| 1. |
- MIrza, Ahmed Akram, 1979-, et al.
(author)
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Effect of thermal conduction on pressure-driven modes in the reversed-field pinch
- 2012
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In: Nuclear Fusion. - : IOP Publishing. - 0029-5515 .- 1741-4326. ; 52:12, s. 123012-
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Journal article (peer-reviewed)abstract
- Classical linearized resistive magnetohydrodynamic (MHD) stability theory predicts unstable pressure-driven modes even at low plasma beta values for the reversed-field pinch (RFP) because of its unfavourable curvature and strong poloidal magnetic field. These resistive g-modes undermine energy confinement and are detrimental to the RFP reactor potential. In the analysis, one aspect is common, which is the usage of the adiabatic energy equation, ignoring the contribution due to thermal conduction effects. However, in recent analysis, stabilization of pressure-driven modes is demonstrated through inclusion of thermal conductivity. In this paper, we compare the results obtained from both classical and thermal conduction modified boundary layer stability analysis with those from a time-spectral resistive linearized MHD code. Ohmic heating and thermal conduction effects are included in the calculations. We have found that thermal conduction effects stabilize pressure-driven resistive g-modes only for very low values of plasma beta. In addition, analytical and numerical investigation of the equilibrium reveal that, for reactor relevant values of S-0 and tearing stable plasmas, the scaling gamma similar to S-0(-1/5) for the growth rate of these modes is weaker than that for the adiabatic case gamma similar to S-0(-1/3).
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| 2. |
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| 3. |
- Scheffel, Jan, 1954-
(author)
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A spectral method in time for initial-value problems
- 2012
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In: American Journal of Computational Mathematics. - : Scientific Research Publishing. - 2161-1211 .- 2161-1203. ; 2:3, s. 173-193
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Journal article (peer-reviewed)abstract
- A time-spectral method for solution of initial value partial differential equations is outlined. Multivariate Chebyshev series are used to represent all temporal, spatial and physical parameter domains in this generalized weighted residual method (GWRM). The approximate solutions obtained are thus analytical, finite order multivariate polynomials. The method avoids time step limitations. To determine the spectral coefficients, a system of algebraic equations is solved iteratively. A root solver, with excellent global convergence properties, has been developed. Accuracy and efficiency are controlled by the number of included Chebyshev modes and by use of temporal and spatial subdomains. As examples of advanced application, stability problems within ideal and resistive magnetohydrodynamics (MHD) are solved. To introduce the method, solutions to a stiff ordinary differential equation are demonstrated and discussed. Subsequently, the GWRM is applied to the Burger and forced wave equations. Comparisons with the explicit Lax-Wendroff and implicit Crank-Nicolson finite difference methods show that the method is accurate and efficient. Thus the method shows potential for advanced initial value problems in fluid mechanics and MHD.
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| 4. |
- Scheffel, Jan, 1954-, et al.
(author)
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Application of the Generalized Weighted Residual Method to stability problems within ideal and resistive MHD
- 2010
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In: 52nd Annual Meeting of the APS Division of Plasma Physics, Chicago, Illinios, USA 8-12 November, 2010.
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Conference paper (peer-reviewed)abstract
- Initial-value stability and transport problems formulated in resistive MHD usually require extensive computations using a very large number of time steps. Although spectral methods are used for the spatial domains, finite steps are traditionally used for the temporal domain with resulting constraints in terms of CFL-like stability conditions for explicit and accuracy-related issues for implicit methods. The Generalized Weighted Residual Method (GWRM) alleviates these problems by representing the time domain in the form of a Chebyshev series. The solution is obtained as an approximate semi-analytical expression through solving a global system of algebraic equations for the expansion coefficients, valid for all time, spatial and physical parameter domains. We demonstrate solutions in terms of eigenvalues and eigenfunctions for the z-pinch, using the linearized ideal MHD equations. Including resistivity, results for resistive g-modes of the reversed-field pinch are also presented.
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| 5. |
- Scheffel, Jan, 1954-
(author)
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Att förstå – betraktelser utifrån en ny teori
- 2010
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In: Filosofisk Tidskrift. - 0348-7482. ; 4, s. 3-15
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Journal article (peer-reviewed)abstract
- Förståelse kan sägas vara den högsta formen av medveten insikt. Kunskap om ett fenomen behöver inte i sig vara tillräcklig för förståelse - de tidiga människorna visste att solen gick upp i öster, men de förstod inte att detta berodde på att jorden är rund och roterar. Förståelsebegreppet är centralt för all vetenskaplig aktivitet, men har mest studerats och tillämpats inom human- och samhällsvetenskaperna. Inom naturvetenskapen har ”förståelse” fått träda i skymundan för ”förklaring”. Vi skall se att detta är olyckligt och att förståelsebegreppet verkligen är av högsta relevans även för naturvetenskapen. Vi får här ett verktyg för att bedöma de yttersta gränserna för våra insikter i omvärlden. Analysen i detta arbete utgår ifrån en ny teori för förståelse, där de två fundamentala elementen är abstraktion och jämförelse. Ett antal intressanta konsekvenser följer, exempelvis visar vi att vissa fenomen aldrig kommer att kunna förstås och att lärandeprocessen ges nya möjligheter.
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| 6. |
- Scheffel, Jan, 1954-
(author)
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Can time-spectral methods improve turbulence modelling?
- 2014
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In: 56th Annual Meeting of the APS Division of Plasma Physics, New Orleans, Louisiana, USA 27-31 October 2014.
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Conference paper (peer-reviewed)abstract
- In computational fusion physics, the widely separated time and space scales often demand extremely long computer simulations and vast memory resources, using finite time steps. Gyrokinetic turbulence modelling at high Reynolds or Lundquist numbers may be allocated millions of CPU hours for parallel processing on supercomputers. It is thus worthwhile to explore new avenues that may alleviate requirements on computer power. Indeed, time-stepping may be completely avoided for initial-value problems. In the recently developed Generalized Weighted Residual Method GWRM [1], temporal, spatial and parameter domains are all handled using a solution ansatz in the form of a sum of Chebyshev polynomials. The coefficients of the ansatz are determined using a weighted residual method for which a new efficient equation solver has been developed [2]. In addition, the temporal and spatial computational region has been successfully treated using subdomain methods in a number of test problems, more efficiently than relevant finite difference methods. The GWRM, however, relies on solution of linear systems of equations in each subdomain, and memory requirement is an issue. In this presentation we will discuss recent subdomain approaches for efficient and convergent modelling of drift-wave turbulence. [1] Scheffel J, Partial Differential Equations: Theory, Analysis and Applications (Nova Science Publishers) p 1-49, 2011.[2] Scheffel J and Håkansson C, Appl. Numer. Math. 59(2009)2430.
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| 7. |
- Scheffel, Jan, 1954-
(author)
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Fund fusion for the sustainable future
- 2010
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In: EU Research. - Bristol : Blazon Publishing. - 2752-4736. ; June, s. 61-63
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Journal article (pop. science, debate, etc.)
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| 8. |
- Scheffel, Jan, 1954-, et al.
(author)
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Resistive pressure driven RFP modes are not removed by heat conduction effects
- 2012
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In: 39th EPS Conference on Plasma Physics 2012, EPS 2012 and the 16th International Congress on Plasma Physics. - 9781622769810 ; , s. 1690-1693
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Conference paper (peer-reviewed)abstract
- During the last decade it has been shown theoretically, numerically and experimentally that current driven, resistive tearing modes can be significantly suppressed in the reversed-field pinch (RFP). In these advanced scenarios, the confinement time can be enhanced by a factor 5-10. Pressure driven resistive instabilities (g-modes) still stand in the way, however, for high RFP confinement. Classical theory [1] shows that the unfavourable RFP curvature inevitably leads to unacceptably large linear growth rates even at high Lundquist numbers. Later theory [2] demonstrates, however, that the classical assumption of adiabatic plasma energy dynamics is inaccurate. The reason is that anomalously large experimental perpendicular heat conduction, together with strong parallel heat conduction, to a certain extent outbalance the pressure terms of the plasma energy equation. Resulting resistive length scales appear to extend the resistive layer at the resonance to allow for fully stable, finite beta RFP configurations. In the present work we show theoretically that the latter result is limited to low beta only and that it scales unfavourably with Lundquist number. Numerical solution, using a novel time-spectral method [3] of the linearised resistive MHD initial-value equations including heat conduction, ohmic heating and resistivity, supports the analytical results
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| 9. |
- Scheffel, Jan, 1954-, et al.
(author)
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Static current profile control and RFP confinement
- 2013
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In: Nuclear Fusion. - : Institute of Physics (IOP). - 0029-5515 .- 1741-4326. ; 53:11, s. 113007-
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Journal article (peer-reviewed)abstract
- Static current profile control (CPC) is shown numerically to substantially enhance plasma confinement in the reversed-field pinch (RFP). By suitable application of an auxiliary electric field and adjustment of its internal location, width and amplitude, strongly decreased levels of dynamo fluctuations are obtained. The simulations are performed using a fully non-linear, resistive magnetohydrodynamic model, including the effects of ohmic heating as well as parallel and perpendicular heat conduction along stochastic field lines. The importance of controlling the parallel current profile in the core plasma to minimize the effects of tearing modes on confinement is thus confirmed. A near three-fold increase in energy confinement is found and poloidal plasma beta increases by 30% from 0.20 to 0.27. The edge heat flux is reduced to a third of that of the conventional RFP. The high-confinement phase is interrupted here by a crash, characterized by a rapid decrease in confinement. A detailed study of the crash phase is carried out by the standard Delta' theory and a fully resistive linearized time-spectral method; the generalized weighted residual method. The analysis suggests that the instability is caused by pressure-driven, resistive g-modes. Inclusion of anisotropic thermal conduction reduces the linear growth rates. As compared with our earlier numerical studies of CPC in the RFP, employing feedback control, the present static control scheme should be more easily implemented experimentally.
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| 10. |
- Scheffel, Jan, 1954-
(author)
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Svar till A. Tollands kommentarer till artikeln Att förstå – betraktelser utifrån en ny teori
- 2012
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In: Filosofisk Tidskrift. - 0348-7482. ; 1, s. 45-52
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Journal article (peer-reviewed)abstract
- I min artikel ”Att förstå – betraktelser utifrån en ny teori” (FT 31:4 Nov 2010) vill jag visa att det finns anledning att förtydliga förståelsebegreppet. Avsevärd möda har, historiskt sett, lagts ned på att definiera och bringa klarhet i begreppen kunskap och förklaring men förståelse, som når längre än vanlig kunskap, har förblivit ett otydligt begrepp. Teorin jag lägger fram i artikeln har som sin kärna en definition av förståelse. Denna utkristalliseras dels naturligt från vår vardagliga användning, dels från behovet av att tydligt visa på vilket sätt förståelse är den djupaste formen av kunskap, av medveten insikt. Först när förståelsebegreppet utgör ett väl format verktyg kan kunskapsteorin nå sin fulla potential. Jag är tacksam gentemot Anders Tolland för att ha kritiskt granskat artikeln och för att han ger mig möjlighet att uttrycka teorin klarare. Tollands kritik berör främst oklarheter avseende innehållet i de abstraktioner som, tillsammans med jämförelser, är centrala element i teorin. Tolland bidrar också till förtydliganden, för vilka jag är mycket tacksam. Särskilt vill jag nämna påpekandena att förståelse dels kan relatera till vad något är, dels till varför det är på det sättet och att förståelse dels är en process, dels ett uppnått tillstånd. I det följande bemöter jag Tollands kritik och anser mig verkligen kunna visa att den framlagda teorin för förståelse är sammanhållen, tydlig och alls icke ”kontra-intuitiv” samt att den utgör ett viktigt, nytt kunskapsteoretiskt verktyg.
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