Automating computations in the virtual Tokamak software system

We describe the concept, functional capabilities, graphic user interface (GUI), and operating technique of a specialized system for distributing the computational burden encountered in solving typical problems of controlled thermonuclear fusion. The system is employed in the Virtual Tokamak simulation modeling complex to automate the distribution of computing on a network of computers, making it possible to dramatically improve the productivity of a researcher??s work. The system is useful in various applications that require massive multivariate calculations using one or more application codes, and for supporting websites that provide computing services using locally stored science-intensive application software.     

基于统计过程控制技术的项目管理可视化控制系统

概述IMCS-SPC模型的总体框架、组成部分以及两大核心技术(多变量统计过程控制技术和虚拟现实可视化技术);详细讨论项目管理者构建IMCS-SPC模型的基本步骤。作为一种采用多元统计分析进行过程控制的可视化决策支持系统,IMCS-SPC为项目管理者提供了一种十分清晰、直观的过程控制方法和工具,可有效提高项目管理效率,以确保项目过程的正常运行。     

Gaussian Packets and Beams with Focal Points in Vector Problems of Plasma Physics

We consider a linearized equation describing plasma motion in a toroidal domain (tokamak) and study the asymptotic forms of steady-state solutions of the Gaussian beam type with a short wave length, which correspond to electric modes. We also study Gaussian wave packets and localized “cigar”-type beams describing the transmission of localized perturbations through the tokamak chamber. We separately consider the case of focal points on a trajectory and the asymptotic forms in a neighborhood of a focal point.     

Simulating the effect of external helical magnetic fields on MHD stability of tokamak plasma

The effect of external helical magnetic fields on the stability of a rotating plasma in an axially symmetric tokamak machine is simulated numerically. Threshold amplitude effects are investigated using the NFTC code for the complete nonlinear dynamical 3-D system of MHD equations. The research was partially funded by Russian Foundation of Basic Research (grant 96-07-89110) and Ministry of Science grants 201.03.002 and 0201.03.003. Translated from Chislennye Metody i Vychislitel'nyi Eksperiment, Moscow State University, pp. 4–14, 1998.     

Solvability of nonlinear boundary-value problems arising in modeling plasma diffusion across a magnetic field and its equilibrium configurations

We study the simplest one-dimensional model of plasma density balance in a tokamak type system, which can be reduced to an initial boundary-value problem for a second-order parabolic equation with implicit degeneration containing nonlocal (integral) operators. The problem of stabilizing nonstationary solutions to stationary ones is reduced to studying the solvability of a nonlinear integro-differential boundary-value problem. We obtain sufficient conditions for the parameters of this boundary-value problem to provide the existence and the uniqueness of a classical stationary solution, and for this solution we obtain the attraction domain by a constructive method.     

Parallel simulation of large scale multibody systems

Virtual prototyping plays an ever increasing role in the engineering disciplines. Nowadays, engineers can rely on powerful tools like object oriented modeling languages, e.g., Modelica. Models written in this language can be simulated by open source software as well as commercial tools. The advantage of this approach is that the engineers can concentrate themselves on modeling, whereas the numerical intricacies of the simulation are handled by the software. On the other hand the simulations are usually slower than implementations which are parallelized and optimized manually. This can lead to computation times which are infeasible in practice, e.g., when a real time simulation is necessary for a hardware-in-the-loop simulation. In this contribution we are concerned with speeding up such automated simulations by parallelization (on desktop hardware as well as HPC systems). We examine the parallelism across the system approaches. Additionally, the influence of the problem formulation on the simulation time is discussed. The implemented methods are demonstrated on engineering examples. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A symplectic mapping for the ergodic magnetic limiter and its dynamical analysis

A model for a new bidimensional sympletic mapping describing magnetic field line trajectories in a tokamak perturbed by ergodic magnetic limiter coils is presented. Numerical examples of these trajectories, computed for plasma described by large aspect-ratio equilibria, simulate the main characteristics of trajectories in the toroidal geometry. Also the importance of the symplecticity of the new mapping regarding certain features of non-linear dynamical analysis, for which a large number of iterations is necessary, is shown. Thus, some standard algorithms, such as the Lyapunov exponents and the rotational transforms, are applied with precision in order to characterize regular and chaotic regions in the parameter space, improving the study of bifurcations, routes to chaos, and diffusion in this system.     

A study of current generation by electron cyclotron waves in magnetic-surface-averaged kinetic model

A two-dimensional magnetic-surface-averaged kinetic model is constructed for current generation by electron cyclotron waves in tokamak plasma. The model allows for toroidal effects, localization of the injected RF energy on a given magnetic surface, and also relativistic effects. Numerical results are reported for the dependence of current generation efficiency on a wide selection of parameters.Translated from Matematicheskoe Modelirovanie i Reshenie Obratnykh Zadach Matematicheskoi Fiziki, pp. 183–200, 1993.     

The effect of radial diffusion on current generation by electron-cyclotron waves in tokamak plasma

The effect of radial diffusion of electrons on current generation by electron-cyclotron waves in a tokamak plasma is studied in the framework of the three-dimensional kinetic model. A numerical solution of the problem is obtained. The results suggest that electron diffusion in the radial direction has a significant effect on the energy spectrum of the excited current. The lower diffusion bound in the velocity space plays an important role in this context.Translated from Matematicheskie Modeli Estestvoznaniya, Published by Moscow University, Moscow, 1995, pp. 27–31.     

Multi-criteria decision aid for the formulation of sustainable technological energy priorities using linguistic variables

Implementation of new and innovative energy technologies is a key mean towards a sustainable energy system. Currently, governments have to decide from an increasingly diverse mix of them, the ones which warrant support, including funding and other incentives for private sector efforts. However, appraising energy technologies in terms of their sustainability is a really complex task, considering the series of uncertainties and implications that have to be encountered so as to obtain realistic and transparent results. In this context, the main aim of this paper is to present a direct and flexible multi-criteria decision making approach, using linguistic variables, to assist policy makers in formulating sustainable technological energy priorities. Furthermore, its software realization will be applied to a number of technologies, in the context of the Greek Technology Foresight Programme, and the results will be presented and discussed.     

Maslov complex germ and high-frequency Gaussian beams for cold plasma in a toroidal domain

Asymptotic vector solutions describing, in the linear approximation, the passage of high-frequency Gaussian beams through an electroneutral plasma occupying a toroidal domain T (modeling a tokamak chamber) are constructed in a fairly effective form by using the Maslov complex germ theory. The particle density and the magnetic field in T are assumed to be given. Based on Radon transforms, the reconstruction of the particle density and the magnetic field from measurements of the characteristics of Gaussian beams after their passage through T is discussed.     

Explorative and dynamic visualization of data in virtual reality

Summary  A software system has been developed for the study of dynamic glyph visualizations in the context of Visual Data Mining in Virtual Reality. The system uses parallel processing to calculate data visualizations in real-time, with real-time interaction and dynamic changes to the view. The system allows morphing between different visualizations, the use of dynamic features like “vibrations” and “rotations” of thousands of objects individually, and dynamic visualization, where the influence of any variable of a dataset with a “reasonable” distribution, can be shown as a dynamic development. It appears that these facilities for dynamic data visualization have a very promising potential, but their optimal use will depend on further developments in the context of their individual practical application.     

Well-posedness of a diffusive gyro-kinetic model

We study a finite Larmor radius model used to describe the ions distribution function in the core of a tokamak plasma, that consists in a gyro-kinetic transport equation coupled with an electro-neutrality equation. Since the last equation does not provide enough regularity on the electric potential, we introduce a simple linear collision operator adapted to the finite Larmor radius approximation. We next study the two-dimensional dynamics in the direction perpendicular to the magnetic field. Thanks to the smoothing effects of the collision and the gyro-average operators, we prove the global existence of solutions, as well as short time uniqueness and stability.     

Object-orientation,Discrete Simulation and the Three-Phase Approach

The three-phase approach provides a simple and robust way to develop discrete computer simulation programs. Object-orientation allows system developers to develop software which can be extended and also makes it impossible for important variables within a software system to be tampered with. This paper shows how the two approaches can be usefully combined and discusses the development of a simulation library, written in C++ and based on these ideas. Limitations of both approaches are also discussed.     

Vector spherical harmonics in 3-D vector tomography

A method of series expansion in terms of vector spherical harmonics intended for inverting line integrated experimental (Doppler) data is proposed to investigate 3-D vector fields in laboratory plasma in spherical tokamak devices. A number of numerical computations demonstrating 3-D reconstructions of model vector fields have been performed to assess the inversion method proposed.     

FronTier and applications to scientific and engineering problems

We report significant developments of the FronTier code and applications in science and engineering. The progress includes the extraction of an independent software library from the front tracking code, robust and accurate locally grid based method, applications to fluid mixing problem, fuel injection jet and fusion pellet injection in a magnetically confined plasma, among other problems. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Simulation of MHD processes in high-temperature plasma

The paper analyzes a number of mathematical models and numerical codes developed for the study of magnetohydrodynamic (MHD) processes in high-temperature tokamak plasma. Various approaches are discussed to numerical solution of the nonlinear problems for systems of MHD equations arising in controlled thermonuclear fusion research.Translated from Metody Matematicheskogo Modelirovaniya, Avtomatizatsiya Obrabotki Nablyudenii i Ikh Primeneniya, pp. 243–259, 1986.     

Fillmore–Springer–Cnops Construction Implemented in <Literal><Emphasis FontCategory="SansSerif">GiNaC</Emphasis></Literal>

This is an implementation of the Fillmore–Springer–Cnops construction (FSCc) based on the Clifford algebra capacities [10] of the GiNaC computer algebra system. FSCc linearises the linear-fraction action of the M?bius group. This turns to be very useful in several theoretical and applied fields including engineering. The core of this realisation of FSCc is done for an arbitrary dimension, while a subclass for two dimensional cycles add some 2D-specific routines including a visualisation to PostScript files through the MetaPost or Asymptote software. This library is a backbone of many result published in [9], which serve as illustrations of its usage. It can be ported (with various level of required changes) to other CAS with Clifford algebras capabilities.