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  • 1
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 8 (2001), S. 1553-1558 
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A simple criterion that allows one to determine whether or not a given wave spectrum will generate zonal flows, is derived and analyzed. In the context of a coupled drift wave–zonal turbulence, the results are pertinent to the limit of small zonal flow damping, γd→0, in which previous analyses found that the turbulence vanishes. However, the practically important issue of the drift wave amplitude threshold for zonal flow excitation was not resolved. In its formal mathematical appearance, the criterion obtained is similar to the well-known Penrose criterion that is used for stability analysis of stellar distributions and particle distributions in plasmas. By contrast, the derived criterion, being applied to wave quanta rather than to particle distribution, shows that even "normal" (wave density decaying with wave number) distributions with an intensity above the threshold should generate zonal flows. This clearly points at the ubiquity of the latter. © 2001 American Institute of Physics.
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  • 2
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 7 (2000), S. 170-177 
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Theoretical studies of mean field electrodynamics for diffusive processes in the electron magnetohydrodynamic (EMHD) model is presented. In contrast to magnetohydrodynamics (MHD), the evolution of the magnetic field here is governed by a nonlinear equation in magnetic field variables. A detailed description of diffusive processes in two dimensions are presented in this paper. In particular, it has been shown analytically that the turbulent magnetic field diffusivity is suppressed from naive quasilinear estimates. It is shown that for complete whistlerization of the spectrum, turbulent diffusivity vanishes. The question of whistlerization of the turbulent spectrum is investigated numerically, and a reasonable tendency towards whistlerization is observed. Numerical studies also show suppression of magnetic field diffusivity in accordance with analytical estimates. © 2000 American Institute of Physics.
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  • 3
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 3 (1996), S. 2903-2911 
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A model for plasma transport near marginal stability is presented. The model is based on subcri- tical resistive pressure-gradient-driven turbulence. Three-dimensional nonlinear calculations based on this model show effective transport for subcritical mean profiles. This model exhibits some of the characteristic properties of self-organized criticality. Perturbative transport techniques are used to elucidate the transport properties. Propagation of positive and negative pulses is studied. The observed results suggest a possible explanation of the apparent nonlocal effects ob- served with perturbative experiments in tokamaks. © 1996 American Institute of Physics.
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  • 4
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 3 (1996), S. 3745-3753 
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The radial structure of tokamak profiles determined by anomalous transport is elucidated by studying the statistical mechanics of a sand pile automaton for which the toppling conditions depend on local gradient, alone. In this representation, the sand pile dynamics is Markovian, and spatial profiles may be obtained from calculated expectation values of the local gradient. The Markovian structure of the dynamics is exploited to analytically derive a local gradient probability distribution function from a generalized kinetic equation. For homogeneous, weak noise, the calculated expectation value of the gradient is well below the marginally stable state. In the over-driven limit (i.e., strong homogeneous noise), a region of super-critical gradient is shown to form near the bottom of the pile. For the case of localized noise, the mean self-organized profile is always sub-critical. These results are consistent with numerical studies of simple automata. Their relevance to and implications for tokamak confinement are discussed. © 1996 American Institute of Physics.
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  • 5
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 2 (1995), S. 1941-1946 
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A turbulent dynamo in a conducting fluid is accompanied by the generation of small-scale magnetic fields, which are much stronger than the mean dynamo-generated magnetic field. These small-scale fields modify the α effect in such a way as to stabilize the dynamo process, α=(α0+β0R⋅/B∇×R)/(1+R2), where α0, β0 are the standard kinematic dynamo parameters, and R is proportional to the mean magnetic field B0, R=B0/(4πρV2/Rm)1/2, ρ is the fluid density, V is the characteristic turbulent velocity, and Rm is the magnetic Reynolds number. The derivation of this formula is illustrated using a simple model—the turbulent dynamo for an asymmetrical top. © 1995 American Institute of Physics.
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  • 6
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 2 (1995), S. 2007-2010 
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: In the presence of a pressure gradient, the phase velocity of drift wave or ion temperature gradient (ITG) mode turbulence is different from the average poloidal E×B rotation velocity of the guiding centers. This results in an E˜×B turbulent particle diffusion being suppressed by the phase shift due to the diamagnetic rotation velocity uθ=(c/enB)dP/dr. This shift cannot be eliminated by a change of frame and affects the plasma transport. For uθ well above the turbulent E˜×B velocity, the radial diffusivity is suppressed as D∝u−3θ. This results in a nonmonotonous particle flux Γ(∇n)(approximately-equal-to)−D0∇n[1+α(∇n)2]−3/2 such that the transport can develop a bifurcation at a realistic density gradient. © 1995 American Institute of Physics.
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  • 7
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 2 (1995), S. 3685-3695 
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A simple dynamic model of spatiotemporally propagating transport barriers and transition fronts from low (L) to high (H) confinement regimes is presented. The model introduces spatial coupling (via transport) into the coupled evolution equations for flow shear and fluctuation intensity, thus coupling the supercritical L to H bifurcation instability to turbulent transport. Hence, fast spatiotemporal front propagation and evolutionary behavior result. The theory yields expressions for the propagation velocity and termination point of an L–H transition front and transport barrier. When the evolution of the pressure gradient, ∇Pi, and the contribution of ∇Pi to sheared electric field, Er′, is included, the ambient pretransition pressure gradient acts as a local source term that drives the evolution of the poloidal velocity shear. The transition may then evolve either as a spatiotemporally propagating front or as a uniform (i.e., nonlocal) fluctuation reduction or quench. The precise route to transition adopted depends on the relative magnitudes of the front transit time, τT, and the fluctuation reduction time, τf, respectively. The relevance of spatiotemporally propagating L–H transition fronts to the very high confinement regime (VH mode) evolution in DIII-D [R. I. Pinsker and the DIII-D Team, Plasma Physics and Controlled Nuclear Fusion Research 1992 (International Atomic Energy Agency, Vienna, 1993), Vol. 1, p. 683] and in the Joint European Torus (JET) [Plasma Physics and Controlled Nuclear Fusion Research 1990 (International Atomic Energy Agency, Vienna, 1991), Vol. 1, p. 27] is discussed. © 1995 American Institute of Physics.
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  • 8
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 1 (1994), S. 1592-1600 
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: From extensive simulation of simple local fluid models of long wavelength drift wave turbulence in tokamaks, it is found that conventional notions concerning directions of cascades, locality and isotropy of spectral transfer, frequencies of fluctuations, and stationarity of saturation do not hold for moderate to long wavelengths (kρs≤1). In particular, at long wavelengths, where spectral transfer of energy is dominated by the E×B nonlinearity, energy is carried to short scale (even in two dimensions) in a manner that is anisotropic and highly nonlocal (energy is efficiently passed between modes separated by the entire spectrum range in a correlation time). At short wavelengths, transfer is dominated by the polarization drift nonlinearity. While the standard dual cascade applies in this subrange, it is found that finite spectrum size can produce cascades that are reverse directed (i.e., energy to high k) and are nonconservative in enstrophy and energy similarity ranges (but conservative overall). In regions where both nonlinearities are important, cross-coupling between the nonlinearities gives rise to large nonlinear frequency shifts which profoundly affect the dynamics of saturation by modifying the growth rate and nonlinear transfer rates. These modifications produce a nonstationary saturated state with large amplitude, long period relaxation oscillations in the energy, spectrum shape, and transport rates. Methods of observing these effects are presented.
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  • 9
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 9 (2002), S. 71-77 
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: An analytical theory of the tails of the probability distribution function (PDF) for the local Reynolds stress (R) is given for forced Hasegawa–Mima turbulence. The PDF tail is treated as a transition amplitude from an initial state, with no fluid motion, to final states with different values of R due to nonlinear coherent structures in the long time limit. With the modeling assumption that the nonlinear structure is a modon (an exact solution of a nonlinear Hasegawa–Mima equation) in space, this transition amplitude is determined by an instanton. An instanton is localized in time and can be associated with bursty and intermittent events which are thought to be responsible for PDF tails. The instanton is found via a saddle-point method applied to the PDF, represented by a path integral. It implies the PDF tail for R with the specific form exp[−cR3/2], which is a stretched, non-Gaussian exponential. © 2002 American Institute of Physics.
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  • 10
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 3 (1996), S. 3023-3031 
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A theory of the relaxation dynamics of the radial electric field toward its neoclassical value in the regime of subsonic poloidal rotation is presented. It is shown that the relaxation occurs via damped oscillations on time scales proportional to the ion transit time. © 1996 American Institute of Physics.
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