# From Liouville's theorem to quasilinear, nonlinear stochastic, and fractional transport, a multi-scale kinetics of plasma turbulence

Source: [From Liouville's theorem to quasilinear, nonlinear stochastic, and fractional transport, a multi-scale kinetics of plasma turbulence](<https://www.sota2.com/research/paper/68fa2cfe1e209131ce855394>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T15:42:19.847Z

Authors: Shaojie Wang

Published: 2013-12-31T07:33:20.000Z

## Abstract

From Liouville's equation, a phase-space multi-scale transport equation is systematically derived. The proposed phase-space multi-scale transport equation based on the first principle indicates that the nonlinear stochastic transport is due to the micro-turbulence scattering while the familiar quasilinear transport is due to the long-range correlation of the meso-scale coherent modes; and more interestingly, it demonstrates a systematic derivation of the fractional transport equation that may provide a new view-angle to understand the anomalous transport observed in plasma turbulence. The multi-scale kinetics suggests a new approach to confinement improvement through the formation of nonlinearly self-organized stable large-scale structures.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1401.0107>)

[PDF](<https://arxiv.org/pdf/1401.0107.pdf>)