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Title: Theory and discretization of ideal magnetohydrodynamic equilibria with fractal pressure profiles

In three-dimensional ideal magnetohydrodynamics, closed flux surfaces cannot maintain both rational rotational-transform and pressure gradients, as these features together produce unphysical, infinite currents. A proposed set of equilibria nullifies these currents by flattening the pressure on sufficiently wide intervals around each rational surface. Such rational surfaces exist at every scale, which characterizes the pressure profile as self-similar and thus fractal. The pressure profile is approximated numerically by considering a finite number of rational regions and analyzed mathematically by classifying the irrational numbers that support gradients into subsets. As a result, applying these results to a given rotational-transform profile in cylindrical geometry, we find magnetic field and current density profiles compatible with the fractal pressure.
Authors:
 [1] ;  [2]
  1. Princeton Univ., Princeton, NJ (United States)
  2. Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
Publication Date:
Grant/Contract Number:
AC02-09CH11466
Type:
Accepted Manuscript
Journal Name:
Physics of Plasmas
Additional Journal Information:
Journal Volume: 24; Journal Issue: 9; Journal ID: ISSN 1070-664X
Publisher:
American Institute of Physics (AIP)
Research Org:
Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
Sponsoring Org:
USDOE
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY
OSTI Identifier:
1395556
Alternate Identifier(s):
OSTI ID: 1395590

Kraus, B. F., and Hudson, S. R.. Theory and discretization of ideal magnetohydrodynamic equilibria with fractal pressure profiles. United States: N. p., Web. doi:10.1063/1.4986493.
Kraus, B. F., & Hudson, S. R.. Theory and discretization of ideal magnetohydrodynamic equilibria with fractal pressure profiles. United States. doi:10.1063/1.4986493.
Kraus, B. F., and Hudson, S. R.. 2017. "Theory and discretization of ideal magnetohydrodynamic equilibria with fractal pressure profiles". United States. doi:10.1063/1.4986493. https://www.osti.gov/servlets/purl/1395556.
@article{osti_1395556,
title = {Theory and discretization of ideal magnetohydrodynamic equilibria with fractal pressure profiles},
author = {Kraus, B. F. and Hudson, S. R.},
abstractNote = {In three-dimensional ideal magnetohydrodynamics, closed flux surfaces cannot maintain both rational rotational-transform and pressure gradients, as these features together produce unphysical, infinite currents. A proposed set of equilibria nullifies these currents by flattening the pressure on sufficiently wide intervals around each rational surface. Such rational surfaces exist at every scale, which characterizes the pressure profile as self-similar and thus fractal. The pressure profile is approximated numerically by considering a finite number of rational regions and analyzed mathematically by classifying the irrational numbers that support gradients into subsets. As a result, applying these results to a given rotational-transform profile in cylindrical geometry, we find magnetic field and current density profiles compatible with the fractal pressure.},
doi = {10.1063/1.4986493},
journal = {Physics of Plasmas},
number = 9,
volume = 24,
place = {United States},
year = {2017},
month = {9}
}