Spheromak as a relaxed state with minimum dissipation

Dasgupta, B.; Ms, Janaki; Bhattacharyya, R.; Dasgupta, P.R.; Watanabe, Takeharu; Sato, Toru

doi:10.1103/physreve.65.046405

Cited by 18 publications

(21 citation statements)

References 19 publications

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“…These various profiles for some of the laboratory plasma devices are shown in our earlier works. [16][17][18][19] The magnetic field com- ponents for reversed field pinch and spheromak obtained from our model correspond to the experimental observations and are similar to those obtained from a force-free model. For the tokamak ͑where the force-free model is not applicable͒, our model predicts magnetic field profile, q-profile that are very close to the experimentally observed profiles.…”

Section: Discussionsupporting

confidence: 83%

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Theory and simulations of principle of minimum dissipation rate

et al. 2008

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We perform a self-consistent, time-dependent numerical simulations of dissipative turbulent plasmas at a higher Lundquist number, typically up to O͑10 6 ͒, using full three-dimensional compressible magnetohydrodynamics code with a numerical resolution of 128 3 . Our simulations follow the time variation of global helicity, magnetic energy, and the dissipation rate and show that the global helicity remains approximately constant, while magnetic energy is decaying faster and the dissipation rate is decaying even faster than the magnetic energy. This establishes that the principle of minimum dissipation rate under the constraint of ͑approximate͒ conservation of global helicity is a viable approach for plasma relaxation.

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Section: Discussionsupporting

confidence: 83%

“…Furthermore this model was applied to produce the observed pressure and q-profile of a tokamak, 17 a field-reversed configuration, 18 and a spheromak configuration. 19 Bhattacharyya and Janaki 20 extended these ideas to address dissipative relaxed states in a two-fluid plasma with external drive.…”

Section: Theoretical Backgroundmentioning

confidence: 99%

Theory and simulations of principle of minimum dissipation rate

et al. 2008

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“…∇×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

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Mathis

2010

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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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“…using the Fourier representation of Eq. (1) along with local algebraic approximations for the MSD's [15,16]. Figure 2(a) shows results for three particle sizes derived from MSD1 and the master MSD2 for a DNA concentration of 397 g=ml (c 13c ).…”

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confidence: 99%