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Numerical studies of current profile control in the reversed-field pinch
KTH, School of Electrical Engineering (EES), Centres, Alfvén Laboratory Centre for Space and Fusion Plasma Physics.
2006 (English)Doctoral 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.

Place, publisher, year, edition, pages
Stockholm: KTH , 2006. , 52 p.
Series
Trita-EE, ISSN 1653-5146 ; 2006:053
Keyword [en]
Reversed-Field Pinch, RFP, Current Profile Control, CPC, DEBS, DEBSP, active control, feedback, MHD.
National Category
Fusion, Plasma and Space Physics
Identifiers
URN: urn:nbn:se:kth:diva-4167ISBN: 91-7178-500-0 (print)OAI: oai:DiVA.org:kth-4167DiVA: diva2:11022
Public defence
2006-11-30, Kollegiesalen (F3), Lindstedtsvägen 26, Stockholm, 10:00
Opponent
Supervisors
Note
QC 20101101Available from: 2006-11-13 Created: 2006-11-13 Last updated: 2010-11-01Bibliographically approved
List of papers
1. Feedback current profile control in the advanced RFP
Open this publication in new window or tab >>Feedback current profile control in the advanced RFP
2004 (English)In: Proceedings of the 31st EPS plasma physics conference, 2004Conference paper, Published paper (Refereed)
National Category
Fusion, Plasma and Space Physics
Identifiers
urn:nbn:se:kth:diva-6331 (URN)
Conference
31st EPS plasma physics conference
Note
QC 20101101Available from: 2006-11-13 Created: 2006-11-13 Last updated: 2010-11-01Bibliographically approved
2. A novel feedback algorithm for simulating controlled dynamics and confinement in the advanced reversed-field pinch
Open this publication in new window or tab >>A novel feedback algorithm for simulating controlled dynamics and confinement in the advanced reversed-field pinch
2005 (English)In: Physics of Plasmas, ISSN 1070-664X, Vol. 12, no 6, 062502- p.Article in journal (Refereed) Published
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.

Keyword
POLOIDAL CURRENT DRIVE; FLUCTUATION; TRANSPORT; BETA
National Category
Engineering and Technology
Identifiers
urn:nbn:se:kth:diva-6332 (URN)10.1063/1.1924556 (DOI)000229700400034 ()2-s2.0-24144484884 (Scopus ID)
Note
QC 20100824Available from: 2006-11-13 Created: 2006-11-13 Last updated: 2010-11-01Bibliographically approved
3. Confinement scaling in the advanced reversed-field pinch
Open this publication in new window or tab >>Confinement scaling in the advanced reversed-field pinch
2006 (English)In: Plasma Physics and Controlled Fusion, ISSN 0741-3335, E-ISSN 1361-6587, Vol. 48, no 11, L97-L104 p.Article in journal (Refereed) Published
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.

Keyword
Electric current control, Electric field effects, Fluid dynamics, Magnetic field effects, Mathematical models, Numerical analysis, Three dimensional computer graphics
National Category
Physical Sciences
Identifiers
urn:nbn:se:kth:diva-6333 (URN)10.1088/0741-3335/48/11/L01 (DOI)000242550000001 ()2-s2.0-33846094480 (Scopus ID)
Note
QC 20100906Available from: 2006-11-13 Created: 2006-11-13 Last updated: 2010-09-06Bibliographically approved
4. Numerical studies of confinement scalings for the dynamo-free reversed-field pinch
Open this publication in new window or tab >>Numerical studies of confinement scalings for the dynamo-free reversed-field pinch
2007 (English)In: Nuclear Fusion, ISSN 0029-5515, E-ISSN 1741-4326, Vol. 47, no 1, 9-16 p.Article in journal (Refereed) Published
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.

Keyword
Computer simulation, Electric conductivity, Joule heating, Magnetohydrodynamics, Optimization, Plasma confinement, Regression analysis, Scaling laws
National Category
Fusion, Plasma and Space Physics
Identifiers
urn:nbn:se:kth:diva-6334 (URN)10.1088/0029-5515/47/1/002 (DOI)000243953900005 ()2-s2.0-33947622628 (Scopus ID)
Note
QC 20100924. Uppdaterad från Accepted till Published (20100924).Available from: 2006-11-13 Created: 2006-11-13 Last updated: 2010-09-24Bibliographically approved
5. Ultra-high beta in numerical simulations of a tearing-mode reduced reversed-field pinch
Open this publication in new window or tab >>Ultra-high beta in numerical simulations of a tearing-mode reduced reversed-field pinch
2007 (English)In: Nuclear Fusion, ISSN 0029-5515, E-ISSN 1741-4326, Vol. 47, no 9, 1184-1188 p.Article in journal (Refereed) Published
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.

Keyword
Betatrons, Computer simulation, Magnetic fields, Magnetohydrodynamics
National Category
Physical Sciences
Identifiers
urn:nbn:se:kth:diva-6335 (URN)10.1088/0029-5515/47/9/015 (DOI)000249968800018 ()2-s2.0-34548236281 (Scopus ID)
Note
QC 20101005. Uppdaterad från Submitted till Published (20101005).Available from: 2006-11-13 Created: 2006-11-13 Last updated: 2010-10-05Bibliographically approved
6. Numerical studies of active current profile control in the reversed-field pinch
Open this publication in new window or tab >>Numerical studies of active current profile control in the reversed-field pinch
2007 (English)In: Plasma Physics and Controlled Fusion, ISSN 0741-3335, E-ISSN 1361-6587, Vol. 49, no 2, 183-195 p.Article in journal (Refereed) Published
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.

Keyword
Algorithms, Feedback control, Numerical methods, Quenching
National Category
Fusion, Plasma and Space Physics
Identifiers
urn:nbn:se:kth:diva-6336 (URN)10.1088/0741-3335/49/2/008 (DOI)000243752000008 ()2-s2.0-34247205360 (Scopus ID)
Note

QC 20100924. Uppdaterad från Submitted till Published (20100924).

Available from: 2006-11-13 Created: 2006-11-13 Last updated: 2016-12-09Bibliographically approved

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