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Pressure driven instabilities in the reversed-field pinch: numerical and theoretical studies
KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
2013 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

According to classical linearized resistive magnetohydrodynamics theory, pressuredriven modes are unstable in the reversed-field pinch (RFP) due to unfavorable magnetic field line curvature. The result is based on the assumption of an adiabatic energy equation where anisotropic thermal conduction effects are ignored as compared to convection and compression. In this thesis the effects of heat conduction in the energy equation have been studied. We have examined these effects on the linear stability of pressure-driven resistive modes using boundary value theory (Δ´ ) and a novel initial-value full resistive MHD code employing the Generalized Weighted Residual Method (GWRM). In the Δ´ method, a shooting technique is employed by integrating from the resistive layer to boundaries. The GWRM method, on the other hand, is a time-spectral Galerkin method in which the fully linearized MHD equations are solved. For detailed computations, efficiency requires the temporal and spatial domains to be divided into subdomains. For this purpose, a number of challenging test cases including linearized ideal MHD equations are treated.

Numerical and analytical investigations of equilibria reveal that thermal conduction effects are not stabilizing for reactor relevant values of Lundquist number, S0, and normalized pressure, βθ, for tearing-stable plasmas. These studies show that growth rate scales as  γ~_ S0−1/5 , which is weaker than for the adiabatic case, γ~_ S0−1/3.

A numerical study of optimized confinement for an advanced RFP scenario including ohmic heating and heat conduction, is also part of this thesis. The fully nonlinear resistive MHD code DEBSP has been employed. We have identified, using both Δ´ and GWRM methods, that the observed crash of the high confinement is caused by resistive, pressure-driven modes.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2013. , xi, 56 p.
Series
Trita-EE, ISSN 1653-5146 ; 2013:017
Keyword [en]
Fusion plasma, thermonuclear, Reversed-field pinch, resistive MHD, resistive g modes, thermal conduction, the boundary value theory
National Category
Fusion, Plasma and Space Physics
Identifiers
URN: urn:nbn:se:kth:diva-121345ISBN: 978-91-7501-722-8 (print)OAI: oai:DiVA.org:kth-121345DiVA: diva2:618541
Public defence
2013-05-17, Sal F3, Lindstedtsvägen 26, KTH, Stockholm, 14:00 (English)
Opponent
Supervisors
Note

QC 20130503

Available from: 2013-05-02 Created: 2013-04-29 Last updated: 2013-05-02Bibliographically approved
List of papers
1. Effect of thermal conduction on pressure-driven modes in the reversed-field pinch
Open this publication in new window or tab >>Effect of thermal conduction on pressure-driven modes in the reversed-field pinch
2012 (English)In: Nuclear Fusion, ISSN 0029-5515, E-ISSN 1741-4326, Vol. 52, no 12, 123012- p.Article in journal (Refereed) Published
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).

Keyword
Magnetohydrodynamic Transport Model, Resistive Instabilities, Toroidal Plasma, Configurations, Systems
National Category
Fusion, Plasma and Space Physics
Identifiers
urn:nbn:se:kth:diva-105494 (URN)10.1088/0029-5515/52/12/123012 (DOI)000311754900015 ()2-s2.0-84870162299 (Scopus ID)
Note

QC 20130109

Available from: 2012-11-21 Created: 2012-11-21 Last updated: 2017-12-07Bibliographically approved
2. Time-spectral solution of initial-value problems – subdomain approach
Open this publication in new window or tab >>Time-spectral solution of initial-value problems – subdomain approach
2012 (English)In: American Journal of Computational Mathematics, ISSN 2161-1211, Vol. 2, no 2, 72-81 p.Article in journal (Refereed) Published
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. 

Place, publisher, year, edition, pages
Scientific Research Publishing, 2012
Keyword
initial-value problem, time-spectral, spectral method, subdomains, domain decomposition
National Category
Fusion, Plasma and Space Physics
Identifiers
urn:nbn:se:kth:diva-91443 (URN)10.4236/ajcm.2012.22010 (DOI)
Note

QC 20121127

Available from: 2012-11-27 Created: 2012-03-15 Last updated: 2013-05-02Bibliographically approved
3. Static current profile control and RFP confinement
Open this publication in new window or tab >>Static current profile control and RFP confinement
2013 (English)In: Nuclear Fusion, ISSN 0029-5515, E-ISSN 1741-4326, Vol. 53, no 11, 113007- p.Article in journal (Refereed) Published
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.

Place, publisher, year, edition, pages
Institute of Physics (IOP), 2013
Keyword
Reversed-Field Pinch, Current Drive, High-Beta, Fluctuation, Reduction
National Category
Fusion, Plasma and Space Physics
Identifiers
urn:nbn:se:kth:diva-121596 (URN)10.1088/0029-5515/53/11/113007 (DOI)000326684400008 ()2-s2.0-84887107572 (Scopus ID)
Note

QC 20131209

Available from: 2013-05-02 Created: 2013-05-02 Last updated: 2017-12-06Bibliographically approved
4. Resistive pressure driven RFP modes are not removed by heat conduction effects
Open this publication in new window or tab >>Resistive pressure driven RFP modes are not removed by heat conduction effects
2012 (English)In: 39th EPS Conference on Plasma Physics 2012, EPS 2012 and the 16th International Congress on Plasma Physics: Volume 3, 2012, 2012, 1690-1693 p.Conference paper, Published 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

National Category
Fusion, Plasma and Space Physics
Identifiers
urn:nbn:se:kth:diva-105504 (URN)2-s2.0-84876917604 (Scopus ID)978-162276981-0 (ISBN)
Conference
39th EPS Conference on Plasma Physics and 16th Int. Congress on Plasma Physics, Stockholm, Sweden, 2-6 July 2012
Note

QC 20130115

Available from: 2012-11-21 Created: 2012-11-21 Last updated: 2013-09-10Bibliographically approved
5. Numerical study of thermal conductivity effects on stability of the reversed-field pinch
Open this publication in new window or tab >>Numerical study of thermal conductivity effects on stability of the reversed-field pinch
2011 (English)Conference paper, Published paper (Refereed)
National Category
Natural Sciences Fusion, Plasma and Space Physics
Identifiers
urn:nbn:se:kth:diva-76038 (URN)2-s2.0-84867632865 (Scopus ID)
Conference
38th EPS Conference on Plasma Physics, Strasbourg, France, 27 June – 1 July 2011
Note
QC 20120413Available from: 2012-02-06 Created: 2012-02-06 Last updated: 2013-05-02Bibliographically approved

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