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| 3. |
- Anderson, Johan, 1973, et al.
(författare)
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A fractional Fokker-Planck model for anomalous diffusion
- 2014
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Ingår i: Physics of Plasmas. - : AIP Publishing. - 1089-7674 .- 1070-664X. ; 21:12, s. aricle no: 122109-
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we present a study of anomalous diffusion using a Fokker-Planck description withfractional velocity derivatives. The distribution functions are found using numerical means forvarying degree of fractionality of the stable Lévy distribution. The statistical properties of thedistribution functions are assessed by a generalized normalized expectation measure and entropyin terms of Tsallis statistical mechanics. We find that the ratio of the generalized entropy andexpectation is increasing with decreasing fractionality towards the well known so-called sub-diffusivedomain, indicating a self-organising behavior.
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| 4. |
- Anderson, Johan, 1973, et al.
(författare)
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Anomalous Diffusion by the Fractional Fokker-Planck Equation and Lévy Stable Processes
- 2018
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Ingår i: Fractional Dynamics and Anomalous Transport in Plasma Science. - Cham : Springer International Publishing. - 9783030044824 ; , s. 77-92
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Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- The work presented here is a review of current developments in modelling anomalous diffusion using a Fokker-Planck description with fractional velocity derivatives and Langevin dynamics where L´evy fluctuations are introduced to model the effect of non-local transport due to fractional diffusion in velocity space. Distribution functions are found using numerical means for varying degree of fractionality of the stable L´evy distribution as solutions to the Fokker-Planck equation and is compared to results from Langevin simulations. The statistical properties of the distribution functions are assessed by a generalized normalized expectation measure and entropy in terms of Tsallis statistical mechanics.
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| 5. |
- Anderson, Johan, 1973, et al.
(författare)
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Fractional Fokker-Planck Equation vs Tsallis’ Statistical Mechanics
- 2013
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Ingår i: Festival-de-Theorie. ; 7, s. 4-
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Konferensbidrag (refereegranskat)abstract
- In this paper we present a study of anomalous diffusion using a Fokker-Planck descriptionwith fractional velocity derivatives. The distribution functions are foundusing numerical means for varying degree of fractionality observing the transitionfrom a Gaussian distribution to a L´evy distribution. The statistical properties of thedistribution functions are assessed by a generalized expectation measure and entropyin terms of Tsallis statistical mechanics. We find that the ratio of the generalizedentropy and expectation is increasing with decreasing fractionality towards the wellknown so-called sub-diffusive domain, indicating a self-organising behavior.
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| 6. |
- Anderson, Johan, 1973, et al.
(författare)
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Modelling phase locking of large-scale modes
- 2021
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Ingår i: Bulletin of the Americal Physical Society. ; 63
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Konferensbidrag (refereegranskat)abstract
- Turbulence is often characterized by energetic couplings between different scales of a flow. However, in the context of turbulence driven transport, such as the case of magnetically confined fusion plasmas or the diffusion of cosmic rays, typical flow structures are identified by dominant modes and the global turbulent state is approximated by a superposition of linear contributions (waves in general). These theoretical studies consider the amplitudes of the fluctuating quantities but disregard the dynamics of the phases by using the so-called random-phase approximation (RPA) for which the existence of a Chirikov-like criterion for the onset of wave stochasticity is assumed. In this approximation one assumes that the dynamical amplitudes have a slow variation compared to the rapid change of the phases. It has been observed that the phase dynamic shows significant departure from the well-known RPA assumptions, with phases locking occasionally (but not in the dissipative high-k range). In non-linear turbulent flow however, three-body interactions between the phases of the various modes is of importance. We will consider examples of synchronization in different fluid system such as Burgers and Navier-Stokes turbulence and in more advanced models such as those for Edge Localized Modes (ELMs) in tokamaks which remain a critical issue for plasma stability and the lifetime of fusion reactors such as ITER.
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| 7. |
- Anderson, Johan, 1973, et al.
(författare)
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Non-Linear Langevin and Fractional Fokker-Planck Equations for Anomalous Diffusion by Levy Stable~Processes
- 2018
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Ingår i: Entropy. - : MDPI AG. - 1099-4300. ; 20:10
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Tidskriftsartikel (refereegranskat)abstract
- The~numerical solutions to a non-linear Fractional Fokker--Planck (FFP) equation are studied estimating the generalized diffusion coefficients. The~aim is to model anomalous diffusion using an FFP description with fractional velocity derivatives and Langevin dynamics where L\'{e}vy fluctuations are introduced to model the effect of non-local transport due to fractional diffusion in velocity space. Distribution functions are found using numerical means for varying degrees of fractionality of the stable L\'{e}vy distribution as solutions to the FFP equation. The~statistical properties of the distribution functions are assessed by a generalized normalized expectation measure and entropy and modified transport coefficient. The~transport coefficient significantly increases with decreasing fractality which is corroborated by analysis of experimental data.
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| 8. |
- Anderson, Johan, 1973, et al.
(författare)
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Non-local transport based on the fractional Fokker–Planck Equation model
- 2018
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- Recently a non-local (non-diffusive) heat flux model based on a fractional derivative of plasma pressure was proposed for the heat transport in the JET tokamak plasmas [1], where the degree $\alpha$ of the fractional derivative i.e. non-locality (non-diffusivity), of the heat flux was defined though a simple power balance analysis of the steady state. The findings showed that the fractional degree in all of the analysed plasmas was $\alpha < 2$ for both ion and electron channels, suggesting that the heat transport in these plasmas is likely to be of a non-local (non-diffusive) nature. Thus, a study of anomalous diffusion of heat transport using a Fokker-Planck description with fractional velocity derivatives while keeping the non-linear terms is strongly called for. The distribution functions are found using numerical means for varying degree of fractionality of the stable L\'{e}vy distribution. The statistical properties of the distribution functions are assessed by a generalized normalized expectation measure and entropy. We find that the ratio of the generalized entropy and expectation is increasing with decreasing fractionality towards the well known so-called sub-diffusive domain, indicating a self-organising behavior. Here it is pertinent to keep in mind that the success of a fractional or non-local diffusion model indicates that there is lack of physics in current transport models, namely the super-diffusive character of heat transport, as such it is not only a simplified transport model. When the experimentally found values of the fractional derivatives are used in the model, within a good agreement the experimental heat fluxes were reproduced.
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| 9. |
- Anderson, Johan, 1973, et al.
(författare)
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Self-organisation of random oscillators
- 2015
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Ingår i: Festival-de-Theorie.
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Konferensbidrag (refereegranskat)abstract
- A model for the stochastic passive advection - diffusion of a scalar with external forcing is further developed by introducing a non-linear phase coupling dynamic between the phases of the stochastic flow and the forcing. The model for the phase coupling dynamic follows the well known Kuramoto model of the limit cycle oscillators with an additional linear coupling term between the phasesthe two stochastic fields. The aim is to study the impact of a collective phase synchronization or self-organisation on the fluctuation level of the scalar through a simple stochastic passive advection - diffusion relation. The results shown here, present a significant impact of the collective phase synchronization on the correlation time of the fluctuations, and on the suppression of the fluctuation amplitudes. The model predicts that in the presence of an additional linear coupling between the phases of the two stochastic fields, the phase synchronizations leads to a localisation as well as strong suppression of the fluctuation amplitudes. While, in the a-synchronized state we observe a predator-prey behavior between the correlations of the two fields and time auto-correlation of the fluctuations decay with an oscillatory trend.
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| 10. |
- Anderson, Johan, 1973, et al.
(författare)
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The Information Length Concept Applied to Plasma Turbulence
- 2024
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Ingår i: Entropy. - 1099-4300. ; 26:6
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Tidskriftsartikel (refereegranskat)abstract
- A methodology to study statistical properties of anomalous transport in fusion plasma is investigated. Three time traces generated by the full-f gyrokinetic code GKNET are analyzed for this purpose. The time traces consist of heat flux as a function of the radial position, which is studied in a novel manner using statistical methods. The simulation data exhibit transport processes with both medium and long correlation length along the radius. A typical example of a phenomenon with long correlation length is avalanches. In order to investigate the evolution of the turbulent state, two basic configurations are studied, one flux-driven and one gradient-driven with decaying turbulence. The information length concept in tandem with Boltzmann–Gibbs and Tsallis entropy is used in the investigation. It is found that the dynamical states in both flux-driven and gradient-driven cases are surprisingly similar, but the Tsallis entropy reveals differences between them. This indicates that the types of probability distribution function are nevertheless quite different since the higher moments are significantly different.
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| 12. |
- Bombarda, F., et al.
(författare)
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Runaway electron beam control
- 2019
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Ingår i: Plasma Physics and Controlled Fusion. - : IOP Publishing. - 1361-6587 .- 0741-3335. ; 61:1
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Tidskriftsartikel (refereegranskat)
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| 19. |
- Fülöp, Tünde, 1970, et al.
(författare)
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Effect of poloidal asymmetry on the impurity density profile in tokamak plasmas
- 2011
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Ingår i: Physics of Plasmas. - 1089-7674 .- 1070-664X. ; 18:3, s. 030703-
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Tidskriftsartikel (refereegranskat)abstract
- The effect of poloidal asymmetry of impurities on impurity transport driven by electrostatic turbulence in tokamak plasmas is analyzed. It is found that if the density of the impurity ions is poloidally asymmetric then the zero-flux impurity density gradient is significantly reduced and even a sign change in the impurity flux may occur if the asymmetry is sufficiently large. This effect is most effective in low shear plasmas with the impurity density peaking on the inboard side and may be a contributing factor to the observed outward convection of impurities in the presence of radio frequency heating.
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| 20. |
- Fülöp, Tünde, 1970, et al.
(författare)
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The role of poloidal asymmetries in impurity transport
- 2011
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Ingår i: 38th EPS Conference on Plasma Physics 2011, EPS 2011. Strasbourg, 27 June - 1 July 2011. - 9781618395931 ; , s. 957-960
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Konferensbidrag (refereegranskat)abstract
- If the density of the impurity ions is poloidally asymmetric then the zero-flux impurity densitygradient (the peaking factor) can be reduced. The convective impurity flux can even change signif the asymmetry is sufficiently large. This effect is most effective in low-shear plasmas with theimpurity density peaking on the inboard side and may be a contributing factor to the observedoutward convection of impurities in the presence of radio frequency (RF) heating.Introduction
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| 22. |
- Garzotti, L., et al.
(författare)
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Simulations of density profiles in JET hybrid discharges
- 2012
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Ingår i: 39th EPS Conference on Plasma Physics 2012, EPS 2012 and the 16th International Congress on Plasma Physics; Stockholm; Sweden; 2 July 2012 through 6 July 2012; Code 96757. - 9781622769810 ; 1, s. 157-160
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Konferensbidrag (refereegranskat)
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| 23. |
- Gürcan, O, et al.
(författare)
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Phase and amplitude evolution in the network of triadic interactions of the Hasegawa-Wakatani system
- 2022
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Ingår i: Physics of Plasmas. - : AIP Publishing. - 1089-7674 .- 1070-664X. ; 29:5
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Tidskriftsartikel (refereegranskat)abstract
- The Hasegawa-Wakatani system, commonly used as a toy model of dissipative drift waves in fusion devices, is revisited with considerations of phase and amplitude dynamics of its triadic interactions. It is observed that a single resonant triad can saturate via three way phase locking, where the phase differences between dominant modes converge to constant values as individual phases increase in time. This allows the system to have approximately constant amplitude solutions. Non-resonant triads show similar behavior only when one of its legs is a zonal wave number. However, when an additional triad, which is a reflection of the original one with respect to the y axis is included, the behavior of the resulting triad pair is shown to be more complex. In particular, it is found that triads involving small radial wave numbers (large scale zonal flows) end up transferring their energy to the subdominant mode which keeps growing exponentially, while those involving larger radial wave numbers (small scale zonal flows) tend to find steady chaotic or limit cycle states (or decay to zero). In order to study the dynamics in a connected network of triads, a network formulation is considered, including a pump mode, and a number of zonal and non-zonal subdominant modes as a dynamical system. It was observed that the zonal modes become clearly dominant only when a large number of triads are connected. When the zonal flow becomes dominant as a "collective mean field,"individual interactions between modes become less important, which is consistent with the inhomogeneous wave-kinetic picture. Finally, the results of direct numerical simulation are discussed for the same parameters, and various forms of the order parameter are computed. It is observed that nonlinear phase dynamics results in a flattening of the large scale phase velocity as a function of scale in direct numerical simulations.
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| 25. |
- Joffrin, E., et al.
(författare)
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Overview of the JET preparation for deuterium-tritium operation with the ITER like-wall
- 2019
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Ingår i: Nuclear Fusion. - : IOP Publishing. - 1741-4326 .- 0029-5515. ; 59:11
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Forskningsöversikt (refereegranskat)abstract
- For the past several years, the JET scientific programme (Pamela et al 2007 Fusion Eng. Des. 82 590) has been engaged in a multi-campaign effort, including experiments in D, H and T, leading up to 2020 and the first experiments with 50%/50% D-T mixtures since 1997 and the first ever D-T plasmas with the ITER mix of plasma-facing component materials. For this purpose, a concerted physics and technology programme was launched with a view to prepare the D-T campaign (DTE2). This paper addresses the key elements developed by the JET programme directly contributing to the D-T preparation. This intense preparation includes the review of the physics basis for the D-T operational scenarios, including the fusion power predictions through first principle and integrated modelling, and the impact of isotopes in the operation and physics of D-T plasmas (thermal and particle transport, high confinement mode (H-mode) access, Be and W erosion, fuel recovery, etc). This effort also requires improving several aspects of plasma operation for DTE2, such as real time control schemes, heat load control, disruption avoidance and a mitigation system (including the installation of a new shattered pellet injector), novel ion cyclotron resonance heating schemes (such as the three-ions scheme), new diagnostics (neutron camera and spectrometer, active Alfven eigenmode antennas, neutral gauges, radiation hard imaging systems...) and the calibration of the JET neutron diagnostics at 14 MeV for accurate fusion power measurement. The active preparation of JET for the 2020 D-T campaign provides an incomparable source of information and a basis for the future D-T operation of ITER, and it is also foreseen that a large number of key physics issues will be addressed in support of burning plasmas.
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