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  • 1
    Electronic Resource
    Electronic Resource
    Statistical theory of resistive drift-wave turbulence and transport (1997)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 4 (1997), S. 2116-2133 
    Details
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Resistive drift-wave turbulence in a slab geometry is studied by statistical closure methods and direct numerical simulations. The two-field Hasegawa–Wakatani (HW) fluid model, which evolves the electrostatic potential and plasma density self-consistently, is a paradigm for understanding the generic nonlinear behavior of multiple-field plasma turbulence. A gyrokinetic derivation of the HW model is sketched. The recently developed Realizable Markovian Closure (RMC) is applied to the HW model; spectral properties, nonlinear energy transfers, and turbulent transport calculations are discussed. The closure results are also compared to direct numerical simulation results; excellent agreement is found. The transport scaling with the adiabaticity parameter, which measures the strength of the parallel electron resistivity, is analytically derived and understood through weak- and strong-turbulence analyses. No evidence is found to support previous suggestions that coherent structures cause a large depression of saturated transport from its quasilinear value in the hydrodynamic regime of the HW model. Instead, the depression of transport is well explained by the spectral balance equation of the (second-order) statistical closure when account is taken of incoherent noise. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.872377
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  • 2
    Electronic Resource
    Electronic Resource
    Submarginal profiles and turbulent transport: An exactly solvable model (1997)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 4 (1997), S. 1342-1356 
    Details
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The possibility that linearly stable ("submarginal") profiles can support turbulent transport in the absence of external noise is considered in the context of a one-dimensional, realizable stochastic model of "almost passive" advection that includes a stability threshold dependent on a critical gradient. The important limits of zero and infinite Kubo number (dimensionless autocorrelation time) are solved analytically. When the stability threshold is linear, it is proven rigorously that, within the context of the model, submarginal profiles do not carry any turbulent flux. A generalization to include a nonlinear stability threshold reminiscent of a subcritical bifurcation supports submarginal profiles. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.872496
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  • 3
    Electronic Resource
    Electronic Resource
    Self-organized criticality, long-time correlations, and the standard transport paradigm : The 41st annual meeting of the division of plasma physics of the american physical society (2000)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 7 (2000), S. 1752-1758 
    Details
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Some aspects of low-frequency, long-wavelength fluctuations are considered. A stochastic model is used to show that power-law time correlations need not arise from self-organized criticality. A formula for the frequency spectrum of uncorrelated, overlapping avalanches is shown to be a special case of the spectral balance equation of renormalized statistical turbulence theory. It is argued that there need be no contradiction between the presence of long-time correlations and the existence of local transport coefficients. © 2000 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.873995
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  • 4
    Electronic Resource
    Electronic Resource
    The roles of shear and cross-correlations on the fluctuation levels in simple stochastic models (2000)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 7 (2000), S. 1148-1157 
    Details
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Highly simplified models of random flows interacting with background microturbulence are analyzed. In the limit of very rapid velocity fluctuations, it is shown rigorously that the fluctuation level of a passively advected scalar is not controlled by the rms shear. In a model with random velocities dependent only on time, the level of cross-correlations between the flows and the background turbulence regulates the saturation level. This effect is illustrated by considering a simple stochastic-oscillator model, both exactly and with analysis and numerical solutions of the direct-interaction approximation. Implications for the understanding of self-consistent turbulence are discussed briefly. © 2000 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.873923
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  • 5
    Electronic Resource
    Electronic Resource
    Generalized weighting scheme for δf particle-simulation method (1994)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 1 (1994), S. 863-874 
    Details
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: An improved nonlinear weighting scheme for the δf method of kinetic particle simulation is derived. The method employs two weight functions to evolve δf in phase space. It is valid for quite general, non-Hamiltonian dynamics with arbitrary sources. In the absence of sources, only one weight function is required and the scheme reduces to the nonlinear algorithm developed by Parker and Lee [Phys. Fluids B 5, 77 (1993)] for sourceless simulations. (It is shown that their original restriction to Hamiltonian dynamics is unnecessary.) One-dimensional gyrokinetic simulations are performed to show the utility of this two-weight scheme. A systematic kinetic theory is developed for the sampling noise due to a finite number of marker trajectories. The noise intensity is proportional to the square of an effective charge qeff=(overdot)q(w¯/D), where w¯ ∼δf/f is a typical weight and D is the dielectric response function.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.870745
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  • 6
    Electronic Resource
    Electronic Resource
    Renormalized dissipation in the nonconservatively forced Burgers equation (2000)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 7 (2000), S. 1064-1067 
    Details
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A previous calculation [P. H. Diamond and T.-S. Hahm, Phys. Plasmas 2, 3640 (1995)] of the renormalized dissipation in the nonconservatively forced one-dimensional Burgers equation, which encountered a catastrophic long-wavelength divergence ∼kmin−3, is reconsidered. In the absence of velocity shear, analysis of the eddy-damped quasi-normal Markovian closure predicts only a benign logarithmic dependence on kmin. The original divergence is traced to an inconsistent resonance-broadening type of diffusive approximation, which fails in the present problem. Ballistic scaling of renormalized pulses is retained, but such scaling does not, by itself, imply a paradigm of self-organized criticality. An improved scaling formula for a model with velocity shear is also given. © 2000 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.873909
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  • 7
    Electronic Resource
    Electronic Resource
    Thermostatted δf (1999)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 6 (1999), S. 1477-1494 
    Details
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The δf simulation method is revisited. Statistical coarse graining is used to rigorously derive the equation for the fluctuation δf in the particle distribution. It is argued that completely collisionless simulation is incompatible with the achievement of true statistically steady states with nonzero turbulent fluxes because the variance W of the particle weights w grows with time. To ensure such steady states, it is shown that for dynamically collisionless situations a generalized thermostat or "W stat" may be used in lieu of a full collision operator to absorb the flow of entropy to unresolved fine scales in velocity space. The simplest W stat can be implemented as a self-consistently determined, time-dependent damping applied to w. A precise kinematic analogy to thermostatted nonequilibrium molecular dynamics is pointed out, and the justification of W stats for simulations of turbulence is discussed. An extrapolation procedure is proposed such that the long-time, steady-state, collisionless flux can be deduced from several short W-statted runs with large effective collisionality, and a numerical demonstration is given. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.873400
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  • 8
    Electronic Resource
    Electronic Resource
    Long-time tails do not necessarily imply self-organized criticality or the breakdown of the standard transport paradigm (1999)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 6 (1999), S. 3731-3734 
    Details
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Numerical measurements and analytical studies are performed on a stochastic model with features relevant to plasma confinement. Although the model lacks crucial features of self-organized criticality (SOC) and its transport can be computed by standard techniques, it nevertheless exhibits intermittency and algebraic time correlations. This suggests that SOC need not be the explanation for observed long-time tails in experimental fluctuation data. Arguments based on the renormalized spectral balance equation, and simulation of a standard nonlinear paradigm, predict a range of Hurst exponents in reasonable agreement with the observations without invoking submarginal dynamics. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.873677
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  • 9
    Electronic Resource
    Electronic Resource
    The clump lifetime revisited: Exact calculation of the second-order structure function for a model of forced, dissipative turbulence (1997)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 4 (1997), S. 655-673 
    Details
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The role of the clump lifetime τcl, logarithmically dependent on small scales, in determining the fluctuation level for forced, dissipative turbulence is reconsidered with the aid of an exactly solvable rapid-change model of passive advection. It is shown in mathematical detail that the common procedure of approximating the steady-state fluctuation level I by τclP, where P is the production rate or source of fluctuations, is invalid when a clean distinction can be made between energy-containing and inertial ranges. The correct result is I(approximate)τDP, where τD is a macroscopic diffusion time that does not depend on the small scales. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.872148
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  • 10
    Electronic Resource
    Electronic Resource
    The role of dissipation in the theory and simulations of homogeneous plasma turbulence, and resolution of the entropy paradox (1994)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 1 (1994), S. 3211-3238 
    Details
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The role of dissipation in the theory and simulations of homogeneous plasma slices is analyzed with the goal of understanding the "entropy paradox,'' which is that a certain positive-definite functional of the perturbed distribution function increases without bound in some situations even though the potentials appear to have achieved a steady state. Confusion arises from an interchange of the limits t→∞ and η→0, where η is a measure of dissipation. It is argued that it is never strictly correct to neglect η; the averaged dissipation approaches a nonzero limit (proportional to the averaged flux) even as η→0. An exactly soluble model is worked out to illustrate the point. In collisionless particle simulations, the particle and heat fluxes may nevertheless saturate with their correct values. The relations of kinetic and fluid entropy balances are discussed with the aid of (1) the Terry–Horton model for collisionless drift waves, and (2) a simple model of the ion-temperature-gradient-driven mode. The rationale for simulations of homogeneous slices of plasma is given, with particular emphasis being placed on the relationship of dissipation in such slices to dissipation in a complete physical domain.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.870475
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