skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

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

Abstract

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:
Research Org.:
Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1395556
Alternate Identifier(s):
OSTI ID: 1395590
Grant/Contract Number:  
AC02-09CH11466
Resource 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)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY

Citation Formats

Kraus, B. F., and Hudson, S. R. Theory and discretization of ideal magnetohydrodynamic equilibria with fractal pressure profiles. United States: N. p., 2017. 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. Fri . "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}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 2 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Fractal structures in the chaotic motion of charged particles in a magnetized plasma under the influence of drift waves
journal, March 2017

  • Mathias, A. C.; Viana, R. L.; Kroetz, T.
  • Physica A: Statistical Mechanics and its Applications, Vol. 469
  • DOI: 10.1016/j.physa.2016.11.049

A universal instability of many-dimensional oscillator systems
journal, May 1979


Fat-fractal scaling exponent of area-preserving maps
journal, February 1987


Self-Affine Fractals and Fractal Dimension
journal, October 1985


Physics of magnetically confined plasmas
journal, January 2005


Three-dimensional magnetohydrodynamic equilibria with continuous magnetic fields
journal, July 2017


Fractal dimensionality for different transport modes in the turbulent boundary plasma of TEXTOR
journal, March 1993


Contributions of plasma physics to chaos and nonlinear dynamics
journal, September 2016


Toroidal Containment of a Plasma
journal, January 1967


Fractal structures in nonlinear dynamics
journal, March 2009

  • Aguirre, Jacobo; Viana, Ricardo L.; Sanjuán, Miguel A. F.
  • Reviews of Modern Physics, Vol. 81, Issue 1
  • DOI: 10.1103/RevModPhys.81.333

A method for determining a stochastic transition
journal, June 1979

  • Greene, John M.
  • Journal of Mathematical Physics, Vol. 20, Issue 6
  • DOI: 10.1063/1.524170

Ideal magnetohydrodynamic equilibrium in a non-symmetric topological torus
journal, February 2014


On Euler's totient function
journal, January 1932


Fat Fractals on the Energy Surface
journal, August 1985


Smoothing and Differentiation of Data by Simplified Least Squares Procedures.
journal, July 1964

  • Savitzky, Abraham.; Golay, M. J. E.
  • Analytical Chemistry, Vol. 36, Issue 8
  • DOI: 10.1021/ac60214a047

Symplectic maps, variational principles, and transport
journal, July 1992