Tearing instability and current-sheet disruption in the turbulent dynamo. (arXiv:2201.07757v2 [astro-ph.HE] UPDATED)
<a href="http://arxiv.org/find/astro-ph/1/au:+Galishnikova_A/0/1/0/all/0/1">Alisa K. Galishnikova</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Kunz_M/0/1/0/all/0/1">Matthew W. Kunz</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Schekochihin_A/0/1/0/all/0/1">Alexander A. Schekochihin</a>
Turbulence in a conducting plasma can amplify seed magnetic fields in what is
known as the turbulent, or small-scale, dynamo. The associated growth rate and
emergent magnetic-field geometry depend sensitively on the material properties
of the plasma, in particular on the Reynolds number ${rm Re}$, the magnetic
Reynolds number ${rm Rm}$, and their ratio ${rm Pm}equiv{rm Rm}/{rm Re}$.
For ${rm Pm} > 1$, the amplified magnetic field is gradually arranged into a
folded structure, with direction reversals at the resistive scale and field
lines curved at the larger scale of the flow. As the mean magnetic energy grows
to come into approximate equipartition with the fluid motions, this folded
structure is thought to persist. Using analytical theory and high-resolution
MHD simulations with the Athena++ code, we show that these magnetic folds
become unstable to tearing during the nonlinear stage of the dynamo for ${rm
Rm}gtrsim 10^4$ and ${rm Re}gtrsim 10^3$. An ${rm Rm}$- and ${rm
Pm}$-dependent tearing scale, at and below which folds are disrupted, is
predicted theoretically and found to match well the characteristic
field-reversal scale measured in the simulations. The disruption of folds by
tearing increases the ratio of viscous-to-resistive dissipation. In the
saturated state, the magnetic-energy spectrum exhibits a sub-tearing-scale
steepening to a slope consistent with that predicted for tearing-mediated
Alfv’enic turbulence. Its spectral peak appears to be independent of the
resistive scale and comparable to the driving scale of the flow, while the
magnetic energy resides in a broad range of scales extending down to the
field-reversal scale set by tearing. Emergence of a degree of large-scale
magnetic coherence in the saturated state of the turbulent dynamo may be
consistent with observations of magnetic-field fluctuations in galaxy clusters
and recent laboratory experiments.
Turbulence in a conducting plasma can amplify seed magnetic fields in what is
known as the turbulent, or small-scale, dynamo. The associated growth rate and
emergent magnetic-field geometry depend sensitively on the material properties
of the plasma, in particular on the Reynolds number ${rm Re}$, the magnetic
Reynolds number ${rm Rm}$, and their ratio ${rm Pm}equiv{rm Rm}/{rm Re}$.
For ${rm Pm} > 1$, the amplified magnetic field is gradually arranged into a
folded structure, with direction reversals at the resistive scale and field
lines curved at the larger scale of the flow. As the mean magnetic energy grows
to come into approximate equipartition with the fluid motions, this folded
structure is thought to persist. Using analytical theory and high-resolution
MHD simulations with the Athena++ code, we show that these magnetic folds
become unstable to tearing during the nonlinear stage of the dynamo for ${rm
Rm}gtrsim 10^4$ and ${rm Re}gtrsim 10^3$. An ${rm Rm}$- and ${rm
Pm}$-dependent tearing scale, at and below which folds are disrupted, is
predicted theoretically and found to match well the characteristic
field-reversal scale measured in the simulations. The disruption of folds by
tearing increases the ratio of viscous-to-resistive dissipation. In the
saturated state, the magnetic-energy spectrum exhibits a sub-tearing-scale
steepening to a slope consistent with that predicted for tearing-mediated
Alfv’enic turbulence. Its spectral peak appears to be independent of the
resistive scale and comparable to the driving scale of the flow, while the
magnetic energy resides in a broad range of scales extending down to the
field-reversal scale set by tearing. Emergence of a degree of large-scale
magnetic coherence in the saturated state of the turbulent dynamo may be
consistent with observations of magnetic-field fluctuations in galaxy clusters
and recent laboratory experiments.
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