# The relativistic electro-vortical field—revisiting magneto-genesis and allied problems

TL;DR: Mahajan et al. as mentioned in this paper proposed a very general Electro-Vortical (EV) field to describe the dynamics of a perfect relativistic fluid, similar to the electromagnetic field Fμν, which unified the macroscopic forces into a single grand force that is the weighted sum of the electromagnetic and the inertial/thermal forces.

Abstract: 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.

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TL;DR: In this paper, the authors construct a magnetic helicity conserving dynamo theory which incorporates a calculated magnetic heli-ity current, which plays a small role in large scale magnetic field generation.

Abstract: We construct a magnetic helicity conserving dynamo theory which incorporates a calculated magnetic helicity current. In this model the fluid helicity plays a small role in large scale magnetic field generation. Instead, the dynamo process is dominated by a new quantity, derived from asymmetries in the second derivative of the velocity correlation function, closely related to the `twist and fold' dynamo model. The turbulent damping term is, as expected, almost unchanged. Numerical simulations with a spatially constant fluid helicity and vanishing resistivity are not expected to generate large scale fields in equipartition with the turbulent energy density. The prospects for driving a fast dynamo under these circumstances are uncertain, but if it is possible, then the field must be largely force-free. On the other hand, there is an efficient analog to the $\alpha-\Omega$ dynamo. Systems whose turbulence is driven by some anisotropic local instability in a shearing flow, like real stars and accretion disks, and some computer simulations, may successfully drive the generation of strong large scale magnetic fields, provided that $\partial_r\Omega >0$. We show that this criterion is usually satisfied. Such dynamos will include a persistent, spatially coherent vertical magnetic helicity current with the same sign as $-\partial_r\Omega$, that is, positive for an accretion disk and negative for the Sun. We comment on the role of random magnetic helicity currents in storing turbulent energy in a disordered magnetic field, which will generate an equipartition, disordered field in a turbulent medium, and also a declining long wavelength tail to the power spectrum. As a result, calculations of the galactic `seed' field are largely irrelevant.

168 citations

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TL;DR: In this paper, it is shown that strong magnetic fields are produced from a zero initial magnetic field during the pregalactic era, when galaxies are first forming, and that the resulting magnetic field represents a galactic magnetic field of primordial origin.

Abstract: It is demonstrated that strong magnetic fields are produced from a zero initial magnetic field during the pregalactic era, when galaxies are first forming. Their development proceeds in three phases. In the first phase, weak magnetic fields are created by the Biermann battery mechanism, acting in shocked parts of the intergalactic medium where caustics form and intersect. In the second phase, these weak magnetic fields are amplified to strong magnetic fields by the Kolmogoroff turbulence endemic to gravitational structure formation of galaxies. During this second phase, the magnetic fields reach saturation with the turbulent power, but they are coherent only on the scale of the smallest eddy. In the third phase, the magnetic field strength increases to equipartition with the turbulent energy, and the coherence length of the magnetic fields increases to the scale of the largest turbulent eddy, comparable to the scale of the entire galaxy. The resulting magnetic field represents a galactic magnetic field of primordial origin. No further dynamo action is necessary, after the galaxy forms, to explain the origin of magnetic fields. However, the magnetic field may be altered by dynamo action once the galaxy and the galactic disk have formed. It is first shown by direct numerical simulations, that thermoelectric currentsassociated with the Biermann battery, build the field up from zero to $10^{-21}$ G in the regions about to collapse into galaxies, by $z\sim3$. For weak fields, in the absence of dissipation, the cyclotron frequency ${\bf \omega_{cyc}}=e{\bf B } /m_H c $ and $ {\bf \omega}/(1+ \chi )$, where ${\bf \omega =
abla \times v }$ is the vorticity and $\chi$ is the degree of ionization, satisfy the same equations, and initial conditions ${\bf \omega_{cyc}=\omega}=0$, so that, ${\bf \omega_{cyc}}({\bf

41 citations

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TL;DR: In this article, the spin-electron acoustic wave mechanism was used to explain the superconductivity of ferromagnetic, ferrimagnetic, and antiferromagnetic materials.

Abstract: We have found the mechanism of the electron Cooper pair formation via the electron interaction by means of the spin-electron acoustic waves. This mechanism takes place in metals with rather high spin polarization, such as ferromagnetic, ferrimagnetic, and antiferromagnetic materials. The spin-electron acoustic wave mechanism leads to transition temperatures 100 times higher than the transition temperature allowed by the electron-phonon interaction. Therefore, spin-electron acoustic waves give the explanation for the high-temperature superconductivity. We find that the transition temperature has strong dependence on the electron concentration and the spin polarization of the electrons.

16 citations

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TL;DR: In this article, the spin-electron acoustic wave mechanism was used to explain the superconductivity of ferromagnetic, ferrimagnetic and antiferromagnetic materials, and the transition temperature has a strong dependence on the electron concentration and the spin polarization of the electrons.

Abstract: We have found the mechanism of the electron Cooper pair formation via the electron interaction by means of the spin-electron acoustic waves. This mechanism takes place in metals with rather high spin polarization, like ferromagnetic, ferrimagnetic and antiferromagnetic materials. The spin-electron acoustic wave mechanism leads to transition temperatures 100 times higher than the transition temperature allowed by the electron-phonon interaction. Therefore, spin-electron acoustic waves give the explanation for the high-temperature superconductivity. We find that the transition temperature has strong dependence on the electron concentration and the spin polarization of the electrons.

13 citations

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TL;DR: In this article, a multispecies degenerate astrophysical plasma consisting of two electron species (at different temperatures): a highly degenerate main component plus a smaller classical relativistic flow immersed in a static neutralizing ion background is studied, and it is shown that the high frequency electromagnetic waves through their strong nonlinear interactions with the electron-acoustic waves can scatter to lower frequencies so that the radiation observed faraway will be spectrally shifted downward.

Abstract: Nonlinear wave-coupling is studied in a multispecies degenerate astrophysical plasma consisting of two electron species (at different temperatures): a highly degenerate main component plus a smaller classical relativistic flow immersed in a static neutralizing ion background. It is shown that the high frequency electromagnetic waves through their strong nonlinear interactions with the electron-acoustic waves [sustained by a multielectron component (degenerate) plasma surrounding a compact astrophysical object] can scatter to lower frequencies so that the radiation observed faraway will be spectrally shifted downward. It is also shown that, under definite conditions, the electromagnetic waves could settle into stationary solitonic states. It is expected that the effects of such structures may persist as detectable signatures in forms of modulated micropulses in the radiation observed far away from the accreting compact object. Both these effects will advance our abilities to interpret the radiation coming out of the compact objects.

12 citations

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TL;DR: In this article, the spontaneous generation of reversed fields in toroidal plasmas is shown to be a consequence of relaxation under constraints, and the onset of the reversed field and other features of this model agree well with observations on ZETA.

Abstract: The spontaneous generation of reversed fields in toroidal plasmas is shown to be a consequence of relaxation under constraints. With perfect conductivity a topological constraint exists for each field line and the final state is not unique. With small departures from perfect conductivity, topological constraints are relaxed and the final state becomes unique. The onset of the reversed field and other features of this model agree well with observations on ZETA.

1,740 citations

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TL;DR: The current understanding of astrophysical magnetic fields is reviewed in this paper, focusing on their generation and maintenance by turbulence, where analytical and numerical results are discussed both for small scale dynamos, which are completely isotropic, and for large scale dynamo, where some form of parity breaking is crucial.

1,548 citations

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TL;DR: In this paper, the integral integral of the velocity field in a fluid of infinite extent due to a vorticity distribution w(x) which is zero except in two closed vortex filaments of strengths K1, K2 was shown.

Abstract: Let u(x) be the velocity field in a fluid of infinite extent due to a vorticity distribution w(x) which is zero except in two closed vortex filaments of strengths K1, K2. It is first shown that the integral
\[
I=\int{\bf u}.{\boldmath \omega}\,dV
\]
is equal to αK1K2 where α is an integer representing the degree of linkage of the two filaments; α = 0 if they are unlinked, ± 1 if they are singly linked. The invariance of I for a continuous localized vorticity distribution is then established for barotropic inviscid flow under conservative body forces. The result is interpreted in terms of the conservation of linkages of vortex lines which move with the fluid.Some examples of steady flows for which I ± 0 are briefly described; in particular, attention is drawn to a family of spherical vortices with swirl (which is closely analogous to a known family of solutions of the equations of magnetostatics); the vortex lines of these flows are both knotted and linked.Two related magnetohydrodynamic invariants discovered by Woltjer (1958a, b) are discussed in ±5.

1,420 citations

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TL;DR: The theory of plasma relaxation is described and developed in this article, which involves reconnection of magnetic field lines in a manner that destroys all the topological invariants of ideal plasma so that only total magnetic helicity survives.

Abstract: The theory of plasma relaxation is described and developed. Turbulence, allied with a small resistivity, allows the plasma rapid access to a particular minimum-energy state. This process involves reconnection of magnetic field lines in a manner that destroys all the topological invariants of ideal plasma so that only total magnetic helicity survives. Although this mechanism, and the equations describing the relaxed state, are similar in all systems, the properties of the relaxed state depend crucially on the topology---toroidal or spherical---of the container and on the boundary conditions. Consequently there are several different types of relaxed state, each with its own special characteristics, which are derived and discussed. The measurements made on many experiments, including toroidal pinches, OHTE, multipinch, and spheromaks, are reviewed and shown to be in striking agreement with the theoretical predictions.

1,216 citations