Fourierspectral element approximation of the ion–electron Braginskii system with application to tokamak edge plasma in divertor configuration
Abstract
Due to the extreme conditions required to produce energy by nuclear fusion in tokamaks, simulating the plasma behavior is an important but challenging task. We focus on the edge part of the plasma, where fluid approaches are probably the best suited, and our approach relies on the Braginskii ion–electron model. Assuming that the electric field is electrostatic, this yields a set of 10 strongly coupled and nonlinear conservation equations that exhibit multiscale and anisotropy features. The computational domain is a torus of complex geometrical section, that corresponds to the divertor configuration, i.e. with an “Xpoint” in the magnetic surfaces. To capture the complex physics that is involved, high order methods are used: The timediscretization is based on a Strang splitting, that combines implicit and explicit high order Runge–Kutta schemes, and the space discretization makes use of the spectral element method in the poloidal plane together with Fourier expansions in the toroidal direction. The paper thoroughly describes the algorithms that have been developed, provides some numerical validations of the key algorithms and exhibits the results of preliminary numerical experiments. In particular, we point out that the highest frequency of the system is intermediate between the ion and electron cyclotron frequencies.
 Authors:
 Lab. J. A. Dieudonné, UMR CNRS 7351, Université de NiceSophia Antipolis, F06108 Nice (France)
 (France)
 Publication Date:
 OSTI Identifier:
 22572351
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Journal of Computational Physics; Journal Volume: 321; Other Information: Copyright (c) 2016 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGORITHMS; CONFIGURATION; DIVERTORS; MAGNETIC SURFACES; NONLINEAR PROBLEMS; PLASMA; TOKAMAK DEVICES
Citation Formats
Minjeaud, Sebastian, INRIA project CASTOR, Pasquetti, Richard, Email: richard.pasquetti@unice.fr, and INRIA project CASTOR. Fourierspectral element approximation of the ion–electron Braginskii system with application to tokamak edge plasma in divertor configuration. United States: N. p., 2016.
Web. doi:10.1016/J.JCP.2016.05.056.
Minjeaud, Sebastian, INRIA project CASTOR, Pasquetti, Richard, Email: richard.pasquetti@unice.fr, & INRIA project CASTOR. Fourierspectral element approximation of the ion–electron Braginskii system with application to tokamak edge plasma in divertor configuration. United States. doi:10.1016/J.JCP.2016.05.056.
Minjeaud, Sebastian, INRIA project CASTOR, Pasquetti, Richard, Email: richard.pasquetti@unice.fr, and INRIA project CASTOR. Thu .
"Fourierspectral element approximation of the ion–electron Braginskii system with application to tokamak edge plasma in divertor configuration". United States.
doi:10.1016/J.JCP.2016.05.056.
@article{osti_22572351,
title = {Fourierspectral element approximation of the ion–electron Braginskii system with application to tokamak edge plasma in divertor configuration},
author = {Minjeaud, Sebastian and INRIA project CASTOR and Pasquetti, Richard, Email: richard.pasquetti@unice.fr and INRIA project CASTOR},
abstractNote = {Due to the extreme conditions required to produce energy by nuclear fusion in tokamaks, simulating the plasma behavior is an important but challenging task. We focus on the edge part of the plasma, where fluid approaches are probably the best suited, and our approach relies on the Braginskii ion–electron model. Assuming that the electric field is electrostatic, this yields a set of 10 strongly coupled and nonlinear conservation equations that exhibit multiscale and anisotropy features. The computational domain is a torus of complex geometrical section, that corresponds to the divertor configuration, i.e. with an “Xpoint” in the magnetic surfaces. To capture the complex physics that is involved, high order methods are used: The timediscretization is based on a Strang splitting, that combines implicit and explicit high order Runge–Kutta schemes, and the space discretization makes use of the spectral element method in the poloidal plane together with Fourier expansions in the toroidal direction. The paper thoroughly describes the algorithms that have been developed, provides some numerical validations of the key algorithms and exhibits the results of preliminary numerical experiments. In particular, we point out that the highest frequency of the system is intermediate between the ion and electron cyclotron frequencies.},
doi = {10.1016/J.JCP.2016.05.056},
journal = {Journal of Computational Physics},
number = ,
volume = 321,
place = {United States},
year = {Thu Sep 15 00:00:00 EDT 2016},
month = {Thu Sep 15 00:00:00 EDT 2016}
}

Twodimensional lithium beam imaging technique has been applied in the spherical tokamak CPD (compact plasma wall interaction experimental device) to study the effects of magnetic field configurations on rf plasma boundary in the absence of any plasma current, and also for the measurement of a twodimensional edge electron density profile. With the present working condition of the diagnostics, the minimum measured electron density can be {approx}1.0x10{sup 16} m{sup 3}; this is considered to be the definition for the plasma boundary. The performance of the lithium sheet beam is absolutely calibrated using a quartz crystal monitor. Experimental results reveal that magneticmore »

Leastsquares autoregressive (maximum entropy) spectral estimation for Fourier spectroscopy and its application to the electron cyclotron emission from plasma
A new procedure for the maximum entropy spectral estimation is studied for the purpose of data processing in Fourier transform spectroscopy. The fitting of the autoregressive model to the interferogram is examined under a leastsquares criterion based on the YuleWalker equations. A practical criterion is suggested for selecting the model order. The principal advantage of the new procedure lies in the enhanced frequency resolution, particularly for small values of the maximum optical path difference of the interferogram. The usefulness of the procedure is ascertained by some numerical simulations and further by experiments with respect to a highly coherent submillimeter wavemore » 
Simulation of Turbulence in the Divertor Region of Tokamak Edge Plasma
Results are presented for turbulence simulations with the fluid edge turbulence code BOUT [1]. The present study is focused on turbulence in the divertor leg region and on the role of the Xpoint in the structure of turbulence. Results of the present calculations indicate that the ballooning effects are important for the divertor fluctuations. The Xpoint shear leads to weak correlation of turbulence across the Xpoint regions, in particular for large toroidal wavenumber. For the saturated amplitudes of the divertor region turbulence it is found that amplitudes of density fluctuations are roughly proportional to the local density of the backgroundmore » 
Edge plasma modeling of limiter surfaces in a Tokamak divertor configuration
During the startup phase of a tokamak the plasma configuration may evolve from a limiter to a divertor configuration. Some of the particle and heat flux from the core will be deposited on material surfaces near the separatrix instead of the divertor plates. Examples of such surfaces include the centerpost in most tokamaks, baffles near the xpoint that create closed divertors, and outboard limiter surfaces. Twodimensional edge plasma models for tokamak divertor configurations typically give detailed information about the particle and heat fluxes on the divertor plates, but yield little or no information about fluxes on these other localized surfacesmore »