Mapping of orthogonal 2D flux coordinates for two nearby magnetic Xpoints to logically rectangular domains
Abstract
The behavior of plasmas in configurations with magnetic null points is of potential interest for a number of systems. Such nulls, sometimes referred to as Xpoints, a name strictly valid only for wellseparated nulls where magnetic separatrices cross at a right angle, may occur in only one component of the magnetic field, such as the poloidal field in a tokamak. Numerical simulations are often used to study and predict turbulence and transport in such systems. For cases with strong magnetic field such that the ion and electron gyrofrequencies are much larger that particle collision frequencies, there is a strong anisotropy in the plasma transport along the magnetic field compared to across the field. Because of the strong anisotropy, it is often advantageous for simulations to use a coordinate system based on magnetic flux surfaces together with a coordinate orthogonal to the flux surfaces. This report presents the topological considerations needed to construct the mapping on an orthogonal fluxsurface mesh onto a logically rectangular domain often used in simulation codes of the divertor region of tokamaks having two nearby Xpoints, thus extending the mapping now common singlenull or wellseparated double nullpoint cases with one null located at the top and bottommore »
 Authors:

 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
 Publication Date:
 Research Org.:
 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
 Sponsoring Org.:
 USDOE National Nuclear Security Administration (NNSA)
 OSTI Identifier:
 1637587
 Report Number(s):
 LLNLTR731515
882801
 DOE Contract Number:
 AC5207NA27344
 Resource Type:
 Technical Report
 Country of Publication:
 United States
 Language:
 English
 Subject:
 Physics  Plasma physics
Citation Formats
Rensink, M. E., and Rognlien, T. D. Mapping of orthogonal 2D flux coordinates for two nearby magnetic Xpoints to logically rectangular domains. United States: N. p., 2017.
Web. doi:10.2172/1637587.
Rensink, M. E., & Rognlien, T. D. Mapping of orthogonal 2D flux coordinates for two nearby magnetic Xpoints to logically rectangular domains. United States. doi:10.2172/1637587.
Rensink, M. E., and Rognlien, T. D. Thu .
"Mapping of orthogonal 2D flux coordinates for two nearby magnetic Xpoints to logically rectangular domains". United States. doi:10.2172/1637587. https://www.osti.gov/servlets/purl/1637587.
@article{osti_1637587,
title = {Mapping of orthogonal 2D flux coordinates for two nearby magnetic Xpoints to logically rectangular domains},
author = {Rensink, M. E. and Rognlien, T. D.},
abstractNote = {The behavior of plasmas in configurations with magnetic null points is of potential interest for a number of systems. Such nulls, sometimes referred to as Xpoints, a name strictly valid only for wellseparated nulls where magnetic separatrices cross at a right angle, may occur in only one component of the magnetic field, such as the poloidal field in a tokamak. Numerical simulations are often used to study and predict turbulence and transport in such systems. For cases with strong magnetic field such that the ion and electron gyrofrequencies are much larger that particle collision frequencies, there is a strong anisotropy in the plasma transport along the magnetic field compared to across the field. Because of the strong anisotropy, it is often advantageous for simulations to use a coordinate system based on magnetic flux surfaces together with a coordinate orthogonal to the flux surfaces. This report presents the topological considerations needed to construct the mapping on an orthogonal fluxsurface mesh onto a logically rectangular domain often used in simulation codes of the divertor region of tokamaks having two nearby Xpoints, thus extending the mapping now common singlenull or wellseparated double nullpoint cases with one null located at the top and bottom of the device. This extension is especially relevant to study the capability of snowflake divertors in tokamaks for reducing the peak heat flux of exhaust plasma on the target plates [13]. The analysis presented here follows the analytic description of the poloidal magnetic field, Bpol, near two closelyspaced Xpoints given by Ryutov [13]. This analysis is applicable to experimental devices where the two Xpoints are generated by distributed poloidal field coils and the plasma core current. This analytic description is used to identify topological features of an orthogonal mesh. A key parameter that specifies the various topology changes is the poloidal angle between the primary Xpoint and the second Xpoint, and the changes are associated with a set of critical angles. Understanding these changes leads to the final step in the mesh construction by identifying the locations of various regions or patches in configuration space and in a corresponding logically rectangular index space. UEDGE [4] and other 2D fluid plasma simulation codes [57] describe the edge plasma of toroidally symmetric tokamak configurations with one or more Xpoints in a divertor region. The 2D spatial mesh is usually based on a magnetic configuration produced by an MHD equilibrium code such as EFIT and written out as one or more “eqdsk” files. As illustrated in Fig. 1, the domain of the simulated plasma consists of several flux tubes bounded by poloidal magnetic flux surfaces. The number and spacing of the flux surfaces defines the “radial” resolution of the mesh. The “radial” direction is locally orthogonal to flux surfaces; the “poloidal” direction is locally parallel to flux surfaces. The “poloidal” resolution of the mesh is defined by the number of cells in the poloidal direction between adjacent flux surfaces. For boundary plasma transport codes used for tokamak configurations such as UEDGE it is convenient, though not necessary, to assume that all flux tubes have the same number of poloidal cells so the mesh is logically rectangular in index space, but does possess internal boundaries linking different subrectangles in the computational domain. The following sections of this report describe indexing schemes that map tokamak magnetic configurations with one or more xpoints in the divertor region(s) onto a rectangular index space. Simulation results from the UEDGE code illustrate the schemes for a few configurations.},
doi = {10.2172/1637587},
journal = {},
number = ,
volume = ,
place = {United States},
year = {2017},
month = {5}
}