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At least 235 records · Page 13

Overview of design and analysis activities for the W7-X scraper element

The Wendelstein 7-X stellarator is in final stages of commissioning, and will begin operation in late 2015. In the first phase, the machine will operate with a limiter, and will be restricted to low power and short pulse. But in 2019, plans are for an actively cooled divertor to be installed, and the machine will operate in steady state at full power. Recently, plasma simulations have indicated that, in this final operational phase, a bootstrap current will evolve in certain scenarios. This will cause the sensitive ends of the divertor target to be overloaded beyond their qualified limit. A high heat flux scraper element (HHF-SE) has been proposed in order to take up some of the convective flux and reduce the load on the divertor. In order to examine whether the HHF-SE will be able to effectively reduce the plasma flux in the divertor region of concern, and to determine how the pumping effectiveness will be affected by such a component, it is planned to include a test divertor unit scraper element (TDU-SE) in 2017 during an earlier operational phase. Several U.S. fusion energy science laboratories have been involved in the design, analysis (structural and thermal finite element, as well as computational fluid dynamics), plasma simulation, planning, prototyping, and diagnostic development around the scraper element program (both TDU-SE and HHF-SE). As a result, this paper presents an overview of all of these activities and their current status.

42 ENGINEERING↗

The interaction of the ITER first wall with magnetic perturbations

Mitigation of the multiple risks associated with disruptions and runaway electrons in tokamaks involves competing demands. Success requires that each risk be understood sufficiently that appropriate compromises can be made. Here the focus is on the interaction of short timescale magnetic-perturbations with the structure in ITER that is closest to the plasma, blanket modules covered by separated beryllium tiles. The effect of this tiled surface on the perturbations and on the forces on structures is subtle. Indeterminacy can be introduced by tile-to-tile shorting. A determinate subtlety is introduced because electrically separated tiles can act as a conducting surface for magnetic perturbations that have a normal component to the surface. A practical method for including this determinate subtlety into plasma simulations is developed. The shorter the timescales and the greater the localization, particularly in the toroidal direction, the more important the magnetic effects of the tiles become.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Finite spatial-grid effects in energy-conserving particle-in-cell algorithms

Finite-grid (or aliasing) instabilities are pervasive in particle-in-cell (PIC) plasma simulation algorithms, and force the modeler to resolve the smallest (Debye) length scale in the problem regardless of dynamical relevance. These instabilities originate in the aliasing of interpolation errors between mesh quantities and particles (which live in the space–time continuum). Recently, strictly energy-conserving PIC (EC-PIC) algorithms have been developed that promise enhanced robustness against aliasing instabilities. In this study, we confirm by analysis that EC-PIC is stable against aliasing instabilities for stationary plasmas. For drifting plasmas, we demonstrate by analysis and numerical experiments that, while EC-PIC algorithms are not free from these instabilities in principle, they feature a benign stability threshold for finite-temperature plasmas that make them usable in practice for a large class of problems (featuring ambipolarity and realistic ion-electron mass ratios) without the need to consider the size of the Debye length. We also demonstrate that this threshold is absent for the popular momentum-conserving PIC algorithms, which are therefore unstable for both drifting and stationary plasmas beyond a threshold in cell size compared to Debye length. Finite-grid (or aliasing) instabilities are pervasive in particle-in-cell (PIC) plasma simulation algorithms, and force the modeler to resolve the smallest (Debye) length scale in the problem regardless of dynamical relevance. These instabilities originate in the aliasing of interpolation errors between mesh quantities and particles (which live in the space–time continuum). Recently, strictly energy-conserving PIC (EC-PIC) algorithms have been developed that promise enhanced robustness against aliasing instabilities. In this study, we confirm by analysis that EC-PIC is stable against aliasing instabilities for stationary plasmas. For drifting plasmas, we demonstrate by analysis and numerical experiments that, while EC-PIC algorithms are not free from these instabilities in principle, they feature a benign stability threshold for finite-temperature plasmas that make them usable in practice for a large class of problems (featuring ambipolarity and realistic ion-electron mass ratios) without the need to consider the size of the Debye length. Finally, we also demonstrate that this threshold is absent for the popular momentum-conserving PIC algorithms, which are therefore unstable for both drifting and stationary plasmas beyond a threshold in cell size compared to Debye length.

97 MATHEMATICS AND COMPUTING↗

A plasma–vacuum interface tracking algorithm for magnetohydrodynamic simulations of coaxial plasma accelerators

The resistive Magneto-hydrodynamic (MHD) model describes the behavior of a strongly ionized plasma in the presence of external electric and magnetic fields. For problems involving the plasma with an open boundary to very low pressure/vacuum regions, the continuum assumption is no longer valid in the entire domain of interest. For example, this is seen in a plasma accelerator where a dense plasma expands into a vacuum background. A common practice to deal with this issue is to assign small values of density and pressure to the vacuum regions and proceed to solve the continuum based MHD equations throughout the domain. We show that this approach fails to produce solutions consistent with the physics of the problem and can give rise to unacceptable artifacts such as spurious shocks. Here, we develop a plasma–vacuum interface tracking approach to mitigate this problem. The plasma–vacuum interface is tracked in a physically consistent manner and the MHD equations are solved only in the regions that contain the plasma. The interface tracking is achieved using a face-flux formulation derived from the theoretical solution to a 1D free expansion problem. Coupled with a threshold based approach, the interface tracking is implemented for both explicit and implicit time stepping frameworks on generalized unstructured grids. Simulations of magnetized thermal plasma jets expanding into a vacuum background indicate plume profiles devoid of the unphysical shock obtained using the small background density approach. In the context of resistive MHD simulations, the interface tracking approach overcomes the numerical stiffness induced by specifying a large background resistivity in the vacuum regions, resulting in significant wall-clock time gains.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Energy and momentum preserving Coulomb collision model for kinetic Monte Carlo simulations of plasma steady states in toroidal fusion devices

A kinetic Monte Carlo model suited for self-consistent transport studies is proposed and tested. The Monte Carlo collision operator is based on a widely used model of Coulomb scattering by a drifting Maxwellian and a new algorithm enforcing the momentum and energy conservation laws. The difference to other approaches consists in a specific procedure of calculating the background Maxwellian parameters, which does not require ensemble averaging and, therefore, allows for the use of single-particle algorithms. This possibility is useful in transport balance (steady state) problems with a phenomenological diffusive ansatz for the turbulent transport, because it allows a direct use of variance reduction methods well suited for single particle algorithms. In addition, a method for the self-consistent calculation of the electric field is discussed. Results of testing of the new collision operator using a set of 1D examples, and preliminary results of 2D modelling in realistic tokamak geometry, are presented.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Tailored ramp-loading via shock release of stepped-density reservoirs

The concept of a gradient piston drive has been extended from that of a single component reservoir, such as a high explosive, to that of a multi-component reservoir that utilizes low density foams and large shocks to achieve high pressures ({approx}3.5 mbar) and controlled pressure vs. time profiles on a driven sample. Simulated and experimental drives shaped through the use of multiple component (including carbonized resorcinol formaldehyde and SiO{sub 2} foam) reservoirs are compared. Individual density layers in a multiple component reservoir are shown to correlate with velocity features in the measured drive which enables the ability to tune a pressure drive by adjusting the components of the reservoir. Pre-shot simulations are shown to be in rough agreement with the data, but post-shot simulations involving the use of simulated plasma drives were needed to achieve an exact match. Results from a multiple component reservoir shot ({approx}3.5 mbar) at the National Ignition Facility are shown.

36 MATERIALS SCIENCE↗

Global Simulation of Plasma Microturbulence at the Petascale & Beyond: Optimizing the GTC Code for Blue Gene/Q (ALCF-2 Early Science Program Technical Report)

Figure 1 shows, schematically, the tokamak device, whose intent is to magnetically confine a high-temperature plasma and produce energy through nuclear fusion. The confined plasma, shown in pink, is toroidal in shape. For several decades now, scientists have been studying and improving these devices, working toward a successful fusion ignition—creating a burning plasma—and sustaining it to generate more power than it took to create it. The next big experimental step will be the International Thermonuclear Experimental Reactor, a twenty billion dollar burning plasma device under construction in France, involving the partnership of seven governments. The human in Figure 2 illustrates the scale of ITER. The magnetic field in the tokamak confines the plasma—ions, electrons, and their heat and momentum. Various kinds of instabilities in the plasma work against that confinement. Turbulent fluctuations can cause transport of particles and energy across the magnetic field lines, toward the outside of the plasma, where it is lost. Loss of plasma and energy, of course, works against confinement and successful fusion. This microturbulence is something the fusion community needs to understand and control. In past and present tokamaks, measurements have shown that the transport of energy and particles caused by microturbulence depends on the size of the tokamak—larger means more transport. This is Bohm scaling. However, theoretical arguments predict that beyond a certain size, which ITER will be beyond, the size dependence goes away, leading to relatively smaller turbulent losses and thus better confinement. This is GyroBohm scaling. The key target of this ESP project is to simulate microturbulent transport for devices of different sizes up through ITER size, and validate and understand GyroBohm scaling.

Tang, William M.↗

Plasma acceleration using a radio frequency self-bias effect

In this work plasma acceleration using a RF self-bias effect is experimentally studied. The experiments are conducted using a novel plasma accelerator system, called Neptune, consisting of an inductively coupled plasma source and a RF-biased set of grids. The plasma accelerator can operate in a steady state mode, producing a plasma flow with separately controlled plasma flux and velocity without any magnetic configuration. The operating pressure at the source output is as low as 0.2 mTorr and can further be decreased. The ion and electron flows are investigated by measuring the ion and electron energy distribution functions both space resolved and with different orientations with respect to the flow direction. It is found that the flow of electrons from the source is highly anisotropic and directed along the ion flow and this global flow of accelerated plasma is well localized in the plasma transport chamber. The maximum flux is about 7.5·10{sup 15} ions s{sup −1} m{sup −2} (at standard conditions) on the axis and decreasing to almost zero at a radial distances of more than 15 cm from the flow axis. Varying the RF acceleration voltage in the range 20–350 V, the plasma flow velocity can be changed between 10 and 35 km/s. The system is prospective for different technology such as space propulsion and surface modification and also interesting for fundamental studies for space-related plasma simulations and investigation of the dynamo effect using accelerated rotating plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Density modulation-induced absolute laser-plasma-instabilities: Simulations and theory

Fluid simulations show that when a sinusoidal density modulation is superimposed on a linear density profile, convective instabilities can become absolutely unstable. This conversion can occur for two-plasmon-decay and stimulated Raman Scattering instabilities under realistic direct-drive inertial confinement fusion conditions and can affect hot electron generation and laser energy deposition. Analysis of the three-wave model shows that a sufficiently large change of the density gradient in a linear density profile can turn convective instabilities into absolute ones. In conclusion, an analytical expression is given for the threshold of the gradient change for a two-slope density profile, which depends on the convective gain only.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Simulations of plasmas and fluids using anti-symmetric models

ALMA (Anti-symmetric, Large-Moment, Accelerated) is a fast, flexible, and scalable toolkit designed to solve hyperbolic conservation law systems in hybrid supercomputers. Here this manuscript describes the theoretical background and implementation of ALMA, which uses the anti-symmetric formulation of fluids to obtain simple, robust, and easily paralellizable code. Practical GPU acceleration is realized on entire applications with an overall gain factor of 2 to 4. ALMA also provides a parallel, GPU accelerated sparse solver based on geometric multigrid, capable of diagonalizing linear systems with 239 unknowns. Here we demonstrate ALMA's scaling and performance in petascale supercomputers and use standard fluid models to verify the overall approach with canonical benchmark problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Comparison of Conservation Behavior in Several Variationally Derived Implementations for Simulating Electromagnetic Plasmas

Variational techniques based on Low's Lagrangian formulation have demonstrated significant improvement in conservation properties as compared to traditional particle-in-cell (PIC) algorithms. Previous work showed that equations derived from a discretized Lagrangian preserve a discretized version of the connection between Lagrangian symmetries and conservation laws, i.e., Noether's theorem. Specifically, a thorough analysis of energy conservation within the new system explained the absence of “grid heating” phenomena. In the present work, variationally derived implementations in a gridded periodic domain were compared to analogous implementations using Fourier bases. Since the Fourier basis allows for exact momentum conservation, this approach enables us to compare the relative merits of exact and approximate momentum conservation. Furthermore, to establish a tangible comparison for numerical methods, we investigate two simple physical examples; (1) the coupling of an electrostatic and electromagnetic plasma wave and (2) an equilibrium supporting Weibel instability.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Fully implicit particle-in-cell algorithms for kinetic simulation of plasmas [Slides]

We have demonstrated, for the first time, a fully implicit, fully nonlinear electrostatic PIC formulation that features: (1) Exact charge conservation (via a novel particle mover strategy). (2) Exact energy conservation (no particle self-heating or self-cooling). (3) Adaptive particle orbit integrator to control errors in momentum conservation. The approach has been shown to be free of CFL and finite-grid numerical instabilities. As a result, the method is able to take time steps many times larger than explicit, and resolutions many times coarser. Central to our implementation is the concept of particle enslavement. We have generalized formulation to use spatial adaptivity via mapped coordinates. he method has much potential for efficiency gains vs. explicit in long-time-scale applications, with the CPU speedup scaling as $(kΛ_D)-^{(d+1)}/N_{FE}$. Minimize the number of nonlinear function evaluations $N_{FE}$ for given $Δt$, $Δx \Rightarrow$ preconditioning! We have formulated and implemented a very efficient moment-based preconditioner. We have ported the algorithm to GPU architectures. We have generalized the algorithm to non-radiative electromagnetic regimes (Darwin model), where, in addition to charge and energy, we also conserve canonical momenta.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗