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  • 1.
    Dahlin, Jon-Erik
    KTH, School of Electrical Engineering (EES), Centres, Alfvén Laboratory Centre for Space and Fusion Plasma Physics.
    Numerical studies of current profile control in the reversed-field pinch2006Doctoral thesis, comprehensive summary (Other scientific)
    Abstract [en]

    The Reversed-Field Pinch (RFP) is one of the major alternatives for realizing energy production from thermonuclear fusion. Compared to alternative configurations (such as the tokamak and the stellarator) it has some advantages that suggest that an RFP reactor may be more economic. However, the conventional RFP is flawed with anomalously large energy and particle transport (which leads to unacceptably low energy confinement) due to a phenomenon called the "RFP dynam".

    The dynamo is driven by the gradient in the plasma current in the plasma core, and it has been shown that flattening of the plasma current profile quenches the dynamo and increases confinement. Various forms of current profile control schemes have been developed and tested in both numerical simulations and experiments.

    In this thesis an automatic current profile control routine has been developed for the three-dimensional, non-linear resistive magnetohydrodynamic computer code DEBSP. The routine utilizes active feedback of the dynamo associated fluctuating electric field, and is optimized for replacing it with an externally supplied field while maintaining field reversal. By introducing a semi-automatic feedback scheme, the number of free parameters is reduced, making a parameter scan feasible. A scaling study was performed and scaling laws for the confinement of the advanced RFP (an RFP with enhanced confinement due to current profile control) have been obtained.

    The conclusions from this research project are that energy confinement is enhanced substantially in the advanced RFP and that poloidal beta values are possible beyond the previous theoretical limit beta βΘ < ½. Scalings toward the reactor regime indicate strongly enhanced confinement as compared to conventional RFP scenarios, but the question of reactor viability remains open.

  • 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 Laws2005In: 32nd EPS Conference on Plasma Physics, Tarragona, Spain 27 June-1 July, P-1.118, 2005, 2005Conference 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 Pinch2005In: 47th APS Division of Plasma Physics Meeting, Denver, Colorado, 24-28 October, 2005, 2005Conference paper (Refereed)
  • 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.
    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.

  • 12.
    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.

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