Steady state operation (SSO) of tokamak plasma is one of the basic requirements for future fusion reactors.
Long pulse high beta operation is one of important missions for ITER. Joint study long pulse high beta
discharges in SSO plasma research field on QUEST and EAST is strongly supporting ITER experimentfrom both experience and theory. In this year, the collaboration research continue focused on the power
balance in SSO high performance discharge and coupling of injected energy and plasma during discharge,
which is benefit for the SSO high beta discharges of EAST and QUEST. A steady-state plasma with aworld-record pulse length of 1056 s was obtained, where the density and the divertor peak heat flux were
well controlled, with no core impurity accumulation, and a new high-confinement and self-organising regime(Super I-mode = I-mode + e-ITB) was discovered and demonstrated.

New results in 2022
To access long-duration plasmas, experiments have been performed in a double-null magnetic configuration
mainly using LHCD and ECRH at Ip =300–400 kA, BT = 2.75 T, R = 1.91 m, and a=0.45 m. BT waschosen to be 2.75 T to simultaneously achieve on-axis ECRH deposition and optimised LHCD power
absorption at 4.6 GHz. The line-averaged electron density ݊ത e was approximately 2×1019 m-3. The
operational conditions were carefully tuned shot-by-shot, keeping the main parameters, such as heating
powers, plasma density, plasma current, and plasma shape, the same.
Both particles and heat exhaust related to plasma–wall interaction must be controlled to operate longpulses. Therefore, real-time feedback control was implemented on EAST using additional relevant
techniques. The plasma configuration is double null (DN) during discharge to avoid excessive heat flux on
PFCs. A powder dropper was used to inject lithium to mitigate impurities and reduce recycling. This
allows control of density and radiated power due to impurities. Note that low particle recycling is favourable
for cryo-pumping, which does not suffer from saturation or release of particles back into the plasma whenin a low recycling regime.
Repeated tests of the plasma control system were performed each day prior to the experiments to minimise
the error due to the offset of integrators of magnetic measurements, which is essential for controlling boththe position (zero shift) and shape of the plasmas. Thus, a stable gap (~4 cm) between the plasma and thewall was maintained in the double-null configuration, ensuring sufficient particle exhaust.
After repetitive discharges of hundreds of seconds, a discharge with a duration of 1056 s was achieved, as
shown in Fig. 1. A total energy of 2 GJ was injected into the plasma, twice as much as the record previously
held by Tore Supra and EAST. The plasma was operated at Ip = 330 kA and ݊തe = 1.81019 m-3; it washeated by a total RF power of 1.65 MW (1.1 MW of LHCD at 4.6 GHz, and 0.55 MW of ECRH). As

shown in the figure, all the main plasma quantities are stationary during the entire discharge. The radiation
power, with tungsten as the major radiating species, is found to be very low (~150 kW). Note that thedischarge is fully non-inductive, i.e., the plasma current is mainly driven by LHCD and a moderatebootstrap current (~37%). As illustrated in Fig. 2, in the 1056 s discharge, which is called the Super Imodewill be described in detail belowthe corresponding lower hybrid current drive efficiency estimatedூ௡ ோby ߟCD = LH ೐ (A/W/݉ଶ ) (23)is ~0.87ʹ1019 A/W/m2 The current drive efficiency in this discharge is௉LHcomparable to the experimental value in L-mode plasma, but slightly lower than that in H-mode plasma,
where ILH and PLH are the lower hybrid driven current and lower hybrid wave power, respectively.

Fig. 1. Waveform of the thousand-second discharge #106915. (A) Plasma current Ip and lineaveraged electron density ݊തe. (B) LHCD, ECRH, and radiated powers. (C) Contour of particle flux
given by the ion saturation current js on the divertor target, with the strike points calculated from EFIT
equilibrium shown in open circles (SP1 and SP2 are outer strike points for two X-points in double-nullconfiguration, respectively). (D) Peak heat flux on the divertor target.

Fig. 2. Lower-Hybrid Current Drive (LHCD) efficiency. Experimental comparison of LHCD
efficiency in the L-mode, H-mode and Super I-mode.
Fig. 3 represents the energy confinement enhancement factor H98 as a function of the pulse length forSuper I-mode (solid red square), standard I-mode (red square), H-mode (blue triangle), L-mode with ITB(violet circle), and standard L-mode without ITB (black diamond) in EAST. Super I-mode has an energy
confinement similar to that of H-mode, but with a pulse length considerably longer than that of H-mode.
Further, compared with standard I-mode, Super I-mode exhibits better energy confinement with a 50%
higher H-factor. Noted that the present Super I-mode was realized with a very high electron temperatureand relatively lower ion temperature. Super I-mode experiments on EAST will be extended towards thecase of high ion temperature.

Fig. 3. Comparison of the energy confinement enhancement factor H98 and the plasma duration.
Various plasma regimes obtained in EAST are compared: Super I-mode (solid red square), standard Imode (red square), H-mode (blue triangle), L-mode with ITB (violet circle), and L-mode without ITB(black diamond).

Discussions
The major motivation of this project is to realize SSO plasma, based on QUEST and EAST device. In
2022 EAST campaign, we focus on the studying of the wave-plasma physics, such as coupling between
LHW power and plasma, for achieving high-parameter SSO of the tokamak. A steady-state plasma with aworld-record pulse length of 1056 s was obtained, where the density and the divertor peak heat flux were
well controlled, with no core impurity accumulation, and a new high-confinement and self-organising regime(Super I-mode = I-mode + e-ITB) was discovered and demonstrated.
In 2023, this subtheme will continue pursue in long pulse high beta discharges and related pedestal structureand edge turbulence transport in SSO plasma on QUEST and EAST. Comparison and combination study
based on the calorimetry and other diagnostics will continue be done on both devices. The combined study
will be helpful for understanding the underlying physics and obtaining improved high performance plasma
on EAST and QUEST. It is benefit for the long pulse high beta discharges of EAST and QUEST.

Acknowledgement and comments:
Work supported by the international joint research at the Joint Usage of Research Centers for Applied
Mechanics for 2022. I would like to thank our host, Professor K. Hanada, who helps a lot during ourremotely research and very appreciate the fruitful discussions and comments. We hope that theinternational joint research at the Joint Usage of Research Centers for Applied Mechanics could continue
to enhance China-Japan cooperation on fusion plasma research in the future.

Co-Publications in 2022-2023:[1] Yunfei Wang, Kazuaki Hanada, Haiqing Liu, Xiang Gao et al., " Hot spots induced by RF-accelerated
electrons in the scrape-off layer on Experimental Advanced Superconducting Tokamak ", Nuclear Fusion(2023) Aceepted manuscript online. DOI 10.1088/1741-4326/acb726[2] Yunfei Wang, Kazuaki Hanada, ……, Xiang Gao, et al., “Guiding center orbit simulation of energetic
particles in tokamak plasma”, Proceedings of the 8th International Exchange and Innovation Conference
on Engineering & Sciences(IEICES 2022).

(Signature)

Xiang Gao

(Name in print) Xiang Gaoᅜ㝿໬᥎㐍ඹྠ◊✲ᴫせ㻌
1R
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RIAM JOINT RESEARCH REPORT SUMMARY (English Form)
1. Research ID: No.6_21NU-5
2. Research Title: The research on the confinement and loss mechanism of alpha particle through the research ofenergetic electron on QUEST
3. Category:International

4. Applicant
Affiliation: Institute of Plasma Physics, Chinese Academy of Sciences
Name: Yinxian Jie
5. RIAM Attendant:

K. Hanada

6. Summary (150~200 words in Japanese or 100~150 words in English):Due to COVID-19 pandemic，this year we worked remotely.
Investigation of loss mechanism of the energetic electron in QUEST provides finallya good assistance of confinement of alpha particle in the international thermo-nuclear
fusion reactor (ITER) and designing fusion devices such as Japan DEMO and CFETR(China Fusion Engineering Test Reactor) in China. So I discussed the task of particle
orbit calculating arranged by Professor K.Hanada with student Mr. Yunfei Wang.

*) Submit either one of Japanese or English forms.

Research subject: The research on the confinement and loss mechanism of alphaparticle through the research of energetic electron on QUESTDue to COVID-19 pandemic，this year we worked remotely.
Soft x-ray spectra system is a very important diagnotic on tokamaks. It is one of the mostwidely used in measuring the palsma electron tempreture and MHD phenomenons. The wholesystem needs modification to get more detail date to get the position of IPN and relevant physicalresearch on QUEST.
The mission of QUEST is to develop the scientific basis for achieving a steady state conditionat sufficiently high beta (~20%), with high confinement and low collisionality. Operating Tokamak at
a high poloidal beta value is usually attactive and this makes the spherical tokamak an interesting
choice for future reactors.The maximum achievable β p, however, is limited by a so called
equilibrium limit, where an inboard poloidal magnetic field null (IPN) appears at the high field sideof the vacuum vessel.Inboard poloidal field null (IPN) configuration in a high Bp discharging wasreported first time on TFTR in 1991. In those discharge the evolution of the poloidal field measured
at the midplane on the inboard side of the TFTR vacuum vessel was studied.As Ip was ramped down,
and Bp increased, the midplane poloidal field decreased and eventually become negative, indicatingthat the separatrix had crossed the coil position and moved into the vacuum vessel. The
separatrixlimited discharge was sustained until the end of the beam heating phase.

In QUEST, suchan IPN configuration is easily achieved under a high magnetic mirror ratio and high Bz/Bt values (≈10%) via electron cyclotron (EC) heating and current drive. A soft x-ray spectra system was set up on
QUEST and got some primary date.The whole system needs modification to get more detail date to
get the position of IPN on QUEST.
Investigation of loss mechanism of the energetic electron in QUEST provides finally a good
assistance of confinement of alpha particle in the international thermo-nuclear fusion reactor (ITER)
and designing fusion devices such as Japan DEMO and CFETR (China Fusion Engineering Test

Reactor) in China.

Co-Publications in 2022-2023:[1] "Hot spots induced by RF-accelerated electrons in the scrape-off layer on Experimental
Advanced Superconducting Tokamak"Wang.Yunfei,...

Jie.Yinxian,.... et al .,Nuclear Fusion （to be

published.）(Signature)(Name in print)

Y. JieYinxian Jieᅜ㝿໬᥎㐍ඹྠ◊✲ᴫせ㻌
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RIAM JOINT RESEARCH REPORT SUMMARY (English Form)

1. Research ID: No.16_22NU-13

 Research Title:
Joint study of calorimetric measurement of heat load and power balance estimation and measurement andsimulation of energetic electrons loss in steady state operation (SSO) plasmas on QUEST and EAST
3. Category: International joint research
4. Applicant
Affiliation: Institute of Plasma Physics, Chinese Academy of Sciences

Name: LIU Haiqing

5. RIAM Attendant: Prof.HANADA Kazuaki

6. Summary (150~200 words in Japanese or 100~150 words in English):Due to COVID-19 pandemic ˈ this year the joint research was done remotely. The
collaboration research focused on hot spots induced by RF-accelerated electrons in the
scrape-off layer on EAST. In 2022, the material of lower divertor has been developed fromgraphite to tungsten, aiming at achieving higher power handling capability and achieving
longer H-mode operations. Combined with the experience of long-pulse operation
accumulated in previous rounds of experiments, EAST achieved a long-pulse highparameter operation with electron ITB with duration 1056.66 s, the plasma configuration
is well controlled with improved confinement, called super I mode.
And I have many fruitful discussions with Prof.Hanada’s doctor student, Mr. Yunfei Wang,on his doctoral research issues. Three Co-Publications are achieved in 2022-2023.

*) Submit either one of Japanese or English forms.

Introduction
Steady state operation (SSO) of magnetic fusion devices is one of the goals for fusion research. In this year, thecollaboration research focused on analyzing and finding the cause of hot spot formation, and comparing the heat load
capacity of tungsten and graphite divertors through calorimetry. Hot spots are the outcomes of interactions between
the plasma and plasma-facing components (PFCs), which frequently hinder the maintenance of high-performance
plasmas through unwanted impurity emissions, such as the longest H-mode discharge on the EAST. Moreover, hotspots can cause the meltdown of PFCs, which results in serious damage to the machine.
Hot spots induced by various radio frequency (RF) power injections have been observed and investigated in EAST
and QUEST. The hot spots may be formed by electrons moving along the magnetic field lines that attack the PFCs
in the entire SOL.
In the present study, the effect of the SOL magnetic configuration on hot spot formation was investigated in a seriesof configuration-control experiments, and the magnetic field line tracking in SOL contributed to an intuitive
explanation. The findings of this study helped achieve the longest H-mode plasma. Moreover, the energy source of
hot spots and the mechanism of hot spot formation were clarified through two-frequency LHW pulse modulation
experiments. These experiments showed that collision damping of LHW is a major mechanism for LHW power
deposition on the SOL, which subsequently leads to hot spot formation. These results were confirmed through power
deposition calculations and a joint simulation between ray-tracing and Fokker–Planck codes.
Recent results in 2022
Preventing impurity emission from hot spots on plasma-facing materials is a critical issue in the maintenance of highperformance plasma on the Experimental Advanced Superconducting Tokamak (EAST). In this study, experimental
and theoretical analyses were performed to investigate the mechanism of hot spot formation. In the upper single nullmagnetic configuration of the EAST, two separatrices were connected to the upper (primary) and lower (secondary)X-points. Experiments on plasma configuration control indicated that the reduction in the gap between the lower(secondary) separatrix and lower hybrid antenna is effective in preventing hot spot formation on the lower divertor,
which frequently emits impurities in long-duration discharges. This effectiveness was quantitatively confirmed bymagnetic field lines tracking simulation and calorimetric measurement of divertors in the experiment. Two-frequency
power modulation of the lower hybrid wave (LHW) was conducted to evaluate power deposition on the scrape-off
layer (SOL) during propagation from the LHW antenna to the main plasma. This experiment clarified that LHWaccelerated electrons in the SOL via collision damping deliver their energies to hot spots along the magnetic fieldline. These findings help alleviate or even eliminate the formation of hot spots and maintain the performance ofplasma.
Stable plasma configurations of seven discharges were established from ~2.3 s using the Equilibrium Fitting (EFIT)
code; at times before 2.3 s, the configuration changes of these seven discharges exhibited the same trends, and hot
spots appeared from ~3 s onwards. Therefore, the temporal evolution (from 3 s to 8 s, at every second) of the positionsof the lower outer strike points for #73 991 to #73 998 (except for #73 996) were calculated based on the EFIT
reconstruction, as shown in figure 1. The circles in figure 1 represent the heights of the lower outer strike points ofthese seven discharges in the cylindrical coordinates. Notably, the hot spot and lower outer strike point (from 3 s to8 s) of all these discharges were on the outer dome of the lower divertor. Figure 6 shows that the distance between
the hot spot and lower outer strike point on the divertor had no obvious relationship with the hot spot formation inthese discharges, because the position of the lower outer strike point for discharges #73 994 and #73 995 (without
hot spots) was almost the same as the discharges with the hot spot.

Figure 1. Temporal evolutions of the height positions of the lower outer strike points in cylindrical coordinates. The
red circles represent the discharges with hot spots, and the blue circles represent the discharges without hot spots.
The black dash line represents the height position of the hot spot on the lower dome, and the green color represents
the estimated hot spot area.

Figure 2. (a) Photograph taken using an IR camera of the vacuum vessel of the EAST and location marks fromzones 1 to 4 for discharge #74 864. (b) Temporal evolution of the average temperature (measured using the IR
camera) for the four zones marked in figure 14(a). (c)–(f) Time derivatives of temperatures for the four zones.
Figure 2(a) is a photograph acquired using the IR camera in port G; the LHW antenna at 4.6 GHz and its two graphite
guard limiters are on the left side of the figure. Figure 14(b) represents the average temperature evolution, and figure2(c)–(f) shows the time derivatives of the temperature of the four zones over time, marked in figure 2(a). Zones 1
and 2 with and without hot spots, respectively, were on the lower outer divertor; zones 3 and 4 were on the upperouter and inner divertor, respectively. Figure 2(b) shows that the temperature in zone 1 was strongly related to theinjection of the LHW at 2.45 GHz; however, after the second heating period of the LHW at 2.45 GHz, the temperaturein zone 1 continuously decreased, related to the injection of the LHW at 4.6 GHz. This indicates that the hot spot
formation in zone 1 was most likely related to the different performances of the two LHWs. This finding isinvestigated in the next section.
The temperatures in zone 3 and 4 changed simultaneously with the injection of the LHWs at 2.45 GHz and 4.6 GHz,
indicating that the heat load of the upper divertor in the USN configuration discharge originated from the core plasma.
Because the time derivative of temperature is directly related to heat flux, figures 2(e) and 2(f) show that the upper
divertor can withstand a large heat flux during an LHW injection. Moreover, the location of the hot spot on the lower
divertor in zone 1 can also withstand a large heat flux compared with that in zone 2 during an LHW injection at 2.45
GHz, as shown in figures 2(c) and 2(d).
We observed that the collision absorption caused by the LHW at 2.45 GHz was 35.2 kW higher than that of the LHW
at 4.6 GHz; this part of energy from the LHW at 2.45 GHz may have caused hot spot formation in the lower divertor,
as shown in figure 2(a).
The frequency spectra pertaining to the LHW at 2.45 GHz (blue) and that of the LHW at 4.6 GHz (red) are shownand compared in figure 3. The spectral widths of the two LHWs were almost the same, meaning that the PDI effectis not the primary cause of hot spot formation.
In cases of #73 993 and #73 994, a difference of 3.82 MJ in module E appeared (within 5 s); this was caused by theslight change of the magnetic configuration in the SOL, with 0.43 MW and 1.48 MW being attributed to the LHW
injections at 2.45 GHz and 4.6 GHz, respectively. This indicates that, in this calculation, more than 0.76 MW (40%of the LHW power) should be deposited in the SOL, and 20% of the LHW power can expected to be deposited in the
SOL through collision damping.

Figure 3. Frequency spectra of the LHWs at 2.45 GHz (red) and 4.6 GHz (blue).
Discussions
This year, the collaboration research focused on the mechanism of the hot spot formation, comparing the heat load
capacity of tungsten and graphite divertors through calorimetry. In this year study, we investigated the mechanisms
underlying the hot spot formation on the lower divertor during the EAST 2017 campaign and found that two factors,

namely the magnetic configuration in the SOL and the energy deposition of the LHW in the SOL, played an importantrole in hot spot formation. By slightly changing the SOL plasma configuration, the hot spot on the lower divertor was
effectively alleviated. This helped achieve a record of steady-state H-mode plasma (#73999) in the EAST for 101.2
s. Experiment analyses and GENRAY/CQL3D simulations showed that the two LHWs had different plasma heating
and current driving efficiencies in the main plasma owing to their different frequencies; the LHW at 2.45 GHz likely
deposits more energy than the LHW at 4.6 GHz in the SOL through collision damping, which leads to hot spot
formation in the LHW modulation experiment.
In this year’s joint research, I have many fruitful discussions with Prof.Hanada’s doctor student, Mr. Yunfei Wang,on his doctoral research issues. Three Co-Publications are achieved in 2022-2023.
In the near future, the EAST aims to realize a higher performance plasma operation with higher power injection;
therefore, it is important to achieve full FoV detection for PFCs on the EAST to monitor the condition of PFCs,
including hot spots. Besides, the mechanism of association between the LHW and plasma should be further
investigated to improve the efficiency of plasma heating and current driving through the LHW to achieve lengthierH-mode operations and noninductive current driving. These results and further joint research on EAST and QUEST
have potential applications in exploring advanced operating modes on CFETR in China and ITER.

Acknowledgement and comments:
Work supported by the international joint research at the Joint Usage of Research Centers for Applied Mechanics for2022. I would like to thank our host, Professor K. Hanada, who helps a lot during our remotely research and very
appreciate the fruitful discussions and comments. We hope that the international joint research at the Joint Usage of
Research Centers for Applied Mechanics could continue to enhance China-Japan cooperation on fusion plasma
research in the future.

Co-Publications in 2021-2022:[1] Yunfei Wang, Kazuaki Hanada, Haiqing Liu, et al., " Hot spots induced by RF-accelerated electrons in the scrapeoff layer on Experimental Advanced Superconducting Tokamak ", Nuclear Fusion (2023) Aceepted manuscript
online. DOI 10.1088/1741-4326/acb726[2] Yunfei Wang, Kazuaki Hanada, ……, Haiqing Liu, et al., “Guiding center orbit simulation of energetic particles
in tokamak plasma”, Proceedings of the 8th International Exchange and Innovation Conference on Engineering &Sciences(IEICES 2022).
[3] Y. Q.Chu, H.Q.Liu, ……, K. Hanada, et al., "MHD effect of internal transport barrier on EAST tokamak", Plasma
Science and Technology 24 (2022) 035102.

(Signature)

Haiqing Liu(Name in print) Haiqing Liuᅜ㝿໬᥎㐍ඹྠ◊✲ᴫせ㻌
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Chonnam National University, Prof. Insu Jeon

Summary
In this research, a novel method is proposed to fabricate stretchable and flexible piezoelectric all gel energy harvesters.
Cellulose, a natural biopolymer, with polyvinylidene difluoride (PVDF), an exceptionally piezo active andbiocompatible synthetic polymer, were integrated in glycerol, a green organic solvent with extremely high-boilingpoint and moderately low-freezing point to synthesize the gels. The prepared glycerol gels (GG) exhibited properties
with the Young’s modulus, tensile strength, compressive strength and piezoelectric charge constant of ~7 MPa, ~2.5
MPa, ~9 MPa and ~2.4 pC N−1, respectively. Moreover, the gels maintained their properties for 7 d over a wide
temperature range (−50 to 80 oC). These properties show that the developed gels are prominent candidates for many
applications in next-generation stretchable and flexible energy harvesting and energy storage devices.

MethodFirst, physically isotropic water-equilibrated (Cellulose/PVDF) (x/y) (where x and y are the initial cellulose and
PVDF concentrations (wt%), respectively) hydrogels were prepared according to the method described in ourprevious report with a slight modification. Aqueous glycerol solutions of 25%, 50%, 75%, and 100% glycerol content
were used to convert hydrogels to glycerol gels (GG) sequentially for 12, 12, 24, and 24 h, respectively. The as
prepared GG was annealed in a closed glass vial at 120 °C for 6 h, whereafter it was slowly cooled to 25°C to obtain
the desired Cellulose/PVDF GG (thickness ≈ 2 mm), which was used for further characterization.
Results
A series of (Cellulose/PVDF) (x/y) glycerol gels were fabricated to realize glycerol gel with optimal composition,using the steps illustrated in Figure 1, and evaluated their properties utilizing tensile tests, and electrical output
measurements.

Figure 1. Fabrication process of (Cellulose/PVDF) (x/y) Glycerol gels.

When the PVDF concentration was increased from 0.5 to 2.5 wt% at a set cellulose concentration of 1 wt%, thevoltage output and the current output of the glycerol gels increased gradually to a maximum value for PVDF 2 wt%
and started decreasing when further increasing the PVDF wt% (Figure 2). Further characterizations were performed
for this optimum composition of Cellulose 1 wt% and PVDF 2 wt% glycerol gel. The piezoelectric output of theglycerol gels strongly depended on the final PVDF concentration and relative cellulose and PVDF concentration in
the gels.

Figure 2. (a) Output voltage density and current density (under 20 N tapping force) of the isotropic (Cellulose/PVDF)
glycerol gels prepared by varying the PVDF concentration in the range of 0.5–2.5 wt% at a set cellulose concentrationof 1 wt%. Cellulose/PVDF (1/2) wt% glycerol gel, (b) tensile stress–strain (500% strain rate per min), (c) compressive
stress–strain (20% strain rate per min), and (d) time evolution of residual strain (100% strain rate per min) curves at
25 °C.

Conclusion
A novel class of gels were developed by integrating cellulose and PVDF, which are bio-friendly, piezo active
polymers, in glycerol, a green organic solvent. Even though there are significant differences in structure andproperties of the polymers, a hybrid gel with excellent electrical and mechanical properties, and extremely highstability over a wide temperature range was fabricated following the proposed fabrication method. Considering these
remarkable properties and facile synthesis, the developed gels are expected to have high potential for numerous
applications in next-generation flexible energy harvesting and energy storage devices.

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ᅜ㝿໬᥎㐍ඹྠ◊✲ሗ࿌᭩
No.18_22RE-2
䝍 䜲 䝖 䝹䠖Coupled numerical framework development of hybrid floating offshore wind turbine(FOWT) and oscillating water column (OWC) wave energy converters with power take-off(PTO) control◊✲௦⾲⪅䠖

ZHANG, DAHAI （Zhejiang University）

ᡤෆୡヰே䠖

๽㻌 ┆⁄Introduction
Offshore wind energy plays an important role in accelerating the transition of global net-zero greenhouse gas
emissions [1]. In deep water areas, the floating offshore wind turbine (FOWT) is regarded as a more feasible andeconomical form than fixed-bottom solutions [2]. However, FOWT still has a high cost of energy (CoE) due tothe expensive floating platform and mooring system. At the same time, there will be more vigorous motions andstructural loads due to the additional motion degree of freedom (DoF), which may increase the failure risk andshorten the operational lifetime.
In order to reduce the CoE and improve the dynamic behaviour of FOWT, many studies have been carried out
on the integrated optimisation of floating platforms [3], wind turbines [4], and mooring system configuration [5]etc. Alternatively, as there usually exists abundant wave energy in deep-sea regions [6], integrating wave energy
converters (WECs) into the floating platform could not only increase the overall energy production [7], but also
possibly reduce the motion responses and structural loads of FOWT by the synergy effect between the floating
platform and WECs [8]. Therefore, combining FOWT with WECs has been widely seen as a promising solution
for improving its power gain and load behaviour [9]. Compared with oscillating-body devices, oscillating watercolumn (OWC) WECs have better reliability due to the structural simplicity, as the only moving component is
the air turbine located above water level. Therefore, incorporating OWC WECs into FOWT could be a more
promising solution in aspects of cost and reliability.

Fig. 1 The aero-hydro-servo-elastic-mooring coupled numerical framework for FOWT-OWC dynamic
analysis.

In this study, an aero-hydro-elastic-servo-mooring coupled numerical framework is introduced for integrated
time-domain analysis of FOWT-OWC hybrid platforms in this work. This framework is established by coupling
the offshore structure hydrodynamic and mooring analysis tool ANSYS-AQWA [10] with the wind turbine aeroelastic code FAST [11]. In particular, the OWC is modelled as an equivalent virtual oscillating body within AQWA
environment so that the time-series of OWC free surface variation could be obtained, and then the OWC PTO
control effect on wave energy production as well as platform motion could also be evaluated. Moreover, themulti-body dynamics of utility-scale wind turbines are described by FAST so that the ultimate and fatigue loads
on critical structures, such as the tower and blades, could be assessed. In order to demonstrate the feasibility ofthe established coupled numerical framework, a DeepCwind-OWC combined design is proposed and seen as
the study case in this work, where the coupled numerical simulation results have been compared and validated
against the experimental data of a 1:50 scale model wave basin test. Furthermore, different OWC PTO control
strategies have been comparatively studied to investigate their influence on platform motion responses, windturbine fatigue loads, as well as overall power production.

Methodology
The coupling between AQWA and FAST is achieved through the user-defined DLL and FAST modules, as
shown in Fig. 1. FAST modules, such as AeroDyn for aerodynamics, ServoDyn for control, and ElastoDyn forstructural dynamics, are completely compiled into the DLL, which could be called by AQWA during timedomain simulations. In particular, the OWC WEC is modelled as an equivalent virtual oscillating body in
AQWA, and the formulations of OWC viscosity correction and PTO control actuation are also compiled into
the DLL. More details of the established numerical framework are described below.

Platform and Mooring Modelling
The hydrodynamic loads of the floating platform are calculated within AQWA based on linear potential flow
theory with viscosity correction. It is assumed that flow is inviscid, incompressible, and irrotational. The addedmass, radiation damping, viscous drag effect, and OWC-platform hydrodynamic interactions are all included in
the AQWA simulation. The motion equation of the platform can be represented in an integral convolution formast
M  Af X (t )  CX (t )  K (t )  ³ R(t  W ) X (W )dW
0

Fhydro (t )  Fmooring (t )  Ftower (t )  FOWC (t )(1)where M is the platform mass, A is the added mass matrix at infinite frequency, C is the damping matrix, K is
the stiffness matrix, R is the velocity impulse function matrix, and Ĳ is the variable of the convolution term. X
denotes the displacement vector. The external loadings include the hydrodynamic loads Fhydro, the mooring loads
Fmooring, the tower-base loads Ftower acting on the platform, and the OWC induced loads FOWC. Besides, thelumped-mass approach is adopted for modelling the mooring system.

Wind Turbine Modelling
FAST is used in the proposed numerical framework to predict the dynamic response and structure loads ofutility-scale horizontal wind turbines mounted on floating platforms. In this work, the HydroDyn module within
FAST is not used since the hydrodynamic loads are calculated in AQWA. The aerodynamics are calculated by
AeroDyn based on the blade element momentum approach. The wind turbine control, including generatortorque control, blade-pitch control, and yaw control, is handled by the ServoDyn module. The wind turbine
blades and tower are modelled as flexible bodies with prescribed mode shapes for structural load calculation,and the dynamics of the turbine could be solved through the ElastoDyn module based on Kane’s equation [12]Fr*  Fr0(2)

where Fr* is the generalised inertia force vector, and Fr is the generalised active force vector.

Oscillating Water Column Modelling
The OWC is modelled as an equivalent point absorber in the proposed framework within AQWA.This rigid
water column with the same density of seawater is assumed to have only one motion DoF along the verticalaxis. Here, the viscous effect is simplified as linear damping, the coefficients of which could be approximatedfrom model test results through parametric identification. Then, the dynamics of the assumed rigid OWC could
be described by the following equation based on the Cummins theory
M OWC  AfOWC z (t )

OWC
OWC
OWC
OWC
OWC
Fbuoy
(t )  Fradiation(t )  Fviscous(t )  Fexcitation(t )  FPTO
(t )

(3)

is the added mass of the point absorber atwhere M OWC is the mass of the equivalent point absorber, AOWCOWC
is the hydrostatic restoring force,
infinite frequency, z is the heave displacement of the point absorber, Fbuoy
OWC
OWC
OWC
Fradiationis the radiated force acting on the body, Fviscousis the viscous damping force, Fexcitationis the excitation
OWC
force acting on the body bottom, and FPTO
denotes the pneumatic force acting on the water free surface. Basedon this approximation approach, the time-domain variations of the OWC free surface and wave power
production could be evaluated within the same numerical dynamic analysis framework of FOWT.

Experimental Validation
In order to evaluate the feasibility of the proposed aero-hydro-elastic-servo-mooring coupled numericalframework, a novel hybrid FOWT-OWC concept is proposed in this work, and numerical simulations for anumber of environmental conditions have been conducted based on the established coupled framework. At thesame time, experimental results for 1:50 scale model wave basin tests are also presented for comparison andvalidation, as shown in Fig. 2.

Fig. 2 Concept Description and the 1:50 Scale model of the DOC concept.
The PTO damping is caused by the air pressure variation inside the OWC chamber due to the free surface
oscillation and the air mass flow through the top outlet. It is assumed that the OWC thermodynamic processes
are isentropic and adiabatic, involving incompressible ideal gas [13]. Thus, the air mass flow through the top
outlet is expected to be equal to the air mass variation in the chamber, which can be represented asm air (t )dª U air (t )  Schamber  L0  z (t ) º¼
dt ¬

(4)

where mair is the air mass in the chamber, ȡair is the air density in the chamber, Schamber is the cross-sectional areaof the chamber, L0 is the vertical distance between the mean sea level and the chamber top, and zሶ is the relative
velocity between the internal free surface and the platform column in the water oscillation direction. Then, theinstantaneous wave power production of each OWC can be obtained by
POWC'p (t )  Schamber  z (t )(5)

ZKHUH¨p is the increased pressure in the chamber relative to the atmospheric pressure. In the experiment, tuning
the valve opening will lead to different PTO damping coefficients, which can be approximated by the following
linearised function
BPTOǻp (t )  Schamberz (t )

(6)

where the BPTO denotes the equivalent PTO damping coefficient [14].
The obtained PTO damping fitting results for 5 ° valve opening under regular waves with different periods areshown in Fig. 3, where a strong linear correlation can be observed. Then, the OWC PTO damping force in theestablished time-domain numerical framework could be determined by the identified linear damping coefficient
table and OWC internal free water surface elevation velocities, thus enabling the OWC PTO control design andassessment for FOWT-OWC hybrid platforms.

Fig.3 PTO damping fitting results for OWC under regular waves with different periods (Į = 5 °).
Results
Regular Wave Tests
The regular wave tests without wind loads have been carried out with different PTO damping configurations.
The examined wave height is 3 m in full scale with a series of typical wave periods from 6 s to 18 s, and four
openings are set to 5 °, 30 °, 60 ° and 90 °.
Experimental and numerical result comparisons for the platform motion RAOs under regular waves withdifferent periods are shown in Fig. 4. It is shown that the numerical results agree well with the measured data,
but still, there are certain deviations. Especially for pitch motion, when the wave period is between 10 s to 16 s,
the numerical model over-predicts the RAO, while it is under-estimated when the wave period is 8 s and 18 s.
It is also worth noting that a resonance peak can be observed for platform pitch motion at the wave periodaround 10 s, which corresponds to the OWC natural frequency [15].

Fig.4 Comparisons of motion RAOs between experimental and numerical results with valve openings 5 ° and
30 °.

Irregular Wind and Wave Tests
To further investigate the prediction performance of the proposed numerical model, two irregular wave tests
with wind loads have also been conducted. The JONSWAP spectrum with factor Ȗ=3.3 is used for irregular wave
generation, and the OWC valve opening is set to 30 ° for these cases. The wind generation system in the wave
basin is used to bring wind loads on the rotor, and the corresponding aerodynamic thrust has been measured by
the 6-Axis force/torque sensor. Then, the obtained data is scaled up and imposed onto the rotor in the numericaltime-domain analysis process in order to ensure the consistency of the aerodynamic loads between experiments
and simulations.
mean

std

max

mean

min

std

max

mean

min

std

max

min

Fig.5 Result comparison of DOC platform motion responses.

mean

std

max

min

mean (OWC2)

std (OWC2)

mean (total)std (total)

Fig.6 Result comparisons of OWC free surface response and power production.

Statistical comparisons of the DOC platform motion responses under selected combined wind-wave test
conditions are presented in Fig. 5, which again shows data consistency. Fig. 6 presents the result comparison of
OWC free surface responses and wave power production, where good agreement can also be observed.
In summary, it can be seen that, compared with scale model wave basin experimental test results, the proposed
numerical framework can well predict the dynamic responses of FOWT-OWC hybrid platforms as well as the
OWC free surface variation and wave power production, demonstrating the feasibility of the established coupled
numerical framework [16].
References[1]

Council G W E. GWEC| GLOBAL WIND REPORT 2021[J]. 2017.

[2]

Michailides C, Gao Z, Moan T. Experimental study of the functionality of a semisubmersible wind turbine combined with flaptype wave energy converters. Renewable Energy, 2016, 93: 675-690.

[3]

Xu S, Murai M, Wang X, et al. A novel conceptual design of a dynamically positioned floating wind turbine[J]. Ocean Engineering,
2021, 221: 108528.

[4]Hegseth J M, Bachynski E E, Martins J R R A. Integrated design optimisation of spar floating wind turbines[J]. Marine Structures,
2020, 72: 102771.

[5]

Xu K, Larsen K, Shao Y, et al. Design and comparative analysis of alternative mooring systems for floating wind turbines inshallow water with emphasis on ultimate limit state design[J]. Ocean Engineering, 2021, 219: 108377.

[6]

Zhang H, Zhou B, Zang J, et al. Optimisation of a three-dimensional hybrid system combining a floating breakwater and a wave
energy converter array[J]. Energy Conversion and Management, 2021, 247: 114717.

[7]

Kamarlouei M, Gaspar J F, Calvario M, et al. Experimental study of wave energy converter arrays adapted to a semi-submersible
wind platform[J]. Renewable Energy, 2022, 188: 145-163.

[8]Perez-Collazo C, Pemberton R, Greaves D, et al. Monopile-mounted wave energy converter for a hybrid wind-wave system[J].
Energy Conversion and Management, 2019, 199: 111971.

[9]

Astariz S, Iglesias G. Selecting optimum locations for co-located wave and wind energy farms. Part I: The Co-Location Feasibility
index[J]. Energy Conversion and Management, 2016, 122: 589-598.

[10] ANSYS A. AQWA Theory Manual [J]. Canonsburg, PA 15317, USA, 2013.
[11] Jonkman J M, Buhl Jr M L. FAST user’s guide[J]. Golden, CO: National Renewable Energy Laboratory, 2005, 365: 366.
[12] Lackner M A, Rotea M A. Passive structural control of offshore wind turbines[J]. Wind energy, 2011, 14(3): 373-388.
[13] Cengel Y A, Boles M A, Kanoglu M. Thermodynamics: an engineering approach[M]. New York: McGraw-hill, 2011.
[14] So R, Bosma B, Ruehl K, et al. Modeling of a wave energy oscillating water column as a point absorber using wec-sim[J]. IEEE
Transactions on Sustainable Energy, 2019, 11(2): 851-858.
[15] Zhang D, Chen Z, Liu X, et al. A coupled numerical framework for hybrid floating offshore wind turbine and oscillating watercolumn wave energy converters[J]. Energy Conversion and Management, 2022, 267: 115933.
[16] Chen Z, Rong Z, Yu H, et al. Control Oriented Modelling of Oscillating Water Column Wave Energy Converters[J/OL].
Proceedings of the CSEE, 2022.

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Offshore Wind Turbines Design and Optimization
Zhiqiang Hu
Marine, Offshore and Subsea Technology, School of Engineering, Newcastle University, UK

Collaboration research between RIAM Kyushu University and MOST group, Newcastle
University was initiated at the beginning of year 2022, aiming to propose an AI-based
interactive Integrated Design and Optimization method. This method is proposed based on theconcept of SADA proposed by Zhiqiang Hu and Peng Chen in year 2020. The fundamentals ofSADA were introduced on RIAM symposium in year 2021 and an engineering practice caseof-study was also presented on RIAM symposium in year 2022. Although the Newcastle
University research team couldn’t attend the RIAM symposiums at Kyushu University inperson due to pandemic, the collaborative research outcomes were disseminated during the
symposiums online.
After the symposium of year 2022, Zhiqiang Hu led his research team and devoted into
investigations on AI+FOWTs, on purpose of improving the SADA concept to a higher level
which is suitable for real engineering practice and benefit offshore wind industry. During theyear of 2022, the collaborative research outcomes are listed as below.
1) The 3rd International Symposium on Novel Computational and Experimental Methods forComplicated Fluid-Structure Interactions was held online at RIAM Kyushu University in
Jan 2022. Zhiqiang Hu made a presentation on the topic of ‘Application of SADA method
on Dynamic Performances Analysis of FOWT: Case of Study with Full-Scale Hywind
Data’.
2) During year 2022, the collaborative research is carried out to propose the AI-basedInteractive Integrated Design method, simplified as IID. This investigation also received
kind support from ORE Catapult UK, as they provided the valuable suggestions andexperiences from UK offshore wind industry. The IID method aims to find a trade-off
design method and reconcile the contradictions between the wind industry and offshore
industry. During the development of floating wind farm in UK, there are existing some
contradictions between wind turbine design companies and offshore companies, due to thecommercial confidential. IID uses AI technology to reconcile this contradiction and it isexpected that the IID method will be proposed by mid of year 2023.
Besides the proposing of IID method, the collaborative research teams also began aninvestigation on the application of IID to digital twin level and propose IID+ method. This
IID+ digital twin will be started in year 2023.
3) Based on the research in year 2022, a collaborative conference paper entitled ‘DynamicPerformance Prediction of Hywind Floating Wind Turbine based on SADA Method andFull-Scale Measurement Data’ has been published on MARTECH Conference 2022. This
paper summaries the advantages of SADA method and its engineering values. The firstauthor, Dr Peng Chen presented this paper online in MARTECH2022 Conference and afruitful discussion was made after the presentation.
In year 2023, the collaborative research between Newcastle University and Kyushu University
will be conducted to a further step. The research will be extended to enhance IID method to ahigher level to be IID+, which will include the digital twin engineering practice. In UK, there
are high demands for the development of digital twin system application for offshore windfarms to effectively reduce cost of O&M. In addition, the research team is also extending
collaborations with experts in Geotechnology field, aiming to build the digital twin system not
only serve for wind farm structures, but also for sea environment monitoring. This is a very
new idea and it is expected more fruitful research outcomes will emerge in year 2023.

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Report for 2022 RIAM International Joint Research Project[22RE-]CFD Simulation of Offshore Wind Turbine in Realistic Ocean
Environment
Ye Li
School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, China

1. Purpose
Offshore wind turbine (OffWT) and onshore wind turbine (OnWT) have different working conditions,design loads and wake characteristics. In-depth analysis of the influence of the incoming atmosphericcharacteristics and wake evolution characteristics of OffWT and OnWT on the design value of wind turbines
is important to reduce the cost and improve the power coefficient. In order to understand the differences
between OffWT and OnWT, this joint research project focuses on the analysis of atmospheric conditions,wakes and their interactions with wind turbine loads. The project also provides an opportunity for researchers,
including but not limited to SJTU and RIAM, to exchange knowledge on the renewable energy research.

2. Research Plan
This research project is planned for two years. FY 2022 is the first year of the project. The major research
topic is the development of wind turbine simulation methods, advanced atmospheric turbulence generation
methods and wave models for the ocean waves, especially on the wake and load analysis of wind turbines
under typical offshore and onshore atmospheric conditions. At the end of FY2023, as the main event of thisinternational joint research project, the 1st International Symposium on Marine Renewable Energy System
Dynamics will be carried out. Researchers involved in this joint research project will present and discuss theirresearch progresses.
The members involved in this collaborative research are shown in the following table.
Researcher’s Name

Name of University
or Institute

Present Status or Grade(graduate students)

Ye Li

SJTU

Professor

Representative person (CFD )Changhong Hu

RIAM

Professor

RIAM Attendant

Zhiteng Gao

SJTU

Assistant Professor

Co-researcher (CFD)

Xiaobo Zheng

SJTU

Associate Professor

Co-researcher (CFD)

Shangming Wang

SJTU

Assistant Professor

Co-researcher (CFD)

Hongliang Wang

SJTU

Assistant Professor

Co-researcher (CFD)

Seiya Watanabe

RIAM

Assistant professor

Co-researcher (CFD)

Yingyi Liu

RIAM

Research Fellow

Co-researcher (CFD)

Researcher role

3. Summary of Collaboration Research
In 2022, due to the epidemic and international travel restriction, the discussions have been made between
the two research groups through the Internet. Main topics that have been studied include (1) next generation
CFD development; (2) wind turbine and wake modeling; (3) advanced atmospheric turbulence generation
methods; (4) machine learning application to hydro- and aerodynamic analysis and (5) related ocean renewableenergy technologies. Most of the research results will be presented at the 1st International Symposium on
Marine Renewable Energy System Dynamics, which will be held in a hybrid way in 24 February 2023.
Research papers related to this joint research project in 2022~2023 are listed as follows.

[1] Fan Z, Li S, Gao Z, Zhang L, Zheng X, Zhu W, Shen W, Sjoholm M, Mikkelsen T, Wang T, Li Y*. On
the importance of wind turbine wake boundary to wind energy and environmental impact. Energy Conversion
and Management, 2023, 277:116664.
[2] Leng J, Wang Q, Li Y*. A geometrically nonlinear analysis method for offshore renewable energy
systems—Examples of offshore wind and wave devices. Ocean Engineering, 2022,250: 110930.
[3] Gao Z, Feng X, Zhang Z, Liu Z, Gao X, Zhang L, Li S, Li Y*. A brief discussion on offshore wind turbinehydrodynamics problem. Journal of Hydrodynamics, 2022, 34(1): 15-30.
[4] Zhang L, Li Y*, Xu Wenhao, et al. Systematic analysis of performance and cost of two floating offshore
wind turbines with significant interactions. Applied Energy, 2022, 321: 119341.
[5] Zheng X and Li Y*. Aerodynamic response of a pitching foil to vortex shedding - some inspiration for thevertical-axis wind turbine. 3rd International Symposium on Novel Computational and Experimental Methods
for Complicated Fluid-Structure Interactions, online, January 21st, 2022.
[6] Zhang L, Li Y, Zhao Z, Hu C, Chen M. Numerical and Experimental Study of a 1MW Semi-submersible
Wave Energy Floating Platform. Renewable Energy. (Under review)[7] Xu W, Li G, Zhao R, Zhang L, Shi H, Li S, Gao Z, Hu C, Li Y. Feasibility analysis of large-scale offshore
vertical-axis wind turbines. Energy Conversion and Management. (Under review)[8] Wang H, Zheng X, Pröbsting S, Li Y, Wang Q, Hu C. An Unsteady RANS Simulation of The Performanceof An Oscillating Hydrofoil at High Reynolds Number. (Under second round review)As a main event of this international joint research project, ‘The 1st International Symposium on Marine
Renewable Energy System Dynamics’ will be held on February 24, 2023. Due to the global pandemic situationof COVID-19, the symposium will be held online. On the symposium, overseas and domestic scholars areinvited to present their recent researches on their recent research results on development of computational andexperimental methods for complicated fluid-structure interactions. The program of the symposium is asfollows.

The 1st International Symposium on
Marine Renewable Energy System Dynamics
Organized by Research Institute for Applied Mechanics, Kyushu University
Date: February 24, 2023 (From 10:10 Japan time)
Venue: Research Institute for Applied Mechanics (RIAM), Kyushu University
6-1 Kasuga-koen, Kasuga, Fukuoka 816-8580, Japan
Online participation:
https://riam-kyushu-u-ac-jp.zoom.us/j/82592030283 (ID: 825 9203 0283, PW:
riam0224)

TIME TABLE
10:10 -10:20

Opening Address by Changhong Hu

Session 1

Advanced CFD for Wind Turbine Simulation

10:20 - 11:00

Takanori Uchida (RIAM, Kyushu University)
Invited LectureWind Turbine Wake Simulation by using RIAM-COMPACT LES Model

11:00 - 11:30

Seiya Watanabe (RIAM, Kyushu University)
Numerical Simulation of Wind Farm by Lattice Boltzmann Method

11:30 - 12:00

Yos Panagaman Sitompul (Tokyo Institute of Technology)
Simulation of Foam Formation Using LBM with MPF Model and AMR Method,
Incorporating a Large Number of Bubbles

12:00 - 13:00
Session 2
13:00 - 13:30

Lunch break
Ocean Renewable Energy Technologies
Ye Li (Shanghai Jiao Tong University, China)

13:30 - 14:00

An overview of China-Australian Jiont Research Center for Offshore Wind and Wave
Energy Harvesting
Yusaku Kyozuka, Yusuke Kitajima, Gin Miake, Yuichi Yokoi (Nagasaki University)
A Wave Energy Convertor Making Use of Eccentric Rotating Mass Device

14:00 - 14:30

Ryoya Hisamatsu, Tomoaki Utsunomiya (Kyushu University)

14:30 - 15:00

Experimental and Theoretical Investigation on the Dynamics of a Water Intake Riser fora Floating OTEC
Lei Li (Zhenjiang Ocean University, China)
Study on Vortex-Induced Motion Characteristics and Suppression of a Circular Cylinder

15:00 - 15:20

Break

Session 3

Offshore Wind Energy Technologies

15:20 - 16:00

Shiu-Wu Chau (National Taiwan University, Taiwan)
Invited Lecture

16:00 - 16:30

Performance Prediction of a 15MW Floating Wind Turbine System Using SemiSubmersible Taida Floating Platform in the Hsinchu Offshore Area
Zhiteng Gao (Shanghai Jiao Tong University, China)
Aerodynamic Characteristics of Wind Turbine in Plateau Area

16:30-17:00

Watchara Tongphong (Korea Maritime & Ocean University, Korea)

17:00 - 17:30

A Fully Coupled Aero-Hydrodynamic Analysis of a 10 MW Floating Offshore Wind
Turbine using High-Fidelity Computational Fluid Dynamics
Xiaobo Zheng (Shanghai Jiao Tong University, China)

17:30 - 18:00

Experimental and numerical study on the aerodynamic response of a pitching foil to thevortex shedding
Zhiqiang Hu (Newcastle University, UK)
Offshore Wind and Artificial Intelligence: real-time monitoring and predictive
maintenance for offshore wind turbines

18:00 - 18:10

Closing Address by Ye Li

Contact:
Changhong HU, Professor
Research Institute for Applied Mechanics, Kyushu University
6-1 Kasuga-koen, Kasuga, Fukuoka 816-8580, Japanᅜ㝿໬᥎㐍ඹྠ◊✲ᴫせ㻌
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Introduction
Ocean waves can supply a significant source of clean and renewable energy due to the vast ocean area on theearth [1]. The ocean wave energy can be harnessed by a wave farm, a group of wave energy converters thatare deployed together in the ocean to generate electricity from the kinetic energy of ocean waves. Wave farms
locate near the coast or offshore and typically consist of multiple devices, such as floating buoys, oscillatingwater columns, or other wave energy converters, that are connected to the electrical grid. A conceptual designof wave farm is shown in Figure 1.
At present, there are some challenges associated with wave farms [2]. Due to that the technology is still in its
early stages of development, the cost of deploying and maintaining wave farms can be high. Additionally,
wave energy converters must be designed to withstand harsh conditions of the ocean environment, which canbe challenging and expensive. This study investigates the multiple scattering of ocean waves in a wave farmconsisting of arrays of heaving point absorbers. A numerical method is proposed to evaluate the annual performance of the wave farm.

Figure 1 A conceptual design of wave farm. Illustration by Alfred Hicks, NREL [3].
Methodology
Let us consider a train of regular incident waves that propagates to the positive x-direction with a small amplitude A, a heading angle E measured from the positive x-axis, and a wave number k, in water of a finite depthh. The ambient wave potential incident to body j can be written as୧௚஺ ୡ୭ୱ୦ ௞൫௭ೕ ା௛൯ ୧௞ൣ൫௫ೕ ା௫ҧ ೕ ൯ ୡ୭ୱ ఉା൫௬ೕ ା௬തೕ ൯ ୱ୧୬ ఉ൧݁,ୡ୭ୱ୦ ௞௛߶௝஺ ൫‫ݔ‬௝ ǡ ‫ݕ‬௝ ǡ ‫ݖ‬௝ ൯ ൌ െ ఠ(1)where ൫‫ݔ‬ҧ௝ ǡ ‫ݕ‬ത௝ ǡ Ͳ൯ refers to the origin of the local coordinate system of body j in terms of the global Cartesian
coordinates and ൫‫ݔ‬௝ ǡ ‫ݕ‬௝ ǡ ‫ݖ‬௝ ൯ refers to an arbitrary spatial point in terms of the local Cartesian coordinates. By
converting the local Cartesian coordinates to the polar coordinates ൫‫ݎ‬௝ ǡ ߠ௝ ǡ ‫ݖ‬௝ ൯, Eq. (1) can be expanded as asummation of partial cylindrical waves incident to the body j in the form of matrices்߶௝஺ ൫‫ݔ‬௝ ǡ ‫ݕ‬௝ ǡ ‫ݖ‬௝ ൯ ൌ ൛ܽ௝ூ ൟ ൛߰௝ூ ൟ,(2)

where ൛ܽ௝ூ ൟ is a scalar vector of expansion coefficients, and ൛߰௝ூ ൟ is a scalar vector of the basis function that is
also named as the incident partial wave component.
In arrays of floating bodies, each individual body experiences not only the ambient incident plane wave but
also the outgoing waves that are scattered from all the other neighboring bodies in the arrays. Based on Graf’s
addition theorem, the scattered waves from body i can be expressed as incident waves to body j as the following equation்߶௜ௌ ሺ‫ݎ‬௜ ǡ ߠ௜ ǡ ‫ݖ‬௜ ሻ ൌ ൛‫ܣ‬௜ௌ ൟ ൣܶ௜௝ ൧൛߰௝ூ ൟ,(3)

where ൛‫ܣ‬௜ௌ ൟ is a scalar vector of the scattering coefficients, and the T-transfer matrix yields
௠௤ൣܶ௜௝ ൧௡௡ ൌ ቊ‫ܪ‬௠ି௤ ൫݇‫ܮ‬௜௝ ൯݁ ୧ఈ೔ೕሺ௠ି௤ሻ ǡ ݊ ൌ Ͳǡ‫ܭ‬௠ି௤ ൫݇௡ ‫ܮ‬௜௝ ൯݁ ୧ఈ೔ೕ ሺ௠ି௤ሻ ሺെͳሻ௤ ǡ ݊ ൒ ͳǤ

(4)Using a so-called diffraction transfer matrix ൣ‫ܦ‬௝ ൧ as the form that is defined in Liu et al. [4] based on the hybrid dipole-source formulation, the scattered wave from body j and all the incident waves to the same bodycan be connected based on the following relation்ேಳ൛‫ܣ‬௝ௌ ൟ ൌ ൣ‫ܦ‬௝ ൧ ቀ൛ܽ௝ூ ൟ ൅ σ௜ୀଵǡ௜ஷ௝ൣܶ௜௝ ൧ ൛‫ܣ‬௜ௌ ൟቁ ǡ ሺ݆ ൌ ͳǡʹǡ ǥ ܰ஻ ሻ,(5)where ܰ஻ is the number of wave energy converters. From Eq. (5), scattering coefficients and the wave potentials can be solved numerically. Wave excitation forces, etc., can be calculated via pressure integration overeach body using matrix operations.

Wave farm assessment
It is common to use the so-called interaction factor to evaluate the performance of arrays of wave energy converters. The interaction factor q is defined as a function of the wave number k and the incident wave angle E[5]‫ݍ‬ሺ݇ǡ ߚሻ ൌ ே

௞

ಳ ௉ೈ

ே

ಳ
ܲ௝ ሺ݇ǡ ߚሻ൯
,
൫σ௜ୀଵ
௠௔௫

(6)

where ܲ௝ ሺ݇ǡ ߚሻ is the maximum absorbed power of each device in the farm, ܲௐ is the time-averaged incident
wave power per unit crest widthܲௐ ൌఘ௚஺మ ఠ
ଶ௞௛ቀͳ ൅ ୱ୧୬୦ ଶ௞௛ቁ.
ସ௞

(7)

At a localised site in irregular waves, the annual power production of a wave farm can be evaluated asܲ஺௡௡௨௔௟ ൌ σ்೛ σுೞ ߖ൫‫ܪ‬௦ ǡ ܶ௣ ൯‫ܬ‬൫‫ܪ‬௦ ǡ ܶ௣ ൯,(8)where ߖ൫‫ܪ‬௦ ǡ ܶ௣ ൯ denotes the occurrence probability and ‫ܬ‬൫‫ܪ‬௦ ǡ ܶ௣ ൯ denotes the power matrix. These are both
functions of the significant wave height ‫ܪ‬௦ and the peak wave period ܶ௣ .

Results
As a wave farm usually comprises several arrays of devices, hydrodynamic interactions amongst arrays areinvestigated first [6]. An example is shown as below. Figure 2 presents the variations of the q-factor vs thedevice spacing s, the wave heading angle E, and the wave angular frequency x for a uniform line array consisting of seven CorPower-like point absorbers. The most distinctive result herein is that there are some remarkable “bright spot” regions, indicating that the wave energy absorption there is locally optimized against wave
conditions. With regard to a uniform line array, it is found that the lower the wave frequency is, the larger thewave heading tends to be in association with the center of a spot region. In addition, the number or the densityof the spot regions are found to increase with the device spacing.

Figure 2. q-factor variation of a uniform line array of wave energy devices against the angular frequency x, thewave heading E, and the device spacing s (h = 100 m): (a) s = 2D, (b) s = 3D, (c) s = 4D, and (d) s = 5D.
References[1] Isaacs, J. D., and Schmitt, W. R., “Ocean energy: Forms and prospects,” Science 207, 265–273 (1980).
[2] Astariz, S., & Iglesias, G. (2015). The economics of wave energy: A review. Renewable and Sustainable Energy Reviews, 45, 397408.
[3] https://www.nrel.gov/water/wave-array.html[4] Liu, Y., Liang, H., Kashiwagi, M., & Cong, P. (2021). Alternative approaches of evaluating diffraction transfer matrix and radiation
characteristics using the hybrid source-dipole formulation. Applied Ocean Research, 114, 102769.
[5] Fitzgerald, C., and Thomas, G., “A preliminary study on the optimal formation of an array of wave power devices,” in Proceedingsof the 7th European Wave and Tidal Energy Conference, Porto, Portugal (2007), pp. 11–14.
[6] Liu, Y., Zheng, S., Liang, H., & Cong, P. (2022). Wave interaction and energy absorption from arrays of complex-shaped point
absorbers. Physics of Fluids, 34(9), 097107.