Ravi Samtaney is a research physicist in the Computational Plasma Physics Group at the Princeton Plasma Physics Laboratory (PPPL), Princeton University. His research interests include magnetohydrodynamics, numerical methods, and high performance computing. He is developing adaptive mesh refinement (AMR) numerical methods for magnetohydrodynamics (MHD). The AMR MHD code is a fully three dimensional nonlinear MHD code in toroidal geometry. It is a unique simulation tool, primarily used for simulating pellet injection into tokamaks, a problem of substantial interest to ITER. Furthermore, he is investigating fully implicit Jacobian- Free Newton-Krylov methods to overcome the temporal stiffness in MHD simulations.

ITER ("The Way" in Latin), a joint international research and development project that aims to demonstrate the scientific and technical feasibility of fusion power, is now under construction at Cadarache, France. Refueling of ITER is a practical necessity due to the burning plasma nature of the experiment, and longer pulse durations. An experimentally proven method of refueling tokamaks is by pellet injection. Pellet injection is currently seen as the most likely refueling technique for ITER. Thus it is imperative that pellet injection phenomena be understood via simulations before very expensive experiments are undertaken in ITER. The emphasis of the present work is to understand the large-scale macroscopic processes involved in the redistribution of mass into a tokamak during pellet injection. Arguably, such large scale processes are best understood using magnetohydrodynamics (MHD) as the mathematical model.

The physical processes of pellet injection in tokamaks span several decades of spatio-temporal scales which has prevented effective simulations of these processes. There is a large disparity between the pellet size and device size (O(10³)). Naive estimates indicate that the number of space-time points required to resolve the region around the pellet for simulation of ITER-size parameters can exceed 10¹⁹. The large range of spatial scales and the need to resolve the region around the pellet is somewhat mitigated by the use of Adaptive mesh refinement (AMR). Our approach is to employ block structured hierarchical meshes as championed by the seminal work of Berger and Oliger [1], and Berger and Colella [2]. We employ the Chombo library for AMR developed by the APDEC SciDAC Center at LBNL for AMR. We have developed an upwind conservative flux-surface coordinate MHD code. A critical component is the modeling of the highly anisotropic energy transfer from the background hot plasma to the pellet ablation cloud via long mean-free-path electrons along magnetic field lines. Further details on the approach can be found in [3].

Figure 1 shows the mesh structure in computational coordinates wherein the pellet is buried within the finest mesh which occupies less than 0.015% of the volume of the coarsest mesh - a visual illustration of the resolving power afforded by the AMR technology. The speed up of these AMR simulations over similar single mesh simulations is estimated to be greater than two orders of magnitude Results from pellet injection from the low-field-side (LFS) and high-field-side (HFS) are presented in Figure 2 in which the top panel shows a time sequence of the density in LFS injection while the bottom panel shows density evolution in HFS injection. The dominant motion of the ablated pellet mass is along field lines accompanied by transport of material across flux surfaces towards the low field side. The interchange instability is the mostly likely cause of the pellet material to move towards the low field side. This observation is also qualitatively consistent with experimental observations leading to the conclusion that HFS pellet injection is a more efficient refueling technique than LFS injection.

It ought to be recognized by the visualization community that several physical applications are beginning to employ adaptive meshes; and developments in data analysis and visualizations of such data would accelerate the speed of discovery. As evident from our graphical presentation of the data, there are still very limited ways of visualizing field quantities on hierarchical adaptive meshes, particularly when the data on each grid is in generalized curvilinear coordinates. Furthermore, our data representation is unique in the sense that the mapping is from cylindrical (as opposed to Cartesian) coordinates to a curvilinear one in which the toroidal angle is preserved. Several visualization packages surveyed do not provide even rudimentary support for hierarchical mapped meshes. Standard visualization techniques such as iso-surfaces, and projections of the field data on 2D planes and 1D curves would be extremely valuable to the scientist in interpreting the simulation data. Going beyond the mundane visualizations one would like to investigate the vector field topology (for magnetic fields in MHD), which ought to be driven by intuitive and interactive ways of picking seed points to generate stream lines, path lines, and streaklines, and extracting information such as local curvature of such streamlines. Other data analysis techniques which are conspicuously missing include volume rendering on hierarchical adaptive mapped meshes, techniques to choose appropriate stencils and specify boundary conditions to obtain derived quantities (such as divergence, curl of vector fields), and interactive ways to identify and quantify correlations among various derived quantities (e.g. 2D histograms, structure functions, convolutions).

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If you publish your work using this data set, please make acknowledgment of VisFiles: The data set is made available by Dr. Ravi Samtaney at the Princeton Plasma Physics Laboratory through US Department of Energy's SciDAC Institute for Ultrascale Visuaization.

[Pellet Data]

 
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