skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Reduced Lorenz models for anomalous transport and profile resilience

Abstract

The physical basis for the Lorenz equations for convective cells in stratified fluids, and for magnetized plasmas imbedded in curved magnetic fields, are reexamined with emphasis on anomalous transport. It is shown that the Galerkin truncation leading to the Lorenz equations for the closed boundary problem is incompatible with finite fluxes through the system in the limit of vanishing diffusion. An alternative formulation leading to the Lorenz equations is proposed, invoking open boundaries and the notion of convective streamers and their back-reaction on the profile gradient, giving rise to resilience of the profile. Particular emphasis is put on the diffusionless limit, where these equations reduce to a simple dynamical system depending only on one single forcing parameter. This model is studied numerically, stressing experimentally observable signatures, and some of the perils of dimension-reducing approximations are discussed.

Authors:
;  [1];  [2]
  1. Department of Physics and Technology, University of Tromsoe, N-9037 Tromsoe (Norway)
  2. (Denmark)
Publication Date:
OSTI Identifier:
20974817
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Plasmas; Journal Volume: 14; Journal Issue: 2; Other Information: DOI: 10.1063/1.2435318; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; APPROXIMATIONS; DIFFUSION; EQUATIONS; MAGNETIC FIELDS; MAGNETOHYDRODYNAMICS; PLASMA

Citation Formats

Rypdal, K., Garcia, O. E., and Association EURATOM-Risoe National Laboratory, OPL-128 Risoe, DK-4000 Roskilde. Reduced Lorenz models for anomalous transport and profile resilience. United States: N. p., 2007. Web. doi:10.1063/1.2435318.
Rypdal, K., Garcia, O. E., & Association EURATOM-Risoe National Laboratory, OPL-128 Risoe, DK-4000 Roskilde. Reduced Lorenz models for anomalous transport and profile resilience. United States. doi:10.1063/1.2435318.
Rypdal, K., Garcia, O. E., and Association EURATOM-Risoe National Laboratory, OPL-128 Risoe, DK-4000 Roskilde. Thu . "Reduced Lorenz models for anomalous transport and profile resilience". United States. doi:10.1063/1.2435318.
@article{osti_20974817,
title = {Reduced Lorenz models for anomalous transport and profile resilience},
author = {Rypdal, K. and Garcia, O. E. and Association EURATOM-Risoe National Laboratory, OPL-128 Risoe, DK-4000 Roskilde},
abstractNote = {The physical basis for the Lorenz equations for convective cells in stratified fluids, and for magnetized plasmas imbedded in curved magnetic fields, are reexamined with emphasis on anomalous transport. It is shown that the Galerkin truncation leading to the Lorenz equations for the closed boundary problem is incompatible with finite fluxes through the system in the limit of vanishing diffusion. An alternative formulation leading to the Lorenz equations is proposed, invoking open boundaries and the notion of convective streamers and their back-reaction on the profile gradient, giving rise to resilience of the profile. Particular emphasis is put on the diffusionless limit, where these equations reduce to a simple dynamical system depending only on one single forcing parameter. This model is studied numerically, stressing experimentally observable signatures, and some of the perils of dimension-reducing approximations are discussed.},
doi = {10.1063/1.2435318},
journal = {Physics of Plasmas},
number = 2,
volume = 14,
place = {United States},
year = {Thu Feb 15 00:00:00 EST 2007},
month = {Thu Feb 15 00:00:00 EST 2007}
}
  • An experimental study of the onset of drift wave and flute interchange instabilities in the Helimak configuration is presented. It is shown that the Helimak offers the opportunity to separate the regions where these instabilities are active and to assess their relative role in cross-field anomalous transport and in the self-organization of exponential plasma density profiles with resilient scale length. Some results indicating a period doubling route to turbulence are also presented.
  • The basic physical concepts underlying the theories of anomalous transport in magnetic confinement devices are reviewed. Anomalous transport is a consequence of electric and/or magnetic fluctuations driven by various linear and/or nonlinear instability mechanisms. The latter saturate by inducing a relaxation of the profiles towards a marginally stable state or/and by nonlinear coupling of the various modes. Specific theoretical models are described, together with their successes and drawbacks in the light of observed characteristics of plasma confinement, a non exhaustive list of which is given. A rough estimate of the nuclear heating power required to balance the anomalous losses inmore » the International Tokamak Experimental Reactor (ITER) is calculated on the basis of the electrostatic drift wave instability model. 58 refs., 7 figs.« less
  • Our work presents a method to adaptively refine reduced-order models a posteriori without requiring additional full-order-model solves. The technique is analogous to mesh-adaptive h-refinement: it enriches the reduced-basis space online by ‘splitting’ a given basis vector into several vectors with disjoint support. The splitting scheme is defined by a tree structure constructed offline via recursive k-means clustering of the state variables using snapshot data. This method identifies the vectors to split online using a dual-weighted-residual approach that aims to reduce error in an output quantity of interest. The resulting method generates a hierarchy of subspaces online without requiring large-scale operationsmore » or full-order-model solves. Furthermore, it enables the reduced-order model to satisfy any prescribed error tolerance regardless of its original fidelity, as a completely refined reduced-order model is mathematically equivalent to the original full-order model. Experiments on a parameterized inviscid Burgers equation highlight the ability of the method to capture phenomena (e.g., moving shocks) not contained in the span of the original reduced basis.« less