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At least 397 records · Page 22

Possible mitigation of tokamak plasma–surface interactions using thermionic divertor plates with inverse sheaths

Recent studies demonstrate that when a plasma-facing surface emits a sufficient flux of electrons, it will form an inverse sheath. In this work, we consider a possibility of using thermionic target plates with inverse sheaths as an innovative divertor operating scenario. We derive an electron heat flux boundary condition for inverse sheaths and show that for given power exhaust into a tokamak scrape-off-layer, an inverse sheath leads to a much lower target plasma electron temperature than a conventional sheath. Low enough target plasma temperatures for radiative divertor detachment could therefore be achieved using inverse sheaths instead of the usual need to inject neutral atoms that compromise the core plasma. Other advantages of inverse sheath detachment over conventional sheath operating scenarios include (a) ion impact energies are as low as possible, minimizing sputtering and tritium implantation, (b) surface recombination heat flux is reduced due to ion flux reduction, and (c) arcs are inhibited due to the sign of the surface electric field. This paper outlines the basic properties of inverse sheath detachment and considers the feasibility of implementation. We offer recommendations for future modeling efforts needed to better understand the effects of thermionic emission in tokamaks and whether inverse sheaths present a viable divertor solution.

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Center for Tokamak Transients Simulations

The major goals for the Center for Tokamak Transients Simulations (CTTS) were to develop detailed numerical simulations of disruptive transients in tokamak experiments and to use them in theoretical studies of the thermal-quench (TQ) and current-quench (CQ) phases of disruption. The University of Wisconsin-Madison component of CTTS contributed relevant development for the NIMROD code (https://nimrodteam.org) and applied it to disruptions that involve global vertical displacement. Code-development contributions include boundary conditions that represent sheath effects which occur when tokamak plasma is in contact with the surrounding vessel wall during vertical displacement events (VDEs). We also implemented a reduced model of energetic runaway electrons (REs) to simulate the effect of these energetic electrons on the CQ phase of tokamak disruptions. Our computations of VDEs include 2D and 3D verification through benchmarks with two other widely used macroscale plasma simulation codes, M3D-C1 and JOREK. Over nonlinear evolution to the final termination of plasma current, the 2D simulation results on magnetic axis location, toroidal current, and halo current track each other well. With the 3D benchmark computation, all three codes found the same qualitative behavior of the asymmetric instabilities having increasing growth rate after contact with the wall, followed by nonlinear excitation of other toroidal harmonics. Our NIMROD computations for an idealized configuration show agreement with an analytical assessment by V. D. Pustovitov [Nucl. Fusion 55, 113032 (2015)] that the plasma and non-ideal wall remain in force-balance such that net forces only result from magnetic stresses over the outer surface of the wall. Our study of the influence of boundary conditions on VDEs shows that extended-MHD simulations of VDEs are sensitive to electron energy transport to the wall and that boundary conditions on flow are only significant to the extent that they influence the electron energy transport. Resistive-MHD NIMROD simulations of the tokamak discharges in the Madison Symmetric Torus show that magnetic perturbations of poloidal wavenumber m=3 lead to chaotic magnetic topology over the edge region, which helps deconfine energetic electrons. A second area of RE study shows that the coupled resistive MHD/reduced RE model reproduces the resistive-hose particle-beam instability. With respect to educational opportunities, this effort involved and supported four graduate students at the University of Wisconsin-Madison and one postdoctoral associate. The results of this study have been disseminated through journal publications, conference presentations, technical reports, and PhD dissertations.

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Comparing particle transport in JET and DIII-D plasmas: gyrokinetic and gyrofluid modelling

The paper models the impact of fueling versus particle transport in the DIII-D and JET tokamaks. Experimentally, it was found that in JET an increase in the density peaking at lower collisionality could be attributed to an increase in core fueling, however on DIII-D, the opposite was observed. In DIII-D, the increase in density peaking was the result of an increase in inward transport, not an increase in core fueling. The paper shows that the difference in temperature gradients and thus turbulence dynamics between the two experiments can explain the experimentally observed discrepancy.

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Boundary, SOL, and Divertor Physics Studies on TCV (Final Report for Research Funded by DoE Award DE-SC0020327)

Research supported under this grant was organized around two diagnostic systems installed on the TCV tokamak located at EPFL in Lausanne, Switzerland: Multi-Spectral Imaging (MSI) and Gas-Puff Imaging (GPI). MSI monitors 2-d time-history images of up to 10 spectral lines, in the visible, using identical views for all wavelengths. The primary application of MSI is to infer 2-d time histories of electron temperature and density in the Scrape-Off-Layer (SOL) of diverted plasmas, utilizing ratios of emission from multiple neutral helium lines. The atomic models are validated against 1-d Thomson scattering measurements. SOL density and temperature maps are analyzed to infer divertor dynamics, including particle and power flows, for a variety of divertor configurations, and specifically as flux expansion along the long-legged outboard divertor is systematically varied. GPI is used to measure details of edge fluctuations in the SOL, particularly as a function of plasma triangularity (δ), including both positive and negative δ. A threshold is found, whereby for δ<-0.3, edge turbulence in the far SOL is completely suppressed. Dynamics of the filamentary turbulence was also analyzed using advance machine learning techniques. Research in support of four PhD theses was carried out within the scope of this Award, including 2 at MIT and 2 at EPFL.

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Detailed characterization of runaway electron driven whistler waves in low-density DIII-D discharges

RE-driven whistler waves during quiescent DIII-D shots have been investigated further. The waves are confirmed to be mostly perpendicularly propagating and are observed for the first time with frequencies up to 700 MHz. Phase-spectral analysis has been used to infer their toroidal mode numbers, n, which are expected to scale with the wavenumber, k, of the mode. Though we derive a theoretical scaling of k ≈ 4n, the measured mode numbers are found to exhibit a very weak dependence on k. In addition, increases in synchrotron emission have been found to consistently lag whistler wave bursts by roughly 3–5 ms, suggesting the waves are causing pitch-angle scattering, since the emitted synchrotron radiation is a strong function of the REs' perpendicular energy. The stronger the wave bursts, the greater the subsequent increase in synchrotron emission. A predator-prey model is used to describe these nonlinear wave-particle interactions, from which the wave damping rates and the loss parameter can be inferred. The damping rates are found to be of the order of (1.6 ± 0.8) × 10 4 /s, and the unitless loss parameter is found to be approximately 2, suggesting that the loss mechanism is diffusive. These observations will serve to validate models of RE-driven waves in tokamak plasmas.

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Directional finite difference method for directly solving 3D gyrokinetic field equations with enhanced accuracy

The gyrokinetic (GK) field equation is a three-dimensional (3D) elliptic equation, but it is often simplified to a set of two-dimensional (2D) equations by assuming that the field does not vary along a specific direction. However, this simplification can introduce inevitable 0th-order numerical errors, as nonlinear mode coupling in toroidal geometry can produce undesirable harmonic modes that violate the assumption. In this work, we propose a novel directional finite difference method (FDM) with a local coordinate transformation to better resolve the target field of interest. The directional FDM can accurately solve 3D GK field equations without simplifications, which can overcome the limitations of conventional methods. The accuracy and efficiency of different FDMs are analyzed in great detail for a variety of geometries, from simple 2D Cartesian coordinates to realistic 3D curvilinear coordinates. The 0th-order numerical errors of simplified 2D GK equations were found to be more problematic for low-harmonic modes and low aspect ratio geometries such as spherical tokamaks. On the other hand, the directional 3D FDM can accurately resolve a much wider range of harmonic modes aligned to the direction of interest, including the low-harmonic modes. In conclusion, we demonstrate that the directional 3D FDM is a highly effective algorithm for solving the 3D GK field equations, achieving accuracy improvements of 10 to 100 times or more, particularly for low-harmonic modes in spherical tokamaks.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Lyapunov-based nonlinear control of nonautonomous systems with individual input constraints

A control algorithm that can locally stabilize a specific class of multi-input multi-output nonautonomous nonlinear dynamical systems while satisfying individual input constraints is developed. The proposed Lyapunov-based state-feedback control law inherently accounts for the actuator amplitude saturation limits without the need for computationally expensive real-time optimization techniques. In addition to the control law, a formal definition for the local “controllable region” within which the controller can asymptotically drive the system states to the origin and satisfy the input saturation limits is also presented. The nonautonomous nature of the system dynamics implies that the “controllable region” continuously evolves with time. Therefore, a sufficient condition to maintain the system states within the “controllable region” is proposed in this work to make practical implementation feasible. The effectiveness of the controller is tested for a specific control problem arising in tokamaks, which are toroidal devices that use strong magnetic fields to confine a plasma (hot ionized gas). Here, the primary emphasis of tokamak research is to regulate the plasma properties around predetermined values to achieve stable plasma confinement. Nonlinear simulations show that the proposed controller can achieve the desired plasma control objectives in a DIII-D tokamak scenario.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Doubling off-axis electron cyclotron current drive efficiency via velocity space engineering

For the first time, experiments on the DIII-D tokamak have demonstrated electron cyclotron current drive with more than double the conventional efficiency by tailoring the wave–particle interactions in velocity space using a novel ‘top launch’ geometry. Steering the EC waves to propagate nearly parallel to the resonance drives current more efficiently by (1) selective damping on electrons with higher parallel velocity v ||, and (2) longer absorption path to compensate for inherently weaker absorption at higher v ||. Experiments using a fixed-injection top launch system find an optimal velocity space interaction for maximum current drive efficiency at ρ ~ 0.5 where the ease of drawing out a high v || electron tail is balanced by sufficient absorption.

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Integrated modeling of boron powder injection for real-time plasma-facing component conditioning

An integrated modeling framework for investigating the application of solid boron (B) powder injection for real-time surface conditioning of plasma-facing components (PFCs) in tokamak environments is presented. Utilizing the DIII-D impurity powder dropper (IPD) setup, this study simulates B powder injection scenarios ranging from milligrams to tens of milligrams per second, corresponding to boron flux rates of 10 20 –10 21 B/s in standard L-mode conditions. The comprehensive modeling approach combines EMC3-EIRENE for simulating the deuterium plasma background and the Dust Injection Simulator (DIS) for the ablation and transport of the boron powder particles. EMC3 trace impurity fluid modeling results show substantial boron transport to the inboard lower divertor, predominantly influenced by the main ion plasma flow. The dependency on powder particle size (5-250 µm) was found to be insignificant for the scenario considered. The effects of erosion and redeposition were considered to reconcile the discrepancies with experimental observations, which saw substantial deposition on the outer divertor plasma-facing components. For this purpose, the WallDYN3D code was updated to include boron sources within the plasma domain and integrated into the modeling framework. The mixed-material migration modeling shows evolving boron deposition patterns, suggesting the formation of mixed B-C layers or predominantly B coverage depending on the powder mass flow rate. While the modeling outcomes at lower B injection rates tend to align with DIII-D experimental observations, the prediction of near-pure boron layers at higher rates has yet to be experimentally verified in the carbon environment of the DIII-D tokamak. The extensive reach of boron layers found in the modeling suggests the need for modeling that encompasses the entire wall geometry for more accurate experimental correlations. This integrated approach sets a precedent for analyzing and applying real-time in-situ boron coating techniques in advanced tokamak scenarios, potentially extendable to ITER.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Exploration of the parameter space of quasisymmetric stellarator vacuum fields through adjoint optimisation

Optimising stellarators for quasisymmetry leads to strongly reduced collisional transport and energetic particle losses compared with unoptimised configurations. Although stellarators with precise quasisymmetry have been obtained in the past, it remains unclear how broad the parameter space is where good quasisymmetry may be achieved. We study the range of aspect ratios and rotational transform values for which stellarators with excellent quasisymmetry on the boundary can be obtained. A large number of Fourier harmonics is included in the boundary representation, which is made computationally tractable by the use of adjoint methods to enable fast gradient-based optimisation and by the direct optimisation of vacuum magnetic fields, which converge more robustly compared with solutions from magnetohydrostatics. Several novel configurations are presented, including stellarators with record levels of quasisymmetry on a surface, three field period quasiaxisymmetric stellarators with substantial magnetic shear, and compact quasisymmetric stellarators at low aspect ratios similar to tokamaks.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Numerical Simulation of Irradiation Induced Swelling for STAR 4.1 Blanket

Here, this article presents the preliminary results of FEM implementation of irradiation-induced swelling, hardening, and creep effect using ANSYS user programmable features (UPFs) applied to material properties. The first liquid metal breeding blanket model for STAR 4.1 tokamak as a part of the virtual prototyping system is under development at Princeton Plasma Physics Laboratory (PPPL). Intense neutron irradiation produces significant changes in the physical and mechanical properties of Fe-(8%–9%)Cr-based reduced activation ferritic martensitic (RAFM) steels. An ANSYS model of the breeding blanket was built to involve these irradiation-induced material property changes with neutron fluence distribution mapped from the MCNP model. Simulation results show that significant structure deformation forms from nuclear swelling, stress, and plastic strain arising from DPA gradient through wall thickness. The material degradation effect is not negligible. This modeling feature can either assist in analyzing the structural behaviors with the influence of nuclear swelling or provide guidance to design the structure to withstand irradiation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Modeling of resistive plasma response in toroidal geometry using an asymptotic matching approach

The method of solving linear resistive plasma response, based on the asymptotic matching approach, is developed for full toroidal tokamaks by upgrading the Resistive DCON code [A.H. Glasser, Z.R. Wang and J.-K. Park, Physics of Plasmas, \textbf{23}, 112506 (2016)]. The derived matching matrix, asymptotically matching the outer and inner regions, indicates that the applied three dimension (3-D) magnetic perturbations contribute additional small solutions at each resonant surface due to the toroidal coupling of poloidal modes. In contrast, the resonant harmonic only affects the corresponding resonant surface in the cylindrical plasma. Since the solution of ideal outer region is critical to the asymptotic matching and is challenging to be solved in the toroidal geometry due to the singular power series solution at the resonant surfaces, systematic verification of the outer region $\Delta^\prime$ matrix is made by reproducing the well known analytical $\Delta^{\prime}$ result in [H.P. Furth, P.H. Rutherford and H. Selberg, The Physics of Fluids, \textbf{16}, 1054-1063 (1073)] as well as by making a quantitative benchmark with the PEST3 code [A. Pletzer and R.L. Dewar, J. Plasma Physics, \textbf{45}, 427-451 (1991)]. Finally, the reconstructed numerical solution of resistive plasma response from the toroidal matching matrix is presented. Comparing with the ideal plasma response, the global structure of the response can be affected by the small finite island at the resonant surfaces.

MHD simulation↗

High Field Side Launch of RF Waves: A New Approach to Reactor Actuators

Launching radio frequency (RF) waves from the high field side (HFS) of a tokamak offers significant advantages over low field side (LFS) launch with respect to both wave physics and plasma material interactions (PMI). For lower hybrid (LH) waves, the higher magnetic field opens the window between wave accessibility and the condition for strong electron Landau damping, allowing LH waves from the HFS to penetrate into the core of a burning plasma, while waves launched from the LFS are restricted to the periphery of the plasma. The lower of waves absorbed at higher yields a higher current drive efficiency as well. In the ion cyclotron range of frequencies (ICRF), HFS launch allows for direct access to the mode conversion layer where mode converted waves absorb strongly on thermal electrons and ions, thus avoiding the generation of energetic minority ion tails. The absence of turbulent heat and particle fluxes on the HFS, particularly in double null configuration, makes it the ideal location to minimize PMI damage to the antenna structure. The quiescent SOL also eliminates the need to couple LH waves across a long distance to the separatrix, as the antenna can be located close to plasma without risking damage to the structure. Improved impurity screening on the HFS will help eliminate the long-standing issues of high Z impurity accumulation with ICRF.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

High Field Side Launch of Lower Hybrid Waves: A Scoping Study for ADX

Launching lower hybrid (LH) waves from the high field side (HFS) of a tokamak offers significant advantages over low field side (LFS) launch with respect to both wave physics and plasma material interactions (PMI). The higher magnetic field opens the window between wave accessibility and the condition for strong electron Landau damping, allowing LH waves from the HFS to penetrate into the core of a burning plasma, while waves launched from the LFS are restricted to the periphery of the plasma. The lower parallel refractive index (n) of waves launched from the HFS yields a higher current drive efficiency as well. The absence of turbulent heat and particle fluxes on the HFS, particularly in double null configuration, makes it the ideal location to minimize PMI damage to the antenna structure. The quiescent SOL also eliminates the need to couple LH waves across a long distance to the separatrix, as the antenna can be located close to plasma without risking damage to the structure.

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Nonlinear, real-time optimization for actuator management in tokamaks

Experiments in DIII-D have been carried out to test a novel actuator management approach in tokamaks. Here, the actuator management scheme is posed as a nonlinear-optimization problem in which the actuator commands are calculated in real time according to the changing control priorities, plasma state, and actuator availability. Such optimization problem is solved using the augmented Lagrangian method, combined with a gradient projection method and a conjugate-gradient iteration algorithm. The algorithmic approach followed in this work does not depend on the particular control objectives or actuators considered, which facilitates its integration with other independently-designed control components within a plasma-control system. In addition, the actuator-management algorithm is able to handle the optimization problem in a computationally efficient manner, making it suitable for real-time implementations. Initial DIII-D results in the steady-state high-q min scenario have demonstrated the capabilities of the actuator manager to perform both simultaneous multiple mission and repurposing sharing, which will be required in ITER.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Computational analysis of ion orbital loss in diverted positive- and negative-triangularity tokamaks

The mechanism of ion orbital loss in diverted negative-triangularity (NT) tokamaks is significantly different from that of positive-triangularity (PT) tokamaks. The orbital loss from the edge of NT tokamaks can be quite large, because the separatrix X-point is located on the outboard side, meaning that trapped ions crossing the separatrix are lost to the inboard divertor plate after a mirror reflection on the side of the strong magnetic field. NT tokamaks have difficulties in building up steep pressure gradients in the edge regions. However, the majority of trapped ions crossing the separatrix in PT tokamaks survive (through complete banana motions) without reaching the X-point region. For NT tokamaks, topological changes in the trapped ion trajectories can be achieved in the presence of the radial electric field, thus reducing the orbital loss, whereas for PT tokamaks, the orbital loss is relatively insensitive to the radial electric field.

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