603 research outputs found
Evolution of primordial magnetic fields in mean-field approximation
We study the evolution of phase-transition-generated cosmic magnetic fields
coupled to the primeval cosmic plasma in turbulent and viscous free-streaming
regimes. The evolution laws for the magnetic energy density and correlation
length, both in helical and non-helical cases, are found by solving the
autoinduction and Navier-Stokes equations in 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 radiation and
matter dominated eras. 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 and the magnetic correlation length evolve asymptotically
with the temperature as and . Here, , , and 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 ,
, , , , and , depend on
the index of the assumed initial power-law magnetic spectrum, , and on the
particular regime, with the order-one constants and
depending also on the cut-off 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 equal to zero.Comment: 38 pages, 4 figures, 2 tables, references added, paraghraph added,
minor changes, results unchanged, to appear in Eur. Phys. J.
On the self-similarity of nonhelical magnetohydrodynamic turbulence
We re-analyze the Olesen arguments on the self-similarity properties of
freely evolving, nonhelical magnetohydrodynamic turbulence. We find that a
necessary and sufficient condition for the kinetic and magnetic energy spectra
to evolve self-similarly is that the initial velocity and magnetic field are
not homogeneous functions of space of different degree, to wit, the initial
energy spectra are not simple powers of the wavenumber with different slopes.
If, instead, they are homogeneous functions of the same degree, the evolution
is self-similar, it proceeds through selective decay, and the order of
homogeneity fixes the exponents of the power laws according to which the
kinetic and magnetic energies and correlation lengths evolve in time. If just
one of them is homogeneous, the evolution is self-similar and such exponents
are completely determined by the slope of that initial spectrum which is a
power law. The latter evolves through selective decay, while the other spectrum
may eventually experience an inverse transfer of energy. Finally, if the
initial velocity and magnetic field are not homogeneous functions, the
evolution of the energy spectra is still self-similar but, this time, the
power-law exponents of energies and correlation lengths depend on a single free
parameter which cannot be determined by scaling arguments. Also in this case,
an inverse transfer of energy may in principle take place during the evolution
of the system.Comment: 4 pages, 1 figure, typos correcte
Evolution of Magnetic Fields in Freely Decaying Magnetohydrodynamic Turbulence
We study the evolution of magnetic fields in freely decaying
magnetohydrodynamic turbulence. By quasi-linearizing the Navier-Stokes
equation, we solve analytically the induction equation in quasi-normal
approximation. We find that, if the magnetic field is not helical, the magnetic
energy and correlation length evolve in time respectively as E_B \propto
t^{-2(1+p)/(3+p)} and \xi_B \propto t^{2/(3+p)}, where p is the index of
initial power-law spectrum. In the helical case, the magnetic helicity is an
almost conserved quantity and forces the magnetic energy and correlation length
to scale as E_B \propto (log t)^{1/3} t^{-2/3} and \xi_B \propto (log t)^{-1/3}
t^{2/3}.Comment: 4 pages, 2 figures; accepted for publication in PR
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