Sparse-grid Discontinuous Galerkin Methods for the Vlasov-Poisson-Lenard-Bernstein Model

Sparse-grid methods have recently gained interest in reducing the computational cost of solving high-dimensional kinetic equations. In this paper, we construct adaptive and hybrid sparse-grid methods for the Vlasov-Poisson-Lenard-Bernstein (VPLB) model. This model has applications to plasma physics and is simulated in two reduced geometries: a 0x3v space homogeneous geometry and a 1x3v slab geometry. We use the discontinuous Galerkin (DG) method as a base discretization due to its high-order accuracy and ability to preserve important structural properties of partial differential equations. We utilize a multiwavelet basis expansion to determine the sparse-grid basis and the adaptive mesh criteria. We analyze the proposed sparse-grid methods on a suite of three test problems by computing the savings afforded by sparse-grids in comparison to standard solutions of the DG method. The results are obtained using the adaptive sparse-grid discretization library ASGarD

Anderson localization of ballooning modes, quantum chaos and the stability of compact quasiaxially symmetric stellarators

The radially local magnetohydrodynamic(MHD) ballooning stability of a compact, quasiaxially symmetric stellarator (QAS), is examined just above the ballooning beta limit with a method that can lead to estimates of global stability. Here MHDstability is analyzed through the calculation and examination of the ballooning modeeigenvalue isosurfaces in the 3-space (s,α,θk); s is the edge normalized toroidal flux, α is the field linevariable, and θk is the perpendicular wave vector or ballooning parameter. Broken symmetry, i.e., deviations from axisymmetry, in the stellarator magnetic field geometry causes localization of the ballooning mode eigenfunction, and gives rise to new types of nonsymmetric eigenvalue isosurfaces in both the stable and unstable spectrum. For eigenvalues far above the marginal point, isosurfaces are topologically spherical, indicative of strong “quantum chaos.” The complexity of QAS marginal isosurfaces suggests that finite Larmor radius stabilization estimates will be difficult and that fully three-dimensional, high-nMHD computations are required to predict the beta limit.Research supported by U.S. DOE Contract No. DEAC02-76CH0373. John Canik held a U.S. DOE National Undergraduate Fellowship at Princeton Plasma Physics Laboratory, during the summer of 2000

Radiative heat exhaust in Alcator C-Mod I-mode plasmas

In order to more completely demonstrate the I-mode regime as a compelling fusion reactor operating scenario, the first dedicated attempts at I-mode radiative heat exhaust and detachment were carried out on Alcator C-Mod. Results conclusively show that within the parameter space explored, an I/L back-transition is triggered prior to meaningful reductions in parallel heat flux, q||, target temperature, Te;tar, and target pressure, pe;tar, at the outer divertor. The exact mechanism for the I/L trigger remains uncertain, but a multi-diagnostic investigation suggests the pedestal regulation physics is impacted promptly by small amounts of N2 seeded into the private flux region. The time delay between when N2 contacts the plasma and the I/L transition is triggered varied from 30-120 ms, approximately 0.7-3 x tE, and the delay varied inversely with I-mode pedestal-top pressure, pe;95. Power and nitrogen influx scans indicate that the I/L transitions are not linked to excessive bulk-plasma impurity radiation. It is also shown that in the subsequent L-mode following nitrogen seeding, q|| and Te;tar can be reduced by factors of ~10. The I/L transition and L-mode exhaust results using N2 are compared to similar attempts using Ne where such q|| and Te;tar reductions in L-mode are limited to factors of 2-3. Implications for the I-mode regime are discussed, including needs for follow-up experiments on other facilities

Divertor heat flux challenge and mitigation in SPARC

Owing to its high magnetic field, high power, and compact size, the SPARC experiment will operate with divertor conditions at or above those expected in reactor-class tokamaks. Power exhaust at this scale remains one of the key challenges for practical fusion energy. Based on empirical scalings, the peak unmitigated divertor parallel heat flux is projected to be greater than 10 GW m-2. This is nearly an order of magnitude higher than has been demonstrated to date. Furthermore, the divertor parallel Edge-Localized Mode (ELM) energy fluence projections (∼11-34 MJ m-2) are comparable with those for ITER. However, the relatively short pulse length (∼25 s pulse, with a ∼10 s flat top) provides the opportunity to consider mitigation schemes unsuited to long-pulse devices including ITER and reactors. The baseline scenario for SPARC employs a ∼1 Hz strike point sweep to spread the heat flux over a large divertor target surface area to keep tile surface temperatures within tolerable levels without the use of active divertor cooling systems. In addition, SPARC operation presents a unique opportunity to study divertor heat exhaust mitigation at reactor-level plasma densities and power fluxes. Not only will SPARC test the limits of current experimental scalings and serve for benchmarking theoretical models in reactor regimes, it is also being designed to enable the assessment of long-legged and X-point target advanced divertor magnetic configurations. Experimental results from SPARC will be crucial to reducing risk for a fusion pilot plant divertor design

Novel SOLPS-ITER simulations of X-point target and snowflake divertors

The design and understanding of alternative divertor configurations may be crucial for achieving acceptable steady-state heat and particle material loads for magnetic confinement fusion reactors. Multiple X-point alternative divertor geometries such as snowflakes and X-point targets have great potential in reducing power loads, but have not yet been simulated widely in codes with kinetic neutrals. This paper discusses recent changes made to the SOLPS-ITER code to allow for the simulation of X-point target and low-field side snowflake divertor geometries. Snowflake simulations using this method are presented, in addition to the first SOLPS-ITER simulation of the X-point target. Analysis of these results show reasonable consistency with the simple modelling and theoretical predictions, supporting the validity of the methodology implemented

Overview of the SPARC tokamak

The SPARC tokamak is a critical next step towards commercial fusion energy. SPARC is designed as a high-field (T), compact (m, m), superconducting, D-T tokamak with the goal of producing fusion gain 2$]]> from a magnetically confined fusion plasma for the first time. Currently under design, SPARC will continue the high-field path of the Alcator series of tokamaks, utilizing new magnets based on rare earth barium copper oxide high-temperature superconductors to achieve high performance in a compact device. The goal of 2$]]> is achievable with conservative physics assumptions () and, with the nominal assumption of, SPARC is projected to attain and MW. SPARC will therefore constitute a unique platform for burning plasma physics research with high density (), high temperature (keV) and high power density () relevant to fusion power plants. SPARC's place in the path to commercial fusion energy, its parameters and the current status of SPARC design work are presented. This work also describes the basis for global performance projections and summarizes some of the physics analysis that is presented in greater detail in the companion articles of this collection

Model for screening of resonant magnetic perturbations by plasma in a realistic tokamak geometry and its impact on divertor strike points

This work addresses the question of the relation between strike-point splitting and magnetic stochasticity at the edge of a poloidally diverted tokamak in the presence of externally imposed magnetic perturbations. More specifically, ad-hoc helical current sheets are introduced in order to mimic a hypothetical screening of the external resonant magnetic perturbations by the plasma. These current sheets, which suppress magnetic islands, are found to reduce the amount of splitting expected at the target, which suggests that screening effects should be observable experimentally. Multiple screening current sheets reinforce each other, i.e. less current relative to the case of only one current sheet is required to screen the perturbation.Comment: Accepted in the Proceedings of the 19th International Conference on Plasma Surface Interactions, to be published in Journal of Nuclear Materials. Version 2: minor formatting and text improvements, more results mentioned in the conclusion and abstrac