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  • 101.
    Scheffel, Jan
    et al.
    KTH.
    Arber, T. D.
    Coppins, M.
    Linear Stability of the Large Larmor Radius Z-pinch1994In: Third International Conference on Dense Z-pinches,  Imperial College, London, 19-23 April 1993, 1994, Vol. 299, p. 75-Conference paper (Refereed)
    Abstract [en]

    For the first time, calculations of large Larmor radius (LLR) effects on the linear stability of realistic Z-pinch equilibria have been performed. The fixed boundary m=0 instability of the pure Z-pinch (no external magnetic field) is considered (free-boundary and m=1 modes are presently under study). We use the Vlasov-Fluid model, where ions are treated fully kinetically and electrons are modelled as a cold, massless fluid. Stability is found to be remarkably sensitive to equilibrium profiles. A flat current equilibrium is increasingly stabilized (smaller growth rate) by LLR effects as the normalized average Larmor radius ε is increased to about 0.1. Complete stabilization cannot be obtained. For larger values of ε the growth rate increases to reach above the small Larmor radius value when ε~0.3. The Bennett equilibrium, however, is increasingly destabilized as ε increases.

  • 102. Scheffel, Jan
    et al.
    Arber, T. D.
    Coppins, M.
    Russell, P. G. F.
    Kinetic Stability of the Finite Electron Temperature Z-pinch1997In: Plasma Physics and Controlled Fusion, ISSN 0741-3335, E-ISSN 1361-6587, Vol. 39, no 4, p. 559-568Article in journal (Refereed)
    Abstract [en]

    Large Larmor radius (LLR) stability of linear m = 0 and m = 1 modes in a Z-pinch has been studied using the Vlasov-fluid model (Arber et al1994 Phys. Rev. Lett. 72 2399; 1995 Phys. Rev. Lett. 74 2698). Ions have been modelled fully kinetically through the Vlasov equation, and electrons are treated as a zero temperature, massless fluid. In the present work an improved Vlasov-fluid model is used to investigate the effect of finite electron temperature on m = 0 modes. An electron energy equation is introduced, and results for both adiabatic and isothermal dynamics are presented. It is found that finite electron temperature has a destabilizing effect in general. As a result, the Z-pinch is only weakly stabilized by LLR effects.

  • 103.
    Scheffel, Jan
    et al.
    KTH.
    Brzozowski, J.
    Hellblom, G.
    Hörling, P.
    Welander, A.
    Extrap Mode Operation on Extrap T1-U1995Report (Other academic)
  • 104.
    Scheffel, Jan
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS).
    Brzozowski, Jerzy
    Hellblom, Göran
    Hörling, Pontus
    Welander, Anders
    Extrap Mode Confinement in Extrap T1-U1997In: Plasma Physics and Controlled Fusion, ISSN 0741-3335, E-ISSN 1361-6587, Vol. 39, p. 973-992Article in journal (Refereed)
    Abstract [en]

    An extensive series of experiments in the Extrap mode has been carried out on Extrap T1-U in an attempt to obtain hot, collisionless discharges. Using no external axial magnetic field, performance has been limited to low temperatures (≤ 15 eV) and low currents (≤ 20 kA) at high loop voltages 1.4 kV, leading to energy confinement times of only a few μs or Alfvén times. The discharge length is typically of the order of greater than 100 Alfve ́n times.

    Imposing a weak axial field (q(a) ≤ 0.15 at peak current) the temperature could be increased to 40 eV at toroidal currents ≤ 60 kA. Energy confinement times up to 15 Alfvén times (≈10 μs) were then obtained.

    The poor confinement is attributed to the weak axial magnetic field, generating strong instability-induced fluctuations and related radial transport in the core plasma. A turbulence core plasma transport model is suggested, based on theoretical evidence of linear instability in the kinetic regime.

    Self-generation of axial magnetic field is observed when the magnetic X-points, generated by the plasma current and an external octupole field, approach or pass beyond the wall.

    Edge transport appears to be dominated by line radiation and heat conduction to the wall along open field lines. 

  • 105.
    Scheffel, Jan
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS).
    Coppins, M.
    Interchange Stable Z-Pinch Equilibria1990In: Workshop on Physics of Alternative Magnetic Confinement Schemes, International School of Plasma Physics, Villa Monastero, Varenna, Italy, October 15-24, 1990., 1990Conference paper (Refereed)
  • 106.
    Scheffel, Jan
    et al.
    KTH.
    Coppins, M.
    m=0 Z-Pinch Stability Reconsidered1991Report (Other academic)
  • 107.
    Scheffel, Jan
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS).
    Coppins, M.
    New Aspects on m=0 Z-pinch Stability1991In: 33rd APS Plasma Physics Meeting 4-8 Nov. 1991, Tampa, Florida, 1991, Vol. 36, article id Paper 5T12Conference paper (Refereed)
  • 108.
    Scheffel, Jan
    et al.
    KTH.
    Coppins, M.
    Reconsideration of the m=0 Z-Pinch Stability1993In: Nuclear Fusion, ISSN 0029-5515, E-ISSN 1741-4326, Vol. 33, p. 101-Article in journal (Refereed)
    Abstract [en]

    Possible paths for obtaining linear stability against the m=0 mode in the Z-pinch are studied. Using a generalized energy principle, the necessary and sufficient Chew-Goldberger-Low (CGL) m=0 stability criterion is derived. This criterion is less restrictive than that of ideal MHD, although it also requires the boundary plasma pressure to be finite. It is shown that the edge pressure cannot be stably upheld by a surface current. By instead assuming a finite pressure external gas, it is found that an edge pressure to on-axis pressure ratio of 0.5 is required for stability of a constant current density profile. A parabolic current density profile lowers the limit to the value 0.17. The growth rates are shown to be monotonically decreasing as a function of the external gas pressure. Detailed derivations of the boundary conditions are also given. The results aid in clarifying the experimental stability of four major Z-pinch experiments. Finite Larmor radius stabilization is hence required to maintain stability in future fibre pinch experiments in vacuum, implying line densities less than 10**19 m**(-1).

  • 109.
    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.

  • 110.
    Scheffel, Jan
    et al.
    KTH, Superseded Departments (pre-2005), Alfvén Laboratory.
    Dahlin, Jon-Erik
    KTH, Superseded Departments (pre-2005), Alfvén Laboratory.
    Schnack, D. D.
    University of Madison, Wisconsin.
    Drake, J. R.
    KTH, Superseded Departments (pre-2005), Alfvén Laboratory.
    Energy Confinement in the Advanced RFP2003In: 45th Annual Meeting of the Division of Plasma Physics; Albuquerque, New Mexico, USA, 27-31 October 2003, 2003Conference paper (Refereed)
    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.

  • 111. Scheffel, Jan
    et al.
    Elevant, T.
    Neutron Spectra from Beam-Heated Fusion Plasmas1980Report (Other academic)
  • 112.
    Scheffel, Jan
    et al.
    KTH.
    Faghihi, M.
    Effect of Gyroviscosity on the Small Axial Wavelength Internal Kink Instability in the Z-pinch1987Report (Other academic)
  • 113.
    Scheffel, Jan
    et al.
    KTH.
    Faghihi, M.
    Finite Larmor Radius Effects on Z-Pinch Stability1989In: Journal of Plasma Physics, ISSN 0022-3778, E-ISSN 1469-7807, Vol. 41, p. 427-439Article in journal (Refereed)
    Abstract [en]

    The effect of finite Larmor radius (FLR) on the stability of m = 1 small-axial-wavelength kinks in a z–pinch with purely poloidal magnetic field is investigated. We use the incompressible FLR MHD model; a collisionless fluid model that consistently includes the relevant FLR terms due to ion gyroviscosity, Hall effect and electron diamagnetism. With FLR terms absent, the Kadomtsev criterion of ideal MHD, 2r dp/dr + m2B2/μ0 ≥ 0 predicts instability for internal modes unless the current density is singular at the centre of the pinch. The same result is obtained in the present model, with FLR terms absent. When the FLR terms are included, a normal-mode analysis of the linearized equations yields the following results. Marginally unstable (ideal) modes are stabilized by gyroviscosity. The Hall term has a damping (but not absolutely stabilizing) effect – in agreement with earlier work. On specifying a constant current and particle density equilibrium, the effect of electron diamagnetism vanishes. For a z–pinch with parameters relevant to the EXTRAP experiment, the m = 1 modes are then fully stabilized over the crosssection for wavelengths λ/a ≤ 1, where a denotes the pinch radius. As a general z–pinch result a critical line-density limit Nmax = 5 × 1018 m–1 is found, above which gyroviscous stabilization near the plasma boundary becomes insufficient. This limit corresponds to about five Larmor radii along the pinch radius. The result holds for wavelengths close to, or smaller than, the pinch radius and for realistic equilibrium profiles. This limit is far below the required limit for a reactor with contained alpha particles, which is in excess of 1020 m–1.

  • 114.
    Scheffel, Jan
    et al.
    KTH.
    Faghihi, M.
    Finite Larmor Radius Effects on Z-Pinch Stability1987Report (Other academic)
  • 115.
    Scheffel, Jan
    et al.
    KTH.
    Faghihi, M.
    Incompressible FLR MHD - a Fluid Model for Stability Analysis of a Fusion Plasma1986Report (Other academic)
  • 116.
    Scheffel, Jan
    et al.
    KTH.
    Faghihi, M.
    Non-Ideal Effects on Internal Kink Stability of a Collisionless  Z-pinch1987In: XIV European Conference on Controlled Fusion and Plasma Physics, Madrid, Spain, June 22-26, 1987, 1987, p. 1111-, article id Contributed Papers IIIConference paper (Refereed)
  • 117.
    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.

  • 118.
    Scheffel, Jan
    et al.
    KTH.
    Lehnert, B.
    Large Debye Distance Effects in a Homogeneous Plasma1988Report (Other academic)
  • 119.
    Scheffel, Jan
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS).
    Lehnert, B.
    Large Debye Distance Effects in a Homogeneous Plasma1989In: Journal of Plasma Physics, ISSN 0022-3778, E-ISSN 1469-7807, Vol. 41, p. 493-Article in journal (Refereed)
    Abstract [en]

    The classical phenomenon of electron plasma oscillations has been investigated from new aspects. The applicability of standard normal-mode analysis of plasma perturbations has been judged from comparisons with exact numerical solutions to the linearized initial-value problem. We consider both Maxwellian and non-Maxwellian velocity distributions. Emphasis is on perturbations for which α*λD is of order unity, where α is the wavenumber and λD the Debye distance. The corresponding large-Debye-distance (LDD) damping is found to substantially dominate over Landau damping. This limits the applicability of normal-mode analysis of non-Maxwellian distributions. The physics of LDD damping and its close connection to large-Larmor-radius (LLR) damping is discussed. A major discovery concerns perturbations of plasmas with non-Maxwellian, bump-in-tail, velocity distribution functions f0(w). For sufficiently large α*λD (of order unity) the plasma responds by damping perturbations that are initially unstable in the Landau sense, i.e. with phase velocities initially in the interval where df0/dw > 0. It is found that the plasma responds through shifting the phase velocity above the upper velocity limit of this interval. This is shown to be due to a resonance with the drifting electrons of the bump, and explains the Penrose criterion.

  • 120.
    Scheffel, Jan
    et al.
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    Lindvall, Kristoffer
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    Generalized Weighted Residual Method; Advancements and Current Studies2016In: 58th Annual Meeting of the APS Division of Plasma Physics, San Jose, California, USA, 31 October – 4 November 2016, 2016Conference paper (Refereed)
    Abstract [en]

    The Generalized Weighted Residual Method (GWRM) is a time-spectral method for solving initial value partial differential equations. The GWRM treats the temporal, spatial, and parameter domains by projecting the residual to a Chebyshev polynomial space, with the variational principle being that the residual is zero. This treatment provides a global semi-analytical solution. However, straightforward global solution is not economical. One remedy is the inclusion of spatial and temporal sub-domains with coupled internal boundary conditions, which decreases memory requirements and introduces sparse matrices. Only the equations pertaining to the boundary conditions need be solved globally, making the method parallelizable in time. Efficient solution of the linearized ideal MHD stability equations of screw-pinch equilibria are proved possible. The GWRM has also been used to solve strongly nonlinear ODEs such as the Lorenz equations (1984), and is capable of competing with finite time difference schemes in terms of both accuracy and efficiency. GWRM solutions of linear and nonlinear model problems of interest for stability and turbulence modelling will be presented, including detailed comparisons with time stepping methods.

  • 121.
    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.
    Optimizing Time-Spectral Solution of Initial-Value Problems2018In: American Journal of Computational Mathematics, ISSN 2161-1203, E-ISSN 2161-1211, Vol. 8, no 1, p. 7-26, article id 82900Article in journal (Refereed)
    Abstract [en]

    Time-spectral solution of ordinary and partial differential equations is often regarded as an inefficient approach. The associated extension of the time domain, as compared to finite difference methods, is believed to result in uncomfortably many numerical operations and high memory requirements. It is shown in this work that performance is substantially enhanced by the introduction of algorithms for temporal and spatial subdomains in combination with sparse matrix methods. The accuracy and efficiency of the recently developed time spectral, generalized weighted residual method (GWRM) are compared to that of the explicit Lax-Wendroff and implicit Crank-Nicolson methods. Three initial-value PDEs are employed as model problems; the 1D Burger equation, a forced 1D wave equation and a coupled system of 14 linearized ideal magnetohydrodynamic (MHD) equations. It is found that the GWRM is more efficient than the time-stepping methods at high accuracies. The advantageous scalings Nt**1.0*Ns**1.43 and Nt**0.0*Ns**1.08 were obtained for CPU time and memory requirements, respectively, with Nt and Ns denoting the number of temporal and spatial subdomains. For time-averaged solution of the two-time-scales forced wave equation, GWRM performance exceeds that of the finite difference methods by an order of magnitude both in terms of CPU time and memory requirement. Favorable subdomain scaling is demonstrated for the MHD equations, indicating a potential for efficient solution of advanced initial-value problems in, for example, fluid mechanics and MHD. 

  • 122.
    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, 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. 

  • 123.
    Scheffel, Jan
    et al.
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    Lindvall, Kristoffer
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    Yik, H. F.
    A time-spectral approach to numerical weather prediction2018In: Computer Physics Communications, ISSN 0010-4655, E-ISSN 1879-2944, Vol. 226, p. 127-135Article in journal (Refereed)
    Abstract [en]

    Finite difference methods are traditionally used for modelling the time domain in numerical weather prediction (NWP). Time-spectral solution is an attractive alternative for reasons of accuracy and efficiency and because time step limitations associated with causal CFL-like criteria, typical for explicit finite difference methods, are avoided. In this work, the Lorenz 1984 chaotic equations are solved using the time-spectral algorithm GWRM (Generalized Weighted Residual Method). Comparisons of accuracy and efficiency are carried out for both explicit and implicit time-stepping algorithms. It is found that the efficiency of the GWRM compares well with these methods, in particular at high accuracy. For perturbative scenarios, the GWRM was found to be as much as four times faster than the finite difference methods. A primary reason is that the GWRM time intervals typically are two orders of magnitude larger than those of the finite difference methods. The GWRM has the additional advantage to produce analytical solutions in the form of Chebyshev series expansions. The results are encouraging for pursuing further studies, including spatial dependence, of the relevance of time-spectral methods for NWP modelling. Program summary: Program Title: Time-adaptive GWRM Lorenz 1984 Program Files doi: http://dx.doi.org/10.17632/4nxfyjj7nv.1 Licensing provisions: MIT Programming language: Maple Nature of problem: Ordinary differential equations with varying degrees of complexity are routinely solved with numerical methods. The set of ODEs pertaining to chaotic systems, for instance those related to numerical weather prediction (NWP) models, are highly sensitive to initial conditions and unwanted errors. To accurately solve ODEs such as the Lorenz equations (E. N. Lorenz, Tellus A 36 (1984) 98–110), small time steps are required by traditional time-stepping methods, which can be a limiting factor regarding the efficiency, accuracy, and stability of the computations. Solution method: The Generalized Weighted Residual Method, being a time-spectral algorithm, seeks to increase the time intervals in the computation without degrading the efficiency, accuracy, and stability. It does this by postulating a solution ansatz as a sum of weighted Chebyshev polynomials, in combination with the Galerkin method, to create a set of linear/non-linear algebraic equations. These algebraic equations are then solved iteratively using a Semi Implicit Root solver (SIR), which has been chosen due to its enhanced global convergence properties. Furthermore, to achieve a desired accuracy across the entire domain, a time-adaptive algorithm has been developed. By evaluating the magnitudes of the Chebyshev coefficients in the time dimension of the solution ansatz, the time interval can either be decreased or increased.

  • 124.
    Scheffel, Jan
    et al.
    KTH.
    Liu, Donghui
    Magnetic Fluctuation Driven Cross-field Particle Transport in the RFP1997In: Physics of Plasmas, ISSN 1070-664X, E-ISSN 1089-7674, Vol. 4, p. 3620-Article in journal (Refereed)
    Abstract [en]

    Electrostatic and electromagnetic fluctuationsgenerally cause cross-field particle transport in confined plasmas. Thus core localized turbulence must be kept at low levels for sufficient energy confinement in magnetic fusion plasmas. Reversed-field pinch (RFP) equilibria can, theoretically, be completely stable to ideal and resistive (tearing) magnetohydrodynamic(MHD) modes at zero beta. Unstable resistive interchange modes are, however, always present at experimentally relevant values of the poloidal beta βθ.An analytical quasilinear, ambipolar diffusion model is here used to model associated particle transport. The results indicate that core density fluctuations should not exceed a level of about 1% for plasmas of fusion interest. Parameters of experimentally relevant stationary states of the RFP were adjusted to minimize growth rates, using a fully resistive linearized MHDstability code. Density gradient effects are included through employing a parabolic density profile. The scaling of particle diffusion (D(r)∝λ**2*n**0.5*T/aB, where λ is the mode width) is such that the effects of particle transport are milder in present day RFP experiments than in future reactor-relevant plasmas.

  • 125.
    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 MHD2010In: 52nd Annual Meeting of the APS Division of Plasma Physics, Chicago, Illinios, USA 8-12 November, 2010, 2010Conference paper (Refereed)
    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. 

  • 126.
    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)
  • 127.
    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 confinement2009In: 51st Annual Meeting of the APS Division of Plasma Physics, Atlanta, Georgia, USA  2-6 November, 2009, 2009Conference paper (Refereed)
    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.

  • 128.
    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

  • 129.
    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 RFP2011In: 53rd Annual Meeting of the APS Division of Plasma Physics, Salt Lake City, Utah, USA 14-18 November, 2011, 2011Conference paper (Refereed)
    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.

  • 130.
    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. 

  • 131.
    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.))
  • 132.
    Scheffel, Jan
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS).
    Schnack, D.
    Numerical Simulation of Reversed-field Pinch Confinement1999Report (Other academic)
  • 133.
    Scheffel, Jan
    et al.
    KTH.
    Schnack, D.
    RFP Confinement - Scalings from Numerical Simulations1999In: 26th EPS Conf. on Contr. Fusion and Plasma Physics, Maastricht, 14 - 18 June 1999, 1999, Vol. 23J, p. 577-580Conference paper (Refereed)
  • 134.
    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.

  • 135.
    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.

  • 136.
    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.

123 101 - 136 of 136
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