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  • 11
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 7 (2000), S. 4590-4599 
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Runaway electrons are calculated to be produced during the rapid plasma cooling resulting from "killer pellet" injection experiments, in general agreement with observations in the DIII-D [J. L. Luxon et al., Plasma Physics and Controlled Nuclear Fusion Research 1986 (International Atomic Energy Agency, Vienna, 1987), Vol. I, p. 159] tokamak. The time-dependent dynamics of the kinetic runaway distributions are obtained with the CQL3D [R. W. Harvey and M. G. McCoy, "The CQL3D Code," in Proceedings of the IAEA Technical Committee Meeting on Numerical Modeling, Montreal, 1992 (International Atomic Energy Agency, Vienna, 1992), p. 489] collisional Fokker–Planck code, including the effect of small and large angle collisions and stochastic magnetic field transport losses. The background density, temperature, and Zeff are evolved according to the KPRAD [D. G. Whyte and T. E. Evans et al., in Proceedings of the 24th European Conference on Controlled Fusion and Plasma Physics, Berchtesgaden, Germany (European Physical Society, Petit-Lancy, 1997), Vol. 21A, p. 1137] deposition and radiation model of pellet–plasma interactions. Three distinct runway mechanisms are apparent: (1) prompt "hot-tail runaways" due to the residual hot electron tail remaining from the pre-cooling phase, (2) "knock-on" runaways produced by large-angle Coulomb collisions on existing high energy electrons, and (3) Dreicer "drizzle" runaway electrons due to diffusion of electrons up to the critical velocity for electron runaway. For electron densities below (approximate)1×1015 cm−3, the hot-tail runaways dominate the early time evolution, and provide the seed population for late time knock-on runaway avalanche. For small enough stochastic magnetic field transport losses, the knock-on production of electrons balances the losses at late times. For losses due to radial magnetic field perturbations in excess of (approximate)0.1% of the background field, i.e., δBr/B≥0.001, the losses prevent late-time electron runaway. © 2000 American Institute of Physics.
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  • 12
    Electronic Resource
    Electronic Resource
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 3 (1991), S. 1807-1817 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A unified theory of temperature gradient-driven trapped ion modes and ballooning instabilities is developed using kinetic theory in banana regimes. All known results such as electrostatic and purely magnetic trapped particle modes and ideal magnetohydrodynamic ballooning modes (or shear Alfvén waves) are readily derived from the present single general dispersion relation. Several new results from ion–ion collision, finite beta stabilization of ion temperature gradient-driven trapped particle modes, and trapped particle modification of ballooning modes are derived and discussed. The interrelationship between these modes is established.
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  • 13
    Electronic Resource
    Electronic Resource
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 3 (1991), S. 363-371 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: In this paper, the effect of current drive on the tearing modes in the semicollisional regime is analyzed using the drift-kinetic equation. A collisional operator is developed to model electron parallel conductivity. For the pure tearing modes the linear and quasilinear growth rates in the Rutherford regimes have been found to have roughly the same forms with a modified resistivity as without current drive. One interesting result is the prediction of a new instability. This instability, driven by the current gradient inside the tearing mode layer, is possibly related to magnetohydrodynamic (MHD) behavior observed in these experiments.
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  • 14
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 28 (1985), S. 2824-2837 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Dissipative trapped particle modes are studied in tandem mirrors by including electron collisions and ion Landau damping. A variational approach is used to obtain a collisional response in terms of the collisionless result plus a collisional term. The collisional term is then self-consistently solved in all collision frequency regimes. When ν/ω(very-much-less-than)1 (ν≡electron collision frequency) and the dissipationless mode is stable through a positive (negative) charge uncovering mechanism, there are two stable waves with phase velocities in the ion (electron) diamagnetic direction. The higher frequency wave with ω∼ω@B|i(ω*e) is destabilized by ion (electron) dissipation while the lower frequency wave is destabilized by electron (ion) dissipation. At high collision frequency (ν〉ω@B|e), the only unstable trapped particle wave has ω∼ω*e, with electron collisions being destabilizing.
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  • 15
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A newly developed continuum gyrokinetic code GYRO has been formulated on a radial grid to operate at finite relative gyroradius in a noncyclic radial annulus with profile variation. The code is used to simulate ion temperature gradient mode turbulence and to demonstrate that gyroBohm scaling can be obtained well above the instability threshold but sufficiently strong profile shear stabilization can break gyroBohm scaling down to Bohm scaling (or worse) near threshold. An adaptive source technique is used to maintain profiles. Clear evidence for nonlocal transport is also found in which the local diffusivity depends on the plasma gradients at some considerable radial distance. © 2002 American Institute of Physics.
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  • 16
    Electronic Resource
    Electronic Resource
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 4 (1992), S. 2402-2413 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The linear theory of the sonic ion-temperature-gradient-driven mode in the presence of sheared poloidal rotation is discussed in the context of a hydrodynamic model. Analytical and numerical calculations show that the growth rate increases for weak shear, but then decreases when the shearing frequency exceeds the mode frequency. This trend is a consequence of the coupling of radial eigenmodes induced by the asymmetric effective potential and the absorption and damping due to resonance between the wave frequency and shearing frequency. The former dominates at weak shear, resulting in destabilization, while the latter dominates for strong shear, resulting in stabilization. Mixing length estimates of the turbulent diffusivity are given, and a novel bifurcation scenario for the L→H transition is discussed.
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  • 17
    Electronic Resource
    Electronic Resource
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 4 (1992), S. 2189-2202 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: An asymptotic theory is described for calculating the mode structure and continuum damping of short-wavelength toroidal Alfvén eigenmodes (TAE). The formalism somewhat resembles the treatment used for describing low-frequency toroidal modes with singular structure at a rational surface, where an inner solution, which for the TAE mode has toroidal coupling, is matched to an outer toroidally uncoupled solution. A three-term recursion relation among coupled poloidal harmonic amplitudes is obtained, whose solution gives the structure of the global wave function and the complex eigenfrequency, including continuum damping. Both analytic and numerical solutions are presented. The magnitude of the damping is essential for determining the thresholds for instability driven by the spatial gradients of energetic particles (e.g., neutral-beam-injected ions or fusion-product alpha particles) contained in a tokamak plasma.
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  • 18
    Electronic Resource
    Electronic Resource
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 3 (1991), S. 68-86 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A kinetic theory of collisionless and dissipative trapped-electron-driven drift wave turbulence in a sheared magnetic field is presented. Weak turbulence theory is employed to calculate the nonlinear electron and ion responses and to derive a wave kinetic equation that determines the nonlinear evolution of trapped-electron mode turbulence. The saturated fluctuation spectrum is calculated using the condition of nonlinear saturation. The turbulent transport coefficients (D, χi, χe), are, in turn, calculated using the saturated fluctuation spectrum. Because of the disparity in the three different radial scale lengths of the slab-like eigenmode: Δ (trapped-electron layer width), xt (turning point width), and xi (Landau damping point), Δ〈xt〈xi, it is found that ion Compton scattering rather than trapped-electron Compton scattering is the dominant nonlinear saturation mechanism. Ion Compton scattering transfers wave energy from short to long wavelengths where the wave energy is shear damped. As a consequence, a saturated fluctuation spectrum ||φ||2(kθ)∼k−αθ (α=2 and 3 for the dissipative and collisionless regimes, respectively) occurs for kθ ρs〈1 and is heavily damped for kθ ρs〉1. The predicted fluctuation level and transport coefficients are well below the "mixing length'' estimate. This is due to the contribution of radial wave numbers x−1t〈kr≤ρ−1i to the nonlinear couplings, the effect of radial localization of the trapped-electron response to a layer of width Δ, and the weak turbulence factor 〈γle/ωk〉k〈1, which enters the saturation level.
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  • 19
    Electronic Resource
    Electronic Resource
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 1 (1989), S. 826-839 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The stability of a Migma disk is reexamined to determine the threshold to the interchange instability. It is shown that a previous calculation [Z. Naturforsch. Teil A 42, 1208 (1987)], which assumes a rigid mode eigenfunction, is inaccurate at the predicted particle number for marginal stability. As a result the integral equation for the system must be solved. A variational method of solution is developed and is shown to give good agreement with a direct numerical solution. The threshold for instability is found to be sensitive to the details of the distribution function. For highly focused systems, where all ions pass close to the axis, the threshold particle number (Nu1) for instability is substantially below that predicted by rigid mode theory (Nrigid) (by a factor ∼8ε2, where ε=r1/rL, r1 is the spread in the distance of closest approach to the axis, and rL the ion Larmor radius). At a higher density, a second band of stability appears that again destabilizes at yet a higher particle number (Nu2). If ε(very-much-less-than)1, Nu2 is substantially below the rigid mode prediction, while for 0.2〈ε〈0.3, Nu2 is comparable to the rigid mode prediction. At moderate values of ε (ε≈0.3–0.4) the second stability band disappears and the instability particle number threshold varies from the rigid stability threshold by a factor of 0.4ε, when ε=0.4, to 0.7ε when ε is about unity. The stability criteria would be consistent with the observed particle storage number obtained in experimental configurations if the spread in ε is sufficiently large.
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  • 20
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 30 (1987), S. 2750-2758 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: In this paper the effect of finite pressure on the ballooning instability in toroidal magnetohydrodynamics (MHD) equilibria of steep boundary stellarators and tokamaks is examined. Ballooning modes tend to arise near the place where the local shear vanishes and the normal curvature (the curvature component perpendicular to the flux surface, pointing away from the magnetic axis) is negative. It is shown how the pressure gradient determines the position of the shearless points, and demonstrated in detail how this effect explains the existence of second stability in tokamaks. For large aspect ratio circular cross-section tokamaks the second stability condition is found to scale as α=const S1.25. Stellarators are inherently more stable because of the negative vacuum shear, which at moderate pressure gradients allows the zero shear point to localize on the inner side of the flux surface. However, at high pressure gradients the Pfirsch–Schlüter current produces a positive mean shear when the total toroidal current on a flux surface is zero. This causes the zero shear point to localize on the outer edge near the vertical extremes of the flux surface. This effect, together with helical contributions to the helical curvature, allows for ballooning instability to arise. At higher pressure gradients, with zero net toroidal current, an unstable ballooning mode which localizes to within a helical period always arises where the normal curvature is unfavorable.
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