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Resonant magnetic perturbation effect on the tearing mode dynamics: Novel measurements and modeling of magnetic fluctuation induced momentum transport in the reversed-field pinch
KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.ORCID iD: 0000-0002-6554-9681
2017 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The tearing mode (TM) is a resistive instability that can arise in magnetically confined plasmas. The TM can be driven unstable by the gradient of the plasma current. When the mode grows it destroys the magnetic field symmetry and reconnects the magnetic field in the form of a so-called magnetic island. The TMs are inherent to a type of device called the reversed-field pinch (RFP), which is a device for toroidal magnetic confinement of fusion plasmas. In the RFP, TMs arise at several resonant surfaces, i.e. where the field lines and the perturbation have the same pitch angle. These surfaces are closely spaced in the RFP and the neighboring TM islands can overlap. Due to the island overlap, the magnetic field lines become tangled resulting in a stochastic magnetic field, i.e. the field lines fill a volume instead of lying on toroidal surfaces. Consequently, a stochastic field results in an anomalously fast transport in the radial direction. Stochastic fields can also arise in other plasmas, for example, the tokamak edge when a resonant magnetic perturbation (RMP) is applied by external coils. This stochastization is intentional to mitigate the edge-localized modes. The RMPs are also used for control of other instabilities. Due to the finite number of RMP coils, however, the RMP fields can contain sidebands that decelerate and lock the TMs via electromagnetic torques. The locking causes an increased plasma-wall interaction. And in the tokamak, the TM locking can cause a plasma disruption which is disastrous for future high-energy devices like the ITER. In this thesis, the TM locking was studied in two RFPs (EXTRAP T2R and Madison Symmetric Torus) by applying RMPs. The experiments were compared with modern mode-locking theory. To determine the viscosity in different magnetic configurations where the field is stochastic, we perturbed the momentum via an RMP and an insertable biased electrode.

In the TM locking experiments, we found qualitative agreement with the mode-locking theory. In the model, the kinematic viscosity was chosen to match the experimental locking instant. The model then predicts the braking curve, the short timescale dynamics, and the mode unlocking. To unlock a mode, the RMP amplitude had to decrease by a factor ten from the locking amplitude. These results show that mode-locking theory, including the relevant electromagnetic torques and the viscous plasma response, can explain the experimental features. The model required viscosity agreed with another independent estimation of the viscosity. This showed that the RMP technique can be utilized for estimations of the viscosity.

In the momentum perturbation experiments, it was found that the viscosity increased 100-fold when the magnetic fluctuation amplitude increased 10-fold. Thus, the experimental viscosity exhibits the same scaling as predicted by transport in a stochastic magnetic field. The magnitude of the viscosity agreed with a model that assumes that transport occurs at the sound speed -- the first detailed test of this model. The result can, for example, lead to a clearer comparison between experiment and visco-resistive magnetohydrodynamics (MHD) modeling of plasmas with a stochastic magnetic field. These comparisons had been complicated due to the large uncertainty in the experimental viscosity. Now, the viscosity can be better constrained, improving the predictive capability of fusion science.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2017. , p. 55
Series
TRITA-EE, ISSN 1653-5146 ; 2017:135
Keywords [en]
RFP, reversed-field pinch, tokamak, tearing mode, RMP, fusion, plasma, resonant magnetic perturbation, stochastic, magnetic, field, viscosity, mode, locking
National Category
Fusion, Plasma and Space Physics
Research subject
Electrical Engineering
Identifiers
URN: urn:nbn:se:kth:diva-218052ISBN: 978-91-7729-549-5 (print)OAI: oai:DiVA.org:kth-218052DiVA, id: diva2:1159102
Public defence
2017-12-13, F3, Lindstedtsvägen 26, Stockholm, 09:00 (English)
Opponent
Supervisors
Note

QC 20171122

Available from: 2017-11-22 Created: 2017-11-21 Last updated: 2017-11-22Bibliographically approved
List of papers
1. The tearing mode locking-unlocking mechanism to an external resonant field in EXTRAP T2R
Open this publication in new window or tab >>The tearing mode locking-unlocking mechanism to an external resonant field in EXTRAP T2R
2014 (English)In: Plasma Physics and Controlled Fusion, ISSN 0741-3335, E-ISSN 1361-6587, Vol. 56, no 10, p. 104001-Article in journal (Refereed) Published
Abstract [en]

The tearing mode (TM) locking and unlocking process due to an external resonant magnetic perturbation (RMP) is experimentally studied in EXTRAP T2R. The RMP produces a reduction of the natural TM velocity and ultimately the TM locking if a threshold in the RMP amplitude is exceeded. During the braking process, the TM slows down via a mechanism composed of deceleration and acceleration phases. During the acceleration phases, the TM can reach velocities higher than the natural velocity. Once the TM locking occurs, the RMP must be reduced to a small amplitude to obtain the TM unlocking, showing that the unlocking threshold is significantly smaller than the locking threshold and that the process is characterized by hysteresis. Experimental results are in qualitative agreement with a model that describes the locking-unlocking process via the balance of the electromagnetic torque produced by the RMP that acts to brake the TM and the viscous torque that tends to re-establish the unperturbed velocity.

Keywords
RMP, locking, hysteresis, RFP, tearing mode
National Category
Fusion, Plasma and Space Physics
Identifiers
urn:nbn:se:kth:diva-155144 (URN)10.1088/0741-3335/56/10/104001 (DOI)000342759900003 ()2-s2.0-84907246910 (Scopus ID)
Note

QC 20141105

Available from: 2014-11-05 Created: 2014-10-31 Last updated: 2017-12-05Bibliographically approved
2. Hysteresis in the tearing mode locking/unlocking due to resonant magnetic perturbations in EXTRAP T2R
Open this publication in new window or tab >>Hysteresis in the tearing mode locking/unlocking due to resonant magnetic perturbations in EXTRAP T2R
2015 (English)In: Plasma Physics and Controlled Fusion, ISSN 0741-3335, E-ISSN 1361-6587, Vol. 57, no 10, article id 104008Article in journal (Refereed) Published
Abstract [en]

The physical mechanisms behind the hysteresis in the tearing mode locking and unlocking to a resonant magnetic perturbation (RMP) are experimentally studied in EXTRAP T2R reversed-field pinch. The experiments show that the electromagnetic and the viscous torque increase with increasing perturbation amplitude until the mode locks to the wall. At the wall-locking, the plasma velocity reduction profile is peaked at the radius where the RMP is resonant. Thereafter, the viscous torque drops due to the relaxation of the velocity in the central plasma. This is the main reason for the hysteresis in the RMP locking and unlocking amplitude. The increased amplitude of the locked tearing mode produces further deepening of the hysteresis. Both experimental results are in qualitative agreement with the model in Fitzpatrick et al (2001 Phys. Plasmas 8 4489)

Place, publisher, year, edition, pages
Institute of Physics Publishing (IOPP), 2015
Keywords
EXTRAP T2R, hysteresis, locking unlocking, resonant magnetic perturbation, reversed-field pinch, tearing modes, Magnetic resonance, Magnetism, Pinch effect, Wave plasma interactions, Resonant magnetic perturbations, Reversed field pinch, Locks (fasteners)
National Category
Fusion, Plasma and Space Physics
Identifiers
urn:nbn:se:kth:diva-177743 (URN)10.1088/0741-3335/57/10/104008 (DOI)000366679100009 ()2-s2.0-84940838273 (Scopus ID)
Note

QC 20151130

Available from: 2015-11-30 Created: 2015-11-25 Last updated: 2017-12-01Bibliographically approved
3. Tearing mode dynamics and locking in the presence of external magnetic perturbations
Open this publication in new window or tab >>Tearing mode dynamics and locking in the presence of external magnetic perturbations
Show others...
2016 (English)In: Physics of Plasmas, ISSN 1070-664X, E-ISSN 1089-7674, Vol. 23, p. 062504-Article in journal (Refereed) Published
Abstract [en]

In normal operation, Madison Symmetric Torus (MST) [R. N. Dexter et al., Fusion Technol. 19, 131 (1991)] reversed-field pinch plasmas exhibit several rotating tearing modes (TMs). Application of a resonant magnetic perturbation (RMP) results in braking of mode rotation and, if the perturbation amplitude is sufficiently high, in a wall-locked state. The coils that produce the magnetic perturbation in MST give rise to RMPs with several toroidal harmonics. As a result, simultaneous deceleration of all modes is observed. The measured TM dynamics is shown to be in qualitative agreement with a magnetohydrodynamical model of the RMP interaction with the TM [R. Fitzpatrick, Nucl. Fusion 33, 1049 (1993)] adapted to MST. To correctly model the TM dynamics, the electromagnetic torque acting on several TMs is included. Quantitative agreement of the TM slowing-down time was obtained for a kinematic viscosity in the order of ν≈10–20 m2/s. Analysis of discharges with different plasma densities shows an increase of the locking threshold with increasing density. Modeling results show good agreement with the experimental trend, assuming a density-independent kinematic viscosity. Comparison of the viscosity estimates in this paper to those made previously with other techniques in MST plasmas suggests the possibility that the RMP technique may allow for estimates of the viscosity over a broad range of plasmas in MST and other devices.

Place, publisher, year, edition, pages
American Institute of Physics (AIP), 2016
Keywords
Tearing mode, viscosity, locking, RFP, RMP, MST, magnetic perturbation, fusion, plasma
National Category
Natural Sciences
Research subject
Physics
Identifiers
urn:nbn:se:kth:diva-194184 (URN)10.1063/1.4953438 (DOI)000379172200055 ()2-s2.0-84974628204 (Scopus ID)
Note

QC 20161019

Available from: 2016-10-19 Created: 2016-10-19 Last updated: 2017-11-29Bibliographically approved
4. Estimation of anomalous viscosity based on modeling of experimentally observed plasma rotation braking induced by applied resonant magnetic perturbations
Open this publication in new window or tab >>Estimation of anomalous viscosity based on modeling of experimentally observed plasma rotation braking induced by applied resonant magnetic perturbations
Show others...
2016 (English)In: 43th European Physical Society (EPS) Conference on Plasma Physics. July 4 – July 8, 2016, European Physical Society (EPS) , 2016Conference paper, Published paper (Refereed)
Place, publisher, year, edition, pages
European Physical Society (EPS), 2016
National Category
Fusion, Plasma and Space Physics
Identifiers
urn:nbn:se:kth:diva-203360 (URN)2-s2.0-85013867240 (Scopus ID)
Conference
43th European Physical Society (EPS) Conference on Plasma Physics. July 4 – July 8, 2016
Note

QC 20170321

Available from: 2017-03-15 Created: 2017-03-15 Last updated: 2017-11-21Bibliographically approved
5. Multiple-harmonics RMP effect on tearing modes in EXTRAP T2R
Open this publication in new window or tab >>Multiple-harmonics RMP effect on tearing modes in EXTRAP T2R
2017 (English)Conference paper, Published paper (Other academic)
National Category
Fusion, Plasma and Space Physics
Identifiers
urn:nbn:se:kth:diva-218046 (URN)
Conference
44th EPS Conference on Plasma Physics, 26/06/2017 to 30/06/2017, Belfast, Northern Irland
Note

QC 20171122

Available from: 2017-11-21 Created: 2017-11-21 Last updated: 2017-11-22Bibliographically approved
6. Dependence of perpendicular viscosity on magnetic fluctuations in a stochastic topology
Open this publication in new window or tab >>Dependence of perpendicular viscosity on magnetic fluctuations in a stochastic topology
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(English)Manuscript (preprint) (Other academic)
National Category
Fusion, Plasma and Space Physics
Identifiers
urn:nbn:se:kth:diva-218050 (URN)
Note

QC 20171122

Available from: 2017-11-21 Created: 2017-11-21 Last updated: 2017-11-22Bibliographically approved
7. Modeled and measured magnetic fluctuation induced momentum transport in the reversed-field pinch
Open this publication in new window or tab >>Modeled and measured magnetic fluctuation induced momentum transport in the reversed-field pinch
Show others...
(English)Manuscript (preprint) (Other academic)
National Category
Fusion, Plasma and Space Physics
Identifiers
urn:nbn:se:kth:diva-218051 (URN)
Note

QC 20171122

Available from: 2017-11-21 Created: 2017-11-21 Last updated: 2017-11-22Bibliographically approved

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