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The tearing mode locking-unlocking mechanism to an external resonant field in EXTRAP T2R
KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.ORCID iD: 0000-0002-9546-4494
KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.ORCID iD: 0000-0002-6554-9681
KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.ORCID iD: 0000-0002-5259-0458
2014 (English)In: Plasma Physics and Controlled Fusion, ISSN 0741-3335, E-ISSN 1361-6587, Vol. 56, no 10, 104001- p.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.

Place, publisher, year, edition, pages
2014. Vol. 56, no 10, 104001- p.
Keyword [en]
RMP, locking, hysteresis, RFP, tearing mode
National Category
Fusion, Plasma and Space Physics
Identifiers
URN: urn:nbn:se:kth:diva-155144DOI: 10.1088/0741-3335/56/10/104001ISI: 000342759900003Scopus ID: 2-s2.0-84907246910OAI: oai:DiVA.org:kth-155144DiVA: diva2:760997
Note

QC 20141105

Available from: 2014-11-05 Created: 2014-10-31 Last updated: 2017-12-05Bibliographically approved
In thesis
1. Tearing mode dynamics in the presence of resonant magnetic perturbations
Open this publication in new window or tab >>Tearing mode dynamics in the presence of resonant magnetic perturbations
2016 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

Magnetically confined fusion (MCF) plasmas are typically subject to several unstable modes. The growth of one mode can limit the plasma energy confinement and might cause a termination of the plasma. Externally applied resonant magnetic perturbations (RMPs) are used to control and to mitigate some of the unstable modes. Examples are, mitigation of edge localized modes and steering of neoclassical tearing mode position for stabilization by electron cyclotron current drive. Consequently, use of RMPs are considered necessary in planned future fusion machines. There are however negative consequences, the RMP interaction with a tearing mode (TM) of the same resonance can cause deceleration of the TM and possibly wall-locking. If a TM is non-rotating relative the machine-wall, it can grow and degrade fusion plasma performance and lead to a plasma disruption. Thus, all fusion confinement machines want to avoid wall-locked modes. Resonant magnetic fields can also be present in the form of machine-error-fields, which can produce the same effects. Clearly, it is of importance to understand the TM-RMP interaction. Typically, the modes with long wavelength are described by magnetohydrodynamic (MHD) theory. Considering the finite plasma resistivity, MHD predicts a mode that tears and reconnects magnetic field lines, called a tearing mode (TM). TMs occur at surfaces where the magnetic field lines close on themselves after a number of (m) toroidal and (n)poloidal turns. These surfaces are resonant in the sense that magnetic field and helical current perturbation has the same helicity, which minimize stabilizing effect of magnetic field line bending. In this thesis, the mechanisms of TM locking and unlocking due to external resonant magnetic perturbations (RMPs) are experimentally studied. The studies are conducted in two MCF machines of the type reversed-field pinch (RFP): EXTRAP T2R and Madison Symmetric Torus (MST). The studied machines exhibit multiple rotating TMs under normal operation. In EXTRAP T2R TM locking and unlocking are studied by application of a single harmonic RMP. Observations show that after the TM is locked, RMP amplitude has to be reduced significantly in order to unlock the TM. In similar studies in MST unlocking is not observed at all after turn-off of the RMP. Hence, in both machines, there is hysteresis in the locking and subsequent unlocking of a tearing mode. Results show qualitative agreement with a theoretical model of the TM evolution when subjected to an RMP. It is shown that the RMP cause a reduction of TM and plasma rotation at the resonant surface. The velocity reduction is opposed by a viscous torque from surrounding plasma. After TM locking, relaxation of the whole plasma rotation is observed, due to the transfer of velocity reduction via viscosity. This results in a reduced viscous resorting torque, which explains the observed hysteresis. The hysteresis is further deepened by the increase in amplitude of a locked mode.

Place, publisher, year, edition, pages
Stockholm: Universitetsservice US AB, 2016. vii, 44 p.
Series
TRITA-EE, ISSN 1653-5146 ; 2015:112
Keyword
Tearing mode, plasma, fusion, reversed-field pinch, RFP, magnetic, confinement, resonant, perturbation, magnetohydrodynamics, MHD, EXTRAP T2R, Madison Symmetic Torus
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Research subject
Physics
Identifiers
urn:nbn:se:kth:diva-180058 (URN)978-91-7595-812-5 (ISBN)
Presentation
2016-01-29, Seminarierummet, Teknikringen 31, KTH, Stcokholm, 13:15 (English)
Opponent
Supervisors
Note

QC 20160111

Available from: 2016-01-11 Created: 2016-01-07 Last updated: 2016-01-11Bibliographically approved
2. Resonant magnetic perturbation effect on the tearing mode dynamics: Novel measurements and modeling of magnetic fluctuation induced momentum transport in the reversed-field pinch
Open this publication in new window or tab >>Resonant magnetic perturbation effect on the tearing mode dynamics: Novel measurements and modeling of magnetic fluctuation induced momentum transport in the reversed-field pinch
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. 55 p.
Series
TRITA-EE, ISSN 1653-5146 ; 2017:135
Keyword
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:nbn:se:kth:diva-218052 (URN)978-91-7729-549-5 (ISBN)
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

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Frassinetti, LorenzoBrunsell, Per R.

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