Example of exponentially enhanced magnetic reconnection driven by a spatially-bounded and laminar ideal flow. (arXiv:2011.11822v4 [physics.plasm-ph] UPDATED)

Example of exponentially enhanced magnetic reconnection driven by a spatially-bounded and laminar ideal flow. (arXiv:2011.11822v4 [physics.plasm-ph] UPDATED)
<a href="http://arxiv.org/find/physics/1/au:+Boozer_A/0/1/0/all/0/1">Allen H Boozer</a>, <a href="http://arxiv.org/find/physics/1/au:+Elder_T/0/1/0/all/0/1">Todd Elder</a>

In laboratory and natural plasmas of practical interest, the spatial scale
$Delta_d$ at which magnetic field lines lose distinguishability differs
enormously from the scale $a$ of magnetic reconnection across the field lines.
In the solar corona, plasma resistivity gives $a/Delta_dsim10^{12}$, which is
the magnetic Reynold number $R_m$. The traditional resolution of the paradox of
disparate scales is for the current density $j$ associated with the
reconnecting field $B_{rec}$ to be concentrated by a factor of $R_m$ by the
ideal evolution, so $ jsim B_{rec}/mu_0Delta_d$. A second resolution is for
the ideal evolution to increase the ratio of the maximum to minimum separation
between pairs of arbitrarily chosen magnetic field lines,
$Delta_{max}/Delta_{min}$, when calculated at various points in time.
Reconnection becomes inevitable where $Delta_{max}/Delta_{min}sim R_m$. A
simple model of the solar corona will be used for a numerical illustration that
the natural rate of increase in time is linear for the current density but
exponential for $Delta_{max}/Delta_{min}$. Reconnection occurs on a time
scale and with a current density enhanced by only $ln(a/Delta_d)$ from the
ideal evolution time and from the current density $B_{rec}/mu_0a$. In both
resolutions, once a sufficiently wide region, $Delta_r$, has undergone
reconnection, the magnetic field loses static force balance and evolves on an
Alfv’enic time scale. The Alfv’enic evolution is intrinsically ideal but
expands the region in which $Delta_{max}/Delta_{min}$ is large.

In laboratory and natural plasmas of practical interest, the spatial scale
$Delta_d$ at which magnetic field lines lose distinguishability differs
enormously from the scale $a$ of magnetic reconnection across the field lines.
In the solar corona, plasma resistivity gives $a/Delta_dsim10^{12}$, which is
the magnetic Reynold number $R_m$. The traditional resolution of the paradox of
disparate scales is for the current density $j$ associated with the
reconnecting field $B_{rec}$ to be concentrated by a factor of $R_m$ by the
ideal evolution, so $ jsim B_{rec}/mu_0Delta_d$. A second resolution is for
the ideal evolution to increase the ratio of the maximum to minimum separation
between pairs of arbitrarily chosen magnetic field lines,
$Delta_{max}/Delta_{min}$, when calculated at various points in time.
Reconnection becomes inevitable where $Delta_{max}/Delta_{min}sim R_m$. A
simple model of the solar corona will be used for a numerical illustration that
the natural rate of increase in time is linear for the current density but
exponential for $Delta_{max}/Delta_{min}$. Reconnection occurs on a time
scale and with a current density enhanced by only $ln(a/Delta_d)$ from the
ideal evolution time and from the current density $B_{rec}/mu_0a$. In both
resolutions, once a sufficiently wide region, $Delta_r$, has undergone
reconnection, the magnetic field loses static force balance and evolves on an
Alfv’enic time scale. The Alfv’enic evolution is intrinsically ideal but
expands the region in which $Delta_{max}/Delta_{min}$ is large.

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