Theory and discretization of ideal magnetohydrodynamic equilibria with fractal pressure profiles
In threedimensional ideal magnetohydrodynamics, closed flux surfaces cannot maintain both rational rotationaltransform 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 selfsimilar 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 rotationaltransform profile in cylindrical geometry, we find magnetic field and current density profiles compatible with the fractal pressure.
 Authors:

^{[1]};
^{[2]}
 Princeton Univ., Princeton, NJ (United States)
 Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
 Publication Date:
 Grant/Contract Number:
 AC0209CH11466
 Type:
 Accepted Manuscript
 Journal Name:
 Physics of Plasmas
 Additional Journal Information:
 Journal Volume: 24; Journal Issue: 9; Journal ID: ISSN 1070664X
 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 threedimensional ideal magnetohydrodynamics, closed flux surfaces cannot maintain both rational rotationaltransform 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 selfsimilar 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 rotationaltransform 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}
}