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Variational Integration for Ideal Magnetohydrodynamics and Formation of Current Singularities.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Variational Integration for Ideal Magnetohydrodynamics and Formation of Current Singularities./
Author:	Zhou, Yao.
Description:	1 online resource (110 pages)
Notes:	Source: Dissertation Abstracts International, Volume: 79-04(E), Section: B.
Contained By:	Dissertation Abstracts International79-04B(E).
Subject:	Plasma physics. -
Online resource:	click for full text (PQDT)
ISBN:	9780355323528

Variational Integration for Ideal Magnetohydrodynamics and Formation of Current Singularities.
Zhou, Yao.

Variational Integration for Ideal Magnetohydrodynamics and Formation of Current Singularities. - 1 online resource (110 pages)

Source: Dissertation Abstracts International, Volume: 79-04(E), Section: B.

Thesis (Ph.D.)--Princeton University, 2017.

Includes bibliographical references

Coronal heating has been a long-standing conundrum in solar physics. Parker's conjecture that spontaneous current singularities lead to nanoflares that heat the corona has been controversial. In ideal magnetohydrodynamics (MHD), can genuine current singularities emerge from a smooth 3D line-tied magnetic field? To numerically resolve this issue, the schemes employed must preserve magnetic topology exactly to avoid artificial reconnection in the presence of (nearly) singular current densities.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2018

Mode of access: World Wide Web

ISBN: 9780355323528Subjects--Topical Terms:

1030958
Plasma physics.
Index Terms--Genre/Form:

554714
Electronic books.

Variational Integration for Ideal Magnetohydrodynamics and Formation of Current Singularities.
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100 1 $a Zhou, Yao. $3 1193254
245 1 0 $a Variational Integration for Ideal Magnetohydrodynamics and Formation of Current Singularities.
264 0 $c 2017
300 $a 1 online resource (110 pages)
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500 $a Source: Dissertation Abstracts International, Volume: 79-04(E), Section: B.
500 $a Advisers: Hong Qin; Amitava Bhattacharjee.
502 $a Thesis (Ph.D.)--Princeton University, 2017.
504 $a Includes bibliographical references
520 $a Coronal heating has been a long-standing conundrum in solar physics. Parker's conjecture that spontaneous current singularities lead to nanoflares that heat the corona has been controversial. In ideal magnetohydrodynamics (MHD), can genuine current singularities emerge from a smooth 3D line-tied magnetic field? To numerically resolve this issue, the schemes employed must preserve magnetic topology exactly to avoid artificial reconnection in the presence of (nearly) singular current densities.
520 $a Structure-preserving numerical methods are favorable for mitigating numerical dissipation, and variational integration is a powerful machinery for deriving them. However, successful applications of variational integration to ideal MHD have been scarce. In this thesis, we develop variational integrators for ideal MHD in Lagrangian labeling by discretizing Newcomb's Lagrangian on a moving mesh using discretized exterior calculus. With the built-in frozen-in equation, the schemes are free of artificial reconnection, hence optimal for studying current singularity formation.
520 $a Using this method, we first study a fundamental prototype problem in 2D, the Hahm-Kulsrud-Taylor (HKT) problem. It considers the effect of boundary perturbations on a 2D plasma magnetized by a sheared field, and its linear solution is singular. We find that with increasing resolution, the nonlinear solution converges to one with a current singularity. The same signature of current singularity is also identified in other 2D cases with more complex magnetic topologies, such as the coalescence instability of magnetic islands.
520 $a We then extend the HKT problem to 3D line-tied geometry, which models the solar corona by anchoring the field lines in the boundaries. The effect of such geometry is crucial in the controversy over Parker's conjecture. The linear solution, which is singular in 2D, is found to be smooth. However, with finite amplitude, it can become pathological above a critical system length. The nonlinear solution turns out smooth for short systems. Nonetheless, the scaling of peak current density vs. system length suggests that the nonlinear solution may become singular at a finite length. With the results in hand, we cannot confirm or rule out this possibility conclusively, since we cannot obtain solutions with system lengths near the extrapolated critical value.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2018
538 $a Mode of access: World Wide Web
650 4 $a Plasma physics. $2 bicssc $3 1030958
650 4 $a Astrophysics. $3 646223
650 4 $a Applied mathematics. $3 1069907
655 7 $a Electronic books. $2 local $3 554714
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690 $a 0596
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710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a Princeton University. $b Astrophysical Sciences - Plasma Physics Program. $3 1193255
773 0 $t Dissertation Abstracts International $g 79-04B(E).
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10622457 $z click for full text (PQDT)