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May 2002

Volume 9, Issue 5, pp. 1491-2445

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back to top Magnetically Confined Plasmas, Heating, Confinement

Ideal magnetohydrodynamic equations for low-frequency waves in toroidal plasmas

O. P. Fesenyuk, Ya. I. Kolesnichenko, H. Wobig, and Yu. V. Yakovenko

Phys. Plasmas 9, 1589 (2002); http://dx.doi.org/10.1063/1.1462633 (7 pages) | Cited 6 times

Online Publication Date: 23 April 2002

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Reduced linear equations of magnetohydrodynamics in high-aspect-ratio toroidal devices are derived, which are intended, first of all, for studying the Alfvén eigenmodes in stellarators and tokamaks. The equations take into account the effects of the plasma pressure and compressibility, which are known to be of importance for toroidicity-induced Alfvén eigenmodes, and are applicable to perturbations with arbitrary perpendicular wavelength. The reduction consists in eliminating high-frequency fast magnetoacoustic waves from the system and is shown not to affect the continuous spectrum of Alfvén and slow magnetoacoustic waves, which, to a large extent, determines the behavior of the waves of interest. © 2002 American Institute of Physics.
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52.55.Fa Tokamaks, spherical tokamaks
52.55.Jd Magnetic mirrors, gas dynamic traps
52.35.Bj Magnetohydrodynamic waves (e.g., Alfven waves)
52.35.Dm Sound waves

The role of clustering effects in interpreting nondiffusive transport measurements in tokamaks

J. P. Graves, R. O. Dendy, K. I. Hopcraft, and E. Jakeman

Phys. Plasmas 9, 1596 (2002); http://dx.doi.org/10.1063/1.1464148 (10 pages) | Cited 11 times

Online Publication Date: 23 April 2002

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Recent measurements in tokamak plasmas provide clear evidence for rapid nondiffusive transport and non-Gaussian fluctuations, and have been widely interpreted in terms of the sandpile and self-organized criticality (SOC) paradigms. Many of the statistical physics inferences that can be drawn from observations of, for example, avalanching transport remain to be explored. This paper will show that the statistical characterization of both experimentally observed and simulated avalanching transport phenomena reveals several points of contact with existing stochastic process models that have seldom been deployed in a plasma physics context. It will be shown that statistical physics techniques developed to model clustering of events can be used to characterize microscopic fluctuations in both local density and flux, as well as the global transport properties to which they give rise. This provides a fresh interpretation for some of the key aspects of observed critical gradient-driven transport phenomenology in tokamaks. In particular it provides new evidence for scale-free correlations in the fluctuations which drive the transport, and quantifies their distribution in terms of few-parameter non-Gaussian models. The correlation properties of density fluctuations can be interpreted in terms of random walk models, whereas flux fluctuations cannot: instead they can be described by the discrete negative binomial distribution, which again indicates clustering. Some of the spatio–temporal correlations considered emulate multichannel measurements in tokamaks, and it is shown how these can be used to characterize the transport of naturally arising coherent structures. © 2002 American Institute of Physics.
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52.55.Fa Tokamaks, spherical tokamaks
52.25.Fi Transport properties
52.25.Gj Fluctuation and chaos phenomena

Effect of combined triangularity and ellipticity on the stability limit of the ideal internal kink mode in a tokamak

H. G. Eriksson and C. Wahlberg

Phys. Plasmas 9, 1606 (2002); http://dx.doi.org/10.1063/1.1464890 (16 pages) | Cited 9 times

Online Publication Date: 23 April 2002

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The effect of combined triangular and elliptical shaping of the plasma cross section on the stability limit of the ideal, internal kink mode in a tokamak is analyzed by means of a computer algebra expansion of the magnetohydrodynamic equations. The work extends the result of a previous investigation of the effect of ellipticity alone on this mode in toroidal plasmas [Wahlberg, Phys. Plasmas 5, 1387 (1998)]. It is shown that, in contrast to the strongly destabilizing effect of (positive) ellipticity alone, the effect of combined positive ellipticity and positive triangularity is stabilizing. The effect is of the same importance as the effect of ellipticity alone if the triangularity of the q=1 surface is of the same order of magnitude as the inverse aspect ratio. When the safety factor at the magnetic axis is close to (but below) unity, the geometrical factor governing the stability of the ideal, internal kink mode is found to be the same as the corresponding factor in the Mercier criterion for shaped tokamaks. © 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

Comparision of neoclassical rotation theory with experiment under a variety of conditions in DIII-D

W. M. Stacey and J. Mandrekas

Phys. Plasmas 9, 1622 (2002); http://dx.doi.org/10.1063/1.1464892 (7 pages) | Cited 11 times

Online Publication Date: 23 April 2002

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A neoclassical theory of gyroviscous radial momentum transport and poloidal and toroidal rotation has been compared with experiment in DIII-D [Luxon, Anderson, Batty et al., Plasma Physics and Controlled Nuclear Fusion Research 1986 (IAEA, Vienna, 1987), Vol. 1, p. 159] discharges in different confinement regimes, with a range of neutral beam powers and with co- and counter-injection, and with various types of dominant impurity species present. Calculated central toroidal rotation velocities and momentum confinement times agreed with experiment over a wide range of these conditions, with one notable exception in which a drift correction may be needed to reduce the gyroviscous toroidal force. Radial distributions of toroidal and poloidal rotation velocities and radial electric field, calculated using the radial distribution of toroidal angular momentum input density, agreed with measured distributions for the one time in an L-mode discharge that was examined in detail. © 2002 American Institute of Physics.
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52.25.Fi Transport properties
52.25.Vy Impurities in plasmas

A comparison of drift wave stability in stellarator and tokamak geometry

J. Anderson, T. Rafiq, M. Nadeem, and M. Persson

Phys. Plasmas 9, 1629 (2002); http://dx.doi.org/10.1063/1.1466820 (8 pages) | Cited 12 times

Online Publication Date: 23 April 2002

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The influence of plasma geometry on the linear stability of electrostatic ion-temperature-gradient driven drift modes (ITG or ηi = Ln/LTi modes) is investigated. An advanced fluid model is used for the ions together with Boltzmann distributed electrons. The derived eigenvalue equation is solved numerically. A comparison is made between an H–1NF [Fusion Technol. 17, 123 (1990)] like stellarator equilibrium, a numerical tokamak equilibrium and the analytical ŝ−α equilibrium. The numerical and the analytical tokamak are found to be in good agreement in the low inverse aspect ratio limit. The growth rates of the tokamak and stellarator are comparable whereas the modulus of the real frequency is substantially larger in the stellarator. The threshold in ηi for the stellarator is found to be somewhat larger. In addition, a stronger stabilization of the ITG mode growth is found for large ϵn( = Ln/R) in the stellarator case. © 2002 American Institute of Physics.
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52.25.Fi Transport properties
52.35.Fp Electrostatic waves and oscillations (e.g., ion-acoustic waves)
52.55.Fa Tokamaks, spherical tokamaks

Drift wave instability near a magnetic separatrix

J. R. Myra, D. A. D’Ippolito, and X. Q. Xu

Phys. Plasmas 9, 1637 (2002); http://dx.doi.org/10.1063/1.1467929 (9 pages) | Cited 1 time

Online Publication Date: 23 April 2002

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It is well known that the pure drift-Alfvén wave (DW) (i.e., in the absence of curvature and toroidal coupling effects) is stabilized by magnetic shear in circular flux surface geometry when the drift frequency is constant radially [P. N. Guzdar, L. Chen, P. K. Kaw, and C. Oberman, Phys. Rev. Lett. 40, 1566 (1978)] as is implicit in a local ballooning analysis. In the edge plasma near a magnetic separatrix, X-point geometry is important and the circular flux surface model does not apply. Using several numerical codes and analytical models, it is found that the DW is robustly unstable in this case. Physically, instability is driven by wave reflection from the steep profile of k⊥ near the X-points, due to magnetic shear and the local minimum of the poloidal magnetic field. It is concluded that a complete set of dimensionless parameters describing edge turbulence must include DW parameters that embody the physics of X-point effects and plasma shaping. © 2002 American Institute of Physics.
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52.35.Kt Drift waves
52.35.Bj Magnetohydrodynamic waves (e.g., Alfven waves)
52.55.Fa Tokamaks, spherical tokamaks

Consideration of multifaceted asymmetric radiation from the edge (MARFE) as a dissipative structure

M. Z. Tokar

Phys. Plasmas 9, 1646 (2002); http://dx.doi.org/10.1063/1.1468233 (8 pages) | Cited 4 times

Online Publication Date: 23 April 2002

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Multifaceted asymmetric radiation from the edge (MARFE) is considered as an example of dissipative structures which develop under critical conditions in different physical and technical systems. The model proposed results in a system of algebraic equation including a relation similar to Maxwell’s Rule that determines such characteristic parameters as the plasma temperature in MARFE, its extent in poloidal and radial directions. Predictions of this approximate approach are compared with the results of one- and two-dimensional numerical simulations. © 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

Local potato-plateau transport fluxes and a unified plateau theory

K. C. Shaing, W. A. Houlberg, and P. I. Strand

Phys. Plasmas 9, 1654 (2002); http://dx.doi.org/10.1063/1.1468856 (5 pages) | Cited 2 times

Online Publication Date: 23 April 2002

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A local potato-plateau transport theory is presented. It is a nonradial averaged version of the original theory [Phys. Plasmas 4, 4331 (1997); 5, 953 (1998)]. The theory unifies conventional plateau theory and the potato-plateau theory. It is applicable at any radius. It is found that the ion heat conductivity is the same as that in the conventional theory in the region close to the magnetic axis. © 2002 American Institute of Physics.
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52.25.Fi Transport properties
52.55.Fa Tokamaks, spherical tokamaks

Short wavelength temperature gradient driven modes in tokamaks

A. Hirose, M. Elia, A. I. Smolyakov, and M. Yagi

Phys. Plasmas 9, 1659 (2002); http://dx.doi.org/10.1063/1.1469025 (8 pages) | Cited 13 times

Online Publication Date: 23 April 2002

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Stability analysis of tokamaks based on a fully kinetic, electromagnetic integral equation code indicates the existence of a temperature gradient driven instability in the short wavelength regime (k⊥ρi)2>1. The mode propagates in the ion diamagnetic direction (ion mode with ωr<0) and requires that both ηi and ηe exceed thresholds. Circulating (untrapped) electrons are not adiabatic and parallel electron dynamics provides destabilization. Trapped electrons are not essential for the mode. Toroidicity has a stabilizing influence and the growth rate does not vanish in the slab limit. The growth rate is approximately proportional to math where s is the magnetic shear parameter. The mode is subject to finite α (ballooning parameter) stabilization as the conventional ηi mode in the long wavelength regime (k⊥ρi)2<1. © 2002 American Institute of Physics.
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52.35.Kt Drift waves
52.55.Fa Tokamaks, spherical tokamaks

Interaction of runaway electrons with lower hybrid waves via anomalous Doppler broadening

J. R. Martín-Solís, R. Sánchez, and B. Esposito

Phys. Plasmas 9, 1667 (2002); http://dx.doi.org/10.1063/1.1470165 (9 pages) | Cited 17 times

Online Publication Date: 23 April 2002

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Due to the relativistic decrease of the electron cyclotron frequency, a cyclotron resonance may appear between runaway electrons and lower hybrid waves. A single particle description of the runaway dynamics [J. R. Martín-Solís et al., Phys. Plasmas 5, 2370 (1998)] is extended to analyze the effect of the interaction of runaway electrons with lower hybrid waves via anomalous Doppler broadening. The conditions under which the resonant interaction can play a role in limiting the runaway energy are established and it is shown that, under typical lower hybrid current drive operation parameters, an efficient wave-particle coupling may occur. Observations of a fast pitch angle scattering event during the current decay phase of Ohmic discharges in the Toroidal Experiment for Technically Oriented Research (TEXTOR) [R. J. E. Jaspers, Ph.D. thesis, Technical University Eindhoven (1995)] are interpreted in terms of such interaction. © 2002 American Institute of Physics.
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52.25.Fi Transport properties
52.35.Mw Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.)
52.35.Hr Electromagnetic waves (e.g., electron-cyclotron, Whistler, Bernstein, upper hybrid, lower hybrid)
52.55.Fa Tokamaks, spherical tokamaks
52.80.-s Electric discharges

Simulations of internal transport barrier formation in tokamak discharges using the GLF23 transport model

J. E. Kinsey, G. M. Staebler, and R. E. Waltz

Phys. Plasmas 9, 1676 (2002); http://dx.doi.org/10.1063/1.1470166 (16 pages) | Cited 35 times

Online Publication Date: 23 April 2002

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Results are presented for simulations of tokamak discharges exhibiting internal transport barriers (ITBs) with significant reductions in the core thermal transport using a comprehensive theory-based model for drift-wave transport. The predicted temperature and toroidal velocity profiles from the GLF23 model are compared against the experimental data for twenty-two L- and high-confinement mode (H-mode) ITB discharges from three large tokamaks including DIII-D [J. L. Luxon and L. G. Davis, Fusion Technol. 8, 441 (1985)], Tokamak Fusion Test Reactor [D. J. Grove and D. M. Meade, Nucl. Fusion 25, 1167 (1985)], and Joint European Torus [P. H. Rebut and B. E. Keen, Fusion Technol. 11, 13 (1987)]. The combined effects of E×B shear and Shafranov shift stabilization of the turbulent transport are essential in reproducing the barriers in the plasma core. Shafranov shift or α-stabilization is found to be an essential ingredient in suppressing the thermal transport due to ion and electron temperature gradient and trapped electron modes that can result in simultaneous electron and ion barriers. Another consequence of α-stabilization is that the power threshold for ITB formation is predicted to decrease for strongly reversed magnetic shear cases in comparison with weakly reversed shear cases. © 2002 American Institute of Physics.
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52.65.-y Plasma simulation
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.)
52.75.-d Plasma devices
52.25.Fi Transport properties

Electromagnetic ion temperature gradient modes of tearing mode parity in high β sheared slab plasmas

Zhe Gao, J. Q. Dong, G. J. Liu, and C. T. Ying

Phys. Plasmas 9, 1692 (2002); http://dx.doi.org/10.1063/1.1471516 (6 pages) | Cited 3 times

Online Publication Date: 23 April 2002

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The ion temperature gradient modes of tearing mode parity are investigated for arbitrary β (=plasma pressure/magnetic pressure) plasmas in a sheared slab. Under the low β limit, the results agree with Reynders’ conclusion that the lowest order (l = 1) mode of tearing mode parity persists after the fundamental mode (l = 0) of drift mode parity is completely stabilized by finite β [J. V. M. Reynders, Phys. Plasmas 1, 1953 (1994)]. However, when the effects of the magnetic gradient drift and the coupling to the compressional Alfvén waves are included, the l = 0 mode is more difficult to stabilize than the l = 1 mode. It is also shown that the l = 1 mode is much easier to stabilize by the magnetic shear than the l = 0 mode. Generally, the l = 1 mode grows faster in the low magnetic shear and low β regime while the l = 0 mode is the dominant eigenmode of ion temperature gradient instability in high β plasmas. © 2002 American Institute of Physics.
Show PACS
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.Kn Thermodynamics of plasmas
52.35.Bj Magnetohydrodynamic waves (e.g., Alfven waves)
52.35.Kt Drift waves
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Fluctuation measurements in tokamaks with microwave imaging reflectometry

E. Mazzucato, T. Munsat, H. Park, B. H. Deng, C. W. Domier, N. C. Luhmann, A. J. H. Donné, and M. J. van de Pol

Phys. Plasmas 9, 1955 (2002); http://dx.doi.org/10.1063/1.1435564 (7 pages) | Cited 21 times

Online Publication Date: 23 April 2002

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To study the mechanism of anomalous transport in tokamaks requires the use of sophisticated diagnostic tools for the measurement of short-scale turbulent fluctuations. In this article, we describe an attempt at developing a technique capable of providing a comprehensive description of plasma fluctuations with k⊥ρi<1, such as those driven by the ion temperature gradient mode in tokamaks. The proposed method is based on microwave reflectometry, and stems from a series of numerical calculations showing that the spatial structure of fluctuations near the cutoff could be obtained from the phase of reflected waves when these are collected with a wide aperture optical system forming an image of the cutoff onto an array of phase sensitive detectors. Preliminary measurements with a prototype apparatus on the Torus Experiment for Technology Oriented Research 94 (TEXTOR-94) [U. Samm, Proceedings of the 16th IEEE Symposium on Fusion Engineering, 1995 (IEEE, Piscataway, NJ, 1995), p. 470] confirm the validity of these conclusions. Technical issues in the application of the proposed technique to tokamaks are discussed in this article, and the conceptual design of an imaging reflectometer for the visualization of turbulent fluctuations in the National Spherical Torus Experiment (NSTX) [M. Ono et al., Nucl. Fusion 40, 557 (2000)] is described. © 2002 American Institute of Physics.
Show PACS
52.25.Gj Fluctuation and chaos phenomena
52.70.Gw Radio-frequency and microwave measurements
52.35.Ra Plasma turbulence
52.25.Fi Transport properties
52.55.Fa Tokamaks, spherical tokamaks
52.55.Ip Spheromaks
84.40.-x Radiowave and microwave (including millimeter wave) technology

Characterization of avalanche-like events in a confined plasma

P. A. Politzer, M. E. Austin, M. Gilmore, G. R. McKee, T. L. Rhodes, C. X. Yu, E. J. Doyle, T. E. Evans, and R. A. Moyere

Phys. Plasmas 9, 1962 (2002); http://dx.doi.org/10.1063/1.1452730 (8 pages) | Cited 13 times

Online Publication Date: 23 April 2002

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One mechanism for transport of energy and particles in a plasma is by discrete, intermittent, uncorrelated events, often called avalanches. This paper reports observations and quantitative characterization of avalanche events in a magnetically confined plasma. The observations are primarily of electron temperature fluctuations. Avalanches are identified by their large spatial scale, up to the system size, by self-similar behavior in the frequency spectrum and the autocorrelation function and by propagation. The two-point cross-correlation function allows determination of a characteristic velocity, which typically varies from several hundred meters per second in the outer part of the plasma to zero or even inward near the axis. This can be interpreted as resulting from the prevalence of negative avalanches (i.e., holes) near the axis. The presence of a long-tailed probability distribution is indicated by a Hurst parameter (H) in the range 0.80 to 0.95, which becomes smaller in the outer quarter of the plasma radius. Density fluctuation spectra from the plasma core also show self-similar behavior. Power transport estimates show that about half of the heat flux is carried by the avalanche events under conditions with no magnetohydrodynamic activity. These observations are qualitatively similar to results of modeling calculations based on drift wave turbulence. It is reasonable to infer that avalanches are the macroscopic manifestation of turbulence which inherently has a small spatial scale and, thus, allow a local, gyro-Bohm scaling process to show global Bohm-type behavior. © 2002 American Institute of Physics.
Show PACS
52.25.Fi Transport properties
52.25.Gj Fluctuation and chaos phenomena
52.35.Ra Plasma turbulence
52.35.Qz Microinstabilities (ion-acoustic, two-stream, loss-cone, beam-plasma, drift, ion- or electron-cyclotron, etc.)
52.55.-s Magnetic confinement and equilibrium
52.25.-b Plasma properties

Energy, particle and impurity transport in quiescent double barrier discharges in DIII-D

W. P. West, M. R. Wade, C. M. Greenfield, E. J. Doyle, K. H. Burrell, N. H. Brooks, P. Gohil, R. J. Groebner, G. L. Jackson, J. E. Kinsey, C. J. Lasnier, J. Mandrekas, G. R. McKee, T. L. Rhodes, G. M. Staebler, et al.

Phys. Plasmas 9, 1970 (2002); http://dx.doi.org/10.1063/1.1456064 (11 pages) | Cited 32 times

Online Publication Date: 23 April 2002

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Quiescent double barrier discharges (QDB) on DIII-D [Luxon et al., Fusion Technol. 8, Part 2A, 441 (1985)] exhibit near steady high performance (βNH ∼ 7) with a quiescent H-mode edge, i.e., free of edge localized modes (ELMs), but with effective particle control and strongly peaked density profiles. These QDB discharges exhibit an internal transport barrier with low ion thermal transport despite incomplete turbulence suppression. Very short correlation lengths, which reduce the transport step size, however, characterize the residual turbulence. This observation is consistent with simulations using the GLF23 [Waltz et al., Phys. Plasmas 4, 2482 (1997)] model, which reproduce the core ion temperature profile even in the presence of finite turbulence. Increased retention of high-Z impurities is observed and core nickel concentrations (an intrinsic impurity in DIII-D) are as high as 0.3%. To quantify impurity transport, trace impurity injection has been performed in steady QDB discharges showing a fast influx followed by a slow pump out. The measured decay times of the core concentration of two nonrecycling impurities, F(Z = 9) and Ca(Z = 22), are 299 and 675 ms, respectively, while the energy confinement time is 111 ms. Time dependent analysis of neon influx yields both diffusivities and inward convection velocities significantly greater than neoclassical predictions in the same region of the plasma where measured ion thermal transport is near neoclassical predictions yet significant turbulence is observed. The boundary of these discharges is characterized by a saturated coherent magnetohydrodynamic mode, the edge harmonic oscillation, which takes the place of ELMs in facilitating particle control by allowing particle transport to the open field lines, where both wall- and cryopumping play a major role in particle exhaust. Hot ( ∼ 5 keV) ions observed in the outer scrape-off layer may enhance wall pumping. © 2002 American Institute of Physics.
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52.25.Fi Transport properties
52.25.Vy Impurities in 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.)
52.40.Hf Plasma-material interactions; boundary layer effects
52.55.Tn Ideal and resistive MHD modes; kinetic modes
52.30.Cv Magnetohydrodynamics (including electron magnetohydrodynamics)
52.35.Ra Plasma turbulence

Edge turbulence imaging in the Alcator C-Mod tokamak

S. J. Zweben, D. P. Stotler, J. L. Terry, B. LaBombard, M. Greenwald, M. Muterspaugh, C. S. Pitcher, K. Hallatschek, R. J. Maqueda, B. Rogers, J. L. Lowrance, V. J. Mastrocola, and G. F. Renda

Phys. Plasmas 9, 1981 (2002); http://dx.doi.org/10.1063/1.1445179 (9 pages) | Cited 129 times

Online Publication Date: 23 April 2002

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The two-dimensional (2D) radial vs poloidal structure of edge turbulence in the Alcator C-Mod tokamak [I. H. Hutchinson, R. Boivin, P. T. Bonoli et al., Nucl. Fusion 41, 1391 (2001)] was measured using fast cameras and compared with three-dimensional numerical simulations of edge plasma turbulence. The main diagnostic is gas puff imaging, in which the visible Dα emission from a localized D2 gas puff is viewed along a local magnetic field line. The observed Dα fluctuations have a typical radial and poloidal scale of ≈1 cm, and often have strong local maxima (“blobs”) in the scrape-off layer. The motion of this 2D structure motion has also been measured using an ultrafast framing camera with 12 frames taken at 250 000 frames/s. Numerical simulations produce turbulent structures with roughly similar spatial and temporal scales and transport levels as that observed in the experiment; however, some differences are also noted, perhaps requiring diagnostic improvement and/or additional physics in the numerical model. © 2002 American Institute of Physics.
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52.70.Kz Optical (ultraviolet, visible, infrared) measurements
52.35.Ra Plasma turbulence
52.55.Fa Tokamaks, spherical tokamaks
52.25.Gj Fluctuation and chaos phenomena
52.65.-y Plasma simulation
52.25.Fi Transport properties

Anderson localization of ballooning modes, quantum chaos and the stability of compact quasiaxially symmetric stellarators

M. H. Redi, J. L. Johnson, S. Klasky, J. Canik, R. L. Dewar, and W. A. Cooper

Phys. Plasmas 9, 1990 (2002); http://dx.doi.org/10.1063/1.1448344 (7 pages) | Cited 2 times

Online Publication Date: 23 April 2002

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The radially local magnetohydrodynamic (MHD) ballooning stability of a compact, quasiaxially symmetric stellarator (QAS), is examined just above the ballooning beta limit with a method that can lead to estimates of global stability. Here MHD stability is analyzed through the calculation and examination of the ballooning mode eigenvalue isosurfaces in the 3-space (s,α,θk); s is the edge normalized toroidal flux, α is the field line variable, and θk is the perpendicular wave vector or ballooning parameter. Broken symmetry, i.e., deviations from axisymmetry, in the stellarator magnetic field geometry causes localization of the ballooning mode eigenfunction, and gives rise to new types of nonsymmetric eigenvalue isosurfaces in both the stable and unstable spectrum. For eigenvalues far above the marginal point, isosurfaces are topologically spherical, indicative of strong “quantum chaos.” The complexity of QAS marginal isosurfaces suggests that finite Larmor radius stabilization estimates will be difficult and that fully three-dimensional, high-n MHD computations are required to predict the beta limit. © 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.Jd Magnetic mirrors, gas dynamic traps
71.23.An Theories and models; localized states

Sustained rotational stabilization of DIII-D plasmas above the no-wall beta limit

A. M. Garofalo, T. H. Jensen, L. C. Johnson, R. J. La Haye, G. A. Navratil, M. Okabayashi, J. T. Scoville, E. J. Strait, D. R. Baker, J. Bialek, M. S. Chu, J. R. Ferron, J. Jayakumar, L. L. Lao, M. A. Makowski, et al.

Phys. Plasmas 9, 1997 (2002); http://dx.doi.org/10.1063/1.1446036 (9 pages) | Cited 99 times

Online Publication Date: 23 April 2002

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Sustained stabilization of the n = 1 kink mode by plasma rotation at beta approaching twice the stability limit calculated without a wall has been achieved in DIII-D by a combination of error field reduction and sufficient rotation drive. Previous experiments have transiently exceeded the no-wall beta limit. However, demonstration of sustained rotational stabilization has remained elusive because the rotation has been found to decay whenever the plasma is wall stabilized. Recent theory [Boozer, Phys. Rev. Lett. 86, 5059 (2001)] predicts a resonant response to error fields in a plasma approaching marginal stability to a low-n kink mode. Enhancement of magnetic nonaxisymmetry in the plasma leads to strong damping of the toroidal rotation, precisely in the high-beta regime where it is needed for stabilization. This resonant response, or “error field amplification” is demonstrated in DIII-D experiments: applied n = 1 radial fields cause enhanced plasma response and strong rotation damping at beta above the no wall limit but have little effect at lower beta. The discovery of an error field amplification has led to sustained operation above the no-wall limit through improved magnetic field symmetrization using an external coil set. The required symmetrization is determined both by optimizing the external currents with respect to the plasma rotation and by use of feedback to detect and minimize the plasma response to nonaxisymmetric fields as beta increases. Ideal stability analysis and rotation braking experiments at different beta values show that beta is maintained 50% higher than the no wall stability limit for durations greater than 1 s, and approaches beta twice the no-wall limit in several cases, with steady-state rotation levels. The results suggest that improved magnetic-field symmetry could allow plasmas to be maintained well above no-wall beta limit for as long as sufficient torque is provided. © 2002 American Institute of Physics.
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52.55.Fa Tokamaks, spherical tokamaks
52.30.-q Plasma dynamics and flow
52.35.Py Macroinstabilities (hydromagnetic, e.g., kink, fire-hose, mirror, ballooning, tearing, trapped-particle, flute, Rayleigh-Taylor, etc.)

Current drive experiments in the helicity injected torus (HIT-II)

A. J. Redd, B. A. Nelson, T. R. Jarboe, P. Gu, R. Raman, R. J. Smith, and K. J. McCollam

Phys. Plasmas 9, 2006 (2002); http://dx.doi.org/10.1063/1.1448832 (8 pages) | Cited 18 times

Online Publication Date: 23 April 2002

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The Helicity Injected Torus [HIT-II: T. Jarboe et al., Phys. Plasmas 5, 1807 (1998)] is a low-aspect-ratio tokamak capable of both inductive (ohmic) and Coaxial Helicity Injection (CHI) current drive. HIT-II is modest in size (major radius R = 0.3 m, minor radius a = 0.2 m, and on-axis toroidal field of up to 0.5 T), but has demonstrated 200 kA of toroidal plasma current, using either CHI or induction separately. The loop voltage, boundary flux, and plasma equilibrium are controlled by a real-time flux feedback system. HIT-II ohmic plasmas exhibit reconnection events during both the current ramp-up and decay, events that relax the current profile while conserving the magnetic helicity. A new operating regime for CHI plasmas, using a double-null divertor (DND) boundary flux, has been explored. DND CHI plasmas exhibit good shot-to-shot reproducibility, low impurity content, minimal shorting current in the absorber region, and EFIT-reconstructed equilibria consistent with significant closed-flux core regions [EFIT: L. Lao et al., Nucl. Fusion 25, 1611 (1985)]. HIT-II DND CHI discharges also exhibit a continuous n = 1 mode at the outer midplane, a mode that has been correlated experimentally with current-profile relaxation. A detailed explanation of helicity injection current drive has been developed, which is consistent with experimental observations of HIT and HIT-II discharges. According to this mechanism, asymmetric distortion of the n = 1 mode structure generates current drive in the core plasma by dynamo action, relaxing the CHI-driven current profile. © 2002 American Institute of Physics.
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52.30.Cv Magnetohydrodynamics (including electron magnetohydrodynamics)
52.55.Fa Tokamaks, spherical tokamaks
52.35.Bj Magnetohydrodynamic waves (e.g., Alfven waves)
52.70.Ds Electric and magnetic measurements

Ideal magnetohydrodynamic ballooning stability boundaries in three-dimensional equilibria

C. C. Hegna and S. R. Hudson

Phys. Plasmas 9, 2014 (2002); http://dx.doi.org/10.1063/1.1446037 (6 pages) | Cited 5 times

Online Publication Date: 23 April 2002

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The impact of three-dimensional geometry on ideal magnetohydrodynamic ballooning mode stability is studied. By using a class of “local 3D equilibria” [C. C. Hegna, Phys. Plasmas 7, 3921 (2000)], the effects of plasma shaping, profile variations and symmetry on local plasma physics properties can be addressed. As an example, a local helical axis equilibrium case is constructed that models the magnetic field spectrum of a quasihelically symmetric stellarator. In this case, the magnetic harmonic structure of the local shear (which can be manipulated via changes in the magnetic geometry) has an important impact on the stability boundaries and eigenvalue properties of three-dimensional equilibria. The presence of symmetry breaking components in the local shear produces localized field-line-dependent ballooning instabilities in regions of small average shear. These effects lower first ballooning stability thresholds and can eliminate the second stability regime. A geometric interpretation of these results is given. © 2002 American Institute of Physics.
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52.30.Cv Magnetohydrodynamics (including electron magnetohydrodynamics)
52.55.Dy General theory and basic studies of plasma lifetime, particle and heat loss, energy balance, field structure, etc.
52.55.Jd Magnetic mirrors, gas dynamic traps

Compatibility between high energy particle confinement and magnetohydrodynamic stability in the inward-shifted plasmas of the Large Helical Device

O. Kaneko, A. Komori, H. Yamada, N. Ohyabu, K. Kawahata, Y. Nakamura, K. Ida, S. Murakami, T. Mutoh, S. Sakakibara, S. Masuzaki, N. Ashikawa, M. Emoto, H. Funaba, M. Goto, et al.

Phys. Plasmas 9, 2020 (2002); http://dx.doi.org/10.1063/1.1448345 (7 pages) | Cited 9 times

Online Publication Date: 23 April 2002

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The experimentally optimized magnetic field configuration of the Large Helical Device [A. Iiyoshi et al., Nucl. Fusion 39, 1245 (1999)], where the magnetic axis is shifted inward by 15 cm from the early theoretical prediction, reveals 50% better global energy confinement than the prediction of the scaling law. This configuration has been investigated further from the viewpoints of high energy particle confinement and magnetohydrodynamic (MHD) stability. The confinement of high energy ions is improved as expected. The minority heating of ion cyclotron range of frequency was successful and the heating efficiency was improved by the inward shift. The confinement of passing particles by neutral beam injection was also improved under low magnetic field strength, and there could be obtained an almost steady high beta discharge up to 3% in volume average. This was a surprising result because the observed pressure gradient exceeded the Mercier unstable limit. The observed MHD activities became as high as beta but they did not grow enough to deteriorate the confinement of high energy ions or the performance of the bulk plasma, which was still 50% better than the scaling. According to these favorable results, better performance would be expected by increasing the heating power because the neoclassical transport can also be improved there. © 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.)
52.50.Qt Plasma heating by radio-frequency fields; ICR, ICP, helicons
52.25.Fi Transport properties
52.30.Cv Magnetohydrodynamics (including electron magnetohydrodynamics)

Alfvén wave cascades in a tokamak

S. E. Sharapov, B. Alper, H. L. Berk, D. N. Borba, B. N. Breizman, C. D. Challis, A. Fasoli, N. C. Hawkes, T. C. Hender, J. Mailloux, S. D. Pinches, and D. Testa

Phys. Plasmas 9, 2027 (2002); http://dx.doi.org/10.1063/1.1448346 (10 pages) | Cited 77 times

Online Publication Date: 23 April 2002

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Experiments designed for generating internal transport barriers in the plasmas of the Joint European Torus [JET, P. H. Rebut et al., Proceedings of the 10th International Conference, Plasma Physics and Controlled Nuclear Fusion, London (International Atomic Energy Agency, Vienna, 1985), Vol. I, p. 11] reveal cascades of Alfvén perturbations with predominantly upward frequency sweeping. These experiments are characterized by a hollow plasma current profile, created by lower hybrid heating and current drive before the main heating power phase. The cascades are driven by ions accelerated with ion cyclotron resonance heating (ICRH). Each cascade consists of many modes with different toroidal mode numbers and different frequencies. The toroidal mode numbers vary from n = 1 to n = 6. The frequency starts from 20 to 90 kHz and increases up to the frequency range of toroidal Alfvén eigenmodes. In the framework of ideal magnetohydrodynamics (MHD) model, a close correlation is found between the time evolution of the Alfvén cascades and the evolution of the Alfvén continuum frequency at the point of zero magnetic shear. This correlation facilitates the study of the time evolution of both the Alfvén continuum and the safety factor, q(r), at the point of zero magnetic shear and makes it possible to use Alfvén spectroscopy for studying q(r). Modeling shows that the Alfvén cascade occurs when the Alfvén continuum frequency has a maximum at the zero shear point. Interpretation of the Alfvén cascades is given in terms of a novel-type of energetic particle mode localized at the point where q(r) has a minimum. This interpretation explains the key experimental observations: simultaneous generation of many modes, preferred direction of frequency sweeping, and the absence of strong continuum damping. © 2002 American Institute of Physics.
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52.55.Fa Tokamaks, spherical tokamaks
52.35.Bj Magnetohydrodynamic waves (e.g., Alfven waves)
52.50.Qt Plasma heating by radio-frequency fields; ICR, ICP, helicons
FREE

Edge localized modes and the pedestal: A model based on coupled peeling–ballooning modes

P. B. Snyder, H. R. Wilson, J. R. Ferron, L. L. Lao, A. W. Leonard, T. H. Osborne, A. D. Turnbull, D. Mossessian, M. Murakami, and X. Q. Xu

Phys. Plasmas 9, 2037 (2002); http://dx.doi.org/10.1063/1.1449463 (7 pages) | Cited 23 times

Online Publication Date: 23 April 2002

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A model based on magnetohydrodynamic (MHD) stability of the tokamak plasma edge region is presented, which describes characteristics of edge localized modes (ELMs) and the pedestal. The model emphasizes the dual role played by large bootstrap currents driven by the sharp pressure gradients in the pedestal region. Pedestal currents reduce the edge magnetic shear, stabilizing high toroidal mode number (n) ballooning modes, while at the same time providing drive for intermediate to low n peeling modes. The result is that coupled peeling–ballooning modes at intermediate n (3<n<20) are often the limiting instability which constrains the pedestal and triggers ELMs. These modes are characterized in shaped tokamak equilibria using an efficient new numerical code, and simplified models are developed for pedestal limits and the ELM cycle. Results are compared to several experiments, and nonideal MHD effects are briefly discussed. © 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.)
52.30.Cv Magnetohydrodynamics (including electron magnetohydrodynamics)
52.55.Fa Tokamaks, spherical tokamaks

Physics and control of resistive wall modes

A. Bondeson, Y. Q. Liu, D. Gregoratto, C. M. Fransson, B. Lennartson, C. Breitholtz, Y. Gribov, and V. D. Pustovitov

Phys. Plasmas 9, 2044 (2002); http://dx.doi.org/10.1063/1.1455000 (7 pages) | Cited 33 times

Online Publication Date: 23 April 2002

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Active feedback stabilization of resistive wall modes in tokamaks is studied both analytically, using large aspect ratio theory, and by means of toroidal computations. Extensive studies show that robust stabilization, with respect to variations in plasma current, pressure and flow velocity, can be achieved with a simple control system using poloidal sensors inside the first wall. The required coil voltages are modest, even for the two-wall structure of a tokamak reactor. © 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.)
28.52.Av Theory, design, and computerized simulation
52.55.Fa Tokamaks, spherical tokamaks
52.65.Kj Magnetohydrodynamic and fluid equation

Control of neoclassical tearing modes in DIII–D

R. J. La Haye, S. Günter, D. A. Humphreys, J. Lohr, T. C. Luce, M. E. Maraschek, C. C. Petty, R. Prater, J. T. Scoville, and E. J. Strait

Phys. Plasmas 9, 2051 (2002); http://dx.doi.org/10.1063/1.1456066 (10 pages) | Cited 8 times

Online Publication Date: 23 April 2002

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The development of techniques for neoclassical tearing mode (NTM) suppression or avoidance is crucial for successful high beta/high confinement tokamaks. Neoclassical tearing modes are islands destabilized and maintained by a helically perturbed bootstrap current and represent a significant limit to performance at higher poloidal beta. The confinement-degrading islands can be reduced or completely suppressed by precisely replacing the “missing” bootstrap current in the island O-point or by interfering with the fundamental helical harmonic of the pressure. Implementation of such techniques is being studied in the DIII-D tokamak [J. L. Luxon et al., Plasma Physics and Controlled Fusion Research (International Atomic Energy Agency, Vienna, 1987), Vol. 1, p. 159] in the presence of periodic q = 1 sawtooth instabilities, a reactor relevant regime. Radially localized off-axis electron cyclotron current drive (ECCD) must be precisely located on the island. In DIII-D the plasma control system is put into a “search and suppress” mode to make either small rigid radial position shifts of the entire plasma (and thus the island) or small changes in the toroidal field (and, thus, the ECCD location) to find and lock onto the optimum position for complete island suppression by ECCD. This is based on real-time measurements of an m/n = 3/2 mode amplitude dBθ/dt. The experiment represents the first use of active feedback control to provide continuous, precise positioning. An alternative to ECCD makes use of the six toroidal section “C-Coil” on DIII-D to provide a large nonresonant static m = 1, n = 3 helical field to interfere with the fundamental harmonic of an m/n = 3/2 NTM. While experiments show success in inhibiting the NTM if a large enough n = 3 field is applied before the island onset, there is a considerable plasma rotation decrease due to n = 3 “ripple.” © 2002 American Institute of Physics.
Show PACS
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
28.52.Av Theory, design, and computerized simulation
52.50.Qt Plasma heating by radio-frequency fields; ICR, ICP, helicons
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