Theory and simulations of principle of minimum dissipation rate

Shaikh, Dastgeer; Dasgupta, B.; Zank, G. P.; Hu, Qiang

doi:10.1063/1.2828539

Cited by 11 publications

(10 citation statements)

References 24 publications

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“…7 in Braithwaite (2008), a selective decay of the total helicity (H) and of the magnetic energy (U Mag ) occurs during the initial relaxation with a stronger decrease in U Mag than that of H. This hierarchy, which is well known in plasma physics (see for example Biskamp 1997;Shaikh et al 2008) justifies the variational method used to derive our configuration (Montgomery & Phillips 1988) while the introduction of I I;1 is justified by the non force-free character of the field in stellar interiors (Reisenegger 2009) and by the stratification, which inhibits the transport of flux and mass in the radial direction (see Sect. 3.2 and Braithwaite 2008).…”

Section: Comparison To Numerical Simulationsmentioning

confidence: 99%

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Relaxed equilibrium configurations to model fossil fields

Duez

Mathis

2010

A&A

132

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Context. The understanding of fossil fields' origin, topology, and stability is one of the corner stones of the stellar magnetism theory. On one hand, since they survive on secular time scales, they may modify the structure and the evolution of their host stars. On the other hand, they must have a complex stable structure since it has been demonstrated that the simplest purely poloidal or toroidal fields are unstable on dynamical time scales. In this context, the only stable configuration found today is the one resulting from a numerical simulation by Braithwaite and collaborators who studied the evolution of an initial stochastic magnetic field, which is found to relax on a mixed stable configuration (poloidal and toroidal) that seems to be in equilibrium and then diffuses. Aims. We investigate an equilibrium field in a semi-analytical way. In this first article, we study the barotropic magnetohydrostatic equilibrium states. Methods. The problem reduces to a Grad-Shafranov-like equation with arbitrary functions. These functions are constrained by deriving the lowest-energy equilibrium states for given invariants of the considered axisymmetric problem, in particular for a given helicity known to be one of the causes of such problems. These theoretical results were applied to realistic stellar cases, the solar radiative core and the envelope of an Ap star, and discussed. In both cases we assumed that the field is initially confined in the stellar radiation zone.Results. The generalization of the force-free Taylor's relaxation states studied in laboratory experiments (in spheromaks) that become non force-free in the self-gravitating stellar case are obtained. The case of general baroclinic equilibrium states will be studied in Paper II.

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Section: Comparison To Numerical Simulationsmentioning

confidence: 99%

“…∇×B αB). Some non force-free relaxed states have been identified in plasma physics (Montgomery & Phillips 1988Dasgupta et al 2002;Shaikh et al 2008) and should be studied in a stellar context in a near future.…”

Section: Fossil Fields Barotropic Relaxation Statesmentioning

confidence: 99%

Relaxed equilibrium configurations to model fossil fields

Duez

Mathis

2010

A&A

132

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“…In the same way, we can show that dR/dt $ À 2 2 /S 2 ð Þ P k k 4 b 2 k goes at a much faster rate that dK/dt. Furthermore, a recent 3D time-dependent simulation of MHD fluids proves this argument (Shaikh et al 2008). It is shown that the energy dissipation rate, R j 2 dV , decays the fastest toward a minimum state.…”

Section: Heuristic Justification Of the Mdrmentioning

confidence: 81%

A Practical Approach to Coronal Magnetic Field Extrapolation Based on the Principle of Minimum Dissipation Rate

Dasgupta

Choudhary

et al. 2008

ApJ

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We present a newly developed approach to solar coronal magnetic field extrapolation from vector magnetograms, based on the principle of minimum dissipation rate ( MDR). The MDR system was derived from a variational problem that is more suitable for an open and externally driven system, like the solar corona. The resulting magnetic field equation is more general than force-free. Its solution can be expressed as the superposition of two linear (constant-) force-free fields (LFFFs) with distinct parameters, and one potential field. Thus, the original extrapolation problem is decomposed into three LFFF extrapolations, utilizing boundary data. The full MDR-based approach requires two layers of vector magnetograph measurements on the solar surface, while a slightly modified practical approach only requires one. We test both approaches against three-dimensional MHD simulation data in a finite volume. Both yield quantitatively good results. The errors in the magnetic energy estimate are within a few percent. In particular, the main features of relatively strong perpendicular current density structures, representative of the non-force-freeness of the solution, are well recovered.

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“…Rather, it is a consequence of the identification of the relaxed structures with minima of the dissipated (viscous + Joule) power. In turn, we have invoked the results of [5], generalized the results of [16], [22], [25], [40] and [41] and shown that the latter identification follows from the structure of Ohm's law and of the viscous stress tensor in our low-β, Λ ≫ 1, weakly dissipative plasma near the Sun. The proof holds for vanishing temperature gradient only, but can easily be generalized to the case of self-similar evolution [2] [13].…”

Section: Discussionmentioning

confidence: 99%

On super-elastic collisions between magnetized plasmoids in the heliosphere

Vita

2018

Eur. Phys. J. D

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Recently, a unique collision between two large-scale magnetized plasmoids produced by coronal mass ejections in the heliosphere has been observed [C. Shen et al., Nature Physics 8, 923-928 (2012)]. Results suggest that the collision is super-elastic, i.e. the total linear kinetic energy of the two plasmoids after the collision is larger than before the collision, and that an anti-correlation exists, i.e. the lower the initial relative velocity of the plasmoids, the larger the relative increase in total kinetic energy. The problemCoronal mass ejections (CMEs) give birth to large-scale plasmoids, originating from the solar atmosphere and expanding and propagating into the heliosphere [1] [2]. The occurrence rate of CMEs is about 4-5 CMEs per day at solar maximum [3], so that encounters and interactions between plasmoids are unavoidable. Nevertheless, inter-plasmoid collisions are far from understood. While collisions between blobs of ordinary gases are heavily affected by mixing, cross-field diffusion is effectively prohibited by sufficiently strong magnetic field.Experiments show that initially well-distinct plasmoids preserve their identity after a collision; historically, these experiments led to the very definition of 'plasmoid' as a 'plasma magnetic entity' with well-distinguished identity and geometrical structure [4]. In the lab, conventional magnetohydrodynamics fails to provide adequate macroscopic description of isolated plasmoids [5] -let alone their mutual interaction. In space, such description requires detailed knowledge of energy balance and state equation [2].Recent observation of a collision between plasmoids [1] suggests that such collisions may be superelastic, i.e. the total linear kinetic energy of the colliding plasmoids after the collision is larger than before the collision. A similar phenomenon is observed in collisions of spheres with elastoplastic plates, where rotational kinetic energy may be transferred into linear kinetic energy [6]. This analogy suggests that the linear kinetic energy in collisions between plasmoids may increase at the expense of the energy of some other degree of freedom, and magnetic energy is an obvious candidate. A preliminary investigation of energy balance supports this point of view; moreover, it has been suggested that the lower the impact velocity, the larger the relative increase of the linear kinetic energy [1]; in contrast, if the relative velocity of colliding plasmoids is too large, then no elastic scattering occurs [7], and the plasmoids may merge into each other.The aim of this work is to investigate this suggestion. We invoke the analogy [8] between plasmoids in the lab and space plasmoids and show how recent progress [5] [9] in the analytical description of the former provide information on the latter. In particular, we show that quantities usually invoked in Hall MHD [10] lead to a simple macroscopic description of interacting plasmoids. Some relevant properties of our plasmoids are discussed in Sec. 2. Secs. 3 and 4 discuss the structure...

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Theory and simulations of principle of minimum dissipation rate

Cited by 11 publications

References 24 publications

Relaxed equilibrium configurations to model fossil fields

Relaxed equilibrium configurations to model fossil fields

A Practical Approach to Coronal Magnetic Field Extrapolation Based on the Principle of Minimum Dissipation Rate

On super-elastic collisions between magnetized plasmoids in the heliosphere

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