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We present a fast and accurate data-driven surrogate model for divertor plasma detachment prediction leveraging the latent feature space concept in machine learning research. Our approach involves constructing and training two neural networks. An autoencoder that finds a proper latent space representation (LSR) of plasma state by compressing the multi-modal diagnostic measurements, and a forward model using multi-layer perception (MLP) that projects a set of plasma control parameters to its corresponding LSR. By combining the forward model and the decoder network from autoencoder, this new data-driven surrogate model is able to predict a consistent set of diagnostic measurements based on a few plasma control parameters. In order to ensure that the crucial detachment physics is correctly captured, highly efficient 1D UEDGE model is used to generate training and validation data in this study. Benchmark between the data-driven surrogate model and UEDGE simulations shows that our surrogate model is capable to provide accurate detachment prediction (usually within a few percent relative error margin) but with at least four orders of magnitude speed-up, indicating that performance-wise, it has the potential to facilitate integrated tokamak design and plasma control. Comparing to the widely used two-point model and/or two-point model formatting, the new data-driven model features additional detachment front prediction and can be easily extended to incorporate richer physics. This study demonstrates that the complicated divertor and scrape-off-layer plasma state has a low-dimensional representation in latent space. Understanding plasma dynamics in latent space and utilizing this knowledge could open a new path for plasma control in magnetic fusion energy research., Comment: 24 pages, 15 figures

The Fusion Energy System Studies (FESS) Fusion Nuclear Science Facility (FNSF) project team in the United States is examining the use of liquid metals (LMs) for plasma-facing components (PFCs). Our...

The steady state radial electric field (Er) is calculated by coupling a plasma transport model with the quasi-neutrality constraint and the vorticity equation within the BOUT++ framework. Based on the experimentally measured plasma density and temperature profiles in Alcator C-Mod discharges, the effective radial particle and heat diffusivities are inferred from the set of plasma transport equations. The effective diffusivities are then extended into the scrape-off layer (SOL) to calculate the plasma density, temperature and flow profiles across the separatrix into the SOL with the electrostatic sheath boundary conditions (SBC) applied on the divertor plates. Given these diffusivities, the electric field can be calculated self-consistently across the separatrix from the vorticity equation with SBC coupled to the plasma transport equations. The sheath boundary conditions act to generate a large and positive Er in the SOL, which is consistent with experimental measurements. The effect of magnetic particle drifts is shown to play a significant role on local particle transport and Er by inducing a net particle flow in both the edge and SOL regions.

A modeling study is reported using new 2D data from DIII-D tokamak divertor plasmas and improved 2D transport model that includes large cross-field drifts for the numerically difficult low anomalous transport regime associated with the H-mode. The data set, which spans a range of plasma densities for both forward and reverse toroidal magnetic field (Bt), is provided by divertor Thomson scattering (DTS). Measurements utilizing X-point sweeping give corresponding 2D profiles of electron temperature (Te) and density (ne) across both divertor legs for individual discharges. The simulations focus on the open magnetic field-line regions, though they also include a small region of closed field lines. The calculations show the same features of in/out divertor plasma asymmetries as measured in the experiment, with the normal Bt direction (ion ∇B drift toward the X-point) having higher ne and lower Te in the inner divertor leg than outer. Corresponding emission data for total radiated power shows a strong inner-divertor/outer-divertor asymmetry that is reproduced by the simulations. These 2D UEDGE transport simulations are enabled for steep-gradient H-mode conditions by newly implemented algorithms to control isolated grid-scale irregularities.

The preliminary conceptual design of the Korean fusion demonstration reactor (K-DEMO) with a major radius of 6.8 m and the fusion power of 2200 MW has been studied since 2012. The overall configuration of the K-DEMO divetor system based on the ITER-like water-cooled tungsten technology is a double-null type symmetric divertor subdivided into 32 toroidal modules for the vertical maintenance. A detached divertor scenario with impurity seeding was considered as the primary approach for the power exhaust to reduce the peak heat flux lower than the engineering limit of 10 MW/m2. The power exhaust performance at the scrap off layer was estimated by using UEDGE-2D code, a two-dimensional fluid transport code for collisional edge plasma and neutral species like N, Ne, and Ar. Particle and heat flux on inboard and outboard divertor targets were calculated for the detached cased depending on parameters such as the impurity seeding rate, pumping rate, and the pedestal density. On the other hand, a magnetic solution like X-divertor, snowflake divertor, and super X-divertor to expand the plasma wet area was considered for K-DEMO since the detached divertor increasing a radiation fraction by impurity seeding might be able to be unstable. However, the extremely high current of poloidal coils was required more than the engineering limit, 20 MA, to form magnetic field lines for the alternative divertors. Based on the physical calculation of the edge plasma, engineering analyses were carried out to find out the thermal and structural reliability. The thermo-hydraulic analysis confirmed thermal stability, whether all comprising materials are operating within their allowable temperature windows when the case of the peak heat flux is set to 10 MW/m2 on the outboard divertor target. The response surface optimization method derived two optimal design candidates employing two kinds of heat sink materials, respectively: the reduced activation ferritic martensitic (RAFM) steel and CuCrZr alloy. The drawbacks and merits of the two materials were definite. The optimal design with applying RAFM steel was vulnerable to withstand thermal and mechanical loads since low thermal conductivity caused too thin thickness of the heat sink. On the other hand, the CuCrZr alloy has critical drawbacks in terms of activation and radioactive waste despite its high thermal conductivity. Meanwhile, preliminary electromagnetic (EM) analysis was carried out to estimate the EM loads caused by the abnormal behaviors of plasma since EM loads are one of the most critical external loads for designing a DEMO divertor.

The Langmuir probe is a standard diagnostic tool for laboratory plasmas, routinely used for edge plasmas in magnetic fusion devices. However, recent studies on the Alcator C-Mod tokamak indicate the possibility of a substantial local plasma perturbation by a negatively biased divertor plate target probe under high recycling conditions when the electron temperature is under ∼10 eV. The effects of the probe perturbation of the plasma are studied using the tokamak edge plasma code UEDGE for parameters relevant to Alcator C-Mod edge. It is found that at sufficiently negative bias voltage, the probe substantially modifies the local plasma characteristics. In particular, this is relevant to the experimentally known “death-ray” phenomenon, where the plasma pressure near the probe strongly exceeds the upstream value. Certain features of the “death-ray” phenomenon are reproduced in the modeling, pointing to interplay of plasma and neutrals transport, atomic physics, and sheath heat-flux boundary conditions (© 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

The development of a new parallel framework for integrated modeling of tokamak plasmas is a primary objective of the SciDAC Framework Architecture for Core-Edge Transport Simulations (FACETS) project. The FACETS code will be used to predict the performance of tokamak discharges and to optimize tokamak discharge scenarios. Novel parallel numerical algorithms and solvers have been developed in the FACETS project in order to simulate the multi-scale dynamics of tokamak plasmas. The status of development of modules for anomalous transport in the FACETS code is described in this paper. Mechanisms that are used for coupling 1D anomalous transport in the plasma core together with 2D transport in the plasma edge (in near separatrix and scrape-off-layer regions) are considered. Results of the first verification studies based on predictive modeling of several analytical and experimental equilibria are presented.

Plasma fluxes to the divertor region in ITER near the magnetic separatrix have been modeled extensively in the past. The smaller, but potentially very important fluxes to the main chamber and outer divertor regions are the focus of the present paper. Two main additions to the usual transport modeling are investigated: namely, convective radial transport from intermittent, rapidly propagating ‘blob’ events, and inclusion of the magnetic flux-surface region beyond the second X-point that actually contacts the main-chamber wall. The two-dimensional fluid transport code UEDGE is use to model the plasma, while the energy spectrum of charge-exchange neutrals to the main chamber wall is calculated by the DEGAS 2 Monte Carlo code. Additionally, the spatial distribution of beryllium sputtered from the main chamber wall is determined in the fluid limit.

The mission of the National Spherical Torus Experiment (NSTX) is to extend the understanding of toroidal physics to low aspect ratio (R/a approximately equal to 1.25) in low collisionality regimes. NSTX is designed to operate with up to 6 MW of High Harmonic Fast Wave (HHFW) heating and current drive, 5 MW of Neutral Beam Injection (NBI) and Co-Axial Helicity Injection (CHI) for non-inductive startup. Initial experiments focused on establishing conditions that will allow NSTX to achieve its aims of simultaneous high-bt and high-bootstrap current fraction, and to develop methods for non-inductive operation, which will be necessary for Spherical Torus power plants. Ohmic discharges with plasma currents up to 1 MA and with a range of shapes and configurations were produced. Density limits in deuterium and helium reached 80% and 120% of the Greenwald limit respectively. Significant electron heating was observed with up to 2.3 MW of HHFW. Up to 270 kA of toroidal current for up to 200 msec was produced noninductively using CHI. Initial NBI experiments were carried out with up to two beam sources (3.2 MW). Plasmas with stored energies of up to 140 kJ and bt =21% were produced.

Benchmarks of DEGAS 2 against EIRENE yield agreement to within 5% and comparable single processor run times. DEGAS 2 demonstrates a nearly linear increase in processing speed with the number of parallel processors. That speed is put to practical use here in the first runs of UEDGE coupled to DEGAS 2. The results of the coupled codes match those of coupled UEDGE and EIRENE. Additional algorithmic improvements such as use of the correlated sampling technique promise to make runs of the coupled UEDGE - DEGAS 2 codes practical for everyday use.

Experimental observations show that when a divertor plasma detaches, radiation regions (fronts) move towards the X-point. This indicates that the localization of the fronts in the divertor is unstable. We study theoretically the stability of detached divertor operation and compare our results with experimental data. We show that the impurity radiation and plasma recombination effects play a crucial role in the evolution of detached plasma parameters. In the tokamak SOL these effects result in the saturation of upstream plasma density and temperature as the total number of particles (ions and neutrals) in the SOL is increased, and cause both impurity radiation and ionization–recombination fronts propagation towards the X-point. These conclusions are supported by experimental data from Alcator C-Mod.

In inductive plasma sources, the rapid spatial decay of the electric field arising from the skin effect produces a large radio frequency (RF) magnetic field via Faraday’s law. It was previously shown that this magnetic field leads to a reduction of the electron density in the skin region, as well as a reduction in the collisionless heating rate. The electron deficit leads to the formation of an electrostatic potential which pulls electrons in to restore quasineutrality. Here the electron density calculation is extended to include both the induced and electrostatic fields. If the wave frequency is not too low, the ions respond only to the averaged fields, and hence the electrostatic field is oscillatory, predominantly at the second harmonic of the applied field. The potential required to establish a constant electron density is calculated and compared with numerical orbit‐code calculations. For times short compared to ion transit times, the quasineutral density is just the initial ion density. For timescal...

The coupled core-edge nonlinear transport code CORSICA 2 is introduced and the structure of its iterative coupling algorithm is briefly discussed. Selected application results are reported that reproduce equilibria in DIII-D discharges with plasma profiles initialized from the experimental data. Simulations for an L-H transition and for a gas puffing experiment in DIII-D plasmas are presented.

In this paper we discuss the present divertor design for the planned TPX tokamak, which will explore the physics and technology of steady-state (1000s pulses) heat and particle removal in high confinement (2--4{times} L-mode), high beta ({beta}{sub N} {ge} 3) divertor plasmas sustained by non-inductive current drive. The TPX device will operate in the double-null divertor configuration, with actively cooled graphite targets forming a deep (0.5 m) slot at the outer strike point. The peak heat flux on, the highly tilted (74{degrees} from normal) re-entrant (to recycle ions back toward the separatrix) will be in the range of 4--6 MW/m{sup 2} with 18 MW of neutral beams and RF heating power. The combination of active pumping and gas puffing (deuterium plus impurities), along with higher heating power (45 MW maximum) will allow testing of radiative divertor concepts at ITER-like power densities.

The features of the fully implicit 2-D fluid code UEDGE are described. The utility of the code is demonstrated by showing bifurcations or multiple solutions of the tokamak edge plasma for both deuterium and impurity injection in the divertor.

We address the problem of calculating the parallel electron heat conduction in a tokamak scrape off layer with non-negligible mean free path. We develop a model distribution function based on pieces of Fokker-Planck solutions, containing: a local Maxwellian at low energies, a modified Spitzer-Harm distribution at energies below where the mean free path equals the distance to the nearest wall, a bounce-averaged distribution at higher energies up to the confining potential energy, a filled-in outgoing loss-cone distribution at still higher energies, and finally an empty loss region at energies such that the mean free path exceeds the length of the field line. The model is compared with Monte Carlo simulations.

Gradients along the magnetic field of the parallel index of refraction N∥ or the magnetic‐field strength B can substantially alter the dynamics of electrons subjected to intense, pulsed electron‐cyclotron waves. Electrons trapped in a phase‐space island, or ‘‘bucket,’’ about a cyclotron resonance tend to remain trapped and be accelerated with the bucket as N∥ and B change. The process can result in a substantial increase in the opacity (with the optical thickness possibly exceeding the linear value) and an improvement in the efficiency with which current can be driven in a tokamak. In this paper, a semiquantitative theory for the absorption and current‐drive efficiency is developed and compared with numerical calculations from a multiparticle orbit code. Applications to heating and current drive in present and future tokamaks are discussed.

The introduction of a powerful new microwave source, the free-electron laser, provides new opportunities for novel heating and current-drive schemes to be used in toroidal fusion devices. This high-power, pulsed source has a number of technical advantages for these applications, and its use is predicted to lead to improved current-drive efficiencies and opacities in reactor-grade fusion plasmas in specific cases. The Microwave Tokamak Experiment at the Lawrence Livermore National Laboratory will provide a test for some of these new heating and current-drive schemes. Although the motivation for much of this research has derived from the application of a free-electron laser to the heating of a tokamak plasma at a frequency near the electron cyclotron frequency, the underlying physics, i.e., the highly nonlinear interaction of an intense, pulsed, coherent electromagnetic wave with an electron in a magnetized plasma including relativistic effects, is of general interest. Other relevant applications include ionospheric modification by radio-frequency waves, high-energy electron accelerators, and the propagation of intense, pulsed electromagnetic waves in space and astrophysical plasmas. This review reports recent theoretical progress in the analysis and computer simulation of the absorption and current drive produced by intense pulses, and of the possible complications that may arise, e.g., parametric instabilities, nonlinear self-focusing, trapped-particle sideband instability, and instabilities of the heated plasma.

Operational details are given for the two-dimensional UEDGE edge-plasma transport code. The model applies to nearly fully-ionized plasmas in a strong magnetic field. Equations are solved for the plasma density, velocity along the magnetic field, electron temperature, ion temperature, and electrostatic potential. In addition, fluid models of neutrals species are included or the option to couple to a Monte Carlo code description of the neutrals. Multi-species ion mixtures can be simulated. The physical equations are discretized by a finite-difference procedure, and the resulting system of algebraic equations are solved by fully-implicit techniques. The code can be used to follow time-dependent solutions or to find steady-state solutions by direct iteration.

A critical requirement for tokamak fusion reactors is the control of the divertor heat load, both the time-averaged value and the impulsive fluxes that accompany edge-localized modes. We propose driving toroidally varying currents through the scrape-off layer (SOL) plasma both to broaden the SOL by inducing radial convection and to control the edge pressure gradient by inducing resonant magnetic perturbations. The generation of additional convective transport via steady-state convective cells or increased turbulence drive requires that the electric potential perturbations exceed a threshold in amplitude that depends on wavelength. The generation of a coherent magnetic perturbation is optimized by choosing the appropriate width and phasing of the biasing region at the target plate in order to optimize the profile of the SOL current. Longer wavelength modes produce a larger effect because they are not sheared as strongly by the magnetic X-point. Generation of the necessary currents is challenging due to the possibly substantial power requirements and the possible need for internal insulators. We analyze passive current-drive mechanisms that rely on puffing and pumping of neutral gas in a toroidally asymmetric fashion using the UEDGE code to model the ITER divertor.

Two‐fluid theory is used to calculate the nonlinear effect of a finite‐amplitude ion‐cyclotron wave on the simple interchange stability of a magnetically confined plasma. The ion‐cyclotron wave nonlinearly modifies interchange stability through ponderomotive effects and coupling to sidebands of the ion‐cyclotron wave. Nonlinear stability criteria for flute modes are derived. The nonuniformity and polarization of the ion‐cyclotron wave significantly influence the results. A theoretical explanation for recent experimental observations in axisymmetric mirror and tandem mirror plasmas of reduced levels of magnetohydrodynamic activity in the presence of ion‐cyclotron resonant heating remains elusive.

Providing lower‐hybrid power in short, intense (GW) pulses allows enhanced wave penetration in reactor‐grade plasmas. We examine nonlinear absorption, ray propagation, and parametric instability of the intense pulses. We find that simultaneously achieving good penetration while avoiding parametric instabilities is possible, but imposes restrictions on the peak power density, pulse duration, and/or r.f. spot shape. In particular, power launched in narrow strips, elongated along the field direction, is desired.

Modified guiding‐center equations are derived for particles experiencing a small‐amplitude electromagnetic wave of arbitrary polarization. The resulting differential equations contain the first‐order wave amplitude explicitly and are relativistically correct. A simple characteristic equation is obtained for the particle trajectory in energy and magnetic‐moment phase space for cases where the Doppler frequency shift for drifts perpendicular to the magnetic field is negligible. Two examples are given to illustrate the behavior of particle trajectories in momentum space.