| 31. |
- 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-
-
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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| 32. |
- Anderson, Johan, 1973, et al.
(författare)
-
High frequency geodesic acoustic modes in electron scale turbulence
- 2013
-
Ingår i: Nuclear Fusion. - : IOP Publishing. - 1741-4326 .- 0029-5515. ; 53:12, s. article nr. 123016-
-
Tidskriftsartikel (refereegranskat)abstract
- In this work the finite β-effects of an electron branch of the geodesic acoustic mode (el-GAM) driven by electron temperature gradient (ETG) modes is presented. The work is based on a fluid description of the ETG mode retaining non-adiabatic ions and the dispersion relation for el-GAMs driven non-linearly by ETG modes is derived. The ETG growth rate from the fluid model is compared with the results found from gyrokinetic simulations with good agreement. A new saturation mechanism for ETG turbulence through the interaction with el-GAMs is found, resulting in a significantly enhanced ETG turbulence saturation level compared with the mixing length estimate. It is shown that the el-GAM may be stabilized by an increase in finite β as well as by increasing non-adiabaticity. The decreased GAM growth rates is due to the inclusion of the Maxwell stress.
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| 33. |
- Anderson, Johan, 1973, et al.
(författare)
-
High Frequency Geodesic Acoustic Modes in Electron Scale Turbulence
- 2012
-
Ingår i: Proceedings 24th IAEA FEC, San Diego 8-13 October 2012.
-
Konferensbidrag (refereegranskat)abstract
- In this work the first demonstration of a high frequency branch of the geodesic acoustic mode (GAM) driven by electron temperature gradient (ETG) modes is presented. The work is based on a fluid description of the ETG mode retaining non-adiabatic ions and the dispersion relation for high frequency GAMs driven nonlinearly by ETG modes is derived. A new saturation mechanism for ETG turbulence through the interaction with high frequency GAMs is found, resulting in a significantly enhanced ETG turbulence saturation level compared to the mixing length estimate.
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| 34. |
- Anderson, Johan, 1973
(författare)
-
Information Geometric Investigation of Solutions to the Fractional Fokker-Planck Equation
- 2020
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Ingår i: Mathematics. - : MDPI AG. - 2227-7390. ; 8:5
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Tidskriftsartikel (refereegranskat)abstract
- A novel method for measuring distances between statistical states as represented by probability distribution functions (PDF) has been proposed, namely the information length. The information length enables the computation of the total number of statistically different states that a system evolves through in time. Anomalous transport can presumably be modeled fractional velocity derivatives and Langevin dynamics in a Fractional Fokker-Planck (FFP) approach. The numerical solutions or PDFs are found for varying degree of fractionality (alpha) of the stable Levy distribution as solutions to the FFP equation. Specifically, the information length of time-dependent PDFs for a given fractional index alpha is computed.
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| 35. |
- Anderson, Johan, 1973, et al.
(författare)
-
Modelling phase locking of large-scale modes
- 2021
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Ingår i: Bulletin of the Americal Physical Society. ; 63
-
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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| 36. |
- Anderson, Johan, 1973, et al.
(författare)
-
Non-Linear Langevin and Fractional Fokker-Planck Equations for Anomalous Diffusion by Levy Stable~Processes
- 2018
-
Ingår i: Entropy. - : MDPI AG. - 1099-4300. ; 20:10
-
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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| 37. |
- Anderson, Johan, 1973, et al.
(författare)
-
Non-local transport based on the fractional Fokker–Planck Equation model
- 2018
-
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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| 38. |
- Anderson, Johan, 1973, et al.
(författare)
-
On the Feynman-alpha formula for fast neutrons
- 2011
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Ingår i: Proceedings 33rd ESARDA 16-20 May, Budapest, Hungary (2011).
-
Konferensbidrag (refereegranskat)abstract
- In this contribution, a stochastic theory for a branching process in a neutron population with two energy levels is investigated. In particular, a variance to mean or Feynman-alpha formula is derived in this generalized scenario using the Kolmogorov forward or master equation theory for the probabilities in a system with a compound Poisson source.
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| 39. |
- Anderson, Johan, 1973, et al.
(författare)
-
Saturation Level of ETG Turbulence
- 2013
-
Ingår i: Festival de Thorie. ; 7, s. 4-
-
Konferensbidrag (refereegranskat)abstract
- In this work the finite β-effects of an electron branch of the geodesicacoustic mode (el-GAM) driven by electron temperature gradient (ETG) modes ispresented. The work is based on a fluid description of the ETG mode retaining nonadiabaticions and the dispersion relation for el-GAMs driven non-linearly by ETGmodes is derived. The ETG growth rate from the fluid model is compared to the resultsfound from gyrokinetic simulations with good agreement. A new saturation mechanismfor ETG turbulence through the interaction with el-GAMs is found, resulting in asignificantly enhanced ETG turbulence saturation level compared to the mixing lengthestimate. It is shown that the el-GAM may be stabilized by an increase in finite β aswell as by increasing non-adiabaticity. The decreased GAM growth rates is due to theinclusion of the Maxwell stress.
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| 40. |
- Anderson, Johan, 1973, et al.
(författare)
-
Secondary instability of electromagnetic ion-temperature-gradient modes for zonal flow generation
- 2011
-
Ingår i: Physics of Plasmas. - 1089-7674 .- 1070-664X. ; 18:072306
-
Tidskriftsartikel (refereegranskat)abstract
- An analytical model for zonal flow generation by toroidal ion-temperature-gradient (ITG) modes, including finite β electromagnetic effects, is derived. The derivation is based on a fluid model for ions and electrons and takes into account both linear and nonlinear β effects. The influence of finite plasma β on the zonal flow growth rate (γ_ZF) scaling is investigated for typical tokamak plasma parameters. The results show the importance of the zonal flows close to marginal stability where γ_ZF/γ_ITG ≫ 1 is obtained. In this region the parameter γ_ZF/γ_ITG increases with β, indicating that the ITG turbulence and associated transport would decrease with β at a faster rate than expected from a purely linear or quasi-linear analysis.
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