Change search
Refine search result
1 - 38 of 38
CiteExportLink to result list
Permanent link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Rows per page
  • 5
  • 10
  • 20
  • 50
  • 100
  • 250
Sort
  • Standard (Relevance)
  • Author A-Ö
  • Author Ö-A
  • Title A-Ö
  • Title Ö-A
  • Publication type A-Ö
  • Publication type Ö-A
  • Issued (Oldest first)
  • Issued (Newest first)
  • Created (Oldest first)
  • Created (Newest first)
  • Last updated (Oldest first)
  • Last updated (Newest first)
  • Disputation date (earliest first)
  • Disputation date (latest first)
  • Standard (Relevance)
  • Author A-Ö
  • Author Ö-A
  • Title A-Ö
  • Title Ö-A
  • Publication type A-Ö
  • Publication type Ö-A
  • Issued (Oldest first)
  • Issued (Newest first)
  • Created (Oldest first)
  • Created (Newest first)
  • Last updated (Oldest first)
  • Last updated (Newest first)
  • Disputation date (earliest first)
  • Disputation date (latest first)
Select
The maximal number of hits you can export is 250. When you want to export more records please use the 'Create feeds' function.
  • 1.
    Brunsell, P R
    et al.
    KTH, Superseded Departments, Alfvén Laboratory.
    Bergsåker, H
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    Brzozowski, J H
    KTH, Superseded Departments, Alfvén Laboratory.
    Cecconello, M
    KTH, Superseded Departments, Alfvén Laboratory.
    Drake, J R
    KTH, Superseded Departments, Alfvén Laboratory.
    Malmberg, J-A
    KTH, Superseded Departments, Alfvén Laboratory.
    Scheffel, J
    KTH, Superseded Departments, Alfvén Laboratory.
    Schnack, D D
    Mode dynamics and confinement in the reversed-field pinch2000In: IAEA-CN-77: Fusion Energy 2000, 2000, p. Paper EXP3/14-Conference paper (Refereed)
  • 2.
    Dahlin, Jon-Erik
    et al.
    KTH, School of Electrical Engineering (EES), Centres, Alfvén Laboratory Centre for Space and Fusion Plasma Physics.
    Scheffel, Jan
    KTH, School of Electrical Engineering (EES), Centres, Alfvén Laboratory Centre for Space and Fusion Plasma Physics.
    A novel feedback algorithm for simulating controlled dynamics and confinement in the advanced reversed-field pinch2005In: Physics of Plasmas, ISSN 1070-664X, E-ISSN 1089-7674, Vol. 12, no 6, p. 062502-Article in journal (Refereed)
    Abstract [en]

    In the advanced reversed-field pinch (RFP), the current density profile is externally controlled to diminish tearing instabilities. Thus the scaling of energy confinement time with plasma current and density is improved substantially as compared to the conventional RFP. This may be numerically simulated by introducing an ad hoc electric field, adjusted to generate a tearing mode stable parallel current density profile. In the present work a current profile control algorithm, based on feedback of the fluctuating electric field in Ohm's law, is introduced into the resistive magnetohydrodynamic code DEBSP [D. D. Schnack and D. C. Baxter, J. Comput. Phys. 55, 485 (1984); D. D. Schnack, D. C. Barnes, Z. Mikic, D. S. Marneal, E. J. Caramana, and R. A. Nebel, Comput. Phys. Commun. 43, 17 (1986)]. The resulting radial magnetic field is decreased considerably, causing an increase in energy confinement time and poloidal beta. It is found that the parallel current density profile spontaneously becomes hollow, and that a formation, being related to persisting resistive g modes, appears close to the reversal surface.

  • 3.
    Dahlin, Jon-Erik
    et al.
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    Scheffel, Jan
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    Advanced Reversed-field Pinch Scaling Laws2005Conference paper (Refereed)
    Abstract [en]

    A series of resistive magnetohydrodynamic numerical simulations are performed to generate scaling laws for energy confinement time τE and poloidal beta βp for the advanced reversed field-pinch (RFP). Strongly improved scaling with basic initial parameters is obtained as compared to the conventional RFP. Early results indicate an improved scaling of τE with plasma current I and line density N compared to the conventional RFP. The improved behaviour of the advanced RFP as compared to the conventional, uncontrolled RFP stems from the introduction of current profile control (CPC). In the present numerical simulations, CPC is performed by implementation of a parameter free automatic feedback algorithm, optimised to reduce the fluctuation caused v × B electric field. The scheme introduces an ad-hoc electric field within the plasma volume, automatically adjusted to dynamically control the plasma into more quiescent behaviour by eliminating current driven tearing mode instabilities and reducing resistive interchange modes.

  • 4.
    Dahlin, Jon-Erik
    et al.
    KTH, Superseded Departments, Alfvén Laboratory.
    Scheffel, Jan
    KTH, Superseded Departments, Alfvén Laboratory.
    Feedback current profile control in the advanced RFP2004In: Proceedings of the 31st EPS plasma physics conference, 2004Conference paper (Refereed)
  • 5.
    Dahlin, Jon-Erik
    et al.
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics. KTH, School of Electrical Engineering (EES), Centres, Alfvén Laboratory Centre for Space and Fusion Plasma Physics.
    Scheffel, Jan
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics. KTH, School of Electrical Engineering (EES), Centres, Alfvén Laboratory Centre for Space and Fusion Plasma Physics.
    Improved Computer Simulations of Energy Confinement in the Advanced Reversed-field Pinch2006In: 33rd EPS Conference on Plasma Phys, 2006Conference paper (Refereed)
    Abstract [en]

    A revised algorithm for numerical simulations of the advanced reversed-field pinch (RFP) is presented. The results show improved scalings of magnetic fluctuations, energy confinement time τE and poloidal beta βθ with basic initial parameters as compared to what has been presented by the authors in earlier studies of the advanced RFP. The improved behaviour of the advanced RFP stems from the introduction of current profile control (CPC), implemented through a scheme of active feedback of the electric dynamo field. The work, which has an optimistic approach and sweeps over a large parameter domain reaching into the reactor relevant region, is theoretical and claims to answer the question of how far CPC can bring the RFP concept in principle. Experimental implementation is thus a later concern. With this scheme, a state with strongly suppressed tearing mode activity is achieved, which allows for a theoretical study of pressure driven resistive g-modes. This is a task that has been very hard to perform in the past, since tearing modes have always dominated the RFP dynamics. Thus it is now possible, for the first time, to investigate whether pressure driven modes, which are persistent in the RFP, are fatal for the confinement of a high-beta RFP configuration or if they can be accepted in a future reactor.

  • 6.
    Dahlin, Jon-Erik
    et al.
    KTH, School of Electrical Engineering (EES), Centres, Alfvén Laboratory Centre for Space and Fusion Plasma Physics.
    Scheffel, Jan
    KTH, School of Electrical Engineering (EES), Centres, Alfvén Laboratory Centre for Space and Fusion Plasma Physics.
    Numerical studies of confinement scalings for the dynamo-free reversed-field pinch2007In: Nuclear Fusion, ISSN 0029-5515, E-ISSN 1741-4326, Vol. 47, no 1, p. 9-16Article in journal (Refereed)
    Abstract [en]

    In the reversed-field pinch (RFP), tearing modes associated with the dynamo are responsible for reduced energy- and particle confinement. In this study, it is observed that by implementing current profile control (CPC) in the RFP, a dynamo-free state can be achieved. The effect of CPC in the RFP is examined by the use of numerical simulations, and scaling laws are presented for confinement parameters. The model is nonlinear MHD in 3D including finite resistivity and pressure. A linear regression analysis is performed on simulation data from a series of computer runs for a set of initial parameter values. Scaling laws are determined for radial magnetic field, energy confinement time, poloidal beta and temperature. Confinement is improved substantially as compared with the conventional RFP - the temperature reaches reactor relevant levels by ohmic heating alone. It is observed that the configuration spontaneously develops into a quasi single helicity state. The CPC scheme is designed to eliminate the fluctuating electric dynamo field Ef ≤ -〈v × B〉, using feedback of an externally imposed electric field. The focus of this study is on obtaining principal theoretical optimization of confinement in the RFP by implementing CPC and to formulate scaling laws for confinement parameters, thus investigating the reactor viability of the concept.

  • 7.
    Dahlin, Jon-Erik
    et al.
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    Scheffel, Jan
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    Scaling Laws of Confinement Parameters for the Advanced Reversed-field Pinch2005Conference paper (Other academic)
  • 8.
    Dahlin, Jon-Erik
    et al.
    KTH, Superseded Departments, Alfvén Laboratory.
    Scheffel, Jan
    KTH, Superseded Departments, Alfvén Laboratory.
    Self-consistent zero-dimensional numerical simulation of a Magnetized Target Fusion Configuration2004In: Physica Scripta, ISSN 0031-8949, E-ISSN 1402-4896, Vol. 70, no 5, p. 310-316Article in journal (Refereed)
    Abstract [en]

    A self-consistent zero-dimensional model of a Magnetized Target Fusion (MTF) configuration is presented. The plasma target is a Field Reversed Configuration (FRC). Model parameters were scanned using a Monte Carlo routine in order to determine an operating point that would correspond to reactor conditions. Albeit the model being intrinsically optimistic, the highest Q-values found only slightly exceed unity. The limited performance is due to the short dwell time of the liner, preventing a large portion of the fuel to burn.

  • 9.
    Dahlin, Jon-Erik
    et al.
    KTH, School of Electrical Engineering (EES), Centres, Alfvén Laboratory Centre for Space and Fusion Plasma Physics.
    Scheffel, Jan
    KTH, School of Electrical Engineering (EES), Centres, Alfvén Laboratory Centre for Space and Fusion Plasma Physics.
    Ultra-high beta in numerical simulations of a tearing-mode reduced reversed-field pinch2007In: Nuclear Fusion, ISSN 0029-5515, E-ISSN 1741-4326, Vol. 47, no 9, p. 1184-1188Article in journal (Refereed)
    Abstract [en]

    In the advanced reversed-field pinch (RFP), current profile control (CPC) enables energy confinement time and poloidal beta to increase substantially as compared with the conventional RFP due to reduced magnetic field stochasticity. Numerical simulations using the three-dimensional non-linear resistive MHD-code DEBSP are performed showing that the poloidal beta is not limited to the m ≤ 0 stability criterion βθ < 1/2. Instead, as tearing modes are diminished, it may approach unity. The beta criterion is theoretically analysed and a new, more general, criterion is derived. Analytic estimates of the resistive tearing and g-mode growth rates are derived for m ≤ 0, and it is shown that both tearing and g-mode growth rates decrease significantly as CPC is employed. Furthermore, quasi-steady state operation with increased confinement due to active control of the current profile is numerically demonstrated for the advanced RFP for a scenario with βθ < 1/2.

  • 10.
    Dahlin, Jon-Erik
    et al.
    KTH, School of Electrical Engineering (EES), Centres, Alfvén Laboratory Centre for Space and Fusion Plasma Physics.
    Scheffel, Jan
    KTH, School of Electrical Engineering (EES), Centres, Alfvén Laboratory Centre for Space and Fusion Plasma Physics.
    Anderson, Jay
    KTH, School of Electrical Engineering (EES), Centres, Alfvén Laboratory Centre for Space and Fusion Plasma Physics.
    Numerical studies of active current profile control in the reversed-field pinch2007In: Plasma Physics and Controlled Fusion, ISSN 0741-3335, E-ISSN 1361-6587, Vol. 49, no 2, p. 183-195Article in journal (Refereed)
    Abstract [en]

    Quenching of the reversed-field pinch (RFP) dynamo is observed in numerical simulations using current profile control. A novel algorithm employing active feedback of the dynamo field has been utilized. The quasi-steady state achieved represents an important improvement as compared with earlier numerical work and may indicate a direction for the design of future experiments. Both earlier and the novel schemes of feedback control result in quasi-single helicity states. The energy confinement time and poloidal beta are observed to be substantially increased, as compared with the conventional RFP, in both the cases. Different techniques for experimental implementation are discussed.

  • 11. Lehnert, B.
    et al.
    Scheffel, Jan
    KTH, Superseded Departments, Alfvén Laboratory.
    On the minimum elementary charge of an extended electromagnetic theory2002In: Physica Scripta, ISSN 0031-8949, E-ISSN 1402-4896, Vol. 65, no 3, p. 200-207Article in journal (Refereed)
    Abstract [en]

    Steady axisymmetric equilibria of an earlier developed extended electromagnetic theory are considered. as based on a nonzero electric field divergence in the vacuum state and Lorentz invariance. The general solutions are derived from a generating function which yields electrically charged particle-like states when its radial part diverges at the origin. For a corresponding electron model, the integrated charge, magnetic moment, mass (energy), and angular momentum still become nonzero and finite, provided that the characteristic radius is made to shrink to that of a point-charge-like state. This removes the problem of an infinite self-energy, and presents a possible alternative to the conventional renormalization process. With the subsidiary quantum conditions on magnetic moment, angular momentum, and magnetic flux. a variational analysis is applied to find an extremum of the electronic charge. The resulting minimum value deviates only by about 3 percent from that of the experimentally determined elementary charge, and it depends only on the velocity of light and Planck's constant. This indicates that the electronic charge may no longer be considered as an independent constant of nature. but can be deduced in terms of these two constants. There could be several possible explanations of the obtained deviation, of which the most probable appears to be due to refinements caused by quantization of the field equations already from the outset.

  • 12.
    Mirza, Ahmed A.
    et al.
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    Scheffel, Jan
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    Numerical study of thermal conductivity effects on stability of the reversed-field pinch2011Conference paper (Refereed)
  • 13.
    MIrza, Ahmed Akram
    et al.
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    Scheffel, Jan
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    Johnson, Thomas
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    Effect of thermal conduction on pressure-driven modes in the reversed-field pinch2012In: Nuclear Fusion, ISSN 0029-5515, E-ISSN 1741-4326, Vol. 52, no 12, p. 123012-Article in journal (Refereed)
    Abstract [en]

    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).

  • 14.
    Scheffel, Jan
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    A new method for obtaining analytical eigenfunctions and growth rates2001Conference paper (Refereed)
    Abstract [en]

    By use of computer math programs, the MHD stability properties of fusion confinement plasmas can now be determined analytically, without further approximations, to high orders in time and space coordinates. We here present results from expanding the linearized ideal and resistive MHD eigenvalue equations for cylinder geometry in radius r. The effect of sheared fluid flow on stability is also included. Not only analytical growth rates, but also analytical forms of the eigenfunctions are obtained. As expected, we find that moderately large expansions provide high accuracy for mildly localized eigenfunctions.

    The method, for linearized eigenvalue problems, is based on expansions of the dependent perturbed variables in powers of the spatial independent variables; e.g. ur, uq, uz, br, bq, bz as functions of rn, with n ≤  nmax, the maximum order of the expansion. The basic, scalar MHD equations can thus be retained without further elimination of variables. The equilibrium state is also expanded in r, retaining desired control coefficients.

    By successively solving the MHD equations at higher orders of r, solutions being exact up to this order are obtained. The indicial equation (at r = 0) is automatically solved in this method. By applying boundary conditions at r = rwall, an implicit equation for the eigenvalue w as function of the mode numbers (m,k) and the equilibrium parameters is obtained. This is similar to the often used, however numerical, shooting method. The number of solutions wi are, as implied by the oscillation theorem, dependent on nmax. The roots are obtained by implicit root solvers or graphically. Compact analytical forms of eigenvalues and eigenfunctions can also be obtained by retaining dominating terms in specified parameter limits.

    Our method can be used for any geometry, and also for nonlinear systems of equations. It thus has a very large potential for efficient and exact analytical investigations of (one- or many-fluid) MHD equations, also including additional physical effects. The calculations require efficient math program routines and high speed and memory computer platforms, wherefore they were difficult to perform earlier. 

  • 15.
    Scheffel, Jan
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    A spectral method in time for initial-value problems2012In: American Journal of Computational Mathematics, ISSN 2161-1211, Vol. 2, no 3, p. 173-193Article in journal (Refereed)
    Abstract [en]

    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.

  • 16.
    Scheffel, Jan
    KTH, School of Electrical Engineering (EES).
    Can time-spectral methods improve turbulence modelling?2014Conference paper (Refereed)
    Abstract [en]

    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.

  • 17.
    Scheffel, Jan
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    Fund fusion for the sustainable future2010In: EU Research, Vol. June, p. 61-63Article in journal (Other (popular science, discussion, etc.))
  • 18.
    Scheffel, Jan
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics. KTH, School of Electrical Engineering (EES), Centres, Alfvén Laboratory Centre for Space and Fusion Plasma Physics.
    Semi-analytical solution of initial-value problems2007Conference paper (Other academic)
    Abstract [en]

    A fully spectral weighted residual method for solution of general initial value partial differential equations has been developed. All time, spatial and physical parameter domains are represented by Chebyshev series, enabling global semi-analytical solutions. The method avoids time step limitations. The spectral coefficients are determined by iterative solution of a linear or nonlinear system of algebraic equations, for which a globally convergent root solver has been developed. Accuracy is controlled by the number of included Chebyshev modes in each dimension. The computational efficiency is shown to increase through the use of sub-domains. It is shown by example that the method may be used for efficient solution of nonlinear initial value problems in fluid mechanics and magnetohydrodynamics.

    1J. Scheffel, ”Semi-analytical solution of initial-value problems”, TRITA-ALF-2004-03, Royal Institute of Technology, Stockholm, Sweden, 2004.

  • 19.
    Scheffel, Jan
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    Solution of systems of nonlinear equations - a semi-implicit approach2006Report (Other academic)
    Abstract [en]

    An iterative method for globally convergent solution of nonlinear equations and systems of nonlinear equations is presented. Convergence is quasi-monotonous and approaches second order in the proximity of the real roots. The algorithm is related to semi-implicit methods, earlier being applied to partial differential equations. It is shown that the Newton-Raphson and Newton methods are special cases of the method. This relationship enables efficient solution of the Jacobian matrix equations at each iteration. The degrees of freedom introduced by the semi-implicit parameters are used to control convergence. When applied to a single equation, efficient global convergence and convergence  to either of the bounding roots makes the method attractive in comparison with methods as those of Newton-Raphson and van Wijngaarden-Dekker-Brent.

  • 20.
    Scheffel, Jan
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    The Time- and Parameter-Generalized Weighted Residual Method2008Report (Other academic)
    Abstract [en]

    A general, fully spectral weighted residual method for solution of initial value partial differential equations is presented. All time, spatial and physical parameter domains are represented by Chebyshev series enabling global semi-analytical, rather than purely numerical, solutions. The method avoids time step limitations. The spectral coefficients are determined by iterative solution of a system of algebraic equations, for which a globally convergent root solver has been developed. Accuracy is controlled by the number of included Chebyshev modes and by the use of spatial subdomains. It is shown by example and by comparisons with the explicit Lax-Wendroff and semi-implicit Crank-Nicholson methods that the method may be used for accurate and efficient solution of nonlinear initial value problems in fluid mechanics and magnetohydrodynamics.

  • 21.
    Scheffel, Jan
    KTH, School of Electrical Engineering (EES).
    Time-Spectral Solution of Initial-Value Problems2011In: Partial Differential Equations: Theory, Analysis and Applications / [ed] Christopher L. Jang, New York: Nova Science Publishers, Inc., 2011, 1, p. 1-49Chapter in book (Refereed)
    Abstract [en]

    A generalized fully spectral weighted residual method (GWRM) for solution of initial value partial differential equations is presented. For all temporal, spatial and physical parameter domains, the solution is represented by Chebyshev series, enabling global semi-analytical solutions. The method avoids time step limitations. The spectral coefficients are determined by iterative solution of a system of algebraic equations, for which a globally convergent root solver has been developed. Accuracy and efficiency are controlled by the number of included Chebyshev modes and by the use of temporal and spatial subdomains. Example applications include the diffusion, Burger and forced wave equations as well as a system of ideal magnetohydrodynamic (MHD) equations. A stiff ordinary differential equation introduces the method. Comparisons with the explicit Lax-Wendroff and implicit Crank-Nicolson finite difference methods show that the method is accurate and efficient. Potential applications of the GWRM are, for example, advanced initial value problems in fluid mechanics and MHD.

  • 22.
    Scheffel, Jan
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    Time-spectral solution of initial-value problems2012Conference paper (Other academic)
    Abstract [en]

    A time-spectral method for solutions of initial-value partial differential equations has recently been developed [1]. The purpose of the method is to avoid inefficient time stepping for problems in plasma physics with widely separated time scales. Temporal, spatial and parameter domains are all treated using an ansatz in the form of a sum of Chebyshev polynomials. The coefficients of the ansatz is determined using a generalized weighted residual method. A new, efficient solver for the resulting algebraic systems of coefficient equations has been developed [2]. In addition, subdomain methods for the temporal and spatial domains are employed [3]. The question is now: to what extent are time-spectral methods really more attractive than finite difference methods? We will report on results concerning accuracy and efficiency for several linear and nonlinear model partial differential equations.

  • 23.
    Scheffel, Jan
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    Why we need fusion energy...2011In: Public Service Review -European Union, ISSN 1472-3395, Vol. 21, p. 620-621Article in journal (Other (popular science, discussion, etc.))
  • 24.
    Scheffel, Jan
    et al.
    KTH, School of Electrical Engineering (EES), Centres, Alfvén Laboratory Centre for Space and Fusion Plasma Physics.
    Dahlin, Jon-Erik
    KTH, School of Electrical Engineering (EES), Centres, Alfvén Laboratory Centre for Space and Fusion Plasma Physics.
    Confinement scaling in the advanced reversed-field pinch2006In: Plasma Physics and Controlled Fusion, ISSN 0741-3335, E-ISSN 1361-6587, Vol. 48, no 11, p. L97-L104Article in journal (Refereed)
    Abstract [en]

    A numerical study of confinement scaling in the advanced reversed-field pinch ( RFP) is presented. In the advanced RFP, the tearing mode activity that dominates conventional RFP plasma fluctuations is reduced by current profile control ( CPC). In this work, theoretical limits for confinement in the advanced RFP are explored, modelling a CPC with internally applied electric fields. The obtained scalings of ion temperature, poloidal beta value, energy confinement time and magnetic field fluctuations indicate strongly improved confinement as compared with the conventional RFP. Reactor relevant on-axis temperatures are obtained using ohmic heating alone. Pressure driven modes persist within the present 3D nonlinear, resistive, single-fluid MHD model, but may be reduced by non-ideal effects.

  • 25.
    Scheffel, Jan
    et al.
    KTH, Superseded Departments, Alfvén Laboratory.
    Dahlin, Jon-Erik
    KTH, Superseded Departments, Alfvén Laboratory.
    Schnack, D. D.
    University of Madison, Wisconsin.
    Drake, J. R.
    KTH, Superseded Departments, Alfvén Laboratory.
    Energy Confinement in the Advanced RFP2003Conference paper (Other academic)
    Abstract [en]

    In earlier numerical studies [1,2] of confinement in the optimized, conventional reversed-field pinch (RFP), the scaling of energy confinement time with plasma current and density was found to be too weak to lead into fusion relevant regimes. In the advanced RFP, however, the detrimental magnetic (dynamo) fluctuations are largely eliminated by the presence of an externally applied electric field. This field is adjusted to generate a tearing mode stable parallel current density profile. Previous studies [3,4] used a gaussian shaped electric field with given width and amplitude that was localised at some minor radius of the plasma. A threefold increase in energy confinement was found, but the three associated parameters made further optimisation difficult. In the present work a new, parameter free scheme for current profile control is introduced. An automatic control system continuously replaces the dynamo electric field. Early results indicate strong energy confinement enhancement.

    [1] J. Scheffel and D. D. Schnack, Phys. Rev. Lett. 85 (2000) 322.[2] J. Scheffel and D. D. Schnack, Nucl. Fusion 40 (2000) 1885.[3] C. R. Sovinec and S. C. Prager, Nucl. Fusion 39 (1999) 777.[4] J. Scheffel and D. D. Schnack, International RFP Workshop, Stockholm 2002.

  • 26.
    Scheffel, Jan
    et al.
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    Håkansson, Cristian
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    Solution of systems of nonlinear equations - a semi-implicit approach2009In: Applied Numerical Mathematics, ISSN 0168-9274, E-ISSN 1873-5460, Vol. 59, no 10, p. 2430-2443Article in journal (Refereed)
    Abstract [en]

    An iterative method for globally convergent solution of nonlinear equations and systems of nonlinear equations is presented. Convergence is quasi-monotonous and approaches second order in the proximity of the real roots. The algorithm is related to semi-implicit methods, earlier being applied to partial differential equations. It is shown that the Newton-Raphson and Newton methods are special cases of the method. The degrees of freedom introduced by the semi-implicit parameters are used to control convergence. When applied to a single equation, efficient global convergence and convergence to a nearby root makes the method attractive in comparison with methods as those of Newton-Raphson and van Wijngaarden-Dekker-Brent. An extensive standard set of systems of equations is solved and convergence diagrams are introduced, showing the robustness, efficiency and simplicity of the method as compared to Newton's method using linesearch.

  • 27.
    Scheffel, Jan
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Fusion Plasma Physics.
    Lindvall, Kristoffer
    KTH, School of Electrical Engineering and Computer Science (EECS), Fusion Plasma Physics.
    SIR—An efficient solver for systems of equations2018In: Software Quality Professional, ISSN 1522-0540, E-ISSN 2352-7110, Vol. 7, p. 59-62Article in journal (Refereed)
    Abstract [en]

    The Semi-Implicit Root solver (SIR) is an iterative method for globally convergent solution of systems of nonlinear equations. We here present MATLAB and MAPLE codes for SIR, that can be easily implemented in any application where linear or nonlinear systems of equations need be solved efficiently. The codes employ recently developed efficient sparse matrix algorithms and improved numerical differentiation. SIR convergence is quasi-monotonous and approaches second order in the proximity of the real roots. Global convergence is usually superior to that of Newton's method, being a special case of the method. Furthermore the algorithm cannot land on local minima, as may be the case for Newton's method with line search. 

  • 28.
    Scheffel, Jan
    et al.
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    MIrza, Ahmed A.
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    Application of the Generalized Weighted Residual Method to stability problems within ideal and resistive MHD2010Conference paper (Other academic)
    Abstract [en]

    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. 

  • 29.
    Scheffel, Jan
    et al.
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    MIrza, Ahmed A.
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    Pressure driven resistive modes in the advanced RFP2008In: 35th EPS Conference on Plasma Physics 2008, EPS 2008 - Europhysics Conference Abstracts: Volume 32, Issue 3, 2008, p. 2014-2017Conference paper (Refereed)
  • 30.
    Scheffel, Jan
    et al.
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    MIrza, Ahmed A.
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    Resistive g-modes and RFP confinement2009Conference paper (Other academic)
    Abstract [en]

    The role of pressure driven resistive modes in the reversed-field pinch remains unclear. It was early shown that unstable resistive g-modes would always exist for an inwardly directed pressure gradient. It now appears that pressure profile smoothing, due to incluson of heat conductivity terms in the energy equation, enables completey stable RFP states at moderate plasma beta. These calculations, apart from being restricted to linearized perturbations, suffer from the use of rather forced scalings, thus their accuracy can be questioned. Also, they have so far only been applied to conventional RFP states, where confinement-limiting tearing fluctuations maintain the reversed axial magnetic field. In the advanced RFP, current profile control has largely eliminated current driven tering modes. Fully nonlinear, numerical studies have shown that energy confinement and poloidal beta increase substantially, but that weak residual modes usually remain. The nature of these residual modes, which limit energy confinement, is studied using a novel semi-analytical, spectral scheme for solving the resistive MHD equations; the generalized weighted residual method (GWRM). Results from the analysis as well as comparisons with the competing linear resistive g-mode theories will be presented.

  • 31.
    Scheffel, Jan
    et al.
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics. KTH, School of Electrical Engineering (EES), Centres, Alfvén Laboratory Centre for Space and Fusion Plasma Physics.
    MIrza, Ahmed A.
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics. KTH, School of Electrical Engineering (EES), Centres, Alfvén Laboratory Centre for Space and Fusion Plasma Physics.
    Resistive pressure driven RFP modes are not removed by heat conduction effects2012In: 39th EPS Conference on Plasma Physics 2012, EPS 2012 and the 16th International Congress on Plasma Physics: Volume 3, 2012, 2012, p. 1690-1693Conference paper (Refereed)
    Abstract [en]

    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

  • 32.
    Scheffel, Jan
    et al.
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    MIrza, Ahmed A.
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    Thermal conductivity effects on resistive g-mode stability of the RFP2011Conference paper (Other academic)
    Abstract [en]

    Tearing modes presently dominate fluctuations in the reversed- field pinch (RFP). Using current profile control techniques, the tearing modes can be removed experimentally. Pressure driven resistive g-modes remain for all equilibria, however, according to classical theory. In the tokamak these modes can be eliminated by curvature effects. Resistive g-modes may cause modest global energy confinement and severly limit the reactor potential of the RFP. Work by Bruno et al, where the energy equation has been supplemented by heat conduction terms, appear to show that heat conduction smoothens pressure gradient effects and stabilises resistive g-modes at low beta. On the other hand, fully numerical studies including heat conduction effects as well as experimental work identify resistive g-mode activity. In this work, we present a detailed computational analysis of linear resistive g-mode stability with and without heat conductivity effects. Both traditional delta prime analysis and a fully resistive code, based on the novel Generalized Weighted Residual Method (GWRM), are used.

  • 33.
    Scheffel, Jan
    et al.
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    Mirza, Ahmed A.
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    Time-spectral solution of initial-value problems – subdomain approach2012In: American Journal of Computational Mathematics, ISSN 2161-1211, Vol. 2, no 2, p. 72-81Article in journal (Refereed)
    Abstract [en]

    Temporal and spatial subdomain techniques are proposed for a time-spectral method for solution of initial-value problems. The spectral method, called the generalized weighted residual method (GWRM), is a generalization of weighted residual methods to the time and parameter domains [1]. A semi-analytical Chebyshev polynomial ansatz is employed, and the problem reduces to determine the coefficients of the ansatz from linear or nonlinear algebraic systems of equations. In order to avoid large memory storage and computational cost, it is preferable to subdivide the temporal and spatial domains into subdomains. Methods and examples of this article demonstrate how this can be achieved. 

  • 34.
    Scheffel, Jan
    et al.
    KTH, Superseded Departments, Alfvén Laboratory.
    Rachlew, Elisabeth
    KTH, Superseded Departments, Physics.
    FUSION i det tjugoförsta århundradet - en vital del av energiförsörjningen2004In: KOSMOS, ISSN 0368-6213, Vol. 1, p. 33-66Article in journal (Other (popular science, discussion, etc.))
  • 35.
    Scheffel, Jan
    et al.
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    Schnack, D. D.
    University of Madison, Wisconsin.
    Confinement Scaling Laws for the Conventional Reversed-field Pinch2000In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 10, p. 322-Article in journal (Refereed)
    Abstract [en]

    A series of high resolution, 3D, resistive MHD numerical simulations of the reversed-field pinch are performed to obtain scaling laws for poloidal beta and energy confinement at Lundquist numbers approaching 106. Optimum plasma conditions are attained by taking the transport coefficients to be classical, and ignoring radiation losses and resistive wall effects. We find that poloidal beta scales as βθ∝I-0.40and that the energy confinement time scales as τE∝I0.34 for fixed I/N, with aspect ratio R/a = 1.25.

  • 36.
    Scheffel, Jan
    et al.
    KTH, Superseded Departments, Alfvén Laboratory.
    Schnack, D. D.
    Confinement scaling laws for the conventional reversed-field pinch2000In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 85, no 2, p. 322-325Article in journal (Refereed)
    Abstract [en]

    A series of high resolution, 3D, resistive MHD numerical simulations of the reversed-field pinch are performed to obtain scaling laws for poloidal beta and energy confinement ar Lundquist numbers approaching 10(6). Optimum plasma conditions are attained by taking the transport coefficients to be classical, and ignoring radiation losses and resistive wall effects. We find that poloidal beta scales as beta(theta) proportional to I-0.40 and that the energy confinement time scales as tau(E) proportional to I-0.34 For fixed I/N, with aspect ratio R/a = 1.25.

  • 37.
    Scheffel, Jan
    et al.
    KTH, Superseded Departments, Alfvén Laboratory.
    Schnack, D. D.
    Numerical studies of confinement scaling in the conventional reversed field pinch2000In: Nuclear Fusion, ISSN 0029-5515, E-ISSN 1741-4326, Vol. 40, no 11, p. 1885-1896Article in journal (Refereed)
    Abstract [en]

    Scaling laws for reversed field pinch (RFP) confinement parameters versus plasma current and density are found from computer simulations. The RFP dynamics at high Lundquist numbers approaching 10(6) is studied using a high resolution, 3-D, resistive MHD numerical code. Optimum plasma conditions are attained by assuming that the transport coefficients are classical, and by ignoring radiation losses and resistive wall effects. Anomalous global transport results from classical parallel heat conduction along stochastic field lines in the plasma core. The pinch parameter is Theta = 1.8 and the aspect ratio is R/a = 1.25. Poloidal beta is found to scale as beta (theta) proportional to (I/N)(-0.40) I-0.40 and energy confinement time as tau (E) proportional to (I/N)(0.34) I-0.34. On-axis temperature scales as T(0) proportional to (I/N)(0.56) I-0.56. Experimental results from T2, RFX and MST agree well with the above numerical results and also with the obtained magnetic fluctuation scaling proportional to S-0.14, where S is the Lundquist number. Thus stochastic core field lines appear to persist also at higher, reactor relevant currents and temperatures in the conventional RFP, indicating the need to further pursue confinement enhancement techniques.

  • 38.
    Scheffel, Jan
    et al.
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    Schnack, Dalton D.
    University of Wisconsin.
    MIrza, Ahmed A.
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    Static current profile control and RFP confinement2013In: Nuclear Fusion, ISSN 0029-5515, E-ISSN 1741-4326, Vol. 53, no 11, p. 113007-Article in journal (Refereed)
    Abstract [en]

    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.

1 - 38 of 38
CiteExportLink to result list
Permanent link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf