Magnetic Fields From QCD Phase Transitions

Tevzadze, Alexander G.; Kisslinger, Leonard S.; Brandenburg, Axel; Kahniashvili, Tina

doi:10.1088/0004-637x/759/1/54

Cited by 84 publications

(114 citation statements)

References 69 publications

(94 reference statements)

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“…In subsequent work he stresses that for constant ν (and η), only the case α = 1 can be realized. For nonhelical MHD, this is indeed compatible with simulations [23][24][25], but not for HD [26] nor for helical MHD [3,18]. In this Letter, we argue that the scaling exponent q is not primarily determined by the initial value of α, as suggested by Eq.…”

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confidence: 75%

Classes of Hydrodynamic and Magnetohydrodynamic Turbulent Decay

2017

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We perform numerical simulations of decaying hydrodynamic and magnetohydrodynamic turbulence. We classify our time-dependent solutions by their evolutionary tracks in parametric plots between instantaneous scaling exponents. We find distinct classes of solutions evolving along specific trajectories toward points on a line of self-similar solutions. These trajectories are determined by the underlying physics governing individual cases, while the infrared slope of the initial conditions plays only a limited role. In the helical case, even for a scale-invariant initial spectrum (inversely proportional to wavenumber k), the solution evolves along the same trajectory as for a Batchelor spectrum (proportional to k 4 ). [7], galaxy clusters [8], and the early Universe [9,10]. In the latter case, cosmological magnetic fields generated in the early Universe provide the initial source of turbulence, which leads to a growth of the correlation length by an inverse cascade mechanism [11], in addition to the general cosmological expansion of the Universe. In the last two decades, this topic has gained significant attention [12]. The time span since the initial magnetic field generation is enormous, but it is still uncertain whether it is long enough to produce fields at sufficiently large length scales to explain the possibility of contemporary magnetic fields in the space between clusters of galaxies [13].In this Letter, we use direct numerical simulations (DNS) of both hydrodynamic (HD) and magnetohydrodynamic (MHD) decaying turbulence to classify different types by their decay behavior. The decay is characterized by the temporal change of the kinetic energy spec- * Electronic address: brandenb@nordita.org † Electronic address: tinatin@andrew.cmu.edu trum, E K (k, t), and, in MHD, also by the magnetic energy spectrum, E M (k, t). Here, k is the wavenumber and t is time. In addition to the decay laws of the energies E i (t) = E i (k, t) dk, with i = K or M for kinetic and magnetic energies, there are the kinetic and magnetic integral scales,We quantify the decay by the instantaneous scaling exponents p(t) ≡ d ln E/d ln t and q(t) ≡ d ln ξ/d ln t. Thus, we study the decay behaviors by plotting p(t) vs. q(t) in a parametric representation. The pq diagram turns out to be a powerful diagnostic tool. Earlier work [8,14,15] has suggested that the decay behavior, and thus the positions of solutions in the pq diagram, depend on the exponent α for initial conditions of the form E ∼ k α e −k/k0 , where k 0 is a cutoff wavenumber. Motivated by earlier findings [2,11] of an inverse cascade in decaying MHD turbulence, Olesen considered the time-dependent energy spectra E(k, t) to be of the form [15]where ξ(t) ∝ t q , with q being an as yet undetermined scaling exponent, and ψ is a function that depends on the dissipative and turbulent processes that lead to a departure from a powerlaw at large k. Moreover, the slope ψ ′ ≡ dψ/dκ with κ = kξ must vanish for κ → 0. This turns out to be a critical restriction. Olesen then makes use of the f...

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confidence: 75%

Classes of Hydrodynamic and Magnetohydrodynamic Turbulent Decay

2017

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“…Moreover, in [158], it has been shown that, starting from suitable initial conditions which should reflect the production mechanism of a magnetic field from a bubble collision in a first-order phase transition, a Batchelor spectrum E B ∝ k 4 is established after a short time interval and at small wavenumbers. Nevertheless, we can always assume that on very large scales (very small wavenumbers k) the initial spectrum satisfies the above requirements, but that on smaller scales, where the gross of the magnetic energy is stored, it behaves like k 2 .…”

Section: Initial Conditionsmentioning

confidence: 99%

“…Nevertheless, we see that convergence in the results, at least for the most recent work and for the case of helical magnetic fields, seems to have been achieved (see, in particular, Refs. [156,158,159,161,162]). …”

Section: Freely Decaying Turbulent Magnetic Fieldsmentioning

confidence: 99%

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Evolution of primordial magnetic fields in mean-field approximation

Campanelli

2014

Eur. Phys. J. C

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We study the evolution of phase-transitiongenerated cosmic magnetic fields coupled to the primeval cosmic plasma in the turbulent and viscous free-streaming regimes. The evolution laws for the magnetic energy density and the correlation length, both in the helical and the non-helical cases, are found by solving the autoinduction and Navier-Stokes equations in the mean-field approximation. Analytical results are derived in Minkowski spacetime and then extended to the case of a Friedmann universe with zero spatial curvature, both in the radiation-and the matterdominated era. The three possible viscous free-streaming phases are characterized by a drag term in the Navier-Stokes equation which depends on the free-streaming properties of neutrinos, photons, or hydrogen atoms, respectively. In the case of non-helical magnetic fields, the magnetic intensity B and the magnetic correlation length ξ B evolve asymptotically with the temperature, T , asHere, T i , N i , and v i are, respectively, the temperature, the number of magnetic domains per horizon length, and the bulk velocity at the onset of the particular regime. The coefficients κ B , κ ξ , 1 , 2 , 3 , and 4 , depend on the index of the assumed initial power-law magnetic spectrum, p, and on the particular regime, with the order-one constants κ B and κ ξ depending also on the cutoff adopted for the initial magnetic spectrum. In the helical case, the quasi-conservation of the magnetic helicity implies, apart from logarithmic corrections and a factor proportional to the initial fractional helicity, power-like evolution laws equal to those in the non-helical case, but with p equal to zero.

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“…Taken at face value, the survival of helical fields to turbulent diffusion may provide rejuvenated credence to pre-galactic mechanisms of large scale field production that produce sufficiently strong helical fields (Field & Carroll 2000;Copi et al 2008;Díaz-Gil et al 2008;Semikoz et al 2012, Tevzadze et al 2012, Kahniashvili et al 2013) because such helical fields could then avoid decay by supernova driven turbulent diffusion over a galactic lifetime in the absence of boundary terms. Although most energy in large scale galactic magnetic fields resides in non-helical toroidal fields, as long as the turbulent decay time for the non-helical field exceeds the linear shear time, we can expect a predominance of non-helical field in a steady state, even without an in situ dynamo to regenerate the poloidal fields: The helical field provides a minimum value below which the toroidal field cannot drop.…”

Section: Helical Field Decaymentioning

confidence: 99%

Magnetic Helicity and Large Scale Magnetic Fields: A Primer

Blackman¹

2016

Space Sciences Series of ISSI

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Magnetic fields of laboratory, planetary, stellar, and galactic plasmas commonly exhibit significant order on large temporal or spatial scales compared to the otherwise random motions within the hosting system. Such ordered fields can be measured in the case of planets, stars, and galaxies, or inferred indirectly by the action of their dynamical influence, such as jets. Whether large scale fields are amplified in situ or a remnant from previous stages of an object's history is often debated for objects without a definitive magnetic activity cycle. Magnetic helicity, a measure of twist and linkage of magnetic field lines, is a unifying tool for understanding large scale field evolution for both mechanisms of origin. Its importance stems from its two basic properties: (1) magnetic helicity is typically better conserved than magnetic energy; and (2) the magnetic energy associated with a fixed amount of magnetic helicity is minimized when the system relaxes this helical structure to the largest scale available. Here I discuss how magnetic helicity has come to help us understand the saturation of and sustenance of large scale dynamos, the need for either local or global helicity fluxes to avoid dynamo quenching, and the associated observational consequences. I also discuss how magnetic helicity acts as a hindrance to turbulent diffusion of large scale fields, and thus a helper for fossil remnant large scale field origin models in some contexts. I briefly discuss the connection between large scale fields and accretion disk theory as well. The goal here is to provide a conceptual primer to help the reader efficiently penetrate the literature.

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Magnetic Fields From QCD Phase Transitions

Cited by 84 publications

References 69 publications

Classes of Hydrodynamic and Magnetohydrodynamic Turbulent Decay

Classes of Hydrodynamic and Magnetohydrodynamic Turbulent Decay

Evolution of primordial magnetic fields in mean-field approximation

Magnetic Helicity and Large Scale Magnetic Fields: A Primer

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