We consider the non-dissipative multi-fluid equations, and demonstrate how multi-Beltrami equilibria emerge as natural relaxed states of the model, representing an evolution towards the minimum energy. General properties of these states are studied, and a wide class of solutions is obtained. We specialize to the cases of double and triple Beltrami states and highlight their connections with the appropriate physical invariants, viz., the generalized helicities and the energy. In particular, we demonstrate that different field configurations can give rise to distinct or identical values of the invariants, depending on the nature of the roots of the multi-Beltrami equation. Moreover, we also highlight equivalences between (outwardly) unconnected models allowing us to treat them in a unified manner. Some observations regarding the nature of the solutions for certain special cases of these models are presented. Potential applications for astrophysical plasmas are also highlighted. © 2015 AIP Publishing LLC.

Mahajan S.M.

Lingam M.

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Multi-fluid systems—Multi-Beltrami relaxed states and their implications

Physics of Plasmas

It is shown that thermal turbulence, not unlike the standard kinetic and magnetic turbulence, can be an effective driver of a mean-field dynamo. In simple models, such as hydrodynamics and magnetohydrodynamics, both vorticity and induction equations can have strong thermal drives that resemble the α and γ effects in conventional dynamo theories; the thermal drives are likely to be dominant in systems that are endowed with subsonic, low-β turbulence. A pure thermal dynamo is quite different from the conventional dynamo in which the same kinetic/magnetic mix in the ambient turbulence can yield a different ratio of macroscopic magnetic/vortical fields. The possible implications of the similarities and differences between the thermal and non-thermal dynamos are discussed. The thermal dynamo is shown to be highly important in the stellar and planetary context, and yields results broadly consistent with other theoretical and experimental approaches. © 2016 Author(s).

A potential thermal dynamo and its astrophysical applications

Extended MHD is a one-fluid model that incorporates two-fluid effects such as electron inertia and the Hall drift. This model is used to construct fully nonlinear Alfvénic wave solutions, and thereby derive the kinetic and magnetic spectra by resorting to a Kolmogorov-like hypothesis based on the constant cascading rates of the energy and generalized helicities of this model. The magnetic and kinetic spectra are derived in the ideal (k &lt; 1/λi), Hall (1/λi &lt; k &lt; 1/λi), and electron inertia (k &gt; 1/λe)regimes; k is the wavenumber and λs = c/ωps is the skin depth of species "s." In the Hall regime, it is shown that the emergent results are fully consistent with previous numerical and analytical studies, especially in the context of the solar wind. The focus is primarily on the electron inertia regime, where magnetic energy spectra with power-law indexes of and are always recovered. The latter, in particular, is quite close to recent observational evidence from the solar wind with a potential slope of approximately -4 in this regime. It is thus plausible that these spectra may constitute a part of the (extended) inertial range, as opposed to the standard "dissipation" range paradigm. © 2016. The American Astronomical Society. All rights reserved.

Astrophysical Journal

EXTENDED MHD TURBULENCE and ITS APPLICATIONS to the SOLAR WIND

Following the idea of MagnetoFluid unification [S. M. Mahajan, Phys. Rev. Lett. 90, 035001 (2003)], a very general Electro-Vortical (EV) field is constructed to describe the dynamics of a perfect relativistic fluid. Structurally similar to the electromagnetic field Fμν, the Electro-Vortical field Mνμ unifies the macroscopic forces into a single grand force that is the weighted sum of the electromagnetic and the inertial/thermal forces. The new effective force may be viewed either as a vortico-thermal generalization of the electromagnetic force or as the electromagnetic generalization of the vortico-thermal forces that a fluid element experiences in course of its evolution. Two fundamental consequences follow from this grand unification: (1) emergences of a new helicity that is conserved for arbitrary thermodynamics and (2) the entire dynamics is formally expressible as an MHD (magnetohydrodynamics) like ideal Ohm's law in which the "electric" and "magnetic" components of the EV field replace the standard electric and magnetic fields. In the light of these more and more encompassing conserved helicities, the "scope and significance" of the classical problem of magneto-genesis (need for a seed field to get a dynamo started) is reexamined. It is shown that in models more advanced than MHD, looking for exotic seed-generation mechanisms (like the baroclinic thermodynamics) should not constitute a fundamental pursuit; the totally ideal dynamics is perfectly capable of generating and sustaining magnetic fields entirely within its own devices. For a specified thermodynamics, a variety of exact and semi exact self-consistent analytical solutions for equilibrium magnetic and flow fields are derived for a single species charged fluid. The scale lengths of the fields are determined by two natural scale lengths: the skin depth and the gradient length of the thermodynamic quantities. Generally, the skin depth, being the shorter (even much shorter) than the gradient length, will characterize the kinetic-magnetic reservoir of short scale energy that will drive the dynamo as well as reverse dynamo action - the creation of large scale magnetic and flow fields. © 2016 Author(s).

The relativistic electro-vortical field - Revisiting magneto-genesis and allied problems

Using the magnetofluid unification framework, we show that the accretion disk plasma (embedded in the background geometry of a black hole) can relax to a class of states known as the Beltrami-Bernoulli (BB) equilibria. Modeling the disk plasma as a Hall magnetohydrodynamics (MHD) system, we find that the space-time curvature can significantly alter the magnetic (velocity) decay rates as we move away from the compact object; the velocity profiles in BB states, for example, deviate substantially from the predicted corresponding geodesic velocity profiles. These departures imply a rich interplay of plasma dynamics and general relativity revealed by examining the corresponding Bernoulli condition representing "homogeneity" of total energy. The relaxed states have their origin in the constraints provided by the two helicity invariants of Hall MHD. These helicities conspire to introduce an oscillatory length scale into the system that is strongly influenced by relativistic and thermal effects. © 2015 American Physical Society.