The evolution of causal magnetic field spectra for incompressible fluid motions,
compressible fluids and for the fully helical case are shown in Fig. 1
and Fig.2 in the simple case where all components are in
equipartition.
Fig. 1: Evolution magnetic field from ref. (1).
In the incompressible
case, even though the correlation scale is growing, there is no "inverse
cascade" in the sense that no power is transferred from small to larger scales.
Fig. 2: Evolution helical magnetic field ref. (1).
The growth of ¦ËB is simply due to the loss of small scale power by dissipation.
On large scales, ¦Ë > ¦ËB the power spectrum is not affected. This is sometimes
called ¡¯passive growth¡¯. This is different for the compressible and the helical
cases. There, the power spectrum grows on scales ¦Ë > ¦ËB and decreases on
scales ¦Ë < ¦ËB which is what we call an inverse cascade.
Fig. 3: Cosmological magnetic fields in present time
from ref. (1).
After standard evolution in hot Universe final cosmological magnetic
fields are present in Fig.3 (see (1) and (2) for details).
References:
(1) R.Durrer, A.Neronov, A and A. Rv. 21 (2013) 62 .
(2) Banerjee R, Jedamzik K (2004) Phys Rev D 70,123003
dates of project April 1 , 2020 - March 31, 2023
Acknowledgments
Financial support of this Project was provided in part by
- ANR, France
- RSF, Russia
