Perturbative studies of transport phenomena in fusion devices

Ryter, F.; Dux, R.; Mantica, P.; Tala, T.

doi:10.1088/0741-3335/52/12/124043

Cited by 43 publications

(139 citation statements)

References 161 publications

(280 reference statements)

Supporting

Mentioning

138

Contrasting

Order By: Relevance

“…The highest frequency that needs to be considered is denoted by N . The Volterra kernels G (1) and G (2) are the complex and frequency dependent equivalents of…”

Section: Volterra Seriesmentioning

confidence: 99%

“…The proper choice to define U (k) is to use the power dependent part of the perturbation u (t) = P (t) as has been used in the Taylor expansion in (5). The deposition profile is part of G (1) and G (2) as the input is purely the time dependent part of the perturbation. Alternatively, we can assume that the heat is locally absorbed such that instead the temperature at the deposition location can be used as input, i.e.,…”

Section: Volterra Seriesmentioning

confidence: 99%

“…Therefore, with the view to improve energy confinement a number of methodologies have been developed to analyze transport. They focus either on the micro-scale level [1], or on the global consequences of turbulence, e.g., temperature (gradient) and transport coefficients such as diffusion [2]. These quantities are generally analyzed in 1D as a function of the dimensionless normalized minor radius ρ, which is permissible due to the device geometry, magnetic field configuration, and relevant time scales of transport [3].…”

Section: Introductionmentioning

confidence: 99%

“…These quantities are generally analyzed in 1D as a function of the dimensionless normalized minor radius ρ, which is permissible due to the device geometry, magnetic field configuration, and relevant time scales of transport [3]. This radial transport is then analyzed in steady-state [4] or in the transient phase, often using a perturbation [2,5,3,6].…”

Section: Introductionmentioning

confidence: 99%

“…Current literature related to LHD points into the direction of a power dependence of transport via the turbulence level [30], which has also been extensively studied at W7-AS [31,32,33]. These and other non-linear transport properties have been analyzed using perturbations (often via the heat pulse diffusivity χ HP ) at different operating points and comparing them to each other and to steadystate results (power balance diffusivity χ P B ) [34,2]. Alternatively, model codes based on the physics are used to fit parameters of the non-linear models, e.g., [20,35].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

New evidence and impact of electron transport non-linearities based on new perturbative inter-modulation analysis

et al. 2017

View full text Add to dashboard Cite

Abstract.A new methodology to analyze non-linear components in perturbative transport experiments is introduced. The methodology has been experimentally validated in the Large Helical Device (LHD) for the electron heat transport channel. Electron cyclotron resonance heating (ECRH) with different modulation frequencies by two gyrotrons have been used to directly quantify the amplitude the non-linear component at the inter-modulation frequencies. The measurements show significant quadratic non-linear contributions, but also the absence of cubic and higher order components. The non-linear component is analyzed using Volterra series, which is the non-linear generalization of transfer functions. This allows to study the radial distribution of the non-linearity of the plasma and to reconstruct linear profiles in the case the measurements were not distorted by non-linearities. The reconstructed linear profiles are significantly different from the measured profiles showing the significant impact the non-linearity can have.

show abstract

“…The highest frequency that needs to be considered is denoted by N . The Volterra kernels G (1) and G (2) are the complex and frequency dependent equivalents of…”

Section: Volterra Seriesmentioning

confidence: 99%

Section: Volterra Seriesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

New evidence and impact of electron transport non-linearities based on new perturbative inter-modulation analysis

et al. 2017

View full text Add to dashboard Cite

show abstract

Retraction statement: Adaptive distributed parameter and input estimation in linear parabolic PDEs

Mechhoud

2016

Adaptive Control & Signal

View full text Add to dashboard Cite

SUMMARYIn this paper, we discuss the on-line estimation of distributed source term, diffusion, and reaction coefficients of a linear parabolic partial differential equation using both distributed and interior-point measurements. First, new sufficient identifiability conditions of the input and the parameter simultaneous estimation are stated. Then, by means of Lyapunov-based design, an adaptive estimator is derived in the infinitedimensional framework. It consists of a state observer and gradient-based parameter and input adaptation laws. The parameter convergence depends on the plant signal richness assumption, whereas the state convergence is established using a Lyapunov approach. The results of the paper are illustrated by simulation on tokamak plasma heat transport model using simulated data.

show abstract

How to Face the Complexity of Plasmas?

Escande

2013

Nonlinear Systems and Complexity

View full text Add to dashboard Cite

This paper has two main parts. The first part is subjective and aims at favoring a brainstorming in the plasma community. It discusses the present theoretical description of plasmas, with a focus on hot weakly collisional plasmas. It comprises two sub-parts. The first one deals with the present status of this description. In particular, most models used in plasma physics are shown to have feet of clay, there is no strict hierarchy between them, and a principle of simplicity dominates the modeling activity. At any moment the description of plasma complexity is provisional and results from a collective and somewhat unconscious process. The second sub-part considers possible methodological improvements, some of them specific to plasma physics, some others of possible interest for other fields of science. The proposals for improving the present situation go along the following lines: improving the way papers are structured and the way scientific quality is assessed in the referral process, developing new data bases, stimulating the scientific discussion of published results, diversifying the way results are made available, assessing more quality than quantity, making available an incompressible time for creative thinking and non purpose-oriented research. Some possible improvements for teaching are also indicated. The suggested improvement of the structure of papers would be for each paper to have a "claim section" summarizing the main results and their most relevant connection to previous literature. One of the ideas put forward is that modern nonlinear dynamics and chaos might help revisiting and unifying the overall presentation of plasma physics.The second part of this chapter is devoted to one instance where this idea has been developed for three decades: the description of Langmuir wave-electron interaction in one-dimensional plasmas by a finite dimensional Hamiltonian. This part is more specialized, and is written like a classical scientific paper. This Hamiltonian approach enables recovering Vlasovian linear theory with a mechanical understanding. The quasilinear description of the weak warm beam is discussed, and it is shown that self-consistency vanishes when the plateau forms in the tail distribution function. This leads to consider the various diffusive regimes of the dynamics of particles in a frozen spectrum of waves with random phases. A recent numerical simulation showed that diffusion is quasilinear when the plateau sets in, and that the variation of the phase of a given wave with time is almost non fluctuating for random realizations of the initial wave phases. This led to new analytical calculations of the average behavior of the self-consistent dynamics when the initial wave phases are random. Using Picard iteration technique, they confirm numerical results, and exhibit a spontaneous emission of spatial inhomogeneities.Non quia difficilia sunt, non audemus, sed quia non audemus, difficilia sunt. It is not because things are difficult that we do not dare, it is because we do not dare that things a...

show abstract

Perturbative studies of transport phenomena in fusion devices

Cited by 43 publications

References 161 publications

New evidence and impact of electron transport non-linearities based on new perturbative inter-modulation analysis

New evidence and impact of electron transport non-linearities based on new perturbative inter-modulation analysis

Retraction statement: Adaptive distributed parameter and input estimation in linear parabolic PDEs

How to Face the Complexity of Plasmas?

Contact Info

Product

Resources

About