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Dec 2002

Volume 9, Issue 12, pp. 4837-5140

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Linear and nonlinear thresholds of neoclassical tearing modes in tokamaks

Hinrich Lütjens and Jean-François Luciani

Phys. Plasmas 9, 4837 (2002); http://dx.doi.org/10.1063/1.1521717 (4 pages) | Cited 19 times

Online Publication Date: 18 November 2002

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The understanding of the physics of neoclassical tearing modes (NTM) is important for the dimensioning of current drive systems used to stabilize these modes in International Thermonuclear Experimental Reactor (ITER) plasmas [R. Aymar et al., Nucl. Fusion 41, 1301 (2001)]. Predictions by theoretical models for the dynamics of NTM’s are compared with full scale numerical magnetohydrodynamical simulations including bootstrap current and transport effects. It is shown that curvature currents are sufficient to generate a nonlinear stability threshold for NTM’s. Furthermore, it is emphasized that at large resistivity NTM’s behave as an ordinary linear instability, which suppresses this nonlinear stability threshold. © 2002 American Institute of Physics.
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52.35.Py Macroinstabilities (hydromagnetic, e.g., kink, fire-hose, mirror, ballooning, tearing, trapped-particle, flute, Rayleigh-Taylor, etc.)
52.55.Fa Tokamaks, spherical tokamaks
52.30.Cv Magnetohydrodynamics (including electron magnetohydrodynamics)
52.65.-y Plasma simulation

A systematic search for new kinetic structures in collisionless current-carrying plasmas

A. Luque, H. Schamel, and J.-M. Grießmeier

Phys. Plasmas 9, 4841 (2002); http://dx.doi.org/10.1063/1.1518013 (4 pages) | Cited 4 times

Online Publication Date: 18 November 2002

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The parameter space of nonlinear electrostatic structures in one-dimensional current-carrying plasmas is surveyed. The region available for physically meaningful solutions is precisely marked out and several new kinds of trapped particle structures, such as an alternating train of electron and ion holes, are found. © 2002 American Institute of Physics.
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52.35.Sb Solitons; BGK modes
52.35.Mw Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.)
52.35.Qz Microinstabilities (ion-acoustic, two-stream, loss-cone, beam-plasma, drift, ion- or electron-cyclotron, etc.)
52.35.Py Macroinstabilities (hydromagnetic, e.g., kink, fire-hose, mirror, ballooning, tearing, trapped-particle, flute, Rayleigh-Taylor, etc.)
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back to top Basic Plasma Phenomena, Waves, Instabilities

The Alfvén resonance in a dusty plasma with a distribution of grain sizes

N. F. Cramer, F. Verheest, and S. V. Vladimirov

Phys. Plasmas 9, 4845 (2002); http://dx.doi.org/10.1063/1.1521419 (6 pages) | Cited 9 times

Online Publication Date: 18 November 2002

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The resonance absorption of low-frequency electromagnetic waves in a dusty magnetized plasma is considered. The dust grains are assumed to carry a proportion of the negative charge of the plasma, and there is assumed to be a distribution of dust sizes, typical of that deduced to be present in interstellar molecular clouds. The resonances and cutoffs of the waves in a homogeneous plasma are discussed. The waves are shown to be damped due to Alfvén resonance, and it is shown that the effects of the distributed dust sizes are to produce a broad spatial region of resonance absorption due to dust cyclotron damping. © 2002 American Institute of Physics.
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52.35.Bj Magnetohydrodynamic waves (e.g., Alfven waves)
52.25.Vy Impurities in plasmas
96.30.Cw Comets
98.38.Dq Molecular clouds, H2 clouds, dense clouds, and dark clouds

Noise driven configuration of dust clusters by molecular dynamics simulation

Bai-Song Xie and Zhi-An Yang

Phys. Plasmas 9, 4851 (2002); http://dx.doi.org/10.1063/1.1518012 (5 pages) | Cited 3 times

Online Publication Date: 18 November 2002

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Molecular dynamics simulations are employed to study the effect of noise on the stationary configuration formation of clusters of two-dimensional dusty plasma. It is found that the noise can induce a new stable cluster configuration that is significantly different from that without noise. And, the tunneling crisis phenomena of nonlinear dynamical system is also exhibited in few body dusty clusters studied under noise. Some implication of results to experiments is also discussed. © 2002 American Institute of Physics.
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52.27.Lw Dusty or complex plasmas; plasma crystals
05.45.-a Nonlinear dynamics and chaos
52.25.Vy Impurities in plasmas

Kelvin–Helmholtz instability in Beltrami fields

A. Ito, Z. Yoshida, T. Tatsuno, S. Ohsaki, and S. M. Mahajan

Phys. Plasmas 9, 4856 (2002); http://dx.doi.org/10.1063/1.1518679 (7 pages) | Cited 5 times

Online Publication Date: 18 November 2002

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The stability of Beltrami flows has been analyzed. The model equation represents the coupling of the Kelvin–Helmholtz (KH) instability with Alfvén waves. In a single Beltrami flow that parallels a force-free magnetic field, the magnetic field reduces the growth rate of the KH instability, while the marginally stable wave number is unchanged. Calculating the marginally stable eigenfunction of a magnetohydrodynamic flow, the necessary and sufficient condition for the exponential stability has been derived. The stability of double Beltrami flows has also been analyzed, which is represented by linear combinations of two Beltrami flows. Coupling of two vortices yields both stabilizing and destabilizing effects depending on the amplitudes and the eigenvalues of two Beltrami functions. © 2002 American Institute of Physics.
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52.35.Py Macroinstabilities (hydromagnetic, e.g., kink, fire-hose, mirror, ballooning, tearing, trapped-particle, flute, Rayleigh-Taylor, etc.)
52.35.Bj Magnetohydrodynamic waves (e.g., Alfven waves)
52.30.Cv Magnetohydrodynamics (including electron magnetohydrodynamics)

Stability analysis of hollow electron columns including compressional and thermal effects: Integrability condition and numerical simulations

G. L. Delzanno, V. I. Pariev, J. M. Finn, and G. Lapenta

Phys. Plasmas 9, 4863 (2002); http://dx.doi.org/10.1063/1.1518680 (8 pages) | Cited 3 times

Online Publication Date: 18 November 2002

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The diocotron spectrum for a simplified fluid model of Malmberg–Penning traps that includes compressional effects due to end curvature with finite temperature is investigated. A class of length profiles for which the linearized eigenvalue equation for perturbations can be integrated by quadratures (integrable cases) has been found. In such cases, there is only algebraic growth when the effective angular frequency has a maximum away from the axis (hollow profile), and the model is mathematically equivalent to the zero curvature (two-dimensional Euler) case. Furthermore, profiles that are slightly nonintegrable (the difference being characterized by a small parameter ε) have been studied, finding that the complex frequency of the unstable l = 1 mode scales as ε2/3. Analytical calculations (to be presented in a companion paper) and numerical simulations are found in agreement. For the density profile used, the growth rate of the unstable mode has a minimum at the plasma temperature of about 5 eV, which might be tested experimentally. © 2002 American Institute of Physics.
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52.35.Py Macroinstabilities (hydromagnetic, e.g., kink, fire-hose, mirror, ballooning, tearing, trapped-particle, flute, Rayleigh-Taylor, etc.)
52.35.Qz Microinstabilities (ion-acoustic, two-stream, loss-cone, beam-plasma, drift, ion- or electron-cyclotron, etc.)
52.65.-y Plasma simulation

Dynamic response of a one-component plasma at moderate coupling

A. Wierling, T. Pschiwul, and G. Zwicknagel

Phys. Plasmas 9, 4871 (2002); http://dx.doi.org/10.1063/1.1522382 (8 pages) | Cited 5 times

Online Publication Date: 18 November 2002

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The dynamic structure factor of one-component plasmas at moderate coupling (Γ = 0.5–8) is studied analytically and by molecular dynamics simulations. The recurrence relation technique is used to derive a parameterization of the dynamic structure factor taking into account analytically accessible moments. These moments are calculated from the pair distribution function obtained within the hypernetted chain approximation. A truncation of the recurrence relations on the level of the second-order memory function is proposed. It is shown, that this presents an efficient way to incorporate collisions. © 2002 American Institute of Physics.
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52.65.Yy Molecular dynamics methods
back to top Nonlinear Phenomena, Turbulence, Transport

Nonlinear dust Bernstein–Greene–Kruskal modes in charge-varying dusty plasmas

Mouloud Tribeche, Taha Houssine Zerguini, and Hocine Houili

Phys. Plasmas 9, 4879 (2002); http://dx.doi.org/10.1063/1.1518682 (8 pages) | Cited 14 times

Online Publication Date: 18 November 2002

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Nonlinear dust Bernstein–Greene–Kruskal (BGK) modes are investigated in a charge-varying dusty plasma. It is found that highly localized structures, solely due to the dust charge variation, can exist. The dust BGK soliton suffers the well-known anomalous damping, the importance of which is roughly proportional to the dust grain velocity. This dissipation causes the soliton amplitude to decay algebraically and the conservation of “soliton mass” leads to the development of a noise tail. © 2002 American Institute of Physics.
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52.35.Sb Solitons; BGK modes
52.27.Lw Dusty or complex plasmas; plasma crystals
52.35.Py Macroinstabilities (hydromagnetic, e.g., kink, fire-hose, mirror, ballooning, tearing, trapped-particle, flute, Rayleigh-Taylor, etc.)
52.35.Qz Microinstabilities (ion-acoustic, two-stream, loss-cone, beam-plasma, drift, ion- or electron-cyclotron, etc.)

Ion soliton observation with laser-induced fluorescence

N. Claire, G. Bachet, and F. Skiff

Phys. Plasmas 9, 4887 (2002); http://dx.doi.org/10.1063/1.1520143 (9 pages) | Cited 3 times

Online Publication Date: 18 November 2002

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A laser-induced fluorescence observation of ion-acoustic waves in a collisionless unmagnetized double plasma multipolar device is presented. The optical pumping effect is found to be critical for the interpretation of fast changes of the ion velocity distribution functions induced by the propagation of a soliton. To take this effect into account, the continuity equation is used. The laser-induced fluorescence diagnostic shows that the separation of solitons requires a small plasma drift in the backward direction (reverse direction of the soliton propagation) and that the precursor ions are in fact a precursor wave. © 2002 American Institute of Physics.
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52.35.Tc Shock waves and discontinuities
52.50.Dg Plasma sources
52.70.Kz Optical (ultraviolet, visible, infrared) measurements

Mean field theory of the coherent to random-phase state transition in three-wave interactions

P. M. Drysdale and P. A. Robinson

Phys. Plasmas 9, 4896 (2002); http://dx.doi.org/10.1063/1.1520536 (9 pages) | Cited 7 times

Online Publication Date: 18 November 2002

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The crossover of three-wave interactions from the coherent monochromatic limit to the wide bandwidth random-phase limit is investigated as the bandwidth of the waves is varied in a system exhibiting nonlinear three-wave oscillations. A recently observed sudden transition between the coherent and incoherent interaction is confirmed. As the bandwidth is increased from the monochromatic limit, it is found that the coherence of the interaction decreases slowly. At the transition point of the interaction the coherence then falls abruptly and nonlinear oscillations cease. An analytic mean-field approach is used to model the transition. Below the transition point, each frequency component of the wave spectra oscillates at its own individual frequency about the aggregate quasicoherent oscillation of the wave as a whole. It is when the frequency component at the spectral edge cannot sustain such oscillations that the system switches to random phase behavior. The analytic model’s estimate of the transition point and other interaction properties agrees semiquantitatively with numerical solutions of the full equations. © 2002 American Institute of Physics.
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52.35.Mw Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.)
42.65.Sf Dynamics of nonlinear optical systems; optical instabilities, optical chaos and complexity, and optical spatio-temporal dynamics

Hall magnetohydrodynamics model of double discontinuities

Y. C. Whang

Phys. Plasmas 9, 4905 (2002); http://dx.doi.org/10.1063/1.1521420 (6 pages)

Online Publication Date: 18 November 2002

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A double discontinuity is a compound structure composed of a slow shock layer and an adjoining rotational discontinuity layer on the postshock side. Since the Hall current effects become important as the magnetic field rotates by tens of degree over a thin rotational layer, steady state solutions based on the Hall magnetohydrodynamics (MHD) theory can show the merging of a rotational layer and a slow shock layer to form the observed compound structure. This model uses a set of modified Rankine–Hugoniot relations to calculate the jump conditions between the upstream region and the interface between the two layers, and uses the Hall-MHD equations to calculate the variations of the plasma and magnetic field in the rotational layer in the downstream of the interface. Four series of solutions are presented to show the effect for each of four governing parameters on the structure of double discontinuities. © 2002 American Institute of Physics.
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95.30.Qd Magnetohydrodynamics and plasmas
52.30.-q Plasma dynamics and flow
96.50.Ry Discontinuities

Zonal flows and transport in ion temperature gradient turbulence

Sheikh Dastgeer, Sangeeta Mahajan, and Jan Weiland

Phys. Plasmas 9, 4911 (2002); http://dx.doi.org/10.1063/1.1523010 (6 pages) | Cited 14 times

Online Publication Date: 18 November 2002

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The nonlinear “Dimits” upshift found in gyrokinetic Cyclone simulations has been recovered in simulations using a reactive fluid model. Its magnitude is in good agreement with the gyrokinetic simulations. The upshift is caused by resonant excitation of zonal flows which also provide an absorbing boundary for long wavelengths in the regime above the nonlinear upshift. In agreement with analytical predictions, magnetic shear has a destabilizing effect in combination with zonal flows. © 2002 American Institute of Physics.
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52.25.Fi Transport properties
52.35.Bj Magnetohydrodynamic waves (e.g., Alfven waves)
52.35.Ra Plasma turbulence
52.65.Tt Gyrofluid and gyrokinetic simulations
52.55.Fa Tokamaks, spherical tokamaks
52.25.Tx Emission, absorption, and scattering of particles
28.52.Cx Fueling, heating and ignition
52.30.Cv Magnetohydrodynamics (including electron magnetohydrodynamics)
52.35.Mw Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.)
52.35.Py Macroinstabilities (hydromagnetic, e.g., kink, fire-hose, mirror, ballooning, tearing, trapped-particle, flute, Rayleigh-Taylor, etc.)
back to top Magnetically Confined Plasmas, Heating, Confinement

Escape patterns, magnetic footprints, and homoclinic tangles due to ergodic magnetic limiters

Elton C. da Silva, Iberê L. Caldas, Ricardo L. Viana, and Miguel A. F. Sanjuán

Phys. Plasmas 9, 4917 (2002); http://dx.doi.org/10.1063/1.1518681 (12 pages) | Cited 23 times

Online Publication Date: 18 November 2002

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The action of a set of ergodic magnetic limiters in tokamaks is investigated from the Hamiltonian chaotic scattering point of view. Special attention is paid to the influence of invariant sets, such as stable and unstable manifolds, as well as the strange saddle, on the formation of the chaotic layer at the plasma edge. The nonuniform escape process associated to chaotic field lines is also analyzed. It is shown that the ergodic layer produced by the limiters has not only a fractal structure, but it possesses the even more restrictive Wada property. © 2002 American Institute of Physics.
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52.55.Fa Tokamaks, spherical tokamaks
05.45.-a Nonlinear dynamics and chaos
05.20.-y Classical statistical mechanics

Unstable ion-temperature-gradient modes in the Wendelstein 7-X stellarator configuration

T. Rafiq, R. Kleiber, M. Nadeem, and M. Persson

Phys. Plasmas 9, 4929 (2002); http://dx.doi.org/10.1063/1.1510665 (10 pages) | Cited 13 times

Online Publication Date: 18 November 2002

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The linear stability of the ion-temperature-gradient modes (ITG) in the electrostatic limit is examined in the short wavelength region by using a two fluid reactive model in fully three-dimensional Wendelstein 7-X (W7-X) stellarator [G. Grieger et al., Plasma Physics and Controlled Nuclear Fusion Research, 1990 (International Atomic Energy Agency, Vienna, 1991), Vol. 3, p. 525] geometry. The spectrum of stable and unstable modes and their real frequencies and eigenfunctions are calculated. The effects of density gradients, temperature gradients, temperature ratios, wavevector, ballooning angle, curvature and local magnetic shear on the ITG mode are also investigated. The frequency and growth rate of the most unstable ITG mode is calculated and visualized for a specific magnetic flux surface. For the equilibrium under investigation both localized and extended eigenmodes are found. The effect of small and large temperature ratios, small and large density gradients as well as large local magnetic shear are all found to be stabilizing. The highest growth rates are found at the outer part of the surface where the local magnetic shear is small and normal curvature is unfavorable. © 2002 American Institute of Physics.
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52.55.Jd Magnetic mirrors, gas dynamic traps
52.35.Py Macroinstabilities (hydromagnetic, e.g., kink, fire-hose, mirror, ballooning, tearing, trapped-particle, flute, Rayleigh-Taylor, etc.)
52.35.Qz Microinstabilities (ion-acoustic, two-stream, loss-cone, beam-plasma, drift, ion- or electron-cyclotron, etc.)

Energetic particle mode stability in tokamaks with hollow q-profiles

F. Zonca, S. Briguglio, L. Chen, S. Dettrick, G. Fogaccia, D. Testa, and G. Vlad

Phys. Plasmas 9, 4939 (2002); http://dx.doi.org/10.1063/1.1519241 (18 pages) | Cited 42 times

Online Publication Date: 18 November 2002

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A thorough analysis of energetic particle modes (EPM) stability and mode structures is presented for tokamaks with hollow q profiles. Focusing on the region near the minimum-q surface, EPM gap modes and resonant EPMs are shown to exist as solutions of the same dispersion relation. By controlling the fast ion distribution function, or, equivalently, their fundamental dynamical properties, a smooth transition between these two classes of modes is obtained within the EPM dispersion relation. When toroidal coupling becomes important, it is demonstrated that EPMs may have either single or double hump radial structures. The local analyses of EPM stability and mode structures near the minimum-q surface are put in the broader framework of EPM stability and EPM induced transport in tokamaks with hollow q profiles and a brief summary is also given of present understanding of such problems based on results of three-dimensional nonlinear hybrid magneto–hydrodynamic–gyrokinetic simulations. Possible implications of present results are discussed in terms of experimental observations and possibilities of designing novel experimental setups to probe, at least conceptually, the complex predictions of theory. © 2002 American Institute of Physics.
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52.55.Pi Fusion products effects (e.g., alpha-particles, etc.), fast particle effects
52.35.Bj Magnetohydrodynamic waves (e.g., Alfven waves)
52.35.Tc Shock waves and discontinuities
52.50.Gj Plasma heating by particle beams

Modeling of stochastic magnetic flux loss from the edge of a poloidally diverted tokamak

T. E. Evans, R. A. Moyer, and P. Monat

Phys. Plasmas 9, 4957 (2002); http://dx.doi.org/10.1063/1.1521125 (11 pages) | Cited 61 times

Online Publication Date: 18 November 2002

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A field line integration code is used to study the loss of edge poloidal magnetic flux due to stochastic magnetic fields produced by an error field correction coil (C–coil) in DIII–D [J. L. Luxon, Nucl. Fusion 42, 614 (2002)] for various plasma shapes, coil currents and edge magnetic shear profiles. We find that the boundary of a diverted tokamak is more sensitive to stochastic flux loss than a nondiverted tokamak. The C–coil has been used to produce a stochastic layer in an ohmic diverted discharge with characteristics similar to those seen in stochastic boundary experiments in circular limiter ohmic plasmas, including (1) an overall increase in recycling, (2) a broadening of the recycling profile at the divertor, and (3) a flattening of the boundary profiles over the extent of the stochastic layer predicted by the field line integration code. Profile flattening consistent with field line integration results is also seen in some high performance discharges with edge transport barriers. The prediction of a significant edge stochastic layer even in discharges with high performance and edge radial transport barriers indicates that either the self-consistent plasma response heals the stochastic layer or that edge stochastic layers are compatible with edge radial transport barriers. © 2002 American Institute of Physics.
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02.50.Ey Stochastic processes
52.25.Fi Transport properties
52.55.-s Magnetic confinement and equilibrium
52.55.Dy General theory and basic studies of plasma lifetime, particle and heat loss, energy balance, field structure, etc.

Self-similar decaying profiles for reversed-field pinches

R. A. Nebel, D. D. Schnack, and T. A. Gianakon

Phys. Plasmas 9, 4968 (2002); http://dx.doi.org/10.1063/1.1521713 (17 pages) | Cited 8 times

Online Publication Date: 18 November 2002

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In previous work it was shown that progress in attaining and maintaining stable mean reversed-field pinch (RFP) profiles can be made by abandoning the steady-state assumption and instead seeking solutions of the pressureless (force-free), one-dimensional transport equations that are separable in time and space [E. J. Caramana and R. A. Nebel, Phys. Fluids 31, 3322 (1988)]. Here these solutions have been extended to two dimensions and therefore the previous formalism is also applicable to toroidal and helical states as well as axisymmetric cylindrical states. Furthermore, the one-dimensional separable solutions are demonstrated to be three-dimensional attractors, provided that the separable profiles are stable to current-driven modes. The sensitivity of these states to the velocity boundary conditions and to dimensionless parameters such as the Lundquist number and the magnetic Prandtl number has been studied. The stability boundary between one-dimensional stable solutions and unstable rampdown solutions has also been explored. Simulations with finite pressure and self-consistent transport clearly show the improved confinement that can be achieved with plasma rampdown. Finally, reactor simulations demonstrate that self-similar tearing mode stable rampdown discharges can lead to pulsed systems that show significant net energy gain. © 2002 American Institute of Physics.
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52.55.Jd Magnetic mirrors, gas dynamic traps
52.65.Kj Magnetohydrodynamic and fluid equation

Resistive stability of magnetic dipole and other axisymmetric closed field line configurations

Andrei N. Simakov, Peter J. Catto, Jesus J. Ramos, and R. J. Hastie

Phys. Plasmas 9, 4985 (2002); http://dx.doi.org/10.1063/1.1515272 (11 pages) | Cited 4 times

Online Publication Date: 18 November 2002

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The stability of axisymmetric plasmas confined by a closed poloidal magnetic field is investigated using magnetohydrodynamic equations with anisotropic resistivity and sound waves retained. It is shown that when the system is axially and up–down symmetric and the plasma beta = (plasma pressure/magnetic pressure) is finite, a resistive instability with a growth rate proportional to the cube root of the resistivity exists at the ideal stability boundary for up–down antisymmetric modes. Both the ideal and resistive stability of a Z-pinch equilibrium and the point dipole equilibrium of Krasheninnikov, Catto, and Hazeltine [Phys. Rev. Lett. 82, 2689 (1999)] are studied in detail. For a Z pinch, ideal instabilities are found to always dominate over resistive instabilities. For the point dipole, ideal up–down antisymmetric modes are always stable, and the only resistive instabilities permitted have a growth rate proportional to the resistivity times the square of the azimuthal mode number. © 2002 American Institute of Physics.
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52.35.Py Macroinstabilities (hydromagnetic, e.g., kink, fire-hose, mirror, ballooning, tearing, trapped-particle, flute, Rayleigh-Taylor, etc.)
52.58.Lq Z-pinches, plasma focus, and other pinch devices

Improved confinement through internal transport barrier formation with lower hybrid current drive in the Hefei Tokamak-7

Bojiang Ding, Guangli Kuang, Yuexiu Liu, Jiafang Shan, Weici Shen, Jiawen Yu, Shengxia Liu, Yuejiang Shi, Yinxian Jie, Baonian Wan, Yanping Zhao, and Jiangang Li

Phys. Plasmas 9, 4996 (2002); http://dx.doi.org/10.1063/1.1516216 (5 pages) | Cited 7 times

Online Publication Date: 18 November 2002

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An improved confinement through internal transport barrier formation with lower hybrid current drive (LHCD) is obtained on the Hefei Tokamak-7 [J. K. Xie et al., Proceedings of the 16th International Conference on Fusion Energy, Montreal, 1996 (International Atomic Energy Agency, Vienna, 1997), Vol. 1, p. 685]. The experimental energy confinement time increases from 14.6 ms (Ohmic discharge phase) to 24.5 ms (LHCD phase), which is consistent with the value predicted by the high confinement mode scaling law of ITER93 (edge localized mode free). The confinement factor H (H = τE/τEITER89P) up to 1.42 is obtained during the improved confinement phase. The analysis shows that the modification of the plasma current profile and E×B are two possible reasons for the confinement improvement. © 2002 American Institute of Physics.
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52.55.Fa Tokamaks, spherical tokamaks
52.25.Fi Transport properties
52.40.Hf Plasma-material interactions; boundary layer effects

Equilibrium of field reversed configurations with rotation. III. Two space dimensions and one type of ion

Artan Qerushi and Norman Rostoker

Phys. Plasmas 9, 5001 (2002); http://dx.doi.org/10.1063/1.1517294 (17 pages) | Cited 1 time

Online Publication Date: 18 November 2002

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A two-dimensional equilibrium model for field reversed configurations (FRCs) with rotation is presented. In a previous paper [N. Rostoker and A. Qerushi, Phys. Plasmas 9, 3057 (2002)] it was shown that a complete description of equilibria for FRCs with rotation is provided by a generalized Grad–Shafranov equation for the plasma flux function. In this paper it is shown how to solve that fundamental equation for the case of two space dimensions and one type of ion. Periodic boundary conditions and a Green’s function are used to convert the original differential equation to an equivalent integral equation. The integral equation is solved by iteration. An iteration algorithm is described which converges to a solution of the generalized Grad–Shafranov equation starting with a one-dimensional trial function. Analytic one-dimensional solutions are shown to be a limiting case of two-dimensional solutions when the applied magnetic field is constant. In addition to rapid convergence for a complex nonlinear problem, the Green’s function method guarantees that the boundary conditions are satisfied in every iteration. © 2002 American Institute of Physics.
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52.58.Lq Z-pinches, plasma focus, and other pinch devices
02.30.Rz Integral equations
02.60.Nm Integral and integrodifferential equations

Models for the pedestal temperature at the edge of H-mode tokamak plasmas

T. Onjun, G. Bateman, A. H. Kritz, and G. Hammett

Phys. Plasmas 9, 5018 (2002); http://dx.doi.org/10.1063/1.1518474 (13 pages) | Cited 54 times

Online Publication Date: 18 November 2002

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Predictive models are developed for the temperature at the top at the edge of type 1 ELMy (edge localized mode) H-mode (high-confinement mode) plasmas. Theory-motivated models are used for the pedestal width and pressure gradient, while the pedestal density is obtained from experimental data in this study. The pedestal pressure gradient is assumed to be limited by the ballooning mode instability and is expressed in terms of the magnetic shear and geometrical factors. The effect of the bootstrap current, which reduces the magnetic shear in the steep pressure gradient region at the edge of the H-mode plasma, is included in the determination of the magnetic shear. Approaches for calculating the magnetic shear, combined with proposed models for the pedestal width, are used to determine the pedestal temperature. The computed pedestal temperatures are compared with more than 500 measured pedestal temperatures for type 1 ELMy H-mode discharges in four tokamaks. Some of the uncertainties in these results are discussed, and directions for future work to improve edge pedestal scalings are described. © 2002 American Institute of Physics.
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52.25.Kn Thermodynamics of plasmas
52.55.Fa Tokamaks, spherical tokamaks
52.35.Py Macroinstabilities (hydromagnetic, e.g., kink, fire-hose, mirror, ballooning, tearing, trapped-particle, flute, Rayleigh-Taylor, etc.)
52.35.Qz Microinstabilities (ion-acoustic, two-stream, loss-cone, beam-plasma, drift, ion- or electron-cyclotron, etc.)
52.25.Fi Transport properties
52.70.-m Plasma diagnostic techniques and instrumentation

Comparing simulation of plasma turbulence with experiment. II. Gyrokinetic simulations

David W. Ross and William Dorland

Phys. Plasmas 9, 5031 (2002); http://dx.doi.org/10.1063/1.1518997 (5 pages) | Cited 19 times

Online Publication Date: 18 November 2002

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The direct quantitative correspondence between theoretical predictions and the measured plasma fluctuations and transport is tested by performing nonlinear gyrokinetic simulations with the GS2 code. This is a continuation of previous work with gyrofluid simulations [D. W. Ross et al., Phys. Plasmas 9, 177 (2002)], and the same L-mode reference discharge in the DIII-D tokamak [J. L. Luxon and L. G. Davis, Fusion Technol. 8, 441 (1985)] is studied. The simulated turbulence is dominated by ion temperature gradient (ITG) modes, corrected by trapped-electron, passing-electron and impurity effects. The energy fluxes obtained in the gyrokinetic simulations are comparable to, even somewhat higher than, those of the earlier work, and the simulated ion thermal transport, corrected for E×B flow shear, exceeds the experimental value by more than a factor of 2. The simulation also overestimates the density fluctuation level. Varying the local temperature gradient shows a stiff response in the flux and an apparent up-shift from the linear mode threshold [A. M. Dimits et al., Phys. Plasmas 7, 969 (2000)]. This effect is insufficient, within the estimated error, to bring the results into conformity with the experiment. © 2002 American Institute of Physics.
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52.35.Ra Plasma turbulence
52.25.Gj Fluctuation and chaos phenomena
52.70.-m Plasma diagnostic techniques and instrumentation
52.25.Fi Transport properties
52.25.Kn Thermodynamics of plasmas

On tokamak equilibria with a zero current or negative current central region

M. S. Chu and P. B. Parks

Phys. Plasmas 9, 5036 (2002); http://dx.doi.org/10.1063/1.1521714 (7 pages) | Cited 22 times

Online Publication Date: 18 November 2002

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Several tokamak experiments have reported the development of a central region with vanishing currents (the current hole). The straightforward application of results from the work of Greene, Johnson and Weimer [Phys. Fluids 14, 671 (1971)] on a tokamak equilibrium to these plasmas leads to the apparent singularities in several physical quantities including the Shafranov shift and casts doubts on the existence of this type of equilibria. In this paper, the above quoted equilibrium theory is re-examined and extended to include equilibria with a current hole. It is shown that singularities can be circumvented and that equilibria with a central current hole do satisfy the magnetohydrodynamic equilibrium condition with regular behavior for all the physical quantities and do not lead to infinitely large Shafranov shifts. Isolated equilibria with negative current in the central region could exist. But equilibria with negative currents in general do not have neighboring equilibria and thus cannot have experimental realization, i.e., no negative currents can be driven in the central region. © 2002 American Institute of Physics.
Show PACS
52.25.Fi Transport properties
52.55.Fa Tokamaks, spherical tokamaks
52.30.Cv Magnetohydrodynamics (including electron magnetohydrodynamics)
52.65.Kj Magnetohydrodynamic and fluid equation
28.52.Av Theory, design, and computerized simulation

Observation and analysis of a resistive mode with interchange parity in negative central shear plasmas in the DIII-D Tokamak

R. Jayakumar, T. C. Luce, T. S. Taylor, A. D. Turnbull, M. R. Wade, M. E. Austin, T. A. Casper, M. A. Makowski, M. S. Chu, L. L. Lao, E. J. Strait, and D. P. Brennan

Phys. Plasmas 9, 5043 (2002); http://dx.doi.org/10.1063/1.1522381 (7 pages) | Cited 1 time

Online Publication Date: 18 November 2002

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A magnetohydrodynamic (MHD) instability which has the characteristics that the displacement phase is in the same direction at all the affected flux surfaces (an interchange-like structure with no phase reversal across a flux surface), has been observed during the L mode in several negative central shear discharges of DIII-D tokamak [J. L. Luxon, P. Anderson, F. Baity et al., Plasma Physics and Controlled Fusion Research 1986 (International Atomic Energy Agency, Vienna, 1987), Vol. I, p. 159]. The instability occurs when the minimum safety factor is around 2.0 and the profile of the safety factor q is deeply reversed in the center. Detailed stability analyses were carried out using standard numerical codes and the high quality magnetic probe, motional Stark effect and electron cyclotron emission (ECE) data. Analysis of the data after the onset shows that the instability has an n = 1 mode number and a growth time of about 400 μs. The electron temperature fluctuations obtained from ECE measurements indicate a localized interchange-like structure early in time, the resistive interchange criterion indicates marginal stability, and ideal mode analyses indicate robust stability with an ideal beta limit of about a factor of 2 higher than the βN value at the time of onset. Therefore this interchange-parity mode is not an ideal MHD mode. The marginal value of the resistive interchange criterion observed only in discharges with the instability, indicates that this is probably a resistive interchange mode. However, some observed characteristics of the instability may require models beyond the linear resistive interchange theory. © 2002 American Institute of Physics.
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52.55.Fa Tokamaks, spherical tokamaks
52.35.Py Macroinstabilities (hydromagnetic, e.g., kink, fire-hose, mirror, ballooning, tearing, trapped-particle, flute, Rayleigh-Taylor, etc.)
52.30.Cv Magnetohydrodynamics (including electron magnetohydrodynamics)
52.70.Ds Electric and magnetic measurements
52.25.Gj Fluctuation and chaos phenomena
back to top Inertially Confined Plasmas, Dense Plasmas, Equations of State

Laser imprint reduction with a short shaping laser pulse incident upon a foam-plastic target

Nathan Metzler, Alexander L. Velikovich, Andrew J. Schmitt, and John H. Gardner

Phys. Plasmas 9, 5050 (2002); http://dx.doi.org/10.1063/1.1517610 (9 pages) | Cited 21 times

Online Publication Date: 18 November 2002

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In the previous work [Metzler et al., Phys. Plasmas 6, 3283 (1999)] it was shown that a tailored density profile could be very effective in smoothing out the laser beam nonuniformities imprinted into a laser-accelerated target. However, a target with a smoothly graded density is difficult to manufacture. A method of dynamically producing a graded density profile with a short “shaping” laser pulse irradiating a foam layer on top of the payload prior to the drive pulse is proposed. It is demonstrated that the intensity and the duration of the shaping pulse, the time interval between the shaping pulse and the drive pulse, and the density ratio between the foam and the payload can be selected so that the laser imprint of the drive pulse is considerably suppressed without increasing the entropy of the payload. The use of the foam-plastic target and a shaping pulse reduces the imprinted mass perturbation amplitude by more than an order of magnitude compared to a solid plastic target. The requirements to the smoothing of the drive and “shaping” laser beams and to the surface finish of the foam-plastic sandwich target are discussed. © 2002 American Institute of Physics.
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52.57.Fg Implosion symmetry and hydrodynamic instability (Rayleigh-Taylor, Richtmyer-Meshkov, imprint, etc.)
52.57.-z Laser inertial confinement
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