Tomographic imaging of resistive mode dynamics in the Madison Symmetric Torus reversed-field pinch
P. FranzL. MarrelliP. PiovesanI. PredebonF. BonomoL. FrassinettiP. MartinG. SpizzoB. E. ChapmanD. CraigJ. S. Sarff
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Abstract:
A detailed study of the dynamics and magnetic topological effects of resistive-tearing modes is presented for different operational regimes in the Madison Symmetric Torus reversed-field pinch [R. N. Dexter et al., Fusion Technol. 19, 131 (1991)]. Soft-x-ray tomography and magnetic measurements, along with numerical reconstruction of magnetic-field lines with the ORBIT code [R. B. White and M. S. Chance, Phys. Fluids 27, 2455 (1984)], have been employed. Magnetic-mode dynamics has been investigated in standard plasmas during the transition to the quasi-single helicity state, in which a single mode dominates the mode spectrum. Single helical soft-x-ray structures are studied with tomography in these cases. These structures are associated with magnetic islands, indicating that helical flux surfaces appear in the plasma. Mode dynamics has also been examined during auxiliary inductive current drive, the goal of which is to reduce the tearing-mode amplitudes. In this case the phenomenology of the soft-x-ray structures appearing in the plasma is more complex. In fact, when a quasi-single helicity spectrum occurs, a single island bigger than in the standard case is usually found. On the other hand, when all modes decrease, two helical soft-x-ray structures are observed, with the same helicity as the two innermost resonant modes. This constitutes the first direct evidence of magnetic-chaos reduction during auxiliary inductive current drive, which is responsible for the achievement of the best confinement in the reversed-field pinch configuration up to now.Keywords:
Reversed field pinch
Helicity
Magnetic helicity
Tearing
<p>Magnetic helicity is a physical quantity of great importance in the study of magnetized plasmas as it is conserved in ideal magneto-hydrodynamics and slowly deteriorating in non-ideal conditions such as magnetic reconnection. A meaningful way of defining a density for helicity is with field line helicity, which, in solar conditions, is expressed by relative field line helicity (RFLH). Here, we study in detail the behaviour of RFLH in the large, well-studied, eruptive solar active region (AR) 11158. The computation of RFLH and of all other quantities of interest is based on a high-quality non-linear force-free reconstruction of the AR coronal magnetic field, and on the recent developments in its computational methodology. The derived photospheric morphology of RFLH is very different than that of the magnetic field or the electrical current, and also manages to depict the large decrease in the value of helicity during an X-class flare of the AR. Moreover, the area of the RFLH decrease coincides with the location of the magnetic structure that later erupted, the flux rope. Based on these results we review the necessary steps one needs to follow in order to identify the locations in an AR where magnetic helicity is more important. This task can provide crucial information for the conditions of an AR, especially during eruptive events.</p>
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We demonstrate that the current helicity observed in solar active regions traces the magnetic helicity of the large-scale dynamo generated field. We use an advanced two-dimensional mean-field dynamo model with dynamo saturation based on the evolution of the magnetic helicity and algebraic quenching. For comparison, we also studied a more basic two-dimensional mean-field dynamo model with simple algebraic alpha-quenching only. Using these numerical models we obtained butterfly diagrams both for the small-scale current helicity and also for the large-scale magnetic helicity, and compared them with the butterfly diagram for the current helicity in active regions obtained from observations. This comparison shows that the current helicity of active regions, as estimated by −A · B evaluated at the depth from which the active region arises, resembles the observational data much better than the small-scale current helicity calculated directly from the helicity evolution equation. Here B and A are, respectively, the dynamo generated mean magnetic field and its vector potential. A theoretical interpretation of these results is given.
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The tearing mode instability is investigated for sharp boundary high-β reversed field pinch configurations which are close to the force-free field configuration. The effects of the conducting wall on the m=0, 1 and 2 modes are discussed for various configurations of this kind, and critical locations of the conducting wall are given.
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It is shown that in magnetohydrodynamics, the shapes of the magnetic energy and magnetic helicity spectra can influence whether the magnetic helicity resistive dissipation time scale is longer, equal to, or shorter than that of magnetic energy. The calculations highlight that magnetic helicity need not always dissipate significantly more slowly than magnetic energy. While this may be implicitly understood in detailed studies of magnetic helicity in plasma devices, it is not sufficiently emphasized in elementary discussions comparing magnetic helicity vs. magnetic energy evolution. Measuring magnetic energy and helicity decay times may provide a posteriori insight into the initial spectra.
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This chapter contains sections titled: Introduction: Utility of the Helicity Concept Gauge Invariant Definitions of Helicity Helicity Conservation in the Sun Solar Wind: Statistical Aspects of Helicity Role of Helicity in the Astrophysical Dynamo Problem Helicity in Laboratory Plasmas
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