Nondiffusive Transport in Plasma Turbulence: A Fractional Diffusion Approach

Del-Castillo-Negrete, Diego B; Carreras, B. A.; Lynch, V. E.

doi:10.1103/physrevlett.94.065003

Cited by 249 publications

(187 citation statements)

References 14 publications

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“…0, this turbulent dispersion is superdiffusive because some structures in the turbulence are relatively static and have large amplitudes relative to the background profile, allowing ions to move large distances through the structures. 36 However, if the fluctuations are reduced below a certain level, c R drops dramatically because the amplitude of the vortex structures is too small for the structures to form connected velocity streamlines between the center and edge of the plasma. This is simply a topological constraint set by the amplitude of the turbulent fluctuations.…”

Section: B Interaction Phasementioning

confidence: 99%

Suprathermal ion transport in simple magnetized torus configurations

et al. 2012

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Inspired by suprathermal ion experiments in the basic plasma experiment TORPEX, the transport of suprathermal ions in ideal interchange mode turbulence is theoretically examined in the simple magnetized torus configuration. We follow ion tracer trajectories as specified by ideal interchange mode turbulence imported from a numerical simulation of drift-reduced Braginskii equations. Using the variance of displacements, σ2(t)∼tγ, we find that γ depends strongly on suprathermal ion injection energy and the relative magnitude of turbulent fluctuations. The value of γ also changes significantly as a function of time after injection, through three distinguishable phases: ballistic, interaction, and asymmetric. During the interaction phase, we find the remarkable presence of three regimes of dispersion: superdiffusive, diffusive, and subdiffusive, depending on the energy of the suprathermal ions and the amplitude of the turbulent fluctuations. We contrast these results with those from a “slab” magnetic geometry in which subdiffusion does not occur during the interaction phase. Initial results from TORPEX are consistent with data from a new synthetic diagnostic used to interpret our simulation results. The simplicity of the simple magnetized torus makes the present work of interest to analyses of more complicated contexts ranging from fusion devices to astrophysics and space plasma physics.

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Section: B Interaction Phasementioning

confidence: 99%

Suprathermal ion transport in simple magnetized torus configurations

et al. 2012

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“…2, 3, 4, 5, 6, 7, 8, 9, 10, applications and enhancements of these techniques were presented. The relevance of fractional calculus in the phenomenological description of anomalous diffusion has been discussed within applications of statistical mechanics in physics, chemistry and biology [11,12,13,14,15,16,17] as well as finance [18,19,20,21,22]; even human travel and the spreading of epidemics were modeled with fractional diffusion [23]. A direct Monte Carlo approach to fractional Fokker-Planck dynamics through the underlying CTRW requires random numbers drawn from the Mittag-Leffler distribution.…”

Section: Introductionmentioning

confidence: 99%

Monte Carlo simulation of uncoupled continuous-time random walks yielding a stochastic solution of the space-time fractional diffusion equation

2008

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We present a numerical method for the Monte Carlo simulation of uncoupled continuous-time random walks with a Lévy α-stable distribution of jumps in space and a Mittag-Leffler distribution of waiting times, and apply it to the stochastic solution of the Cauchy problem for a partial differential equation with fractional derivatives both in space and in time. The one-parameter MittagLeffler function is the natural survival probability leading to time-fractional diffusion equations. Transformation methods for Mittag-Leffler random variables were found later than the well-known transformation method by Chambers, Mallows, and Stuck for Lévy α-stable random variables and so far have not received as much attention; nor have they been used together with the latter in spite of their mathematical relationship due to the geometric stability of the Mittag-Leffler distribution. Combining the two methods, we obtain an accurate approximation of space-and time-fractional diffusion processes almost as easy and fast to compute as for standard diffusion processes.

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“…Although these assumptions are reasonable and physical realizable, recent experiments and numerical simulations have shown that there are cases in which fluctuations in turbulent plasmas exhibit Lévy statistics. For example, Lévy statistics has been observed in electrostatic edge turbulence in tokamaks and stellarators [11], and in numerical simulations of pressure-gradient driven plasma turbulence [12]. …”

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confidence: 99%