17th Technical Meeting on Energetic Particles and Theory of Plasma Instabilities in Magnetic Confinement Fusion

6 Dec 2021, 08:30 → 10 Dec 2021, 17:50 Europe/Vienna

Virtual Event

william heidbrink (UC Irvine)

Webex Links (password sent via email)

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Monday, Dec 6, 2021 2:00 pm | 4 hours | (UTC+01:00) Vienna

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Tuesday, Dec 7, 2021 2:00 pm | 4 hours | (UTC+01:00) Vienna

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Wednesday, Dec 8, 2021 2:00 pm | 3 hours 10 minutes | (UTC+01:00) Vienna

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Thursday, Dec 9, 2021 2:00 pm | 3 hours 30 minutes | (UTC+01:00) Vienna

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Friday, Dec 10, 2021 2:00 pm | 3 hours 50 minutes | (UTC+01:00) Vienna

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EPPI2021_Fom B.pdf

EPPI2021_Form A.pdf

EPPI2021_Info Sheet.pdf

Monday 6 December

Opening and Welcome

1 Opening Remarks

Speaker: Mr Matteo Barbarino (International Atomic Energy Agency)

2 Opening Remarks

Speaker: William W. Heidbrink (University of California Irvine)

Effects of Energetic Particles in Magnetic Confinement Fusion Devices

Convener: Taina Kurki-Suonio (Aalto University)

3 Unstable beta-induced ion temperature gradient (BTG) eigenmodes in JET plasmas with ITBs and elevated monotonic q-profiles.

Abstract:
JET deuterium experiments in an advanced tokamak scenario with an internal transport barrier (ITB) exhibit unstable electromagnetic (EM) perturbations in the sub-TAE frequency range. In JET pulse number (JPN) 92054, a high-beta plasma ($\beta_N = \beta_T B_T a / I_P \sim 4.38 [\%Tm/MA]$) with high power neutral beam injection (NBI), $P_{NBI} = 25.1 MW$, contained EM perturbations identified as beta-induced ion temperature gradient (BTG) eigenmodes and not beta-induced Alfvén eigenmodes (BAE) nor beta-induced Alfvén acoustic eigenmodes (BAAE) which are often destabilised in similar plasma conditions. The EM perturbations are localised near the $q=2$ magnetic surface related to the ITB, and their frequency correlates well with the BTG characteristic frequency (ion diamagnetic frequency, $\omega_i^*$) and the thermal ion temperature gradient ($\nabla T_i$). BTG modes are the most unstable modes due to the high thermal ion temperature gradient in the ITB, high thermal ion temperature compared to thermal electron temperature ($T_i / T_e > 1$), and a high ion beta. Three well-defined conditions for BTG modes to exist, defined by BTG analytical theory [1], are fulfilled in JPN 92054: (1) a positive relative ion temperature gradient, (2) ion beta higher than a critical value, and (3) a low magnetic shear. BTG theory also predicts a mode location in the vicinity of a rational magnetic surface, a frequency scaling with $\omega_i^*$, and a coupling between Alfvén and drift waves. We have performed linear gyrokinetic simulations with validated plasma profiles and equilibrium, and find a mode with features resembling those of the experimental and theoretical BTG modes; specifically the mode is kinetically driven by thermal ions, is localised near the $q=2$ magnetic surface, has a dominant Alfvénic polarisation, and its frequency scales with $\omega_i^*$ dependent on the toroidal mode number ($n$). Parts of this work have been reported in [2].

BTG modes are also observed in more recent JET plasmas during energetic particle scenario experiments aimed at studying alpha-particle driven AEs, performed in JET 2019/2020 deuterium campaigns. Reflectometer diagnostic data confirm that the mode location is around the $q=2$ magnetic surface. We also present evidence for a systematic correlation between the BTG mode stability and the neutron rate roll-over (i.e. $d(R_{NT})/dt$ transiting from positive to negative).

References:
[1] A. B. Mikhailovskii and S. E. Sharapov. Beta-induced Temperature-gradient Eigenmodes in Tokamaks. Kinetic Theory. JET Joint Undertaking Reports, JET–P(98)12:1–16, 1998.
[2] N. Fil, et al. Interpretation of electromagnetic modes in the sub-TAE frequency range in JET plasmas with elevated monotonic q-profiles. Physics of Plasmas, Accepted, 2021.

Acknowledgments:
This work has been carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training programme 2014-2018 and 2019-2020 under grant agreement No 633053 and from the RCUK [grant number EP/T012250/1]. The views and opinions expressed herein do not necessarily reflect those of the European Commission.
This work was supported by U.S. Department of Energy (DOE) through DEFG02-99ER54563, DE-AC05-00OR22725 and DE-AC02-05CH11231).

Speaker: Dr Nicolas Fil (UKAEA, CCFE)

2021-12-06_IAEA-EPPI_BTG-modes_clean.pdf

4 Hybrid simulations of of beta-induced Alfven eigenmode with reversed safety factor profile

Based on the experimental parameters in HL-2A tokamak, the linear stability and nonlinear dynamics of BAE with reversed safety factor $q$ profile are investigated by using kinetic-MHD code M3D-K. It is found that the ($m/n=3/2$) BAE is excited by co-passing energetic ions with $q_{min}=1.5$ in linear simulation, and the mode frequency is consistent with experimental meuasurement. The simulation results show that the energetic ions $\beta_h$, the injection velocity $v_0$ and orbit width parameter $\rho_h$ of energetic ions are important parameters determining the drive on BAE. The effect of $\rho_h$ is determined by the orbital averaging, while the effect of $v_0$ is associated with the fraction of resonant ions. Furthermore, the effect of $q_{min}$ (with fixed shape of $q$ profile) is studied, and it is found that: when $q_{min} \le 1.5$, the excited modes are BAEs, which are located near $q=1.5$ rational surfaces; when $q_{min} > 1.5$, the excited modes are reversed-shear Alfven eigenmodes (RSAEs), which are localized around $q=q_{min}$ surfaces. Nonlinear simulation results show that the nonlinear dynamics of BAE depends on the EP drive. For strongly driven case, firstly, redistribution and transport of engetic ions are trigged by $3/2$ BAE, which raised the radial gradient of energetic ions distribution function near $q=2$ rational surface, and then an EPM ($m/n=4/2$) is driven in nonlinear phase. Finally, these two instabilities triggered significant redistribution of energetic ions, which results in the repetitive and mostly-downward frequency chirping of $3/2$ BAE. For weakly driven case, there are no $4/2$ EPM being driven and repetitive chirping in nonlinear phase, since the radial gradient near $q=2$ rational surface is small and almost unchanged.

Speaker: Sizhe Duan (University of Science and Technology of China)

5 Implementation of ion cyclotron resonance frequency heating in a kinetic-MHD hybrid code: MEGA

Ion cyclotron resonance frequency (ICRF) heating has been chosen as one of the fundamental auxiliary heating systems in many present-day fusion devices, as well as the upcoming ITER. Energetic ions generated by ICRF heating with energies up to several hundred-keV or several MeV can drive a variety of Alfven eigenmodes, such as reversed-shear, toroidal and ellipticity Alfven eigenmodes (RSAE, TAE, EAE). The destabilized Alfven eigenmodes will significantly modify the energetic ion distribution. Accurate evaluations of energetic ion distributions in present-day devices and the prediction in future burning plasmas require considering the interactions between Alfven eigenmodes and energetic ions during the distribution formation process. Additionally, the destabilized Alfven eigenmodes have a wide variety of nonlinear dynamics during the ICRF generated energetic ion pitch-angle scattering and slowing-down processes [1].

In this work, we have extended the MEGA code [2], which is a hybrid simulation code for energetic particles interacting with an MHD fluid, by implementing the ICRH acceleration, source, sink, and collisions. Both Coulomb collisions [3] and a quasilinear ICRF operator for wave–particle interactions [4,5] are solved by Monte Carlo method. We applied the extended MEGA code to an ICRF minority heating scenario in the Large Helical Device (LHD). The heating efficiencies, minority ion distributions, and AE stabilities at different RF input power and resonance layer locations in LHD will be presented.

References
[1] H.L. Berk, B.N. Breizman, and M.S. Pekker, Phys. Rev. Lett. 76, 1256 (1996).
[2] Y. Todo and T. Sato, Phys. Plasmas, 5, 1321 (1998).
[3] C.F.F. Karney, Comput. Phys. Rep., 4, 183 (1986).
[4] T.H. Stix., Nucl. Fus., 15, 737 (1975).
[5] S. Murakami et al., Nucl. Fus., 46, S425 (2006).

Speaker: Jialei Wang (National Institute for Fusion Science)

6 Modeling of the nonlinear resonant interaction between ELMs and fast-ions in tokamaks using MEGA

Edge localized modes (ELMs) are periodic magnetohydrodynamic (MHD) instabilities driven by sharp pressure gradients and current densities at the plasma boundary that will likely lead to transient, and intolerable, energy and particle losses in ITER. Although the ELM nature is still under intense investigation, their behavior and their consequences in a burning plasma with a significant fraction of energetic (supra-thermal) ions is completely missing. Recent experimental observations have shown the ejection and acceleration of energetic ions during ELM crashes [1, 2], indicating a strong interplay between the energetic particle population at the plasma edge and the electromagnetic perturbation developed during an ELM crash. A good understanding of the interaction between energetic ions and ELMs is mandatory to develop ELM control techniques for burning plasmas as well as to be able to predict their impact on the plasma, including fast-ion confinement.

In this work, the nonlinear hybrid kinetic-MHD MEGA code [3] has been used to study the interaction between energetic particles and ELMs in an ASDEX Upgrade H-mode plasma [4]. The simulations show, for the first time, the strong impact that energetic particles kinetic effects have on the spatio-temporal structure of ELMs in tokamaks. Energetic ions kinetic effects modify the ELM linear growth rate, crash timing, frequency pattern, and spatial structure. In the nonlinear phase, energetic ions impact the shear and tend to extend the ELM radial ballooning structure to regions deeper in the plasma. Strong energetic ion transport is observed during the ELM crash. The results presented here may help explaining the frequency pattern and fast-ion losses observed during ELMs in several tokamaks worldwide [5] and, thus, may help improving our predictive capabilities and control techniques for future fusion devices. The implications of our simulation results for ITER will be discussed.

References
[1] M. Garcia-Munoz et al., Nucl. Fusion 53, 123008 (2013).
[2] J. Galdon-Quiroga et al., Phys. Rev. Lett. 121, 025002 (2018).
[3] Y. Todo et al., Phys. Plasmas 5, 1321 (1998).
[4] A.F. Mink et al., Nucl. Fusion 58, 026011 (2018).
[5] F.M. Laggner et al., Nucl. Mater. Energy 19, 479 (2019).

Speaker: Jesus Dominguez-Palacios (University of Seville)

O63_DominguezPalacios.pdf

7 Effects of distribution functions in global gyrokinetic simulations of energetic particle driven Alfvénic and EGAM instabilities in ITER and ASDEX Upgrade

In recent years, there has been significant progress with global electromagnetic gyrokinetic codes in modelling Alfvén Eigenmodes (AEs) and other energetic particle (EP) driven instabilities in realistic equilibria, for example, simulations with the gyrokinetic code ORB5 [1] of Energetic Particle Modes (EPMs) and Energetic-particle-driven Geodesic Acoustic Modes (EGAMs) in ASDEX Upgrade (AUG) [2,3] and toroidal Alfvén Eigenmodes (TAEs) in ITER [4].

While the previous work addressed the realistic density and temperature profiles and equilibria of the experiments considered, the distribution function of the EPs was typically modelled using a Maxwellian (for AEs) or a Bump-on-tail (for EGAMs). For quantitative predictions or comparisons to experiments, a more realistic distribution for alpha particles in ITER (isotropic slowing down), or for neutral beam injected (NBI) particles in AUG is required.

We report on work done in ORB5 to handle general distribution functions in addition to the analytical choices already implemented. This framework has been used to couple the output from the NBI solver RABBIT [5] to be used as the background distribution in ORB5. The same framework was used to verify the implementations of analytical distribution functions and their gradients, and was used to implement a semi-analytic anisotropic slowing down distribution function.

Also, a comparison for the ITER 15MA scenario between TAEs driven by Maxwellian and slowing down distribution functions, where the mode growth due to EPs with a isotropic slowing down is found to be larger than in the case of a Maxwellian.

In the case of ASDEX Upgrade, following the so-called "NLED-AUG" case (#31213) [6], we focus on EPs from NBI injection. These are taken from RABBIT, but also comparisons have been performed with analytical anisotropic distribution functions, which help to parameterize the observed behaviour.
With these simple analytical distribution functions, we can compare the phase space gradients at the positions of the maximum power exchange in linear simulations.

Finally, we report on efforts ongoing to model AEs in an ITER pre-fusion power operation (PFPO) scenario, and the associated coupling of NBI data from the Integrated Modelling & Analysis Suite (IMAS) database.

[1] E. Lanti, et al., Computer Physics Communications 251, 107072 (2020)
[2] I. Novikau et al., Physics of Plasmas 27, 042512 (2020)
[3] F. Vannini et al., Physics of Plasmas 27, 042501 (2020)
[4] T. Hayward-Schneider et al., Nucl. Fusion 61, 036045 (2021)
[5] M. Weiland et al., Nucl. Fusion 58 082032 (2018)
[6] Ph. Lauber et al, EX1/1 Proc. 27th IAEA FEC (2018)

Speaker: Thomas Hayward-Schneider (Max Planck Institute for Plasma Physics)

Hayward-Schneider_EPPI_2021.pdf

8 Impurity holes induced by energetic electrons during electron cyclotron resonance heating in tokamaks with helical core

Tungsten accumulation is one of the main challenges for successful operation of ITER and future reactors. For this reason, various techniques have been developed recently in order to mitigate such accumulation. One of such methods is the application of wave heating, in particular electron cyclotron resonance heating (ECRH) deposited close to the plasma center.

Recent 3D equilibrium calculations have revealed that ITER plasmas in the hybrid scenario are prone to spontaneous helical core formation [1]. Such helical cores with dominant mode numbers m/n=1/1 are routinely observed between sawtooth crashes in ASDEX Upgrade discharges with central ECRH [2]. The long-standing mystery of these shots, which motivated present work, is deeply hollow tungsten density profile between crashes, which manifests itself by inverted sawteeth on the soft X-ray signals.

In the present contribution it is shown that ECRH-generated energetic electrons are responsible for the tungsten hole [3]. Such electrons 'run away' along RF-induced quasi-linear diffusion path in velocity space and form strongly anisotropic population with banana tips accumulated at cyclotron resonance position on the magnetic surface. When cyclotron resonance is located on the high-field side, as in the ASDEX experiments described in [2], magnetic drift of the energetic electrons' banana guiding centers bacomes 'reversed', i.e. it is directed in the co-current direction and can balance the opposite electric drift associated with positive radial electric field $E_r$. As a result, banana guiding centers of energetic electrons become trapped in the n=1 toroidal 'ripple' of the magnetic field induced by internal kink, which generates strong non-ambipolar flux of the hot electrons, $\Gamma_e^{hot}$, due to super-banana motion. For relarive density of hot electrons ~ few %, this resonant flux exceeds by order of magnitude the flux of non-resonant thermal ions, which for kink-distorted equilibrium was estimated in [4]. The ambipolarity condition thus becomes $\Gamma_e^{hot}(E_r)=0$. The stable root of this equation (i.e. a stable fixed point of the radial current balance $(1+2q^2)(c^2/V_A^2)\partial E_r/\partial t-e\Gamma_e^{hot}(E_r)=0$) yields a self-consistent 'electron' root with $E_r\sim +10 kV/m$ (in the frame with static internal kink). Trace tungsten should respond adiabatically to this root, i.e. with Boltzmann distribution, $\nabla n_Z/n_Z=ZE_r/T_i>0$, which corresponds to the deep hole, consistent with experiment [2].

This results imply that high-field side ECRH can be a viable option to prevent tungsten accumulation in the hybrid ITER discharges prone to spontaneous helical core formation [1], since recent modeling suggests that helical core itself augments impurity accumulation [5].

1. A. Wingen et al., Nucl. Fusion 58, 036004 (2018).
2. M. Sertoli et al., Nucl. Fusion 55, 113029 (2015).
3. V.S. Marchenko, Phys. Plasmas 27, 022516 (2020).
4. S.V. Putvinskij, Nucl. Fusion 33, 133 (1993).
5. M. Raghunathan et al., Plasma Phys. Control. Fusion 59, 124002 (2017).

Speaker: Victor Marchenko (Institute for Nuclear Research, Kyiv, Ukraine)

9 Verification and validation of gyrokinetic and kinetic-MHD simulations for internal kink and fishbone instabilities in DIII-D and ITER

Verification and validation of the internal kink instability in tokamak have been performed for both gyrokinetic (GTC) and kinetic-MHD codes (GAM-solver, M3D-C1-K, NOVA, XTOR-K). Using realistic magnetic geometry and plasma profiles from the same equilibrium reconstruction of the DIII-D shot #141216, these codes exhibit excellent agreements for the growth rate and mode structure of the n=1 internal kink mode in ideal MHD simulations by suppressing all kinetic effects. The simulated radial mode structure agrees quantitatively with the electron cyclotron emission measurement after adjusting, within the experimental uncertainty, the q=1 flux-surface location in the equilibrium reconstruction. Equilibrium plasma pressure gradient and compressible magnetic perturbation strongly destabilize the kink, while poloidal variations of the equilibrium current density stabilize the kink. Furthermore, kinetic effects of thermal ions are found to decrease the kink growth rate in kinetic-MHD simulations, but increase the kink growth rate in gyrokinetic simulations, due to the additional drive of the ion temperature gradient and parallel electric field. Kinetic thermal electrons are found to have negligible effects on the internal kink instability.
The validated MHD capability of GTC is then applied to study the NBI/alpha fishbone instability in ITER plasmas. Fishbone modes are found unstable for a pre-fusion baseline and 15 MA steady-state scenarios. DIII-D discharges similar to the ITER scenarios have been identified to validate GTC simulation results. Fishbone modes are found unstable in these DIII-D plasmas as well, with similar mode structures to those found in ITER simulations.

Speaker: Guillaume Brochard (University of California, Irvine)

10 Effect of anisotropic fast ions on internal kink mode stability in DIII-D negative and positive triangularity plasmas

Recent DIII-D experiments show that sawteeth can be strongly affected by anisotropic fast ions from Neutral Beam Injection (NBI) in both negative and positive triangularity plasma configurations. Fast ions from co-current NBI are stabilizing for the sawtooth stability, resulting in longer sawtooth periods. On the other hand, fast ions from counter-current NBI are destabilizing, leading to small and frequent sawteeth. The relative change in the sawtooth period and amplitude can be more than 50%. The observation appears to hold in both plasma shapes. Non-perturbative toroidal modeling, utilizing the magnetohydrodynamic-kinetic hybrid stability code MARS-K, reveals an asymmetric dependence of the stability of the (1,1) internal kink mode on the injection direction of neutral beams, being consistent with the experimentally observed sawtooth behavior. The MARS-K results suggest that anisotropic fast ions strongly affect the mode growth rate and frequency through both adiabatic (fluid) and non-adiabatic (kinetic) contributions. The asymmetry of the (1,1) kink mode instability relative to the beam injection direction is mainly due to the non-adiabatic contribution of passing fast ions, which stabilize (destabilize) the internal kink with the co-(counter-) current beam injection. The mode growth rate of the internal kink mode with co-(counter-) current beam injection can be increased (decreased) by a factor of 2 compared with the fluid limit. Trapped particles are always stabilizing due to precessional drift resonances. Modeling also shows that fast ions affect the n = 1 internal kink in a similar manner in both negative and positive triangularity plasmas, albeit being more unstable in the negative triangularity case. This similarity is mainly attributed to the fact that the mode is localized inside the q=1 flux surface, with very similar eigenmode structures in both negative and positive configurations. Furthermore, MARS-K modeling indicates that other factors, such as the plasma rotation, the plasma resistivity, or the presence of a resistive/ideal wall, have much weaker effects on the mode stability as compared to that of the drift kinetic resonance effects of fast ions in DIII-D.

*Supported by the US DOE under DE-FC02-04ER54698, DE-SC0020337, and DE-AC52-07NA27344.

Speaker: Dr Deyong Liu (University of California, Irvine)

2021IAEAEP_Sawtooth_MARSK.pdf

11 Conceptual design of DIII-D experiments to diagnose the lifetime of spin polarized fuel

The D-T fusion cross-section in magnetically confined plasmas is increased by 50% when the spins of both nuclei are polarized along the magnetic field[1], offering promise for a significant increase in fusion energy output with no additional requirement on plasma confinement. Theoretically [1], depolarization mechanisms from field inhomogeneities or collisions are weak in the core of a tokamak but the polarization lifetime has never been measured. The goal of this study is to assess the feasibility of lifetime measurements on the DIII-D tokamak using relative changes in charged fusion product (CFP) loss measurements that depend upon the differential fusion cross section dσ/dΩ. Relative measurements are preferred over absolute measurements of the total reaction rate for two reasons. First, changes in relative measurements with polarization are insensitive to uncertainties in plasma parameters, while the reaction rate is not. Second, dσ/dΩ changes when only one species is polarized but the cross section does not. Relative changes in the escaping CFP pitch, poloidal, and energy distributions are all sensitive to changes in dσ/dΩ.

Three scenarios are considered. In the first, a tensor-polarized deuterium pellet is injected into an L-mode hydrogen background plasma that includes neutral beam injection (NBI) of unpolarized deuterium and compared to an unpolarized pellet of similar size and velocity. The effect of polarization on dσ/dΩ is controversial for D-D but almost certainly is non-zero [2], so the persistence of changes in 3-MeV proton signals yields a lifetime measurement. The second scenario substitutes unpolarized 3He NBI for D NBI and utilizes both 15-MeV proton and 3.7-MeV alpha detection. In nuclear physics, D-3He and D-T are nearly identical mirror reactions, so the expected change in dσ/dΩ is well known. In the third scenario, vector-polarized D and 3He pellets are injected into a hot hydrogen plasma to produce thermonuclear reactions.

The calculations utilize realistic plasma scenarios from TRANSP and energy-resolved CFP count rates evaluated with FIDASIM [3]. Initial results for the D-D scenario show that the pitch and energy distributions of 3-MeV protons are sensitive to changes in dσ/dΩ for a port on the midplane; signal levels are also practical.

[1] R.M. Kulsrud et al., Nucl. Fusion 26 (1986) 1443.

[2] H.M. Hofmann and D. Fick, Phys. Rev. Lett. 52 (1984) 2038.

[3] W.W. Heidbrink et al., Plasma Phys. Control. Fusion 63 (2021) 055008.

This work is supported by the U.S. Department of Energy under DE-SC0021624, DE-SC0019253 and DE-FC02-04ER54698.

Speaker: Alvin V. Garcia (University of California, Irvine)

12 Negative triangularity shaping effects on Alfvén eigenmodes in DIII-D plasma

Linear numerical simulations using FAR3d indicate that negative triangularity (NT) shaping of plasma in DIII-D lowers the growth rate of energetic particle (EP) driven Alfvén eigenmodes (AEs) as compared to the positive triangularity (PT) shaping of plasma [1]. Recently, there is a renewed interest in the NT shaping for its benefits of reduced microturbulence, better thermal confinement and high normalized beta achievable in fusion plasmas [2,3]. An investigation based on the effects of NT plasma shape on the EP driven AE activity in DIII-D is performed using the gyrofluid code - FAR3d. Numerical simulations performed at a discrete time determine AEs at similar frequencies as observed in the experiments. However, the lower growth rates in NT plasma are not due the negative triangularity shape but are caused by different fast ion density profile and lower q-values in the NT discharge as compared to the PT discharge. We also compared FAR3d results with linear gyrokinetic simulations using the GTC code to include more damping physics and observed similar trends of lower AE growth rates with NT plasma shaping. However, DIII-D experiments did not report any significant advantage of NT shaping for suppressing AEs induced fast ion transport [4]. The study of nonlinear state of the EP driven AEs and the associated fast ion transport can be readily performed using the nonlinear version of FAR3d. The linear simulations shall be extended to the nonlinear regime for long simulation times to compare the saturation mechanism and fast ion transport in the NT and PT regimes. Our findings should lead to new physical insights regarding the benefits of NT shaping of the plasmas in fusion devices.

*This material is based upon work supported by the U.S. Department of Energy, Office of
Science, Office of Fusion Energy Sciences under Awards DE-AC05-00OR22725, DE-FC02-
04ER54698, the U.S. DOE SciDAC ISEP Center, and project 2019-T1/AMB-13648 founded by the Comunidad de Madrid and Comunidad de Madrid (Spain).

References:
[1] Y. Ghai, D. A. Spong, J. Varela, L. Garcia and M. A. Van Zeeland, ‘Effect of plasma shaping
on energetic particle drive Alfvén eigenmodes in DIII-D, Nuclear Fusion (2021) (In Press) https://doi.org/10.1088/1741-4326/ac2bc0.
[2] Camenen Y., Pochelon A., Behn R. et al., Nuclear Fusion, 47, 510-516 (2007).
[3] Austin M.E. et al., Phys. Rev. Lett., 122, 115001 (2019).
[4] M. Van Zeeland et al., Nuclear Fusion, 59, 086028 (2019).

Speaker: Yashika Ghai

Tuesday 7 December

Transport of Energetic Particles

Convener: William W. Heidbrink (University of California Irvine)

13 Numerical Studies on Saturated Kink and Sawtooth Induced Fast Ion Transport in JET

This presentation examines the energetic particle transport induced by saturated kink modes and sawtooth crashes in JET deuterium plasmas. It is known that kink mode-resonant transport[1-3] and phase-space redistribution from sawtooth crashes[4-5] can drive strong fast ion transport with dependencies on particle pitch and energy. Measurements with JET's Faraday cup fast ion loss detector array have shown that the internal kink growth phase preceeding sawtooth crashes produces substantial fast ion losses.[6] This report will numerically investigate the dominant energetic particle transport mechanism with a detailed examination of the fast ion phase-space dependencies, resonances, topological effects, and induced losses associated with the long-lived, resonant, kink mode and non-resonant sawtooth crash. The ORBIT-kick model[7] forms the basis of the transport studies with realistic fast ion distributions produced from TRANSP[8]. A recently created reduced model for sawtooth induced transport[9] is compared against the standard Kadomtsev model within TRANSP while the saturated kink modes are modeled with ideal MHD codes and analytic theory. Figure 1 compares ORBIT calculated and ECE meaasured $T_e$ fluctuations for the saturated kink with methods based from [9] and demonstrates the power of the reduced modeling framework. The simulations are further validated against experiment with a newly developed synthetic Faraday cup fast ion loss detector[10] in addition to scintillator probe, neutron, and gamma-ray spectroscopy measurements.

[1] Ya. I. Kolesnichenko, V. V. Lutsenko, et al. 1998 Phys. Plasmas 5 2963
[2] Ya. I. Kolesnichenko, V. V. Lutsenko, et al. 2000 Nucl. Fusion 40 1325
[3] R. Farengo et al. 2013 Nucl. Fusion 53 043012
[4] D. Kim, M. Podesta, D. Liu, and F. M. Poli 2018 Nucl. Fusion 58 082029
[5] D. Kim et al. 2019 Nucl. Fusion 59 086007
[6] P. J. Bonofiglo et al. 2020 Rev. Sci. Instrum. 91 093502
[7] M. Podesta et al. 2017 Plasma Phys. Control Fusion 59 095008
[8] doi:10.11578/dc.20180627.4
[9] M. Podesta et al. 2021 Plasma Phys. Control Fusion Submitted
[10] P. J. Bonofiglo et al. 2021 Nucl. Fusion Submitted

Speaker: Phillip Bonofiglo (Princeton Plasma Physics Laboratory)

Bonofiglo_IAEAEP_2021.pdf

14 Numerical study of helium ash and fast particle dynamics in a sawtoothing tokamak plasma

We study the effect of a sawtooth crash on the dynamics of MeV-class fast deuterons, as produced by ion cyclotron heating, and alpha particles in the energy range 35-3500 keV, resembling helium ash and newly-born fusion alphas. The simulations are performed using the hybrid code MEGA [1], which solves visco-resistive MHD equations for the bulk plasma and drift-kinetic equations with gyroaveraging [2] for fast ions.

The internal disruption is simulated in a scenario resembling a tokamak plasma in the Joint European Torus (JET) with strong central heating as realized with 3-ion RF heating schemes [3]. The domain size and time scale of the crash match observations. Meanwhile, the profile of the safety factor q is chosen to be fairly flat as considered for ITER steady-state scenarios, with the on-axis q value lying only slightly below unity.

Both current and pressure gradients play a role, so that the phenomenology of the internal disruption is sensitive to simulation parameters. When pressure effects dominate (e.g., for lower resistivity or higher beta), the dominant toroidal mode number n can have values of 2 or greater. We focused primarily on cases where the n=1 component is dominant. Our two main results may be summarized as follows:

1. Although linear stabilization of the internal disruption could not be simulated with our model due to resistivity and pressure effects [4], we observe that reconnection of the plasma core saturates prematurely in the nonlinear regime when MeV-class deuterons are present and interact with the MHD modes. The island seen in magnetic Poincare plots is distorted into a tear-drop shape. This result suggests that nonlinear effects should be taken into account when interpreting delayed sawtooth crashes or monster sawteeth in experiments.

2. Mono-energetic, nearly isotropic alpha particles with energies 35 keV, 350 keV or 3.5 MeV are modeled as passive tracers and followed during an n=1 sawtooth crash lasting less than 0.5 ms. The initial peak of the alpha particle density profile is localized in the disrupting domain. While the 35 keV profile flattens, the 3.5 MeV profile undergoes relatively little change. Mass and velocity scans reveal that the better confinement of fast alphas can be explained as a synergy of four factors: (i) high transit frequency, (ii) field and orbit helicities close to unity, (iii) large magnetic drifts, and (iv) rapidity of the crash. While slow alphas are displaced by the electric drifts like an MHD fluid, the parallel speed and magnetic drifts of fast alphas are sufficiently large to compensate the displacement. This finding motivates the use of moderate sawtooth activity in a fusion reactor to remove helium ash without compromising fast alpha confinement [5].

[1] Todo et al., Phys. Plasmas 5 (1998) 1321; Phys. Plasmas 12 (2005) 012503.
[2] Bierwage et al., Nucl. Fusion 56 (2016) 106009.
[3] Kazakov et al., Phys. Plasmas 28 (2021) 020501. Nocente et al., Nucl. Fusion 60 (2020) 124006.
[4] Bondeson et al., Phys. Fluids B 4 (1992) 1889.
[5] Bierwage et al., submitted to Phys. Rev. Lett. (2021). Preprint: http://arxiv.org/abs/2109.03427.

Speaker: Andreas Bierwage (National Institutes for Quantum and Radiological Science and Technology)

2021-12-07_EPPI_Bierwage_main.pdf

15 Energetic Ion Transport due to Energetic Particle Continuum Mode in Deuterium LHD Plasmas

Energetic particle transport due to the energetic-particle-driven magnetohydrodynamic (MHD) instabilities in existing fusion devices has been intensively studied in order to find a way to control/reduce the energetic deuterium-tritium fusion born alpha particle transport in a future fusion reactor. In the hydrogen Large Helical Device (LHD) plasma experiment, a study of energetic ion transport/loss due to energetic-particle-driven MHD instabilities such as toroidal Alfvén eigenmode and energetic particle continuum mode (EPM), has been performed using comprehensive energetic particle diagnostics [1, 2]. By starting the deuterium plasma experiment in LHD, information of the energetic particles confined in the plasma core region can be obtained by neutron diagnostics because neutrons are mainly created by the so-called beam-thermal reactions. The transport of helically-trapped beam ion due to the energetic-particle-driven resistive interchange mode has been visualized using the vertical neutron camera and orbit following numerical simulation [3].
Energetic particle transport due to EPM, whose frequency is sufficiently low compared with toroidal Alfvén frequency, has been studied in relatively low-field conditions. The energetic particle diagnostic, i.e., the fast ion loss detector [4], and neutron diagnostics, i.e., neutron flux detector [5] are simultaneously utilized to understand the transport and loss of energetic particles. Three intensive negative-ion-based neutral beam injectors inject the deuterium beam into the low-density LHD deuterium plasma in these discharges. The bursting EPM excited by significant beam ion pressure gradient having the mode number of $m/n$ of 2/1 and the magnetic fluctuation amplitude of $\sim3×10^{-5}$ T is observed by the magnetic probe position located on the vacuum vessel. The frequency of EPM sweeps from 40 kHz to 20 kHz within 1 ms. The neutron flux detector shows that EPM induces approximately a 10% decrease in total neutron emission rate, suggesting ~10% loss of the beam ions. The fast ion loss detector measurement shows that fast ions rate corresponds to energy/pitch angle of 60-180 keV/~35 degrees and 120-180 keV/~55 degrees increases significantly due to EPM. The EPM enhances the transport of energetic ions having co-going transit and transition orbits.
[1] K. Toi et al 2011 Plasma Phys. Control. Fusion 53 024008.
[2] M. Isobe et al 2010 Contrib. Plasma Phys. 50 540.
[3] K. Ogawa et al 2020 Nucl. Fusion 60 112001.
[4] K. Ogawa et al 2009 J. Plasma Fusion Res. Ser. 8 655.
[5] K. Ogawa et al 2018 Plasma Fusion Res. 13 3402068.

Speaker: Dr Kunihiro Ogawa (National Institute for Fusion Science)

16 Precession direction reversal and rapid energetic particle pressure redistribution in a Large Helical Device Plasma

The understanding of energetic particle (EP) dynamics in plasmas is crucial for the conception and operation of magnetic confinement devices. These energetic particles have an energy much higher than the thermal energy of the bulk plasma, and despite their low density, can destabilize magnetohydrodynamics (MHD) modes. These modes can provoke the rapid ejection of energetic particles from the plasma core, rendering them unable to deposit their energy on the bulk plasma, and thus reducing the fusion efficiency rate. These energetic particle modes have been observed and found to cause transport such as the fishbone instability, EP driven Alfvén Eigenmodes.
In the Large Helical Device (LHD), an Energetic particle driven InterChange mode (EIC) was observed in 2015 [1]. This mode, destabilized when a perpendicular neutral beam injection was active, has an $m/n=1/1$ mode structure (m and n being poloidal and toroidal mode numbers respectively) and is located close to the plasma edge at the $\iota=1$ surface, and it caused significant energetic particle losses from the plasma core. Its observation motivates the present numerical study of energetic particle driven by majority trapped energetic particles in the LHD.
This work, done using the kinetic-MHD hybrid code MEGA [2], focuses on an $m/n=2/1$ mode observed numerically. It is shown to grow with a high growth rate and finite frequency, before experiencing a rapid frequency chirping at saturation, that leads to a frequency sign inversion during a short time. At the same time, a reversal in the precession drift direction of the trapped particles that interact strongly with the mode is observed, and is shown to be responsible for the rapid energetic particle pressure redistribution.
A free boundary condition is implemented in this model to allow studying the $m/n=1/1$ EIC mode located at the plasma edge, as well its interaction with the previously discussed $m/n=2/1$ mode located more inward.

[1] X. D. Du et al., Phys. Rev. Lett., 114, 155003 (2015)
[2] Y. Todo, Phys. Plasmas 13, 082503 (2006)

Speaker: Malik Idouakass (NIFS)

17 Simulation study of energetic-particle driven off-axis fishbone instabilities in tokamak plasmas

Kinetic-magnetohydrodynamic hybrid simulations were performed to investigate the linear growth and the nonlinear evolution of off-axis fishbone mode (OFM) destabilized by trapped energetic ions in tokamak plasmas. The spatial profile of OFM is mainly composed of $m/n = 2/1$ mode inside the $q=2$ magnetic flux surface while the $m/n = 3/1$ mode is predominant outside the $q=2$ surface, where $m$ and $n$ are the poloidal and toroidal mode numbers, respectively, and $q$ is the safety factor. The spatial profile of the OFM is a strongly shearing shape on the poloidal plane, suggesting the nonperturbative effect of the interaction with energetic ions. The frequency of the OFM in the linear growth phase is in good agreement with the precession drift frequency of trapped energetic ions, and the frequency chirps down in the nonlinear phase. Two types of resonance conditions between trapped energetic ions and OFM are found. For the first type of resonance, the precession drift frequency matches the OFM frequency, while for the second type, the sum of the precession drift frequency and the bounce frequency matches the OFM frequency. The first type of resonance is the primary resonance for the destabilization of OFM. The resonance frequency, which is defined based on precession drift frequency and bounce frequency for each resonant particle, is analyzed to understand the frequency chirping. The resonance frequency of the particles that transfer energy to the OFM chirps down, resulting in the chirping down of the OFM frequency. A detailed analysis of the energetic ion distribution function in phase space shows that the gradient of the distribution function along the $E′=const.$ line drives or stabilizes the instability, where $E′$ is a combination of energy and toroidal canonical momentum and conserved during the wave-particle interaction. The distribution function is flattened along the $E′=const.$ line in the nonlinear phase leading to the saturation of the instability. The waveform distortion as a unique characteristic of OFM is observed in the simulations and attributed to the higher-n harmonics which are generated through MHD nonlinearity. The physical mechanism for the waveform distortion will be discussed.

Speaker: Hanzheng Li

18 Estimation of the magnetic field mode structure of EIC event applying data assimilation method in LHD

It is known that MHD instability driven by energetic particles called EIC is excited in high ion temperature mode with high power perpendicular NBI heating in LHD [1]. The EIC has been observed by measuring temperature fluctuations and local magnetic field fluctuations, but the overall structure of the EIC is not well understood.

In this study, we introduce a data assimilation method based on the drift kinetics analysis code GNET-TD in a three-dimensional magnetic field configuration to reproduce the magnetic field fluctuation structure of the EIC. Data assimilation is the technique for determining the optimal state of a dynamic system by combining observation data with a numerical model. We use Ensemble Kalman Filter (EnKF) as a sequential data assimilation method to estimate the structure of magnetic field fluctuations from the observed experiment data. EnKF is successfully introduced to an integrated transport simulation [2].

We use two types of measurements, FIDA (Fast-ion Dα) and neutron emission rate measurements during the EIC as observation data for data assimilation. FIDA measures the Doppler-shifted light emitted as a result of the charge exchange reaction between fast ions and beam neutrals and estimates the velocity and position information of the fast ions. For simulating FIDA signals, we used FIDASIM code [3] which was developed as a neutral beam and fast-ion diagnostic modeling suite.

[1] X.D. Du et al., Phys. Rev. Lett. 114, 155003 (2015).
[2] Y. Morishita et al., Nucl. Fusion 60, 056001 (2020).
[3] B. Geiger et al., Plasma Phys. Control. Fusion 62, 105008 (2020).

Speaker: Kosuke Suzuki (Kyoto University)

19 Hybrid kinetic-MHD modelling of fast-ion flow induced by Alfvén instabilities measured by an imaging neutral particle analyzer

An imaging neutral particle analyzer (INPA) [1] provides energy and radially resolved measurements of the confined fast-ion (FI) population ranging from the high-field side to the edge on the midplane of the DIII-D tokamak. In recent experiments, a neutral beam modulation technique is employed to diagnose FI flow in the INPA-interrogated phase-space driven by multiple, marginally unstable Alfvén Eigenmodes (AEs). The INPA enables unprecedented phase-space resolution, required to identify the key features of this FI flow: (1) A phase-space ‘hole’ at the injected energy and $q_{min}$; (2) FI migration towards the plasma edge at lower energies; (3) The formation of a high-energy tail above beam injection energy in the plasma core, showing the first experiment evidence of inward FI transport induced by AEs, as seen in figure 1a.

The hybrid kinetic-MHD MEGA code [2] is used to reproduce the radial location and frequency of the modes observed in the experiment, as well as the associated FI transport. At the INPA-interrogated pitch angle, reversed shear Alfvén eigenmodes (RSAE) are found to create phase-space islands near the $q_{min}$ location on the low-field side of the plasma. On the magnetic axis, these islands cover the topological boundary between passing and stagnation orbits. These islands induce flattening of the FI population along constant $E^{'}=nE+ωP_{ϕ}$, explaining the observed prompt FI pile-up in the plasma core at a few keV higher than the neutral beam injection energy.

To quantitatively reproduce the time-resolved phase space flow measured by the INPA, multi-phase simulations are performed including realistic neutral beam injection and collisions. These simulations combine sequential phases of purely kinetic with hybrid modelling, enabling simulation of the entire beam modulation period. During consecutive hybrid phases, an RSAE consistent with the experiment grows and saturates, redistributing the injected FI. Forward modelling of the instrument response [3] is applied to the simulated FI population. As seen in figure 1b, the synthetic INPA images are in good agreement with the measurement near the injection energy. The simulations track the FI redistribution at different pitch angles within the INPA range, confirming that the measured FI flow follows streamlines defined by the intersection of phase-space surfaces of constant magnetic moment μ and constant E$^{'}$.

[1] X. Du et al., Nuclear Fusion 58, 082006 (2018)
[2] Y. Todo et al., Phys. Plasmas 5, 1321 (1998)
[3] X. Du et al., Nuclear Fusion 60, 112001 (2020)
*Supported by US DOE contracts DE-AC05-00OR22725, DE-AC02-09CH11466, DE-SC0018270, DE- SC0021201, and DE-FC02-04ER54698.

Speaker: Dr Javier Gonzalez-Martin (University of California, Irvine)

20 Fast-ion Transport Induced by Edge Localized Modes

Edge localized modes (ELMs) are inherent to a transport barrier at the tokamak plasma edge. While there have been extensive theoretical as well as simulational studies on the ELM characteristics, there are relatively few studies on the effects of ELMs on fast-ion transport [1]. Here, by employing the nonlinear gyrokinetic theory, we develop a theoretical analysis of the fast-ion transport induced by ELMs, including the effects such as finite Larmor radius, finite drift orbit width, realistic magnetic field geometry, and magnetically trapping of particles. The derived transport equation allows a detailed discussion for the relative importance of various contributions. In particular, it demonstrates the transport scaling of fast-ions by ELMs, and further clarifies the energy and pitch angle dependence of the radial diffusivity. The findings provide a plausible explanation for the experimental observations [1, 2, 3].

Work supported by the European Research Council (ERC) under the European Unions Horizon 2020 research and innovation programme (grant agreement No. 805162).

References
[1] M. Garcia-Munoz, et al., Plasma Phys. Control. Fusion, 55, 124014 (2013)
[2] J. Galdon-Quiroga, et al., Phys. Rev. Lett, 121, 025002 (2018)
[3] J. Galdon-Quiroga, et al., Nucl. Fusion, 59, 066016 (2019)

Speaker: Dr Haotian Chen (University of Seville)

21 Fast-Ion losses during the current ramp-up and disruptions of the ASDEX Upgrade tokamak

Beam ion losses have been observed in AUG discharges during the plasma current ramp-up phase and during disruptions. The velocity-space of the escaping, and ccelerated, beam ions has been measured with the poloidal FILD array available at AUG [1]. Tomographic reconstruction techniques [2] applied to the FILD data revealed, with unprecedented detail, the velocity-space distribution of the lost ions. These reconstructions have shown that the losses during the ramp-up phase present a feature at energiesgreater than the NBI injection one. The accelerated lost beam ions are located in a narrow interval of gyroradii and have similar pitch angles than the non-accelerated promptlosses. For the disrupting discharges investigated here, there is an initial phase where the confinement of fast-ions is severely lost followed by another one where this confinement is recovered, before the termination of the plasma. During the phase of loss of fasi-ion confinement, widely spread losses in pitch are detected; after it, the usual beam prompt losses (pitch and energy localized) reach the scintillator, as in HL-2A tokamak[3]. ASCOT [4] kinetic full-orbit simulations, will be done to assess the possible mechanisms leading to acceleration and pitch redistribution.

[1]M. Garcia-Munoz et al., Rev. Sci. Instrum. 80, 053503 (2009).
[2]J. Galdon-Quiroga et al., Plasma Phys. Control. Fusion 60, 105005 (2018)
[3]Y.P. Zhang et al 2015 Nucl. Fusion 55, 113024 (2015)
[4]E.Hirvijokietal et al. Computer Phys Comm. 185 1310–132 (2014)

Speaker: Jose Rueda Rueda (University of Seville)

IAEA_JoseRueda_FIL

22 Experimental study of RMP induced fast-ion transport using FIDA spectroscopy at the ASDEX Upgrade tokamak

Resonant magnetic field perturbation (RMP) coils are used in multiple fusion devices to mitigate magnetohydrodynamic (MHD) instabilities known as edge localised modes. The coils produce a radial magnetic field component that is small compared to the toroidal field strength, but breaks the axi-symmetry of the flux surfaces near the edge. This increases heat and particle transport at the plasma edge which reduces the pressure and gradients that drive the instability [1]. Additionally, it has been found that the use of RMP coils lead to enhanced fast-ion losses [2, 3, 4]. Recent work has shown that RMPs produce an edge resonant transport layer (ERTL) inside the plasma separatrix that leads to enhanced fast-ion transport in this region [5]. However, a quantitative study on the impact of RMPs on the fast-ion density profile including the radial extent of modifications is yet to be performed on the ASDEX Upgrade tokamak (AUG). Previous studies have relied on measurements from static fast-ion loss detectors (FILDs) which do not provide radial information of the confined fast-ion density. The availability of a dedicated edge fast-ion D-alpha (FIDA) diagnostic at AUG [6] allows to now additionally measure the distribution function of confined fast-ions near the edge.

Dedicated discharges have been performed during the 2021 experimental campaign to investigate the impact of RMPs on the edge fast-ion density. Configuration scans of n=2 applied perturbation fields and coil current scans to vary the perturbation strength have been carried out. A strong response in the FIDA emission profile is observed when the RMP coils are applied. Modulation of the field perturbation by means of rigidly rotating the perturbations has allowed to make use of the light ion beam probe [7] method to calculate the RMP induced fast-ion displacement from FIDA measurements. These are compared to values calculated from FILD measurements as well as predicted values from modelling using the full fast-ion orbit code ASCOT5 [8]. A combined analysis of the FIDA and FILD measurements as well as those from the diamagnetic loop diagnostic is performed to asses the reduction in fast-ion content. Lastly, the radial impact of the RMP coils on the fast-ion density profile is characterised and compared to numerical predictions which include for the effect of plasma response to the perturbation fields.

[1] W. Suttrop et al, Fusion Eng. Des. 88, 446-453 (2013)
[2] M. Garcia-Munoz et al, Nucl. Fusion 53, 123008 (2013)
[3] M. A. Van Zeeland et al, Nucl. Fusion 55, 073028 (2015)
[4] K. G. McClements et al, Plasma Phys. Control. Fusion 57, 075003 (2015)
[5] L. Sanchis et al. Plasma Phys. Control. Fusion 61, 014038 (2019)
[6] A. Jansen van Vuuren et al, Rev. Sci. Instrum. 90, 103501 (2019)
[7] X. Chen et al, Rev. Sci. Instrum. 85, 11E701 (2014)
[8] E. Hirvijoki et al., Comput. Phys. Commun. 185 (2014)

Speaker: Anton Jansen van Vuuren (University of Seville)

Anton_IAEA.pdf

23 Fast Ion Losses and Plasma Response Induced by externally Applied Magnetic Perturbations on DIII-D

Externally applied resonant magnetic perturbations (RMPs), which are useful for suppressing Edge Localized Modes, modify the axisymmetric equilibrium fields on DIII-D, altering the confinement of fast ions and leading to increased prompt losses from beam ions born inside the last closed flux surface (LCFS). The light ion beam probe (LIBP) technique [1] uses beam ions to probe internal magnetic perturbations and infer the displacement of fast ion orbits traversing through them using signals from a scintillator-based fast ion loss detector (FILD).
A rigidly rotating n=1 RMP was applied to several DIII-D discharges in both L-mode and H-mode with a magnetic spectrum created by displacing the phase of the upper and lower internal coils by $\Delta\phi_{UL}=240°$. The internal coils on DIII-D consist of two sets of 6 window frame coils in the outer wall: One above the midplane, and one above. The total n=1 perturbation includes both the vacuum fields generated by the internal coils and the fields internally generated by the plasma response. Magnetic coils located at the midplane on the low-field-side measured lower plasma responses after transitioning from L-mode into H-mode: a decrease of 34% for the $B_r$ measurements and 50% for the $B_p$ measurements; however, analysis of losses from a co-injected tangential neutral beam show that losses induced by the RMPs account for a larger fraction of prompt losses in H-mode. The ratio of losses fluctuating at the RMP rotation frequency to constant prompt losses, $\Delta F/\bar{F}$, increased by 62% after the transition into H-mode.
Simulations of the plasma response using M3D-C1 show a decrease in average amplitude of the response in H-mode near the outer midplane, consistent with experimental findings. Using these fields to follow particles in the code ASCOT5 shows that the RMP induced losses are concentrated mostly at the outer midplane and vessel floor, with FILD-impacting ions being born inside the LCFS.
[1] X.Chen et al, Rev Sci Instrum 85, 11E701 (2014)
Work supported by US DOE under DE-FC02-04ER54698, DE-SC0020337

Speaker: Kenneth Gage (UCI)

IAEA21_Gage.pdf

Wednesday 8 December

Runaway Electrons, Disruptions, and Diagnostics

Convener: Tünde Fülöp (Chalmers University of Technology)

24 Simulations of Disruption Mitigation in ITER with Two-Stage Shattered Pellet Injection

The currently envisaged method for disruption mitigation in ITER is to use massive material injection. One of the injection schemes considered is a two-stage shattered pellet injection (SPI), with a pre-disruption diluting deuterium injection followed by a neon injection aiming to radiatively dissipate the plasma energy content [1]. It was recently shown [1] that it will likely be possible to increase the plasma density by at least an order of magnitude, thus strongly reducing the plasma temperature, without unacceptably accelerating the onset of the thermal quench. In this work [2], we perform numerical simulations assessing the performance of such a mitigation scheme in an ITER-like setting, with a particular focus on runaway electron generation.

These studies are performed with the integrated tool DREAM [3,4], designed to evolve the 1D configuration space and 2D momentum space dynamics during tokamak disruptions. In this work, DREAM has been extended with the ability to simulate SPI based on a statistical model for the shattering [5], and the neutral gas shielding model for the ablation [6]. The effects of a finite spread and $E\times$$B$ drift of recently ablated material relative to the shards can also be studied using a depsition kernel with a finite width and shift. We determine, within this model, the degree of pellet shattering resulting in the most efficient use of the injected material for a given pellet size, and study the subsequent thermal quench, current quench and runaway electron dynamics over a wide range of pellet sizes. We also study the influence of impurity transport and drifts on the final density profile, and discuss the consequences for the two-stage SPI scheme.

Our studies indicate that the diluting deuterium injection can efficiently reduce the hot-tail runaway generation, by allowing for a moderate temperature equilibration of the superthermal electron population between the injections. During non-nuclear operation, in the absence of impurity transport, the maximum runaway current is found to be reduced to acceptable levels with realistic two-stage injection parameters. On the other hand, during nuclear operation, the unavoidable runaway seed from tritium decay and Compton scattering was found to be amplified to several mega-amperes by the avalanche mechanism for all investigated injection parameters. The reason is that the intense cooling from the injected material leads to a high induced electric field and a substantial recombination, resulting in an enhanced avalanche multiplication. The success of the two-stage injection scheme requires that the density increase reach the plasma core. Our initial studies suggest that the penetration depth might be significantly altered by impurity transport and drifts, as well as the interaction between the shards via their effect on the background plasma, indicating a need for further studies.

[1] E. Nardon et al, Nucl. Fusion 60 126040 (2020).
[2] O. Vallhagen, Master's thesis, https://hdl.handle.net/20.500.12380/302296 (2021).
[3] M. Hoppe et al, Comp. Phys. Comm. 268 108098 (2021).
[4] I. Svenningsson et al, Phys. Rev. Lett. 127 035001 (2021).
[5] P. Parks, General Atomics Tech. Rep. GA-A28352 (2016).
[6] P. Parks, Theory and Simulation of Disruptions Workshop (2017).

Speaker: Oskar Vallhagen

25 Investigation of Alfvénic activity during the current quench in ASDEX-Upgrade

During the current quench in ASDEX Upgrade (AUG) disruptions, created by massive gas injection (MGI) to study runaway electron (RE) physics [1], Alfvénic activity is visible in the 300-800 kHz range. An example is presented in figure 1. These modes are analysed as potential runaway electron mitigation candidates [2]. With the help of a mode tracing algorithm, we classified the mode behaviour for 180 discharges. We found these modes to be ubiquitous in shots which had the primary goal of RE generation. We performed a systematic statistical analysis using 38 selected parameters (describing pre- and post-disruption plasma, RE behaviour, mode behaviour, etc.) and found no significant effect of the mode characteristics on the formation of the subsequent RE beam [3]. Global Alfvén eigenmodes (GAEs) are investigated as the most likely candidates. Changes in the Alfvén continuum are proposed as a possible cause for the strong frequency sweeping of the observed modes.

[1] G. Pautasso et al., Nuclear Fusion 60, 086011 (2020).
[2] A. Lvovskiy et al., PPCF 60, 124003 (2018).
[3] P. Heinrich, MSc thesis (2021). http://hdl.handle.net/21.11116/0000-0008-ED5A-9

Speaker: Paul Heinrich (IPP Garching)

26 Fast wave excited by runaway electrons in disruptive plasma

Kinetic instabilities in the MHz range have been observed during current quench in DIII-D disruption experiments (A. Lvovskiy et al., PPCF 60, 124003 (2018)). These instabilities are correlated with the RE loss happening at the beginning of disruption. In this work we use a MHD-kinetic code M3D-C1-K to simulate the excitation of this instability. It is found that this mode lies in the fast wave branch, which is similar to the compressional Alfvén eigenmode (CAE) and has large parallel magnetic field component. The mode frequency from the simulation has a qualitative agreement with experiments. The mode structure for different toroidal mode number was analyzed. The wave can have resonance with high energy trapped runaway electrons, which have precession frequency close to the mode frequency.

The excited mode has the potential to increase the diffusion of runaway electron and can play a role in RE mitigation, thus provides an alternative approach to dissipate RE beam during the current quench.

Speaker: Chang Liu (Princeton Plasma Physics Laboratory)

slides.pdf

27 Polarized imaging of visible synchrotron emission from runaway electron plateaus in DIII-

Post-disruption runaway electron (RE) beams can carry majority of flattop current and loss of RE confinement could be detrimental for continuous safe operation of tokamaks. Synchrotron emission (SE) is a great diagnostic tool for in-flight high-energy REs, but since it depends on both runaway electron density nRE and pitch angle θ, to understand RE evolution from SE, an independent measure of pitch angle is necessary. In this work we study polarized visible RE SE as a way to constrict the RE phase space and interpret data in RE mitigation experiments.
In DIII-D runaway plateau discharges, synchrotron emission was imaged in several repeat discharges with a linear polarizer in vertical (PZ) or horizontal (PX) orientation. Image average <Pz>/<Px> ratio, ranging ~ 3-14, is found to be a valuable tool to isolate pitch angle change.
Leading synthetic diagnostics tools were used to analyze SE polarization by generating SE images and modeling <Pz>/<Px> vs. θ dependence. For easier comparison of images simulated with: 1) guiding center and hollow cone radiation model in SOFT [1] and 2) full orbit and full angular radiation model in KORC [2], mono-energy (20 MeV) and mono-pitch angle (0.2 rad) RE beams were initialized in both codes and, due to analysis approach, in KORC allowed to evolve.
Simulated images reproduced experimental images well under given assumptions and returned polarization ratios 7 and 5.8, which gives ground for subsequent use of synthetic polarization ratio vs. θ to infer measured pitch angle.
SE decrease following D2 massive gas injection (MGI) into RE plateau was assumed to be related to the purge of impurities by MGI, causing a rapid drop in pitch angle due to decreased pitch angle scattering and was used to recover pitch angle evolution based on <Pz>/<Px> ratio parametrization obtained from SOFT and KORC for 20 MeV REs.
Measured/inferred pitch angle time evolution was compared with values from kinetic test particle simulations combined with a 1D impurity radial diffusion model [3], in equilibrium and non-equilibrium cases. The comparison showed good agreement in values, and while differences in the rate of change indicate further effects should be considered, considering SE polarization increases accuracy diagnosing confined high-energy REs.
[1] Hoppe, NF 58 026032, 2018
[2] Carbajal, PPCF 59 124001, 2017
[3] Hollmann, PoP 27 042515, 2020

Work supported by US DOE under DE-FC02-04ER54698, DE-FG02- 07ER54917, DE-AC05-00OR22725, DE-AC52-07N27344, DE-FG02-04ER54744, and DE-AC05-06OR23100

Speaker: Zana Popovic (UCSD)

28 Determination of Runaway Electron Distribution Parameters from Synchrotron Radiation Measurements

Runaway electrons (RE) in a tokamak can deposit a significant quantity of energy onto the plasma facing components and therefore represent a threat to ITER and next step fusion devices. This contribution presents the Runaway Electron Imaging Spectroscopy (REIS) diagnostic, designed to collect spectra and images produced by the RE synchrotron radiation emission. The system is composed of spectrometers covering the range from 0.4 µm up to 5 µm and a fast CCD camera. We show how the RE energy, pitch angle, radial density profile and total number can be inferred through the comparison of REIS experimental images and spectra with simulations. Results of the application of this method to the study of the RE dynamics in FTU discharges will be discussed.

Speaker: Chiara Monti (ENEA)

REIS_IAEA_2021_12_08_Monti.pdf

29 Orbit Weight Functions for Neutron Emission and One-step Reaction Gamma-Ray Spectroscopy Diagnostics

Fast-ion distribution functions in the MeV-range can be diagnosed by neutron emission spectroscopy (NES) and gamma-ray spectroscopy (GRS). For a given fast-ion distribution function and diagnostic energy bin, a measurement signal will have contributions originating from various fast-ion orbits [Ref1][Ref2]. These contributions depend on the sensitivity of the diagnostic in orbit phase space, which can be mapped using weight functions. Velocity-space weight functions have previously been used to map the sensitivity in 2D velocity space[Ref3][Ref4][Ref5]. In this work, we present and discuss 3D orbit weight functions for the Joint European Torus NES diagnostic TOFOR[Ref6], an NE213-scintillator[Ref7] and a high-purity germanium GRS diagnostic[Ref8]. The complicated three-dimensional structures of these so-called orbit sensitivities can be mapped by varying the fast-ion energy while tracing out the topological boundaries between different orbit types. Furthermore, the sensitivity is found to vary depending on the diagnostic energy bin of interest, as determined by the requirement to produce a sufficient amount of up- or down-shift of the nominal birth energy of neutrons from D(D,n)$^{3}$He and gammas from T(p,$\gamma$)$^{4}$He. Using this approach, signal contribution split into orbit types is presented for the first time.

--- References ---
[Ref1] H. Järleblad et al, Rev. Sci. Instrum. 92, 043526 (2021)
[Ref2] L. Stagner & W. W. Heidbrink, Phys. Plasmas 24, 092505 (2017)
[Ref3] M. Salewski et al, Nucl. Fusion 58, 096019 (2018)
[Ref4] J. Eriksson et al, Plasma Phys. Control. Fusion 61, 014027 (2019)
[Ref5] B.S. Schmidt et al, Rev. Sci. Instrum. 92, 053528 (2021)
[Ref6] M. Gatu Johnson et al, Nucl. Instrum. Methods Phys. Res., Sect. A 591, 417 (2008)
[Ref7] F. Binda et al, Rev. Sci. Instrum. 85, 11E23 (2014)
[Ref8] M. Tardocchi et al, Phys. Rev. Letters 107, 205002 (2011)

Speaker: Henrik Järleblad (DTU Physics, Technical University of Denmark)

H_Jaerleblad_et_al_IAEA_08122021.pdf

Collective Phenomena (High Frequency Modes)

Convener: Tünde Fülöp (Chalmers University of Technology)

30 Characterization of ion cyclotron emission in the DIII-D tokamak

Fast-ion losses and radiation expected in fusion reactors challenge conventional fast-ion diagnosis techniques that rely on delicate components such as scintillating plates and cameras. Passive measurement of coherent ion cyclotron emission (ICE) via magnetic pickup loops offers a robust diagnostic alternative but requires improved experimental resolution and more detailed theory. To this end, the ICE diagnostic on DIII-D has been upgraded [1] to enable detailed mode characterization including determination of toroidal mode number, approximate polarization at the plasma edge, comparison of low and high-field side signal amplitude, and extension of the upper frequency limit into the lower hybrid range.

Dedicated experiments have been performed on the DIII-D tokamak to explore the dependence of ICE amplitude and spectrum on both thermal plasma and fast ion properties [2]. A database of nearly 200 shots has been constructed to investigate centrally-localized ICE in DIII-D L-mode plasmas. These discharges feature both hydrogen and deuterium beams in configurations varied over energy (55–81 kV), pitch (v||/v), radial origin (near-tangential or near-perpendicular), direction of injection (co- vs. counter-plasma current), and tilt (on- or off-axis). ICE depends strongly on the character of these highly anisotropic distributions. Moving counter-current neutral beams off-axis significantly decreases both the number of harmonics excited and their amplitude (cf. co-injecting beams [2]). On a finer scale, frequency splitting of the harmonics is common for many fast-ion distributions. For example, the dominant ~2fcD harmonic excited by the high-power co-current tangential beam is split into bands spaced roughly 100–200 kHz apart in high BT plasmas, and the number of sidebands changes over the course of the beam pulse. The thermal ion population can also influence ICE, as increasing the hydrogen to deuterium ratio in mixed species shifts the dominant harmonic excited by the co-current beams from ~2 fcD to ~4 fcD, where fcD is the ion cyclotron frequency at the magnetic axis.

Work supported by US DOE DE-SC0018270, DE-FC02-04ER54698, and DOE DE-SC0021201.
[1] G. H. DeGrandchamp, Rev. Sci. Instrum. 92, 033543 (2021)
[2] K. E. Thome, Nucl. Fusion 59, 086011 (2019)

Speaker: Genevieve DeGrandchamp (University of California, Irvine)

31 Theory for control of sub-cyclotron Alfvén instabilities and implications for anomalous electron energy transport in tokamaks

High frequency ($\omega <\omega_{ci}$) compressional (CAE) and global (GAE) Alfvén eigenmodes are routinely driven unstable by super-Alfvénic neutral beam ions in spherical tokamaks such as NSTX(-U) and MAST(-U). These instabilities have also been observed in the conventional tokamaks DIII-D and AUG, where the beam ions are typically sub-Alfvénic. In NSTX, the presence of strong CAE/GAE activity was experimentally linked to the anomalous flattening of electron temperature profiles at high beam power, potentially limiting fusion performance. Specifically, CAEs and GAEs can effectively channel energy away from the core [2,3], resulting in presently unpredictable modifications to the core plasma heating. In addition, early NSTX-U operations serendipitously discovered the robust stabilization of counter-propagating GAEs with relatively small amounts of off-axis beam injection [4]. A detailed understanding of the preferential conditions for CAE/GAE excitation and stabilization, therefore, is vital to predicting and controlling their effects on thermal plasma confinement.
A comprehensive set of 3D hybrid kinetic-MHD simulations, using the HYM code, has been performed for a wide range of beam parameters, providing a wealth of information on CAE and GAE destabilization in realistic spherical tokamak configurations. This study is unique in that it uses a full orbit kinetic description of the energetic beam ions, necessary to capture the Doppler-shifted cyclotron resonances which mediate the instability. Furthermore, new instability conditions have been derived for CAEs and GAEs using perturbative linear theory in order to complement and interpret the simulation results. The simulations demonstrate that the excitation of CAEs vs GAEs has a complex dependence on the fast ion injection velocity and geometry. It is found that the analytic instability conditions accurately describe key properties of the unstable modes in the simulations, offer a straightforward and generalizable explanation of the GAE stabilization observed in NSTX-U, and resolve puzzling observations from past DIII-D experiments. A cross validation between the theoretical stability bounds, simulation results, and a large database of experimental measurements in NSTX shows favorable agreement for both the unstable CAE and GAE spectra’s dependence on fast ion parameters. Based on these insights, new mechanisms for the stabilization of CAEs and GAEs are identified in order to aid the investigation of their role in anomalous electron energy transport in future NSTX-U experiments. The combined numerical and analytical approach developed in this work lays the foundation for a powerful predictive capability for effective control of sub-cyclotron Alfvén instabilities and the energy transport which they induce.

*Supported by US DOE via DE-AC02-09CH11466 and DE-SC0011810.
[1] D. Stutman et al, Phys. Rev. Lett. 102, 115002 (2009)
[2] Y.I. Kolesnichenko et al, Phys. Rev. Lett. 104, 075001 (2010)
[3] E.V. Belova et al, Phys. Rev. Lett. 115, 015001 (2015)
[4] E.D. Fredrickson et al, Phys. Rev. Lett. 118, 265001 (2018)

Speaker: Jeff Lestz (UC Irvine)

IAEA21_Lestz.pdf

Thursday 9 December

Collective Phenomena (Alfven and Low Frequency Modes)

Convener: Huishan Cai (University of Science and Technology of China)

32 Theoretical Studies of Low-frequency Alfven Modes in Tokamak Plasmas

Linear wave properties of the low-frequency Alfven modes (LFAMs) observed in the DIII-D tokamak experiments with reversed magnetic shear [Nucl. Fusion 61, 016029 (2021)] are theoretically studied and delineated based on the general fishbone-like dispersion relation. By adopting the representative experimental equilibrium parameters, it is found that, in the absence of energetic ions, the LFAM is a kinetic ballooning mode instability of reactive-type with a dominant Alfvenic polarization. More specifically, due to diamagnetic and trapped particle effects, the LFAM can be coupled with the beta-induced Alfven-acoustic mode in the low-frequency region (frequency much less than the thermal-ion transit and/or bounce frequency); or with the beta-induced Alfven eigenmode in the high frequency region (frequency higher than or comparable to the thermal-ion transit frequency); resulting in reactive-type instabilities. Moreover, the ‘Christmas light’ and ‘mountain peak’ spectral patterns of LFAMs as well as the dependence of instability drive on the electron temperature observed in the experiments can be theoretically interpreted by varying the relevant physical parameters. Conditions when dissipative-type instabilities may set in are also discussed.

Speaker: Dr Ruirui MA (Southwestern Institute of Physics)

33 Gyrokinetic simulation study of BAE and LFM properties in DIII-D plasma

We present results of simulation study of low-frequency Alfvenic modes in sub-TAE (Toroidal Alfven Eigenmodes) range in DIII-D, in particular, BAE (Beta-induced AE) and LFM (low-frequency mode) [1-3]. Using the Gyrokinetic Toroidal Code (GTC) [4], we have performed gyrokinetic simulations of BAE and LFM in DIII-D plasmas and identified LFM by comparing its properties to those of BAE [5]. Fast ion density scan has revealed a continuous change rather than a sudden transition from LFM to BAE with increasing fast ion density. We also have found that LFM linear dispersion has a non-monotonic dependence on radial shift of thermal pressure, implying that the relative position of qmin with respect to the pressure gradient peak contributes to the appearance of the mountain peak in the observed LFM activities [1]. GTC isotope study have yielded a robust 1/mi1/2 scaling of BAE and LFM linear dispersions for different thermal ion mass mi [3]. Note that both modes appear to have wide ranges of toroidal mode number n=3~9 with similar linear growth rates. Results of nonlinear BAE simulations motivated by this finding will be presented. This work was supported by DOE SciDAC ISEP and used computing resources at ORNL (DOE Contract DE-AC05-00OR22725) and NERSC (DOE Contract DE-AC02-05CH11231), and experimental data from DIII-D National Fusion Facility (DOE Contract DE-FC02-04ER54698).

[1] W.W. Heidbrink et al., Nucl. Fusion 61 (2021) 016029.
[2] W.W. Heidbrink et al., Nucl. Fusion 61 (2021) 066031
[3] W.W. Heidbrink et al., Nucl. Fusion 61 (2021) 106021.
[4] Z. Lin et al., Science 281 (1998) 1835.
[5] G.J. Choi et al., Nucl. Fusion 62 (2021) 066007.

Speaker: Gyungjin Choi (Seoul National University)

34 Toroidal Alfvén eigenmodes excited by energetic electrons in EAST low-density plasmas

Operation in the quiescent regime with a large number of energetic particles (EEs) in specific energy range (~ 150–250 keV) have been achieved during the flattop of EAST low-density Ohmic discharges. Toroidal Alfvén eigenmodes (TAEs) excited by EEs are well demonstrated both in the deuterium plasmas and the helium plasmas. The resonance condition for EEs to drive TAEs is discussed and well satisfied for these experimental conditions. The frequencies of these TAEs are in good agreement with ideal MHD theory, after correcting the mass of ion according to the ratio of deuterium to helium for helium plasmas. The energy threshold for EEs to drive TAEs and the plasma operation regime are obtained on the EAST tokamak by statistical results of a series of experiments. Two different slope trends have been observed between the mode frequencies and the Alfvén frequency, analysis show that it is caused by their different radial positions, measured data from reflectometry system and simulated calculations by GTAW code further confirm this results. Moreover, experimental results show that the radial positions that TAEs located are mainly determined by the distribution and evolution of EEs, and threshold for exciting the TAEs is strongly related to populations of EEs. In addition, the damping rates of the TAEs are found to be very sensitive to the energy distribution due to the change of electron density, experiments with different density decay rates are carried out, which verified this results.

Speaker: Xiang Zhu (Shenzhen University)

35 Nonlinear reversed shear Alfvén eigenmode saturation due to spontaneous zonal current generation

Energetic particles (EPs), especially alpha particles, can excite collective shear Alfvén wave (SAW) instability in tokamak plasmas，and in turn affects the behavior of EPs, resulting in EPs transport loss. Notably, reversed shear Alfvén eigenmodes (RSAE) can be preferentially excited by core localized EPs [1], with their frequency and radial localization directly determined by local safety factor minimum . Understanding the excitation, evolution and saturation of RSAE is important to the future study of magnetic confined controllable nuclear fusion.
The nonlinear zero frequency zonal structure (ZFZS) excitation by RSAE is an important channel of the RSAE saturation. The zonal structure (ZS), including the zonal flow (ZF) and the zonal current (ZC), are known to play important self-regulatory roles on microscale drift wave type instabilities by scattering drift waves into short radial wavelength stable domains [2,3].
RSAE frequency may sweep between those of toroidal Alfvén eigenmode (TAE) and beta-induced Alfvén eigenmode (BAE). Based on the work of the TAE [4] and BAE [5] nonlinearly exciting the ZFZS, in this work, we use the nonlinear gyrokinetic theory to study the nonlinear RSAE self-modulation due to ZFZS excitation. Different from TAE confined in the middle of two rational surfaces and BAE confined on the rational surface, the frequency and radial location of the RSAE is determined by , and we obtain a more general dispersion relation describing the modulational instability dispersion relation of ZFZS excitation by AEs. At the same time, we propose a unique channel of RSAE saturation, which is similar with the mechanisms proposed in [6,7] of TAE saturation. Due to the generation of ZC, the SAW continuum and q-profile may be directly modulated, which further modifies the coupling between RSAE and SAW continuum, resulting to RSAE nonlinear saturation.
References
[1] T. Wang, et al., Nucl. Fusion 60, 126032 (2020)
[2] L. Chen, et al., Phys. Plasmas 7, 3129 (2000)
[3] Z. Lin, et al., Science 281, 1835 (1998)
[4] L. Chen, F. Zonca, Phys. Rev. Lett. 109, 145002 (2012)
[5] Z. Qiu, et al., Nucl. Fusion 56, 106013 (2016)
[6] F. Zonca, et al., Phys. Rev. Lett. 74, 698 (1995)
[7] L. Chen, et al., Plasma Phys. Control. Fusion 40, 1823 (1998)

Speaker: Shizhao Wei

36 Nonlinear simulations of Alfvén eigenmodes in CFQS plasmas

Quasi-axisymmetric (QA) device combines the advantages of both tokamak and stellarator, and thus, it can be considered as a disruption-free tokamak and it excites the interests of the fusion community. Alfvén eigenmode (AE) is an important issue for magnetic confinement fusion because it enhances energetic particle (EP) transport and degrades heating performance. Nowadays, a QA device named CFQS is being constructed, and the first plasma will be generated soon. Thus, the research of EP-related instabilities in QA configuration becomes significant and urgent.

The simulation is conducted using MEGA code which is a hybrid simulation code for EPs interacting with a magnetohydrodynamic (MHD) fluid. The equilibria are calculated using HINT code with bootstrap currents 20 kA and 5 kA, respectively. In the 20 kA bootstrap current case, 6 islands appear on the edge, while in the 5 kA bootstrap current case, the islands disappear and the magnetic field on the edge region becomes stochastic.

The instability in CFQS in three-dimensional form is shown for the first time. Both global Alfvén eigenmode (GAE) and toroidal Alfvén eigenmode (TAE) are found in CFQS with and without magnetic island. The dominant mode numbers are $m/n = 3/1$ for GAE and $m/n = 5/2$ for TAE. Strong mode coupling is found under the condition of a very low field period $N_{fp}$ value. This result is consistent with theoretical prediction, and it is similar to the simulation of FAR3d code. For GAE, the mode frequency 79 kHz does not depend on energetic particle pressure or energetic particle beam velocity, while the growth rate increases with energetic particle pressure, and the growth rate is maximum for the energetic particle beam velocity of $0.5v_A$ where $v_A$ is Alfvén velocity. For TAE, similarly, the mode frequency 125 kHz does not depend on energetic particle pressure, energetic particle beam velocity, or peak value of energetic particle pitch angle. The growth rate increases with energetic particle pressure, roughly decreases with the increasing of the peak value of energetic particle pitch angle, and the growth rate is maximum for the energetic particle beam velocity of $0.5v_A$. The resonant condition $f_{mode} = n f_φ − l f_θ$ is confirmed. For GAE, $n = 1$ and $l = 2$, and for TAE, $n = 2$ and $l = 4$. Nonlinear simulation results of AE in CFQS are shown for the first time. GAE frequency chirps in the nonlinear saturated phase, and TAE is similar to that. Hole and clump structures are formed in the pitch angle and energy phase space. The particles comprising the hole and clump are kept resonant with the GAE or TAE during the mode frequency chirping. Finally, during the mode activities, energetic particles are lost from the core region. For the present simulation, the transport caused by GAE is stronger than that of TAE.

Speaker: Hao WANG (National Institute for Fusion Science)

37 Simulation of EP-driven nonlinear collective effects using Landau closure methods

The long time-scale nonlinear simulation of energetic particle (EP) instabilities is critical to studies of fast ion transport since this allows inclusion of mode-coupling induced zonal flows/currents, and transfers of energy to longer and shorter scales. These processes, which are important in evaluating the impact of EP instabilities on heating efficiency, can evolve over much longer timescales than the initial growth and saturation. Also, the predator-prey cycles associated with zonal flow/current effects drives significant intermittency, which is important in the consideration of heat flux variations on plasma-facing components. The FAR3d global gyro-Landau moments model provides an efficient kinetically-closed model for simulation of energetic particle driven instabilities. FAR3d uses hybrid MPI/OpenMP parallelization methods that allow good scaling to the strongly coupled, high toroidal mode number regime of ITER. This work presents the first sustained long-term (~ 50,000 Alfvén times) FAR3d simulations of the above effects, demonstrated using selected discharges from the DIII-D tokamak. The initial growth, saturation levels (peak \delta B_{\theta}/B ~ 0.001, \delta Te ~ 3.4 eV), frequency spectrograms (f ~ 90 kHz), and intermittency (periodic burst interval ~ 0.1 msec, time averaged bursts 1 to 2 msec) are in similar ranges as observations. Two-dimensional zonal structures are obtained in the saturated phase for both the poloidal flows and perturbed toroidal currents. Collective EP transport levels and fast ion density gradient flattening are calculated and show significant levels of EP transport. Future areas for improvement in the FAR3d model include extension to higher moments, improved treatment of phase mixing from drift resonances, transport evaluation using tracer particle orbits, and closure relations optimized for the effect of non-Maxwellian distributions.

*This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Fusion Energy Sciences under Awards DE-AC05-00OR22725, DE-FC02-04ER54698, the U.S. DOE SciDAC ISEP Center, and project 2019-T1/AMB-13648 founded by the Comunidad de Madrid and Comunidad de Madrid (Spain).

Speaker: Donald Spong (Oak Ridge National Laboratory)

FAR3d-Talk-Dspong.pdf

FAR3d-Talk-Dspong.pptx

38 Measurements of Alfven Eigenmode stability in JET D and T plasmas

We present recent measurements and analyses of Alfven Eigenmode (AE) stability in JET D and T plasmas. Stable AEs are resonantly excited by an array of eight in-vessel, toroidally-spaced antennas with independent power and phasing. Databases of stable AE frequencies, net damping rates $\gamma < 0$, and toroidal mode numbers have been assembled for various isotope mixes, and trends are explored. In addition, we highlight two distinct cases when radiative and collisional damping dominate the experimentally measured damping rates, confirmed by MHD modeling. Unstable AEs – including low frequency BAEs to high frequency EAEs – from approximately 2000 plasmas have been compiled into a database; trends in the saturation amplitudes, growth rates $\gamma > 0$, and poloidal/toroidal mode numbers are investigated. Finally, we hope to show preliminary results from JET’s DT campaign, from which the contribution of alpha drive to AE stability could be assessed.

Speaker: Dr Roy Tinguely (MIT PSFC)

Tinguely_IAEA-EP2021_slides_211209_toShare.pdf

39 Observation and interpretation of tornado modes coupled to near-axis Alfvén cascade eigenmodes in JET sawtoothing plasmas

The seeming coupling between fast upwards frequency sweeping modes and tornado modes in a set of JET sawtoothing discharges was investigated. The frequency sweeping modes were identified as near-axis Alfvén cascade eigenmodes associated with a very flat yet strictly monotonic q-profile near the axis, in contrast with the common reversed-shear scenarios. The evolution of the modes’ frequency during the post-sawtooth regime, characterized by a gradually decreasing q-profile, was numerically reproduced and the transition from cascade modes to tornado modes was demonstrated to occur when the q profile takes specific values on-axis given by q0=(n-1/2)/n, with n the toroidal mode number of the mode. An MHD spectroscopy technique based on this result is proposed to track the evolution of q0 when such transitions are observed. Calculations of the resonant interaction between the modes and an ICRH-heated hydrogen minority population indicate the population contributed to driving the mode unstable.

Speaker: Rui Calado (Instituto de Plasmas e Fusão Nuclear, Instituto Superior Técnico, 1049-001 Lisboa, Portugal)

Presentation_TFM_ConfRehearsal.pdf

40 Plasma rotation caused by destabilized eigenmodes and improved plasma performance

Spatial channelling (SC) is a phenomenon of the transfer of the energy and momentum across the magnetic field by destabilized eigenmodes [1-3]. Energy transfer deteriorates or improves plasma confinement, depending on the energy flux direction. In particular, inward SC of alpha-particle energy by fast magnetoacoustic modes (FMM) may have played a role in the improved confinement and anomalous ion heating [4], which took place in JET DTE1 experiments with D-T plasmas [5]. The momentum SC could be another mechanism favourable for plasma confinement in these experiments: The momentum transfer leads to sheared plasma rotation, tending to suppress turbulence in the region of mode location. In particular, our analysis of JET DTE1 data shows that the best parameters were achieved in the discharge where plasma rotation frequency was highest, except for the near-axis region (D-T discharge #42847). TAE activity was absent in these experiments, only ICE which presumably is associated with FMM was observed. This may support the assumption of Ref. [4] that FMM could be responsible for the SC (the structure of modes leading to ICE was not measured).

There are other experiments confirming improved plasma characteristics in rotating plasmas. In particular, high fusion performance at high $T_i/T_e$ in JET-ILW baseline plasmas with high NBI heating power was observed, which correlated with high rotation frequency [6]. Correlation between high rotation frequency and confinement was also observed in DIII-D; furthermore, it was found in super H-mode experiments that high rotation, not high pedestal, plays the essential role in achieving very high confinement $H_{98y2}>1.5$ [7].

We developed a theory of the momentum SC, which includes the study of momentum emission and its radial distribution. It is found that, the momentum SC, in contrast to the energy SC, can take place even in the absence of spatial mismatch of drive and damping during energetic-ion-driven instabilities. The developed theory is applied to the ITER 15 A baseline scenario, employing predictive calculation of drive /damping of TAEs in Ref. [8].

References
[1] Kolesnichenko Ya.I., Yakovenko Yu.V., Lutsenko V.V. 2010 Phys. Rev. Lett. 104 075001.
[2] Kolesnichenko Ya.I., Yakovenko Yu.V., Lutsenko V.V., Weller A., White R.B. 2010 Nucl. Fusion 50 084011.
[3] Kolesnichenko Ya.I., Tykhyy A.V., White R.B. 2020 Nucl. Fusion 60 112006.
[4] Kolesnichenko Ya.I., Lutsenko V.V., Tyshchenko M.H., Weisen H., Yakovenko Yu.V., JET Contributors 2018 Nucl. Fusion 58 076012.
[5] Thomas P., 28th EPS Conf. on Contr. Fus. and Plasma Phys., Funchal 2001.
[6] Kim Hyun-Tae et al. 2018 Nucl. Fusion 58 036020.
[7] Ding S. et al. 2020 Nucl. Fusion 60 034001.
[8] Pinches S.D. et al. 2015 Phys. Plasmas 22 021807.

Speaker: Prof. Yaroslav Kolesnichenko (Institute for Nuclear Research)

41 Energetic Particle-Induced Geodesic Acoustic Modes on DIII-D

The energetic particle-induced geodesic acoustic mode (EGAM) causes loss of injected beam ions on DIII-D [1, 2]. The EGAM is a global [3] n=0, m=0 predominantly electrostatic mode with typical fundamental frequencies between 20-40 kHz. (n and m are toroidal and poloidal mode numbers.) While EGAMs commonly appear in amplitude bursts, they can be continuous, sweep in frequency, or oscillate in both frequency and amplitude. Additionally, strong modes can have more than one fundamental frequency and often excite higher harmonics.

A database of around 900 shots is compiled using the current ramp phase, or first second, of the discharge. EGAMs are most easily excited by the counter-injected beams; in these plasmas, EGAMs expel counter-circulating fast ions across the loss boundary [2]. EGAMs occur less often during co-injection and virtually never occur in off-axis injection. The EGAM amplitude and frequency is diagnosed using spectrograms from the magnetic probes. During counter beam injection, the mode frequency is found to have the strongest linear correlation with qmin, with a correlation coefficient around -0.702. While the mode amplitude increases with qmin, it initially increases with the pitch angle scattering time at mid-radius until PAS ~ 0.3 s and then decreases. In the figure below, a clear boundary for stability is shown within the operating space of qmin and poloidal beta for modes excited by the counter injected beam. The modes tend to be more unstable at higher qmin and lower poloidal beta, with a stronger dependence on qmin. Further investigation of a single discharge characterizes the nonlinear burst cycle. The period between each successive burst is observed to slightly increase as the current increases.

*Work supported by US DOE under DE-FC02-04ER54698 and DE-SC0020337

[1] R. Nazikian et al, PRL 101, 185001 (2008); G.J. Kramer et al, PRL 109, 035003 (2012)
[2] R.K. Fisher et al, NF 52, 123015 (2012)
[3] M.A. Van Zeeland et al, NF 50, 084002 (2010)

Speaker: Daniel Lin (University of California, Irvine)

2021_IAEA_Lin.pdf

Friday 10 December

Control of Energetic Particle Confinement

Convener: Masatoshi Yagi (National Institutes for Quantum and Radiological Science and Technology, Rokkasho Fusion Institute)

42 Mitigation of AE induced ICRF fast-ion losses using deuterium NBI in the ASDEX Upgrade tokamak

The confinement of fast-ions, such as those generated by neutral beam injection (NBI), ion cyclotron resonance heating (ICRH) or fusion products, is of paramount importance for future fusion reactors to ensure a good plasma heating efficiency and the device integrity. Toroidicity induced Alfven Eigenmodes (TAEs) have been shown, both experimentally and numerically, to increase the radial fast-ion transport, eventually causing deleterious fast-ion losses [1].
In this work we present the mitigation of TAE induced fast-ion losses of ICRH origin using deuterium NBI in the ASDEX Upgrade tokamak. The experiment is carried out in deuterium plasmas with Bt=2.5 T and Ip=0.7 MA. The TAEs are driven by a fast-ion population generated by the application of 3.7 MW of on-axis hydrogen minority ICRH, together with up to ~4 MW of ECRH power in counter-ECCD configuration. These TAEs are observed to cause coherent fast-ion losses, as measured by a scintillator based fast-ion loss detector (FILD1). Phases of up to 900 ms and 2.5 MW of NBI heating are added. In these phases, either partial or full suppression of the TAE induced fast-ion losses is observed, depending on the level of applied ECRH power, while the TAE activity is maintained. An overall reduction in the total fast-ion loss level is also observed. The mitigation/recovery of the coherent fast-ion losses appears with a time delay of the order of tens of ms with respect to the NBI on/offset. Such an effect has been observed for NBI sources Q3 and Q8, with a main injection energy of 60 and 93 keV respectively. Tomographic reconstructions of the FILD signal reveal clear changes in the velocity-space of the losses during the mitigation phase. During the NBI on/off phases, FIDA and NPA measurements show changes in the H and D distribution functions, while a clear increase in the ion temperature and toroidal rotation of the plasma is measured, as well as a change in the frequency and toroidal mode numbers of the TAEs.
Measurements point out two possible effects that might explain this mitigation: (a) a modification of the hydrogen and deuterium fast-ion distribution functions during the NBI phases due to the 2nd harmonic D ICRF absorption and (b) a modification of the TAE structure due to changes in the kinetic profiles. In order to clarify which plays the dominant role, modelling of the hydrogen and deuterium fast-ion distribution functions with and without NBIs has been performed with the PION code, while the effect of the NBIs on the TAEs will be studied by means of the LIGKA code.
These experimental results show that, by an appropriate arrangement of the auxiliary heating systems, AE induced fast-ion losses could be mitigated or suppressed even in the case in which the control of the AE activity is not possible.

[1] M.Garcia-Munoz et al, Plasma Phys. Control. Fusion 61 054007 (2019)

Speaker: Joaquin Galdon-Quiroga (University of Seville)

Galdon_IAEA_TM_EP_2021_v3.pdf

43 Mitigation of Alfvén Eigenmodes in negative triangularity plasmas at TCV

Recent experiments at TCV have shown a strong mitigation of Toroidal Alfvén Eigenmodes (TAEs) in negative triangularity (NT) plasma compared to its counterpart experiment in positive triangularity (PT). In order to better understand the underlying physics mechanisms, non-linear simulations with positive ( δ = +0.4) and negative ( δ =- 0.4) triangularities have been carried out with the hybrid kinetic-magnetohydrodynamic code MEGA [1]. Realistic and anisotropic initial fast-ion distributions have been used, showing a significant mitigation of the AE amplitude and growth rate.

Synthetic fast-ion losses show a significant reduction in heat loads (from fast-ions) in NT compared to the PT, using a 2D wall [2] for the TCV case. Significant differences are observed when comparing the power exchange between the confined FI population and the modes, showing a lower energy delivery from the fast-ion population to the wave in the negative triangularity case. Single-n toroidal mode and multi-n simulations are compared to determine the impact of the non-linear interaction between the different modes and their impact on the fast-ion transport and loss. Different pitch-angle and energy distributions are studied to assess whether the effects are dependent on the initial fast-ion distribution in phase-space.

[1] Y. Todo and T. Sato, Physics of Plasmas 5 1321 (1998)
[2] P. Oyola et al., Review of Scientific Instruments 92 043558 (2021)

Speaker: Pablo Oyola (Universidad de Sevila)

IAEA_EPPI_Oyola_2021_submission.pdf

44 Stochastic diffusion of fast ions in Wendelstein-line stellarators: numerical experiment and extension of theory

Confinement of fast ions belongs to most difficult challenges facing a stellarator fusion reactor. Theory suggests a number of optimization schemes aimed to improve it, see, e.g., overview [1]. In particular, the quasi-isodynamic approach is employed in Wendelstein 7-X and Helias reactors. However, first numerical studies have shown that some fraction of 3.5 MeV alphas in a quasi-isodynamic reactor is lost [2] (because quasi-isodynamicity cannot be perfect), which was confirmed recently [3]. Theory explained this fact by a stochastic (collisionless) diffusion of transitioning ions (the particles with orbits transforming between the locally trapped and locally passing states) [4,5]. A way to mitigate these losses was suggested in [6]. Favourable / unfavourable effects of the radial electric field on the fast ion confinement were predicted [7,8].

In this work, we applied the collisionless code ORBIS (Orbits in Stellarators) [6] to verify the mentioned theoretical findings. The code visualizes the motion of particle guiding centers. The observation and an analysis of particle motion have clearly shown that making the separatrix between localized particles and locally passing particles [$\kappa^2(r,\vartheta)=1$] closed in the plasma volume, as suggested in Ref. [6], prevents the particle loss, see Fig. 1. Moreover, it was found that the closed separatrix improves the confinement of localized ions. In addition, a detailed consideration of particle motion has shown that transitioning particles in the locally passing state undergo a diffusion – the effect missing in previous theories. Therefore, the theory of stochastic diffusion was extended correspondingly. Numerical calculations were carried out for W7-X and a Helias reactor, plasmas with and without electric field were considered. These results may pave the way to further optimization of Wenelstein-line-stellarators.
References
[1] P. Helander, Rep. Prog. Phys. 77 (2014) 087001.
[2] W. Lotz, P. Merkel, J. Nuhrenberg, E. Strumberger, Plasma Phys. Control. Fusion 34 (1992) 1037.
[3] M. Drevlak, J. Geiger, P. Helander, Yu. Turkin, Nucl. Fusion 54 (2014) 073002.
[4] C.D. Beidler, Ya.I. Kolesnichenko, V.S. Marchenko, I.N. Sidorenko, H. Wobig, Phys. Plasmas 8 (2001) 2731.
[5] A.V. Tykhyy, Ukr. J. Phys. 63 (2018) 495.
[6] A.V. Tykhyy, Ya.I. Kolesnichenko, Yu.V. Yakovenko, A. Weller, A. Werner, Plasma Phys. Control. Fusion 49 (2007) 703.
[7] Ya.I. Kolesnichenko, V.V. Lutsenko, A.V. Tykhyy, A. Weller, A. Werner, H. Wobig, J. Geiger, Phys. Plasmas 13 (2006) 072504.
[8] A.V. Tykhyy, Ya.I. Kolesnichenko, Plasma Phys. Control. Fusion 63 (2021) 075019.

Fig. 1. The area (in black) where a transitioning 3.5-MeV alpha particle was confined for a long time. The red line is the plasma edge in flux coordinates. Calculations were carried out for a Helias reactor with the separatrix [$\kappa^2(r,\vartheta)=1$] located inside the radius $r_{max}\approx0.82a$ ($a$ being the minor plasma radius). The particle was launched at a point on the $r=0.25a$ flux surface. We observe that the region of diffusion is restricted by $r_{max}$. Calculations were carried out for $\Delta t=1$s. The orbit has covered the whole region $0< r< r_{max}$ by $\Delta t=0.2$s; no change of this region was observed after that.

Speaker: Anton Tykhyi (Institute for Nuclear Research, Kyiv, Ukraine)

Multiscale Physics and Instabilities in Burning Plasmas

Convener: Masatoshi Yagi (National Institutes for Quantum and Radiological Science and Technology, Rokkasho Fusion Institute)

45 Global gyrokinetic study of magnetic shaping effect in reversed magnetic shear plasmas

One of the challenges in gyro-kinetic shaping study is the impact of reversed magnetic shear to the trapped electron mode (TEM) instability, which can only be handled by global gyro-kinetic simulations with kinetic electron response. The configuration with reversed magnetic shear is widely used in recent experiments since it provides the formation of internal transport barrier (ITB) structures and enhanced confinement in many devices [1]. However, the relation between plasma shaping effect and drift-wave instabilities in reversed magnetic shear plasmas has not been well understood. In this work, we extend the linear, δf version of global gyrokinetic code GKNET with kinetic electrons to the cylindrical coordinates (R,φ,Z), in which the effects from multi flux-surfaces are included, to study the shaping effect on linear drift-wave instabilities with reversed magnetic shear. The numerical equilibrium obtained from a fixed-boundary MHD equilibrium code TASK/EQ is utilized [2], and connect with GKNET code through the interface code IGS [3].

Detailed cross-verifications for hybrid-electron code and full-kinetic code are performed using Cyclone-based circular equilibria, in which all electrons are treated kinetically in the full-kinetic case and only trapped electrons are treated as kinetic in the hybrid case. The full-kinetic electron case shows a destabilizing effect from non-adiabatic passing electrons, resulting in larger linear growth rate in Ion Temperature Gradient (ITG) mode and Trapped Electron Mode (TEM) instabilities compared to the hybrid one. This result is also agreed with recent ORB5 full-kinetic electron calculations [4].

Based on equilibria with reversed magnetic shear, the influence of magnetic shaping on linear TEM instability is studied using the GKNET full-kinetic version. Due to the variations of shaping profiles and Shafranov shift under reversed magnetic shear, local temperature/density gradient and magnetic shear show different variations along the straight-field-line poloidal angle χ_θ in outboard mid-plane. Since linear TEMs mainly “feels” an averaged gradient near χ_θ~0 in the low field side, corresponding variations are responsible for the shaping effects on linear TEMs. In details, elongation is found to stabilize linear TEMs due to reduction of effective temperature and density gradient around χ_θ~0. As for triangularity, χ_θ distributions of gradients and shear show different tendency with triangularity. Figure (a) indicates that the negative triangularity case gives much larger local electron temperature gradient around χ_θ~0 than zero and positive triangularity cases. On the other hand, magnetic shears near the peak gradient location are nearly zero for all cases with different triangularity. As a result, the negative triangularity shows destabilizing effect to linear TEMs seen in figure (b) which is different to the findings in normal shear (monotonic safety factor profile) case previously [5].

[1] Ida K and Fujita T Plasma Physics and Controlled Fusion 2018 60 033001
[2] Fukuyama A, et al. APS Conf. 2002:QP1.042.
[3] Nakata M, et al. Plasma and Fusion Research 2014 9 1403029-1403029
[4] Dominski J, et al. Physics of Plasmas 2017 24 022308
[5] Camenen Y, et al. Nuclear fusion 2007 47 510

Speaker: Wei WANG (National Institutes for Quantum Science and Technology (QST))

46 Quantitative linear stability of TAEs in JET ITB scenarios designed for alpha driven modes in DT

The destabilization of toroidal Alfven eigenmodes (TAEs) by alpha particles requires special conditions in current tokamaks, and DT operation of JET provides this rare opportunity [1]. The unambiguous observation of these modes is anticipated to be difficult, and the operation in DT is potentially limited by the availability of tritium and the allowable neutron wall activation, which might result in a reduced number of attempts that can be made at JET. The linear stability of ICRH driven TAEs during DT preparation experiments must therefore be completely understood, with careful accounting for fast and thermal plasma effects and comparison with experiment.
We demonstrate that in JET-like conditions, it is sufficient to use an incompressible cold plasma model for the TAE to reproduce the experimental adiabatic features such as frequency and position. Quantitative calculations with the full-orbit perturbative code HALO [2] during the internal transport barrier (ITB) afterglow were carried out, including full 3D constant of motion ICRH and NBI distribution functions. The core-localised modes that are predicted to be most strongly driven by minority ICRH fast ions correspond to the modes observed in the DD experiment, and conversely, modes that are predicted to be not driven are not observed. Large sensitivity of the linear growth rate to the ICRH tail was observed because of the implied uncertain population of resonant trapped particles. Linear damping rates from the thermal plasma due to a variety of mechanisms are calculated with both perturbative and non-perturbative codes, such as CASTOR-K [3] and GTC [4]. We show that analytical estimates for Landau damping can be too low by at least an order of magnitude in these experiments, owing to the neglect of higher order sideband resonances.

This work has been carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training programme 2014-2018 and 2019-2020 under grant agreement No 633053 and from the RCUK Energy Programme (grant number EP/P012450/1). The views and opinions expressed herein do not necessarily reflect those of the European Commission.

[1] Dumont R J,et al. 2018 Scenario development for the observation of alpha-driven instabilities in JET DT plasmas Nucl. Fusion 58
[2] Fitzgerald M et al. 2020 HALO: A full-orbit model of nonlinear interaction of fast particles with eigenmodes Comput. Phys. Commun. 252 106773
[3] Borba D et al. 1999 CASTOR-K: Stability Analysis of Alfvén Eigenmodes in the Presence of Energetic Ions in Tokamaks J. Comput. Phys. 153 101–38
[4] Lin Z 1998 Turbulent Transport Reduction by Zonal Flows: Massively Parallel Simulations Science (80-. ). 281 1835–7

Speaker: Michael Fitzgerald

47 Regulation of Alfven eigenmodes by microturbulence in fusion plasmas

Recent theoretical and experimental studies have suggested possible effects of microturbulence on Alfven eigenmode (AE) saturation and energetic particle (EP) transport in fusion plasmas. Zonal flows can be nonlinearly generated by, and in turn, suppress both the AE and microturbulence. EP Scattering by the microturbulence can affect phase space dynamics in the nonlinear AE-EP interaction. Unstable AE can also be scattered to shorter wavelength damped modes due to modulation by the microturbulence.
In the current work, the cross-scale coupling between AE and microturbulence is studied in state-of-the-art integrated simulations using the global gyrokinetic toroidal code (GTC) with comprehensive physics and kinetic treatment of all particle species. GTC simulations of the DIII-D tokamak experiment find that reversed shear Alfven eigenmodes (RSAE) excited by energetic ions from the neutral beam injection can saturate by self-generated zonal flows. However, the saturated amplitude and EP transport level are much higher than experimental levels at nonlinear saturation, but quickly diminish to very low levels after the saturation when background microturbulence is artificially suppressed. In contrast, in simulations coupling micro-meso scales, the RSAE amplitude and EP transport decrease drastically at the saturation but increases to the experimental levels after the saturation due to regulation by thermal ion temperature gradient (ITG) microturbulence. In the quasi-steady state ITG-RSAE turbulence, the resulting RSAE amplitude agrees very well with experimental measurements using electron cyclotron emission (ECE), and the microturbulence density fluctuation amplitude of 0.5-0.8% has the right order of the integrated low-k density fluctuation amplitude of 0.3-0.4% from beam emission spectroscopy (BES) measurement.

     This work was supported by DOE SciDAC ISEP and used computing resources at ORNL (DOE Contract DE-AC05-00OR22725) and NERSC (DOE Contract DE-AC02-05CH11231), and experimental data from DIII-D National Fusion Facility (DOE Contract DE-FC02-04ER54698).

Speaker: Pengfei Liu (University of California, Irvine)

48 Integrated, self-consistent quasilinear modeling of fast ion relaxation in tokamaks

The success of burning plasma devices relies on their ability to confine fusion alpha particle products long enough for them to transfer a substantial fraction of their energies to the reacting thermal particles via collisions. It is, therefore, essential to develop efficient and robust capabilities to predict the level of energetic ion losses in tokamak experiments. This work self-consistently constructs from first principles a resonance-broadened quasilinear plasma transport theory that incorporates Fokker-Planck dynamical friction (drag) and scattering for marginally-unstable modes resonating with an energetic minority species. Recent analytic developments show that drag fundamentally changes the structure of the wave-particle resonance, breaking its symmetry and leading to the shifting and splitting of resonance lines. In contrast, scattering broadens the resonance in a symmetric fashion. Comparison with fully nonlinear simulations shows that the proposed quasilinear system preserves the exact instability saturation amplitude and the corresponding particle redistribution of the fully nonlinear kinetic theory. The broadened quasilinear model has been designed to efficiently evolve amplitudes of several interacting Alfvén modes, in regimes of both overlapping and isolated resonances, while self-consistently relaxing the fast ion distribution function in the presence of collisions and turbulence.
An integrated, quasilinear numerical framework to quantify the losses of fast ions in tokamaks that is both fast and comprehensive has been realized through the development of the Resonance Broadened Quasilinear (RBQ) code. It formulates the quasilinear diffusive beam ion relaxation in action variables (i.e., in both the canonical toroidal momentum and the unperturbed particle kinetic energy) via a generalized alternating direction implicit method. The developed framework employs realistic eigenstructures, mode damping rates and wave-particle interaction matrices. Rigorous verification exercises have been undertaken in limiting cases in which there exist analytical solutions for single mode saturation levels. The quasilinear simulation output provide mappings of fast ion flows that are useful in informing phase-space engineering solutions for neutral-beam-driven instabilities. The simulations are integrated with TRANSP with the calculated neutron loss rate, yielding reasonable quantitative agreement compared with measurements from DIII-D, which suggests that the integrated model is a promising predictor of fast ion confinement in scenario development studies.

This work was supported by the US Department of Energy under Contract Nos. DE-AC02-09CH11466 and DE-FC02-04ER54698.

Speaker: Vinicius Duarte (Princeton Plasma Physics Laboratory)

49 Fast-ion transport optimization using the integrated TGLF-EP+Alpha Alfvén eigenmode transport model

Control of Alvfén eigenmodes (AEs) driven by energetic neutral beam injection (NBI) ions in DIII-D is explored with the TGLF-EP+Alpha model. TGFL-EP+Alpha is a reduced model assuming stiff-transport informed by DIII-D experiments and nonlinear gyrokinetic simulations. In DIII-D shot 180625, neutron deficit below classical predictions (a proxy for AE transport of fast ions) is experimentally reduced by up to 35% by moving NBI off axis and/or moving electron cyclotron current drive to on-axis. TGLF-EP+Alpha captures these trends, predicting the evolving neutron signal to well within 10% over the entire current ramp. Adding in the energetic-particle diffusivity predicted to in TGLF-EP to the power-balance analysis brings TGLF thermal-ion temperature profiles into much better agreement with measurements as well. The physics-based TGLF-EP+Alpha model improves over ad hoc energetic particle diffusivity currently used in integrated modeling workflows. It’s inexpensive enough for scenario optimization and validated over a wide parametric range.
Work supported by U.S. Department of Energy under Grants DE-FG02-95ER54309, DE-FC02-08ER54977, DE-SC0018108, DE-AC05-00OR22725, and DE-FC02-04ER54698.

Speaker: Eric Bass (UC San Diego)

50 Feasibility of kinetic stability analysis in time-dependent simulations and applications for predictions and design of controlled plasma discharges

An interface for kinetic stability analysis has been implemented in TRANSP, motivated by recent advances in the calculation of fast ion transport induced by MHD and Alfvénic Eigenmodes [1] in time-dependent simulations and by the need for predicting accurate evolution of fast ion pressure profiles for the interpretation, prediction and design of controlled plasma discharges. Similar efforts are ongoing in the ITER IMAS framework [2].
As a proof-of-concept, the new interface has been coupled with the FAR3d code [3], which is capable of both initial-value and eigensolver calculations using a Gyro-Landau closure model to identify unstable Alfvén eigenmodes in tokamaks and stellarators. Preliminary results will be presented and discussed at this meeting for a well analyzed discharge on DIII-D [4,5] and for a JET deuterium discharge that has been converted to an equivalent DT discharge for predictive studies [6]. The time-dependent simulations will focus on the calculation of stability for an entire discharge to produce a synthetic spectrum of Alfvén eigenmodes for a user-selected range of toroidal mode numbers and frequencies. The results from the time dependent simulation will be compared with time slice analysis for the DIII-D case, in which unstable modes were experimentally observed [4,5]. The comparison makes it possible to assess the uncertainties when kinetic stability analysis is performed at each time step for which the equilibrium is calculated, without direct supervision by the user. Applications for predictive simulations for the design of dedicated experiments targeted to steady state exploration and stability control will also be discussed.

[1] M. Podestà et al., Plasma Phys. Control. Fusion 59, 095008 (2017)
[2] V. A.Popa, TUM Munich 2020 and ITER-IMAS project
[3] D. A. Spong, Nucl. Fusion 53, 053008 (2013); J. Varela et al., Nucl. Fusion 57 (2017) 046018
[4] C. Collins et al, phys. Rev. letters 116, 095001 (2016)
[5] S. Taimourzadeh et al, Nucl. Fusion 59 (2019) 066006
[6] M. Podestà et al., Extension of the energetic particle transport "kick model" in TRANSP to multiple fast ion species, to be submitted to PPCF

Speaker: Francesca Poli (PPPL)

fmpoli_friday.pdf

51 Multiscale Chirping modes Driven by Thermal Ions in a Plasma with Reactor-relevant Ion Temperature

A thermal ion driven bursting instability with rapid frequency chirping, assessed to be an Alfvénic ion temperature gradient mode [1], has been observed in plasmas having reactor-relevant temperature in the DIII-D tokamak [2] (see the Fig. 1). The modes are excited over a wide spatial range from macroscopic device size to micro-turbulence size and the perturbation energy propagates across multiple spatial scales. The radial mode structure is able to expand from local to global in ∼ 0.1 ms, and it causes magnetic reconnection in the plasma edge, which can lead to a minor disruption event. The ηi (=∂ln$T_i$/∂ln$n_i$) exceeds the theory-predicted threshold for the destabilization of Alfvénic continuum due to compressibility of core ions. The most unstable modes belong to the strongly coupled kinetic ballooning mode and β-induced Alfvénic eigenmodes branch [3]. The key features of the observation are successfully reproduced by linear analysis solving the electromagnetic gyrokinetic equations (CGYRO code) [4]. Since the mode is typically observed in high ion temperature >10 keV and high-β plasma regime, the manifestation of the mode in future reactors should be studied with development of mitigation strategies, if needed.

https://i.ibb.co/9tH68Wt/001.jpg

*Supported by the US DOE under DE-FC02-04ER54698

[1] F. Zonca, L. Chen and R.A. Santoro, Plasma Phys. Controlled Fusion 38 2011 (1996).
[2] X.D. Du, R.J Hong, W.W. Heidbrink, X. Jian et al., Phys. Rev. Lett. 127, 025001 (2021).
[3] I. Chavdarovski and F. Zonca, Phys. Plasmas 21, 052506 (2014).
[4] J. Candy, E. Belli and R. Bravenec, J. Comput. Phys. 324, 73 (2016).

Speaker: Xiaodi Du (General Atomics)

Closing

52 Closing and Announcement of 18th Meeting

Speakers: Matteo Barbarino (International Atomic Energy Agency), Matthew John Hole (Australian National University)