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Title: Nonlinear energy principle for model current sheets

Abstract

It is demonstrated on the basis of exact invariants of nonlinear Vlasov equation and model current sheets that the change in magnetic topology (i.e., reconnection) in a finite closed system leads to the conversion of magnetic-field energy to particle energy. It is also shown that the volume-averaged conversion efficiency diminishes as the spatial average is taken over larger and larger system size, while it increases when the system size becomes smaller. This finding may have an important implication for numerical simulation of reconnection processes under finite geometry.

Authors:
;  [1];  [2]
  1. Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742-2431 (United States)
  2. (United States)
Publication Date:
OSTI Identifier:
20782432
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Plasmas; Journal Volume: 13; Journal Issue: 1; Other Information: DOI: 10.1063/1.2151181; (c) 2006 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; BOLTZMANN-VLASOV EQUATION; CHARGED-PARTICLE TRANSPORT; COMPUTERIZED SIMULATION; EFFICIENCY; GEOMETRY; MAGNETIC FIELDS; MAGNETOHYDRODYNAMICS; NONLINEAR PROBLEMS; PLASMA; PLASMA SIMULATION; TOPOLOGY

Citation Formats

Yoon, Peter H., Lui, Anthony T.Y., and Applied Physics Laboratory, Johns Hopkins University, Johns Hopkins Road, Laurel, Maryland 20723-6099. Nonlinear energy principle for model current sheets. United States: N. p., 2006. Web. doi:10.1063/1.2151181.
Yoon, Peter H., Lui, Anthony T.Y., & Applied Physics Laboratory, Johns Hopkins University, Johns Hopkins Road, Laurel, Maryland 20723-6099. Nonlinear energy principle for model current sheets. United States. doi:10.1063/1.2151181.
Yoon, Peter H., Lui, Anthony T.Y., and Applied Physics Laboratory, Johns Hopkins University, Johns Hopkins Road, Laurel, Maryland 20723-6099. Sun . "Nonlinear energy principle for model current sheets". United States. doi:10.1063/1.2151181.
@article{osti_20782432,
title = {Nonlinear energy principle for model current sheets},
author = {Yoon, Peter H. and Lui, Anthony T.Y. and Applied Physics Laboratory, Johns Hopkins University, Johns Hopkins Road, Laurel, Maryland 20723-6099},
abstractNote = {It is demonstrated on the basis of exact invariants of nonlinear Vlasov equation and model current sheets that the change in magnetic topology (i.e., reconnection) in a finite closed system leads to the conversion of magnetic-field energy to particle energy. It is also shown that the volume-averaged conversion efficiency diminishes as the spatial average is taken over larger and larger system size, while it increases when the system size becomes smaller. This finding may have an important implication for numerical simulation of reconnection processes under finite geometry.},
doi = {10.1063/1.2151181},
journal = {Physics of Plasmas},
number = 1,
volume = 13,
place = {United States},
year = {Sun Jan 15 00:00:00 EST 2006},
month = {Sun Jan 15 00:00:00 EST 2006}
}
  • In the present paper we revisit the energy principle associated with magnetic reconnection. In the earlier approach the boundary of the system was freely adjusted to always contain one full period of the magnetic islands. In view of the fact that in simulations of reconnection such an adjustment of the boundary size is not feasible, in the present paper we reconsider a fixed boundary problem. It is shown that the energy conversion is almost negligible in such a situation. It is thus concluded that the choice of appropriate boundary conditions is critically important in the study of the energy conversionmore » by magnetic reconnection. The present finding also points to the likelihood that the study of reconnection in two dimensions in a fixed boundary system may not reveal any appreciable magnetic field-to-particle energy conversion in an overall sense, although the present idealized theoretical approach cannot address the possibility of local heating and acceleration. This does not necessarily mean that the energy conversion by reconnection is not an efficient source of particle energization, for in nature the system is not limited by any artificial boundaries. The present finding instead only points to the possible limitation of studying the reconnection by a two-dimensional fixed-boundary system.« less
  • Nonlinear evolution of three dimensional electron shear flow instabilities of an electron current sheet (ECS) is studied using electron-magnetohydrodynamic simulations. The dependence of the evolution on current sheet thickness is examined. For thin current sheets (half thickness =d{sub e}=c/ω{sub pe}), tearing mode instability dominates. In its nonlinear evolution, it leads to the formation of oblique current channels. Magnetic field lines form 3-D magnetic spirals. Even in the absence of initial guide field, the out-of-reconnection-plane magnetic field generated by the tearing instability itself may play the role of guide field in the growth of secondary finite-guide-field instabilities. For thicker current sheetsmore » (half thickness ∼5 d{sub e}), both tearing and non-tearing modes grow. Due to the non-tearing mode, current sheet becomes corrugated in the beginning of the evolution. In this case, tearing mode lets the magnetic field reconnect in the corrugated ECS. Later thick ECS develops filamentary structures and turbulence in which reconnection occurs. This evolution of thick ECS provides an example of reconnection in self-generated turbulence. The power spectra for both the thin and thick current sheets are anisotropic with respect to the electron flow direction. The cascade towards shorter scales occurs preferentially in the direction perpendicular to the electron flow.« less
  • A calculation is presented that accounts for rapid nonlinear growth of the {ital m}=1 kink-tearing instability. The equilibrium analysis contained in the Rutherford theory (Phys. Fluids {bold 16}, 1903 (1973)) of nonlinear tearing-mode growth is generalized to islands for which the constant-{psi} approximation is not valid. Applying the helicity-conservation assumption introduced by Kadomtsev ({ital Plasma Physics and Controlled Nuclear Fusion Research} (IAEA, Vienna, 1977), Vol. I, p. 555), the presence of a current-sheet singularity is shown that gives rise to a narrow tearing layer and rapid reconnection. This rapid reconnection, in turn, justifies the use of the helicity conservation assumption.more » The existence of a family of self-similar {ital m}=1 equilibrium islands is demonstrated. The formalism introduced here is shown to apply both to the case of the {ital m}=1 kink-tearing mode and to the case of forced reconnection. These two cases are compared and contrasted.« less
  • The MHD stability of a compact torus is analyzed with the help of a nonlinear variational principle. An unstable mode is found for an entire class of configurations in which the plasma is enclosed in a long cylindrical chamber. One possilbe version of the evolution of this mode in the nonlinear stage is studied. Some possible methods for stabilizing the unstable mode are discussed.