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The application of a bundling technique to model the diverse charge states of tungsten impurity species in total-f gyrokinetic simulations is demonstrated. The gyrokinetic bundling method strategically groups tungsten ions of similar charge, optimizing computational efficiency. The initial radial configuration of these bundles and their respective charges are derived from a coronal approximation and the quasi-neutrality of the plasma. A low-density JET H-mode like plasma is simulated using the neoclassical version of XGC across the entire plasma volume, spanning from the magnetic axis to the divertor. An accumulation of tungsten is observed at the pedestal top, as a result of low-Z tungsten ions moving inward from the scrape-off-layer (SOL) into the core region and high-Z tungsten ions moving outward from the core into the pedestal. This organization of the fluxes cannot be captured by a single tungsten-ion simulation. Large up-down poloidal asymmetries of tungsten form in the pedestal and strongly influence the direction of neoclassical fluxes. The temperature screening effect and its correlation with asymmetries is analyzed.
Finally, an update on recent neoclassical and turbulence simulations of the WEST tokamak including tungsten and nitrogen impurities will be presented. Preliminary results on the prediction of tungsten accumulation near the axis will be discussed.
Future devices like ITER will have limited capacity to drive toroidal rotation, increasing the risk of instabilities like resistive wall modes. Fortunately, many experiments have found that tokamak plasmas rotate “intrinsically”, that is, without applied torque. The modulated-transport model shows that such rotation may be caused by the interaction of ion drift-orbit excursions with the strong spatial variation of the turbulent momentum diffusivity [1]. The model predicts intriguing qualitative behavior, such as a strong dependence of edge intrinsic toroidal rotation on the major-radial position of the X-point, which was subsequently measured on TCV [2]. The model has also been experimentally validated through further dedicated tests [3, 4], as well as via application in the new European whole-device transport model IMEP [5]. However, certain applications will require a relaxation of the underlying assumptions. In particular, the original model required the turbulent momentum diffusivity to decay exponentially in the radial direction, while experiments often exhibit a more complicated variation. In this work, we generalize the modulated-transport model to allow the turbulent momentum diffusivity to depend on space in an axisymmetric but otherwise arbitrary way. To enable this generality, we assume that the normalized diffusivity is weak, roughly equivalent to assuming that the pedestal-top ion transit time is short compared to the transport time across the pedestal, a condition that is almost always met for experimental applications. Given the increased flexibility, along with a technically much easier calculation, the new approach may serve as a basis for future extensions, including shaped geometry and trapped particles as well as the retention of momentum transport by neutrals.
[1] T. Stoltzfus-Dueck, Phys. Rev. Lett. 108, 065002 (2012).
[2] T. Stoltzfus-Dueck et al., Phys. Rev. Lett. 114, 245001 (2015).
[3] J. A. Boedo et al., Phys. Plasmas 23, 092506 (2016).
[4] A. Ashourvan, B. A. Grierson, D. J. Battaglia, S. R. Haskey, and T. Stoltzfus-Dueck, Phys. Plasmas 25, 056114 (2018).
[5] T. Luda et al., Nucl. Fusion 61, 126048 (2021).
Axisymmetric modes in elongated plasmas are normally associated with a well-known ideal instability resulting in a vertical shift of the whole plasma column. This vertical instability is stabilized by means of passive feedback consisting of eddy currents induced by the plasma motion in a nearby wall and/or in plasma-facing components. When a thin resistive wall is considered, the n=0 mode dispersion relation can be studied analytically with reduced ideal MHD models and is cubic. Under relevant conditions, two roots are oscillatory and weakly damped. These oscillatory modes present Alfvénic frequency and are dependent on plasma elongation and on the relative position of the plasma boundary and of the wall. The third root is unstable and represents the so- called resistive wall mode (RWM) [1]. We focus on the two oscillatory modes, dubbed Vertical Displacement Oscillatory Modes (VDOM), that can be driven unstable due to their resonant interaction with energetic ions.
The fast ion drive, involving MeV ions in present days tokamak experiments such as JET, may overcome dissipative and resistive wall damping, setting an instability threshold, as described in Ref. [2]. The effects of energetic particles are added within the framework of the hybrid kinetic-MHD model. An energetic ion distribution function with ∂F/∂E > 0 is required to drive the instability, achievable with pitch angle anisotropy or with an isotropic distribution in velocity space with regions of positive slope as a function of energy. The latter situation can be achieved by considering losses of fast ions or due to fast ion source modulation [3-4]. The theory presented here is partly motivated by the observation of saturated n=0 fluctuations reported in [4,5], which were initially interpreted in terms of a saturated n=0 Global Alfvén Eigenmode (GAE). Modeling of recent JET discharges using the NIMROD [6] extended-MHD code will be presented, focusing on mode structure and frequency dependence. It is early for us to conclude whether the mode observed at JET is a VDOM rather than a GAE, nevertheless, we discuss the main points of distinction between GAE and VDOM that may facilitate their experimental identification.
References
[1] T. Barberis, et al. 2022, J.Plasma Phys. 88, 905880511
[2] T. Barberis, et al 2022 Nucl. Fusion 62 06400
[3] Ya.I. Kolesnichenko and V.V. Lutsenko 2019 Nucl. Fusion 59 126005
[4] V. G. Kiptily et al 2022 Plasma Phys. Control. Fusion 64 064001
[5] H. J. C. Oliver et al. 2017 Phys. Plasmas 24, 122505
[6] C. Sovinec et al. and the NIMROD Team 2004 J. Comp. Phys. 195 355
We discuss recent progress in understanding the role of transport physics in density limit phenomena. Our approach is one which combines theory and experiment. Contrary to the conventional wisdom that the density limit is enforced by MHD instability, findings indicate that the L−mode density limit is associated first with the degradation of the edge E × B shear layer. The latter occurs for k‖² vₜₕₑ² / ω νₑᵢ<1. Shear layer decay leads to strongly enhanced turbulence spreading and increased production of density 'blobs'. Interestingly, the spreading flux increases more rapidly with increasing n / n_G than does the particle flux. Shear layer decay is linked to a decline in zonal flow production.
A simple model for flow, fluctuation and density evolution reveals that the edge density will increase with edge heat flux (power). This favorable trend results from increased Reynolds stress flow drive at higher power. It provides physical insight into the power scaling of density limit, now observed in experiments. A scaling of n ∼ P^(1/3) is suggested for the case of ITG turbulence.
We briefly discuss recent density limit experiments in negative triangularity plasmas, as well as aspects of the H−mode density limit phenomenon. Implications for burning plasma are discussed.
Contributions from Ting Long, SWIP ; Rameswar Singh ,UCSD ; Rongjie Hong, UCLA and DIII−D ; Zheng Yan, Univ Wisc and DIII−D ; and George Tynan, UCSD are acknowledged.
Starting from the assumption that saturation of plasma turbulence driven by temperature-gradient instabilities in fusion plasmas is achieved by a local energy cascade between a long-wavelength outer scale, where energy is injected into the fluctuations, and a small-wavelength dissipation scale, where fluctuation energy is thermalized by particle collisions, we formulate a detailed phenomenological theory for the influence of perpendicular flow shear on magnetized-plasma turbulence. Our theory introduces two distinct regimes, called the weakly and strongly sheared regimes, each with its own set of scaling laws for the scale and amplitude of the fluctuations and for the level of turbulent heat transport. We discover that the ratio of the typical radial and poloidal wavenumbers of the fluctuations, i.e., their aspect ratio, plays a central role in determining the dependence of the turbulent transport on the imposed flow shear. Our theoretical predictions are found to be in excellent agreement with numerical simulations of two models of magnetized plasma turbulence: (i) an electrostatic fluid model of slab electron-scale turbulence, and (ii) Cyclone-base-case gyrokinetic ion-scale turbulence.
We present the first local delta-f nonlinear gyrokinetic (GK) simulations based on a gyro-moment (GM) approach, which exploits the projection of the distribution functions onto a Hermite-Laguerre velocity- space basis. We first demonstrate that, in contrast to gyrofluid models, the GM approach reproduces the Dimits shift, notably, with a coarser velocity space resolution than the continuum GK GENE code. In addition, we reveal that the choice of collision operator model (Dougherty, Sugama, Lorentz and Landau) significantly impacts the level of turbulent transport through multi-species zonal flow damping.
In addition, we show for the first time that the GM approach is able to bridge the gap between GK and reduced fluid modelling by its exact equivalency to the model of Ivanov et al. 2020 when considering the same limits. Leveraging its efficiency and multi-fidelity capability, we finally use the GM approach to explore the impact of triangularity in realistic DIII-D edge conditions across a range of models, spanning from GK electron-ion multi-scale simulations to the reduced fluid limit.
Turbulence is one of the key ingredients in shaping H-mode pedestals. Identifying the relevant turbulent transport mechanisms in a pedestal, however, is a great scientific and numerical challenge. Here, we address this challenge by global, nonlinear gyrokinetic simulations of two pedestals: One from ASDEX Upgrade (Type-I ELMy H-mode) and one from JET (hybrid scenario H-mode). The global simulations permit to calculate heat fluxes due to ion-scale turbulence in the steep gradient region encompassing the full pedestal from top to foot. They are supported by detailed characterizations of gyrokinetic instabilities via local, linear simulations at pedestal top, center and foot as well as dedicated nonlinear electron-scale heat flux calculations. Simulations are performed with the gyrokinetic, Eulerian, delta-f code GENE (genecode.org) and employ a new code upgrade of its global, electromagnetic model that enables stable simulations at experimental plasma beta values.
In both investigated pedestals from AUG and JET, we find turbulent transport to have a complex radial structure that is multi-scale and multi-channel. Electron transport in the AUG pedestal is found to transition in scale. At the pedestal top ion-scale TEM/MTM instabilities fuel electron transport whereas in the pedestal center electron-scale ETG transport takes over. Turbulent ion heat flux is present at the pedestal top and strongly reduces towards the steep gradient region. Magnetic shear is found to locally contribute to the stabilization of microinstabilities and reduction of heat flux. In the JET pedestal, transport due to ITG is found to play a much more important role, particularly on the pedestal top/ outer core. In both pedestals, ExB shear is confirmed to strongly reduce heat fluxes in the global, nonlinear simulations. We discuss implications of our results for the applicability of quasi-linear transport models in the pedestal.
Understanding the formation of large-scale structures in weakly magnetized plasmas represents a crucial step towards developing predictive design capabilities for E×B devices dedicated to investigating fundamental plasma physics phenomena. MISTRAL is such a device based at PIIM laboratory to study plasmas in cross-field configuration (E⊥B). The formation of coherent rotating structures in MISTRAL is supposed to be due to an interplay between various instabilities and the E×B flow. However, a definitive understanding of which instabilities are accountable for their emergence and the specific triggers involved remains elusive. An experimental investigation of MISTRAL plasmas has been performed to lay the basis for the theoretical modeling. A two-fluid model has been developed to discuss the linear stability of rotating plasma columns. Prior works have demonstrated that rotating plasma columns are susceptible to centrifugal flute modes. However, most of the existing models rely on the low-frequency approximation (LFA), which holds true when the instability frequency and equilibrium flow frequency are considerably smaller than the ion-cyclotron frequency. This assumption is challenged in numerous laboratory plasma devices, including weakly magnetized plasma columns like MISTRAL. To address this limitation, a radially global dispersion relation describing the centrifugal instability without the LFA has been derived and linear stability analysis is performed. A comparison has been made between the results obtained using the dispersion relation with the radially local approximation and those obtained using the radially global dispersion relation. This comparison revealed the non-applicability of the local solution to MISTRAL-like plasma systems. Due to the high fraction of neutrals in the present plasma system, the model is further extended to include the effects due to ion-neutral collisions. In this first step, the ion-neutral collision frequency is assumed to be small as compared to the ion-cyclotron frequency. The dispersion relation is then solved with finite ion-neutral collisionality and the linear stability analysis is conducted.
In magnetic confinement fusion plasmas, many instabilities have a flute mode character. The field-aligned coordinates bring the benefit of efficient resolution of parallel mode structure along the magnetic field direction. However, the curvilinear coordinates make equations and codes more complex especially in high order PDE.
The Compile-time Symbolic Solver (CSS) is developed to solve PDEs and ODEs in finite difference method from vector equations directly. CSS is a general-purpose finite difference framework for generating finite difference codes easily and greatly reducing the risk of implementation mistakes.
For physics model, CSS supports arbitrary equations in arbitrary curvilinear coordinates and multiple boundaries for both PDEs and ODEs. For memory distribution, N-dimension distribution grids with hybrid TBB and MPI parallelization in arbitrary dimensions are implemented. For numerical method, CSS employs Method of Line in numerical difference with arbitrary grid points and offset. The N-dimension B-spline is implemented with arbitrary orders for pushing particles. CSS employs PARDISO to solve matrix problem and Runge–Kutta method for time advance. CSS is a C++20 template metaprogramming code which guarantee zero-overhead at runtime. Furthermore, the instruction optimization makes the codes generated by CSS much faster than usual codes.
We have used CSS to generate the Gyrokinetic-MHD Hybrid Code GMEC, 3D Field and the Particle calculation code FP3D and a fluid ITG code. For GMEC, we propose a new shifted metric method which is able to stabilize numerical instabilities and avoid the interpolation from MHD field-align grids to particle flux coordinate grids at the same time. The equilibriums can be analytical ones or numerical ones calculated by VMEC or DESC. We have used GMEC to simulate ballooning modes (IBM) with or without the diamagnetic drift term and tearing modes. The simulation results agree well with those of the eigenvalue code MAS. The n=20 IBM costs only 17 seconds using 448 cores. We have also used GMEC to simulate energetic particle-driven TAEs in a circular equilibrium and a CFETR equilibrium. The results of an n=3 TAE agree well with those of M3D-K code.
We have also used CSS to generate the test particle code FP3D for calculation of magnetic surfaces, rotation transform, particle orbits and neoclassical transport in both tokamaks and stellarators. We have used FP3D to simulate ripple losses in EAST tokamak and neoclassical transport coefficient in NCSX. The results are consistent with previous results. FP3D has been used in design and optimization of stellarators successfully.
[1] P. Y. Jiang, et al. CSS: Compile-time symbolic solver for finite difference method. To be submitted.
[2] P. Y. Jiang, et al. GMEC: Gyrokinetic-MHD Hybrid Code. To be submitted. [3] P. Y. Jiang, Z. C. Feng, G. D. Yu, and G. Y. Fu, FP3D: A code for calculating 3D magnetic field and particle motion. Submitted to POP.Accurately predicting lower hybrid current drive (LHCD) in the weak-damping regime is an outstanding challenge, which suggests important physics is missing in present-day ray-tracing/Fokker-Planck (RTFP) models. In this work, the impact of filamentary scrape-off layer (SOL) turbulence on LH waves is investigated using a new multi-scale scattering model. When coupled to an RTFP code, the resulting simulations of LHCD in Alcator C-Mod show RF power deposition profiles robustly peaked on-axis, leading to good agreement with experimental Motional Stark Effect and hard X-ray measurements. Therefore, it is shown that the rotation of the perpendicular wave-vector due to SOL turbulence is sufficient to bridge the discrepancy between simulation and experiment. Notably, this model predicts an asymmetric broadening of the transmitted wave-spectrum, which is attributed to full-wave scattering effects in the presence of spatially coherent turbulence. This asymmetry leads to rotation of incident power away from the plasma core when SOL densities are sufficiently high. RTFP modeling shows this effect plays a significant role in the anomalous drop in LHCD efficiency observed at high densities.
The multi-scale scattering model has two steps. (1) Single filament-wave interactions are solved in full-wave formalism using a Mie-scattering technique. (2) Multiple of these filament-wave interactions are modeled using the radiative transfer approximation, in which a photon’s scattering probability depends on the statistical properties of the filament population. The radiative transfer equation (RTE) is then solved using a Monte Carlo scattering term in a ray-tracing model, allowing for self-consistent coupling to RTFP codes. For verification and comparison against other models, the RTE is also solved in a simple slab geometry using a Markov chain. This model shows good agreement with ray-tracing in the Wentzel-Kramer-Brillouin (WKB) limit, and predicts greater, asymmetric scattering beyond the WKB limit. Good agreement is also found with numeric full-wave solutions at sufficiently low filament packing-fraction, which is consistent with the validity limit of the radiative transfer approximation.
It should be emphasized that this multi-scale scattering model retains many important full-wave effects while remaining computationally inexpensive, allowing fast parameter scans and inter-shot analysis. In addition, this model is highly applicable to the modeling of electron cyclotron wave scattering since the radiative transfer approximation is increasingly valid for waves at higher k.
B. Biswas et al., “Spectral broadening from turbulence in multiscale lower hybrid current drive simulations,” Nuclear Fusion, 63, 1 (2022).
B. Biswas et al., “A hybrid full-wave Markov chain approach to calculating radio-frequency wave scattering from scrape-off layer filaments,” Journal of Plasma Physics, 87, 5 (2021).
This is joint work with M. O'Neil, L. Greengard, and L.-M. Imbert-Gerard
Since the work of Sauter in 1931 it is known that quantum electrodynamics (QED) exhibits a so-called "critical" electromagnetic field scale, at which the quantum interaction between photons and macroscopic electromagnetic fields becomes nonlinear. One prominent example is the importance of light-light interactions in vacuum at this scale, which violates the superposition principle of classical electrodynamics. Furthermore, an electromagnetic field becomes unstable in this regime, as electron-positron pairs can be spontaneously created from the vacuum at the expenses of electromagnetic-field energy (Schwinger mechanism). Unfortunately, the QED critical field scale is so high that experimental investigations are challenging. One promising pathway to explore QED in the nonlinear domain with existing technology consists in the combination of modern (multi) petawatt optical laser systems with highly energetic particles. The suitability of this approach was first demonstrated in the mid-1990s at the seminal SLAC E-144 experiment. Since then, laser technology continuously developed, implying the dawn of a new era of strong-field QED experiments. For instance, the basic processes nonlinear Compton scattering and Breit-Wheeler pair production are expected to influence laser-matter interactions and in particular plasma physics at soon available laser intensities. Therefore, a considerable effort is being undertaken to include these processes into particle-in-cell (PIC) codes used for numerical simulations.
In the first part of the talk the most prominent nonlinear QED phenomena are presented and discussed on a qualitative level. Afterwards, the mathematical formalism needed for calculations with strong plane-wave background fields is introduced with an emphasize on fundamental concepts. Finally, the nonlinear Breit-Wheeler process is considered more in depth. In particular, the semiclassical approximation is elaborated, which serves as a starting point for the implementation of quantum processes into PIC codes.