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

Title: Two-fluid physics and field-reversed configurations

Abstract

In this paper, algorithms for the solution of two-fluid plasma equations are presented and applied to the study of field-reversed configurations (FRCs). The two-fluid model is more general than the often used magnetohydrodynamic (MHD) model. The model takes into account electron inertia, charge separation, and the full electromagnetic field equations, and it allows for separate electron and ion motion. The algorithm presented is the high-resolution wave propagation scheme. The wave propagation method is based on solutions to the Riemann problem at cell interfaces. Operator splitting is used to incorporate the Lorentz and electromagnetic source terms. The algorithms are benchmarked against the Geospace Environmental Modeling Reconnection Challenge problem. Equilibrium of FRC is studied. It is shown that starting from a MHD equilibrium produces a relaxed two-fluid equilibrium with strong flows at the FRC edges due to diamagnetic drift. The azimuthal electron flow causes lower-hybrid drift instabilities (LHDI), which can be captured if the ion gyroradius is well resolved. The LHDI is known to be a possible source of anomalous resistivity in many plasma configurations. LHDI simulations are performed in slab geometries and are compared to recent experimental results.

Authors:
;  [1];  [2]
  1. Tech-X Corporation, 5621 Arapahoe Avenue - Suite A, Boulder, Colorado 80303 (United States)
  2. (United States)
Publication Date:
OSTI Identifier:
20975039
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Plasmas; Journal Volume: 14; Journal Issue: 5; Other Information: DOI: 10.1063/1.2742570; (c) 2007 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; ALGORITHMS; DRIFT INSTABILITY; ELECTRONS; FIELD-REVERSED THETA PINCH DEVICES; LOWER HYBRID CURRENT DRIVE; LOWER HYBRID HEATING; MAGNETOHYDRODYNAMICS; MHD EQUILIBRIUM; PLASMA; PLASMA DIAMAGNETISM; PLASMA FLUID EQUATIONS; PLASMA SIMULATION; REVERSE-FIELD PINCH; REVERSED-FIELD PINCH DEVICES

Citation Formats

Hakim, A., Shumlak, U., and Aerospace and Energetics Research Program, University of Washington, Seattle, Washington 98195-2600. Two-fluid physics and field-reversed configurations. United States: N. p., 2007. Web. doi:10.1063/1.2742570.
Hakim, A., Shumlak, U., & Aerospace and Energetics Research Program, University of Washington, Seattle, Washington 98195-2600. Two-fluid physics and field-reversed configurations. United States. doi:10.1063/1.2742570.
Hakim, A., Shumlak, U., and Aerospace and Energetics Research Program, University of Washington, Seattle, Washington 98195-2600. Tue . "Two-fluid physics and field-reversed configurations". United States. doi:10.1063/1.2742570.
@article{osti_20975039,
title = {Two-fluid physics and field-reversed configurations},
author = {Hakim, A. and Shumlak, U. and Aerospace and Energetics Research Program, University of Washington, Seattle, Washington 98195-2600},
abstractNote = {In this paper, algorithms for the solution of two-fluid plasma equations are presented and applied to the study of field-reversed configurations (FRCs). The two-fluid model is more general than the often used magnetohydrodynamic (MHD) model. The model takes into account electron inertia, charge separation, and the full electromagnetic field equations, and it allows for separate electron and ion motion. The algorithm presented is the high-resolution wave propagation scheme. The wave propagation method is based on solutions to the Riemann problem at cell interfaces. Operator splitting is used to incorporate the Lorentz and electromagnetic source terms. The algorithms are benchmarked against the Geospace Environmental Modeling Reconnection Challenge problem. Equilibrium of FRC is studied. It is shown that starting from a MHD equilibrium produces a relaxed two-fluid equilibrium with strong flows at the FRC edges due to diamagnetic drift. The azimuthal electron flow causes lower-hybrid drift instabilities (LHDI), which can be captured if the ion gyroradius is well resolved. The LHDI is known to be a possible source of anomalous resistivity in many plasma configurations. LHDI simulations are performed in slab geometries and are compared to recent experimental results.},
doi = {10.1063/1.2742570},
journal = {Physics of Plasmas},
number = 5,
volume = 14,
place = {United States},
year = {Tue May 15 00:00:00 EDT 2007},
month = {Tue May 15 00:00:00 EDT 2007}
}
  • After extensive experimentation on the Translation, Confinement, and Sustainment rotating magnetic-field (RMF)-driven field reversed configuration (FRC) device [A. L. Hoffman et al., Fusion Sci. Technol. 41, 92 (2002)], the principal physics of RMF formation and sustainment of standard prolate FRCs inside a flux conserver is reasonably well understood. If the RMF magnitude B{sub {omega}} at a given frequency {omega} is high enough compared to other experimental parameters, it will drive the outer electrons of a plasma column into near synchronous rotation, allowing the RMF to penetrate into the plasma. If the resultant azimuthal current is strong enough to reverse anmore » initial axial bias field B{sub o} a FRC will be formed. A balance between the RMF applied torque and electron-ion friction will determine the peak plasma density n{sub m}{proportional_to}B{sub {omega}}/{eta}{sup 1/2}{omega}{sup 1/2}r{sub s}, where r{sub s} is the FRC separatrix radius and {eta} is an effective weighted plasma resistivity. The plasma total temperature T{sub t} is free to be any value allowed by power balance as long as the ratio of FRC diamagnetic current, I{sup '}{sub dia}{approx_equal}2B{sub e}/{mu}{sub o}, is less than the maximum possible synchronous current, I{sup '}{sub sync}=<n{sub e}>e{omega}r{sub s}{sup 2}/2. The RMF will self-consistently penetrate a distance {delta}{sup *} governed by the ratio {zeta}=I{sup '}{sub dia}/I{sup '}{sub sync}. Since the FRC is a diamagnetic entity, its peak pressure p{sub m}=n{sub m}kT{sub t} determines its external magnetic field B{sub e}{approx_equal}(2{mu}{sub o}p{sub m}){sup 1/2}. Higher FRC currents, magnetic fields, and poloidal fluxes can thus be obtained, with the same RMF parameters, simply by raising the plasma temperature. Higher temperatures have also been noted to reduce the effective plasma resistivity, so that these higher currents can be supported with surprisingly little increase in absorbed RMF power.« less
  • The nonlinear interactions of time-varying magnetic fields with plasmas is investigated in the regime of electron magnetohydrodynamics. Simple magnetic field geometries are excited in a large laboratory plasma with a loop antenna driven with large oscillatory currents. When the axial loop field opposes the ambient field, the net field can be reversed to create a field-reversed configuration (FRC). In the opposite polarity, a strong field enhancement is produced. The time-varying antenna field excites whistler modes with wave magnetic fields exceeding the ambient magnetic field. The resulting magnetic field topologies have been measured. As the magnetic topology is changed from FRCmore » to strong enhancement, two propagating field configurations resembling spheromaks are excited, one with positive and the other with negative helicity. Such 'whistler spheromaks' propagate with their null points along the weaker ambient magnetic field, with the current density localized around its O-line. In contrast, 'whistler mirrors' which have topologies similar to linear whistlers, except with B{sub wave}>B{sub 0}, have no null regions and, therefore, broad current layers. This paper describes the basic field topologies of whistler spheromaks and mirrors, while companion papers discuss the associated nonlinear phenomena as well as the interaction between them.« less
  • Two-dimensional field-reversed equilibria bounded by a conducting cylinder are computed. The computation is made possible by using a global constraint and by using a computational algorithm that is protective of the initial guess. A pressure profile is used that has sufficient generality to match experimentally produced configurations. It is found that for some choices of separatrix radius and separatrix beta, no equilibria exist. The reasons for loss of equilibrium are discussed and an example of a configuration near loss of equilibrium conditions is given.
  • An interpretive method is developed for extracting details of the fully two-dimensional (2D) “internal” structure of field-reversed configurations (FRC) from common diagnostics. The challenge is that only external and “gross” diagnostics are routinely available in FRC experiments. Inferring such critical quantities as the poloidal flux and the particle inventory has commonly relied on a theoretical construct based on a quasi-one-dimensional approximation. Such inferences sometimes differ markedly from the more accurate, fully 2D reconstructions of equilibria. An interpreter based on a fully 2D reconstruction is needed to enable realistic within-the-shot tracking of evolving equilibrium properties. Presented here is a flexible equilibriummore » reconstruction with which an extensive data base of equilibria was constructed. An automated interpreter then uses this data base as a look-up table to extract evolving properties. This tool is applied to data from the FRC facility at Tri Alpha Energy. It yields surprising results at several points, such as the inferences that the local β (plasma pressure/external magnetic pressure) of the plasma climbs well above unity and the poloidal flux loss time is somewhat longer than previously thought, both of which arise from full two-dimensionality of FRCs.« less
  • A two fluid model is used to derive an analytical equilibrium for elongated field reversed configurations containing shear in both the electron and ion velocity profiles. Like some semiempirical models used previously, the analytical expressions obtained provide a satisfactory fit to the experimental results for all radii with a few key parameters. The present results reduce to the rigid rotor model and the infinite conductivity case for a specific choice of the parameters.