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Charged particle dynamics in the presence of nonGaussian Lévy electrostatic fluctuations [electronic resource].
Washington, D.C. : United States. Dept. of Energy. Office of Science ; Oak Ridge, Tenn. : distributed by the Office of Scientific and Technical Information, U.S. Dept. of Energy, 2016Full orbit dynamics of charged particles in a 3dimensional helical magnetic field in the presence of stable Levy electrostatic fluctuations and linear friction modeling collisional Coulomb drag is studied via Monte Carlo numerical simulations. The Levy fluctuations are introduced to model the effect of nonlocal transport due to fractional diffusion in velocity space resulting from intermittent electrostatic turbulence. The probability distribution functions of energy, particle displacements, and Larmor radii are computed and showed to exhibit a transition from exponential decay, in the case of Gaussian fluctuations, to power law decay in the case of Levy fluctuations. The absolute value of the power law decay exponents are linearly proportional to the Levy index. Furthermore, the observed anomalous nonGaussian statistics of the particles' Larmor radii (resulting from outlier transport events) indicate that, when electrostatic turbulent fluctuations exhibit nonGaussian Levy statistics, gyroaveraging and guiding centre approximations might face limitations and full particle orbit effects should be taken into account.
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On the anisotropic advectiondiffusion equation with time dependent coefficients [electronic resource].
Washington, D.C. : United States. Dept. of Energy. Office of Science ; Oak Ridge, Tenn. : distributed by the Office of Scientific and Technical Information, U.S. Dept. of Energy, 2017The advectiondiffusion equation with time dependent velocity and anisotropic time dependent diffusion tensor is examined in regard to its nonclassical transport features and to the use of a nonorthogonal coordinate system. Although this equation appears in diverse physical problems, particularly in particle transport in stochastic velocity fields and in underground porous media, a detailed analysis of its solutions is lacking. In order to study the effects of the timedependent coefficients and the anisotropic diffusion on transport, we solve analytically the equation for an initial Dirac delta pulse. Here, we discuss the solutions to three cases: one based on powerlaw correlation functions where the pulse diffuses faster than the classical rate ~t, a second case specically designed to display slower rate of diffusion than the classical one, and a third case to describe hydrodynamic dispersion in porous media
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A statistical study of gyroaveraging effects in a reduced model of driftwave transport [electronic resource].
Washington, D.C. : United States. Dept. of Energy. Office of Science ; Oak Ridge, Tenn. : distributed by the Office of Scientific and Technical Information, U.S. Dept. of Energy, 2016Here, a statistical study of finite Larmor radius (FLR) effects on transport driven by electrostatic driftwaves is presented. The study is based on a reduced discrete Hamiltonian dynamical system known as the gyroaveraged standard map (GSM). In this system, FLR effects are incorporated through the gyroaveraging of a simplified weakturbulence model of electrostatic fluctuations. Formally, the GSM is a modified version of the standard map in which the perturbation amplitude, K_{0}, becomes K_{0}J_{0}($\hat{p}$), where J_{0} is the zerothorder Bessel function and $\hat{p}$ s the Larmor radius. Assuming a Maxwellian probability density function (pdf) for $\hat{p}$ , we compute analytically and numerically the pdf and the cumulative distribution function of the effective driftwave perturba tion amplitude K_{0}J_{0}($\hat{p}$). Using these results, we compute the probability of loss of confinement (i.e., global chaos), P_{c} provides an upper bound for the escape rate, and that P_{t }rovides a good estimate of the particle trapping rate. Lastly. the analytical results are compared with direct numerical MonteCarlo simulations of particle transport.
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