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  • 1
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 8 (2001), S. 475-490 
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The nonlinear time-dependent equations of resistive magnetohydrodynamics are solved in simply connected domains to investigate spheromak formation and sustainment with electrostatic current drive. Spheromak magnetic fields are generated in three-dimensional computations as the nonlinear state resulting from an unstable pinch. Perturbations convert continuously supplied toroidal magnetic flux into poloidal magnetic flux, leading to "flux amplification" of field embedded in the electrodes. Relaxation of the axisymmetric component of the parallel current profile can be substantial, and the final nonlinear state is steady over a wide range of parameters. However, for sufficiently large values of Lundquist number or sufficiently large applied potential, nonsteady final states are observed with periodic relaxation events in some cases. Under most conditions, the saturated configuration exhibits chaotic scattering of the magnetic field lines. Conditions just above the marginal point of pinch instability sustain large closed flux surfaces in steady state; a weakly kinked pinch current threads the toroidal region of closed flux surfaces and imposes stellarator-like helical transform. Closed flux surfaces also form during decay, due to reduced fluctuation levels and average toroidal current driven directly by inductive electric field.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 8 (2001), S. 1505-1513 
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Recent theoretical work [R. A. Nebel and D. C. Barnes, Fusion Technol. 38, 28 (1998); D. C. Barnes and R. A. Nebel, Phys. Plasmas 5, 2498 (1998)] has suggested that a tiny oscillating ion cloud (referred to as the periodically oscillating plasma sphere or POPS) may undergo a self-similar collapse that can result in the periodic and simultaneous attainment of ultrahigh densities and temperatures. However, a major uncertainty in this plasma system is the behavior of the electron cloud that forms a virtual cathode. Here it is demonstrated that the required electron cloud (which forms a harmonic oscillator potential) is susceptible to an instability related to buoyancy-driven modes present in compressible fluids. Although it is demonstrated that no absolutely stable profiles with uniform electron density exist, stable profiles that are close to the required harmonic oscillator potential are found. A simple two-stream analysis indicates that kinetic effects lead to a critical limit in λD/a above which the virtual cathodes are stable. This result is consistent with previous experimental observations. © 2001 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 3 (1996), S. 3983-3997 
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The self-consistent evolution of a pair of initially straight and either parallel or antiparallel magnetic flux tubes with prescribed boundary twist is studied using fully compressible three-dimensional (3-D) resistive magnetohydrodynamics (MHD). 3-D visualization techniques specially designed for divergence free vector fields are employed to investigate topological changes in the field lines and current lines associated with 3-D reconnection in the system. Four cases are studied, corresponding to either parallel or antiparallel initial magnetic fields and to the same or opposite sign of footpoint twist. It is found that in the case with antiparallel field and opposite twist, so that the currents are parallel, the evolution proceeds in two phases. In the first phase, a series of topological changes involving magnetic nulls (where B=0) create an X-type closed field line. In the second phase, the X-type line serves as the separator for reconnection, allowing field lines from the two tubes to merge and form loops. The magnetic field lines exhibit spatial chaos and chaotic scattering. The observed reconnection involves the X-type closed field line with evident current sheets. Later in time, the X-type line changes to an O-type closed field line, surrounded by a ring of toroidal flux surfaces. Reconnection continues until there emerges a final steady state having two reconnected loops and a toroidal ring of flux surfaces in between. The torus of magnetic surfaces has zero current in steady state because it is not connected by field lines to the twist imposed at the boundary. It is discussed how it is possible that such a region of zero current density can exist. The other three cases involve breaking of the ideal MHD flux constraint and changes in topology, but without localized current sheets, i.e., without reconnection. Implications for coronal loop interaction are discussed. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 4 (1997), S. 1238-1248 
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The rf combined trap for confining a non-neutral plasma by a combination of rf fields and a uniform magnetic field is introduced. The particle motion is studied in such a trap in which the rf fields are given by the TM011 mode. The aim is to determine limits on a focus at the center for low angular momentum particles. Such a focus allows densities in excess of the local Brillouin limit. The motion is described in terms of an effective potential consisting of the ponderomotive potential Vpon(r,z) plus a radial potential mΩc2r2/8 due to the magnetic field Bz plus a centrifugal potential pθ2/2mr2. Near the origin r=0, z=0, the equations reduce to a pair of Mathieu equations for the r and z motions. For certain parameters the system is quasispherically symmetric, i.e. the effective ponderomotive frequencies Ωr, Ωz in r and z are equal. In this case the Brillouin limit for a uniform density plasma is shown to equal the usual cylindrical limit. Numerical integration of the ponderomotive equations is shown for parameters near those giving quasispherical symmetry. There is resonance for Ωr/Ωz=1, giving m=2, n=2 islands. The islands limit the size of the focus at the origin, even for pθ=0. For particles with large effective energy Eeff, there can also be chaos, depending on the elongation L/a of the rf cavity. It is found that the deleterious effect of islands and chaos on the focus is minimized by having the elongation L/a close to unity and having particles trapped deeply in the ponderomotive well. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 7 (2000), S. 839-843 
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Previous work [D. C. Barnes and R. A. Nebel, Phys. Plasmas 5, 2498 (1998)] has demonstrated the existence of a one-dimensional self-similar oscillating ion solution which remains in local thermodynamic equilibrium at all times during an oscillation in a harmonic oscillator potential. Here it is shown that all spherically symmetric distributions, in which x, y, and z are independent, are of this form. However, in a real device the density profile will be truncated due to the presence of a wall or conductor. Particle simulations of these truncated profiles are presented and compared with the idealized solutions in the proper limits. Results are also interpreted in terms of rigid rotor rotation in phase space as is appropriate for a harmonic oscillator. Next, it is demonstrated that the deviations from Maxwellian velocity distributions that are observed when the plasma contracts will be quickly rethermalized during the expansion phase. Energy throughput resulting from this rethermalization is discussed. © 2000 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 4 (1992), S. 2758-2768 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A fluid equilibrium consisting of a periodic array of counter-rotating vortices is found to be unstable to the generation of one-dimensional sheared flow along the direction of periodicity. This instability is inviscid (exists for zero viscosity μ) or viscous (with growth rate γ∼μ3/4) depending on the elongation of the vortices. Nonlinearly, the instability goes through a vortex reconnection or "peeling'' phase in which one of the vortices per period is destroyed, leading to a state with a chain of islands. Without a source, the flow evolves to pure one-dimensional shear flow, which decays because of viscosity on a much longer time scale. In the presence of a source driving the initial vortices, the flow evolves to an equilibrium having vortex flow plus shear flow and, for sufficiently high Reynolds number, having only one vortex per periodicity length rather than two, i.e., with islands.
    Type of Medium: Electronic Resource
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  • 7
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The comments of Montgomery and Matthaeus on the authors' paper1, have been answered. The results do not contradict those of Montgomery and Matthaeus but for simple case considered, transition to shear flow state and shape of initial vortices is explained. (AIP)
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 9 (2002), S. 1164-1176 
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The nonlinear regime of the parallel velocity shear–tearing instability is studied numerically using a two-dimensional reduced, resistive magnetohydrodynamics model. In this instability, a sheared parallel velocity profile interacts with the perpendicular dynamics via the magnetic field curvature. Linearly, it has been shown [J. M. Finn, Phys. Plasmas 2, 4400 (1995)] that, in the inviscid limit, such interaction alters the classical behavior of the tearing instability, resulting in increased growth rates for classically tearing-unstable regimes (Δ′〉0), and destabilizing classically tearing-stable regimes, leading to an electrostatic mode as Δ′→−∞. These trends are seen to hold with finite viscosity as long as the perpendicular plasma viscosity is of the order or smaller than the plasma resistivity. Nonlinearly, it is found that a self-consistent perpendicular shear flow and a reversed (stabilizing) density gradient develop. For favorable curvature, the latter implies an anomalous pinch effect. The shear flow generation mechanism is found, using quasilinear theory, to be related to asymmetries (tilting) introduced by the magnetic curvature coupling term. In the classically tearing-stable regime, the nonlinear behavior is very rich, including relaxation-oscillation phenomena and chaotic behavior. The potential implications of the nonlinear regime of this instability for the plasma confinement are also discussed. © 2002 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 4 (1992), S. 488-491 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A periodic array of convection cells is subject to a "shear flow'' instability. The generation of the sheared flow is a consequence of "peeling'' of the convection cells. Fluid simulations demonstrate that the efficiency of shear flow generation is high. Implications for understanding poloidal rotation in tokamaks are discussed.
    Type of Medium: Electronic Resource
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