Session YO05: MFE: Edge Instabilities, Transport, and Helium Exhaust

Comparison of the new BOUT++ fluid edge code Hermes-3 to SOLEDGE2D-EIRENE in an example ST40 predictive scenario

Axisymmetric tokamak edge transport simulations are essential tools for interpretation of experimental data and the design of future devices and operating scenarios. Hermes-3 is a new open-source fluid edge plasma code written under the BOUT++ framework. Combining the features of SD1D and Hermes-2, it allows for self-consistent simulation of edge plasma in 1D, 2D or 3D with an arbitrary number of species for both steady state and unsteady/turbulent regimes.

In this study, Hermes-3 is configured in steady-state 2D axisymmetric transport mode and compared to the edge code SOLEDGE2D-EIRENE in an example predictive double null diverted configuration of ST40, the privately-funded spherical tokamak owned and operated by Tokamak Energy. Although available in both codes, drifts, currents and impurities are not evolved for simplicity. The equations in each code are currently under review to confirm applicability to spherical tokamaks.

While both codes feature similar plasma models, Hermes-3 features fluid neutrals and a grid terminating at an arbitrary magnetic surface while SOLEDGE2D has kinetic neutrals with a grid extending to the wall. The impact of this in the large ST40 vessel region has been found to be significant and the performance of Hermes-3 has been enhanced through improved neutral boundary conditions. In addition, the impact of the Hermes-3 field-orthogonal grid is compared to the SOLEDGE2D grid which supports both field and target orthogonality.   

The impact of net power and edge particle source on the electron density pedestal of Alcator C-Mod

Understanding plasma transport and fueling at the edge of tokamak plasmas is critical to predicting the density and performance in next-generation reactors. Existing experimental data, combined with high-fidelity simulations of neutral kinetics, allows insight into important atomic/plasma processes that determine plasma profiles. To this end, SOLPS-ITER is run interpretively on Alcator C-Mod discharges with varied particle and energy content. We consider a scan of the net power (P_net), both with/without active cryopumping, and track changes in recycling particle fluxes and edge electron density (n_e) and temperature gradients. We use measurements from edge Thomson scattering and a Lyman-alpha camera to simultaneously constrain n_e and the neutral density. Experimentally, we observe degradation in the pedestal quality when P_net drops past ~2.4 MW. As this approaches the L-H power threshold, we see a dramatic rise in effective particle diffusivity at the location of maximum n_e gradient, by about an order of magnitude. Computationally, we attempt to model the change in transport by solving for particle and heat diffusivities that uniquely reproduce experimental plasma profiles as well as measured ionization source. We thus supplement experimental 1D findings with a 2D picture of transport and fueling in a high-density machine opaque to neutrals.   

Stochastic modelling of blob-like filaments in the scrape-off layer

A stochastic model has been developed in order to describe the dynamics of intermittent fluctuations due to radial motion of blob-like filaments in the scrape-off layer (SOL) of magnetically confined plasma [1-3]. Uncorrelated pulses move radially outwards with a random distribution of amplitudes, sizes and velocities. The pulses have a fixed shape and an exponentially decaying amplitude due to parallel drainage towards the divertor plates. In its simplest form, the model predicts exponentially decreasing average radial profiles [2].

 

More generally, we investigate the implications of a distribution of blob velocities and correlations with the amplitudes. When pulse velocities depend on the instantaneous amplitude, the filaments will eventually stagnate in the SOL. A broad distribution of pulse velocities leads to non-exponential profiles with strongly increased intermittency and large-amplitude fluctuations in the far-SOL [3].

 

It is demonstrated that this explains many features from experimental measurements. This includes the formation of a shoulder structure in the average density profile with broad far-SOL profiles, high relative fluctuation levels throughout the SOL, and strong intermittency with positively skewed and flattened probability density functions in the far-SOL. These results will be discussed in the context of experimental measurements in tokamak plasmas.

 

References

[1] O. E. Garcia, Phys. Rev. Lett. 108, 265001 (2012)

[2] O. E. Garcia et al., 23, 052308 (2016)

[3] J. M. Losada et al., Phys. Plasmas 30, 042518 (2023)   

HeRMES: Helium Retention Mechanism Experiment in a Stellarator

The issue of helium ash build-up poses a significant obstacle to achieving commercial fusion from both scientific and economic perspectives. The inability to effectively remove thermalized alphas from the plasma decreases the operational regime to realize ignition. Current plans to remove helium ash involve the use of large pump ducts that increase reactor size. This increases construction costs and thus hinders fusion reactors from being economically competitive. Previous experiments at the University of Illinois Urbana-Champaign (UIUC) showed helium recycling being reduced up to 85% during lithium evaporations into helium plasmas. The Helium Retention Mechanism Experiment in a Stellarator (HeRMES) is the next experimental campaign to be conducted at UIUC to study helium retention effects in the Hybrid Illinois Device for Research and Applications (HIDRA). HeRMES aims to identify the mechanism associated with helium retention observed from in-operando lithium evaporations in HIDRA helium plasmas. HeRMES consists of several plasma shots where lithium induces a low-recycling regime in HIDRA and conditions such as gas flow and ECRH power are adjusted during this regime.The HIDRA Materials Analysis Test-stand will be utilized to perform thermal desorption spectroscopy post-evaporation to investigate the potential trapping of helium in lithium. HeRMES will provide critical information for addressing the issue of helium ash and will advance the development of future plasma-facing components.   

Effects of plasma-wall self-organization on density limit and ignition condition of a burning tokamak plasma

The impurity radiation in a tokamak affects the amount of heat flux reaching the wall target plates, determining the plasma conditions in the target region and the subsequent impurity production and radiation inside plasma. Such a plasma-wall self-organization (PWSO) has been proposed as a potential machanism for the tokamak density limit [D.F. Escande NF 2022]. In this work, the PWSO model has been extended to evaluate the effects of PWSO on the density limit and the ignition condition of a burning tokamak plasma. Based on a 1D transport model including the PWSO, the α-particle heating is found to enhance the tokamak density limit. On the other hand, the results reveal that the inclusion of the PWSO leads to an increased value of the fusion triple product required for ignition, which can be attributed to the power deposition on the wall target plates that is excluded from the transport energy loss. The impurity fraction near density limit and ignition condition can be self-consistently determined based on the power deposition on the wall target plates and the sputtering properties of the target material in our calculation.   

The Effect of ETG Transport on the Electron Temperature Pedestal

ETG turbulence likely constrains the electron temperature profile in the pedestal in many scenarios. We present simple formulas for ETG pedestal transport extracted from a database of nonlinear gyrokinetic simulations. These formulas are surprisingly simple and accurate when taking into account a few physically-motivated parameters and accounting for certain geometric factors. They are accurate in the steep gradient region for both spherical and standard aspect ratio tokamaks. The strongest parameter dependences are the normalized inverse electron temperature gradient (a/LTe) (to the second power) and eta=Ln/LTe (to the third power). These dependences result in strong sensitivity to both the electron temperature and density gradients. The dependence on Zeff and temperature ratio can also be important. We apply these models to predicting electron temperature profiles in various pedestal scenarios. In scenarios where ETG transport is insufficient to account for the electron thermal transport (i.e. it over predicts the temperature), we posit that MTM is also active and formulate reduced models for its contribution. This work represents an initial step toward more comprehensive (i.e., accounting for transport in addition to MHD limits) modeling of pedestal structure.   

Role of EHO-like modes in Inter-ELM Particle Transport during type-I ELMy DIII-D H-mode Discharges

Edge harmonic oscillation (EHO)-like modes, observed during the inter-ELM period of regular type-I ELMing H-mode discharges of the DIII-D tokamak, are investigated for the role they may play in the inter-ELM particle transport. The appearance of the EHO-like modes correlates with higher D_α levels while their disappearance correlates with a sharp decrease in D_α. ELITE calculations show that the MHD stability is close to the peeling boundary in the inter-ELM period. These pedestal localized modes (~10 kHz and its harmonics) are observed in the measurement of flow oscillations by Doppler backscattering (DBS), density fluctuations by beam emission spectroscopy (BES), and magnetic fluctuations by magnetic probes. They are also observed in the ion saturation current measurements by Langmuir probes, which suggests their role in inter-ELM particle transport. BES measurements show that the modes rotate in ion diamagnetic direction in lab frame and have k_θ~0.1–0.3 cm^-1. Linear CGYRO simulation indicates that kinetic ballooning modes are most unstable in the region where EHO-like modes are measured which might explain the inter-ELM particle transport.

This work was supported by the US Department of Energy under grants DE-SC0019352 and DE-FC02-04ER54698.   

A Chapman-Enskog-like (CEL) Kinetic Closure Approach in NIMROD

When simulating the macroscopic dynamics of high temperature magnetized plasmas, a fluid description has limitations due to approximations commonly employed in the closure problem. Rigorous closure methods exist in higher collisionality regimes, but many processes become intrinsically kinetic in lower collisionality regimes. While heuristic forms have proven useful for mimicking some of this kinetic closure physics, this effort seeks to close the plasma fluid equations self-consistently in all collisionality regimes.

In particular, a Chapman-Enskog-like (CEL) kinetic closure approach [1] has recently been added to the plasma fluid code NIMROD [2,3]. This CEL implementation allows for a rigorous kinetic closure of NIMROD’s fluid model by evolving a kinetic equation in the presence of a self-consistent background Maxwellian defined by temporally and spatially evolving density, temperature and fluid velocity (evolved using the fluid equations).

We employ this new closure scheme in a resonant field error penetration problem in tokamak geometry. A kinetic ion response is used to accurately describe the ion flow dynamics in toroidal geometry. Numerical stability considerations relevant to the coupled CEL-fluid evolution approach in NIMROD are discussed. [1] J. J. Ramos, Phys. Plasmas extbf{17}, 082502 (2010). [2] C. Sovinec, et. al. , Nonlinear magnetohydrodynamics with high-order finite elements, J. Comp. Phys. extbf{195} (2004) 355 [3] J. R. Jepson, et. al. , Phys. Plasmas extbf{28} (2021) 082503.   

Investigating Micro-Tearing Mode and Drift-Alfven Instability in Pedestal Turbulence

The micro-tearing mode (MTM) has been suggested as one of the potential driving mechanisms for pedestal electron temperature heat turbulence transport. In our study, we derive the dispersion relations of MTM under various limiting cases and compare them with various MTM models. Additionally, we investigate the instability of the drift Alfven wave (DAW) by incorporating the impact of time-dependent thermal forces using Hassam's collisional fluid model. Our finding indicates distinct instability characteristics of MTM and DAW at different rational surface locations. Specifically, MTM exhibits instability near the rational surface, whereas DAW instability occurs away from the rational surface. To simulate the micro-tearing mode, we implement the Hassam's model into BOUT++ framework. Employing a shifted-circle tokamak geometry, our linear global simulations reveal that the growth rate of the linear MTM decreases as collisionality increases, aligning with theoretical expectations. Furthermore, our nonlinear global simulation demonstrates that MTM generates chains of magnetic islands. In the late nonlinear stage, these magnetic islands overlap, leading to the emergence of chaotic magnetic fields. Notably, in the absence of energy source, the initial value simulation shows that MTMs can also trigger crashes in the electron temperature profile due to stochastic and magnetic transport, similar to the effects of ELMs.   

Ballooning Mode in a Stochastic Magnetic Field—A Quasi-mode Model

Recently, Minjun Choi et al. employed entropy-complexity analysis to pedestal temperature fluctuations with RMP switched on, revealing a reduction in the predictability of pedestal turbulence. Given that peeling-ballooning mode is a likely mechanism of ELM, studying how a stochastic magnetic field affects ballooning mode is beneficial to our understanding of these results. Due to the fact that models for ballooning mode are set up in a torus while theories involving RMP focus on resonant surfaces in a cylinder, reconciling these two different geometries is necessary to develop a comprehensive theory. Since quasi-mode is the counterpart of ballooning mode in a cylinder, we choose to study quasi-mode first, and then extend the results to ballooning mode.

In this work, a multi-scale model of quasi-mode in a stochastic magnetic field is presented. The insights we have gained regarding the ballooning mode are:

1. To maintain ▽·J=0 at all scales, a microturbulence is driven.

2. The scaling of the resultant turbulent viscosity is larger than that in our study on interchange mode. This can be attributed to the variations in mode structure.

3. Stochastic magnetic fields can stabilize mode growth by enhancing the effective inertia, reducing the effective drive, and boosting mixing.

4. A non-trivial correlation develops between velocity fluctuations and magnetic perturbations. This could explain the reduction in the predictability of the pedestal turbulence.

Experiments for future investigations are also proposed.   

Investigation of helium exhaust dynamics at the ASDEX Upgrade tokamak with full-tungsten wall

An efficient removal of helium "ash" from burning plasmas is necessary to avoid fuel dilution and degradation of plasma confinement. Extrapolations of helium exhaust towards reactor-grade tokamaks rely on a deep understanding of the underlying physics mechanisms. The investigation presented herein was performed at the ASDEX Upgrade (AUG) tokamak. This is an ideal test environment thanks to the optimized divertor geometry, an extensive diagnostic coverage and the presence of plasma-facing components (PFCs) made of tungsten, which is an increasingly relevant candidate for the PFCs in ITER and DEMO. To interpret the experimentally observed exhaust dynamics in H-mode plasmas we developed a novel multi-reservoir particle balance model. This simulates plasma transport and wall retention in a self-consistent way, and disentangles the contributions of active pumping and wall pumping to the observed helium behavior. We found that the limited performance of the AUG pumping system and the high retention capability of helium in the plasma-exposed tungsten surfaces quantitatively play a similar role in hindering an efficient exhaust. As such, the role of the walls as particle reservoirs for helium should be taken into account also in future devices, and emphasizes the need for efficient active pumping systems.   

Modeling blob and hole-like impurity transport in the scrape-off layer of DIII-D

A novel blob and hole-like impurity transport model has been implemented within the Monte Carlo SOL impurity transport code DIVIMP and subsequently benchmarked on DIII-D. Simulation results obtain simultaneous quantitative agreement with estimates of tungsten density at multiple locations. The model uses blob measurements from a reciprocating Langmuir probe as input. The blob/hole-like transport model hypothesizes that impurities encountering blobs/holes experience the same E_pol x B_T drift as the blobs/holes. Blobs carry impurities away from the core and holes transport impurities into the core. Simulations using blob/hole-like impurity transport are successfully performed on two DIII-D L-mode discharges with the outer strike point on W tiles: one in an open divertor configuration, and another in a slot-like closed divertor configuration. TGYRO simulations using soft X-ray data of W concentration predict core profiles of W density up to the ~separatrix (n_W~10¹⁵ m^-3). 3DLIM simulations constrained by W surface deposition patterns on far-SOL collector probes estimate the W density within the far-SOL (n_W~10¹² m^-3). DIVIMP with blob/hole-like transport matches the W density within 25% for both TGYRO and 3DLIM estimates by assuming impurities travel with blobs/holes for 10 us at a time.   

Helium pumping and NBI fueling the burning plasma in low recycling tokamak regimes.

The present high-recycling plasma regimes remain questionable for burning plasma due to inavoidable disruptions. The altenative is low recycling regimes relying on plasma pumping by lithium + fueling by NBI. Not sensitive to thermal conduction and PSI (replaced by collisionless flow of 15-20 keV electrons and ions to lithium), these regimes implement the best possible confinement (determined by particle diffusion) suitable for fusion amplification Q=5-10 even in the JET tokamak. Moreover at 50 % recycling, half of plasma energy is lost to the side walls (covered by Li) in disperse manner. The simplicity of Li-wall-fusion gives the hope on disruption avoidance and on removing the major regulation obstacle for burning DT plasmas. The technology of continuously flowing liquid lithium allows for the real-time recuperation of unburned tritium by absorbing it from plasma and delivering to outside facility as T solution in liquid Li. This invalidates the existing misconception on lithium incompatibility with DT plasma. This presentation, aiming to 150-200 MW DT neutron source (R/a=4/1 m, b/a=1.6, 1 m thick blanket), addresses helium exhaust pumping, and fueling by NBI. The sufficient sink for ionized helium seems to be realistic, while negative-ion NBI would allow to fuel the burning plasma at a proper plasma density and magnetic field. Even with H-plasma JET device is uniquely suitable for implementation of the best possible confinement and getting key data on He impurity pumping and on fueling with extra D NBI beam.