Judgment of paradigms for magnetic reconnection in coronal loops Allen H Boozer Columbia University New York NY 10027

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Judgment of paradigms for magnetic reconnection in coronal loops

Allen H Boozer

Columbia University, New York, NY 10027

ahb17@columbia.edu

(Dated: October 6, 2022)

The traditional paradigm for magnetic ﬁeld lines changing connections ignores magnetic ﬁeld line

chaos and requires an extremely large current density, jmax ∝Rm, ﬂowing in thin sheets of thickness

1/Rm, where Rmis the magnetic Reynolds number. The time required for a general natural evolution

to take a smooth magnetic ﬁeld into such a state is rarely considered. Natural evolutions generally

cause magnetic ﬁeld lines to become chaotic. A fast change in ﬁeld line connections then arises on

the timescale deﬁned by the evolution multiplied by a ln(Rm) factor, and the required maximum

current density scales as ln(Rm). Even when simulations support the new paradigm based on chaos,

they have been interpreted as supporting the old. How this could happen is an important example

for plasma physics of Kuhn’s statements about the acceptance of paradigm change and on Popper’s

views on the judgment of truth in science.

In 1962, Thomas Kuhn wrote [1] what the En-

cyclopaedia Britannica described as one of the most

inﬂuential works of history and philosophy written in

the 20th century [2]. He discussed the importance of

paradigms in science and how diﬃcult it is for a sci-

entiﬁc community to accept a change in paradigm.

The physics of changes in the connections of mag-

netic ﬁeld lines illustrates Kuhn’s point in a problem

of great importance in both natural and laboratory

plasmas.

The traditional paradigm for changes in ﬁeld line

connections was clearly stated by Schindler, Hesse,

and Birn in their paper on general magnetic recon-

nection [3]. To obtain changes in ﬁeld line connec-

tions at a rate consistent with plasmas with large

magnetic Reynolds numbers, Rm∼108to 1020 , an

intense current density, jmax ∝Rmmust arise in

sheets of thickness ∝1/Rm. Hundreds of papers

have been written on ways such an extreme current

density can be maintained if it were initially present,

but the way an arbitrary magnetic ﬁeld could evolve

into such a state is rarely considered.

Papers by a number authors emphasize that

chaotic magnetic-ﬁeld-line trajectories fundamen-

tally change the paradigm of magnetic reconnection

from that of Schindler et al. Chaos enters the the-

ory of turbulent magnetic reconnection, and this

topic was reviewed [4] by Lazarian, Eyink, Jafari,

Kowal, Li, Xu, and Vishniac in 2020. Eric Priest

has been associated with a large body of work on

three-dimensional structures that tend to concen-

trate currents and thereby lead to enhanced recon-

nection [5]. In particular, he is known for his work

on quasi-separatrix layers, which are essentially re-

gions of ﬁeld line chaos. Reid, Parnell, Hood, and

Browning [6], have simulated a case in which the

footpoint motions of magnetic ﬁeld lines do not di-

rectly make the lines chaotic but drive large-scale

instabilities that do.

FIG. 1: A perfectly conducting cylinder of height Land

radius aencloses an ideal pressureless plasma. All of

the sides of the cylinder are ﬁxed except the top, which

ﬂows with a speciﬁed velocity ~vt. Initially, ~

B=B0ˆz.

Each point ~xbon the bottom of the cylinder deﬁnes a

line of ~

Bthat in an ideal evolution intercepts a speciﬁc

point on the top ~xtwith ∂~xt(~x0, t)/∂t =~vt(~xt, t) and

~x0≡~xtat t= 0. The case of primary interest is when

~vtis divergence free and chaotic. This means the 2 ×2

Jacobian matrix ∂~xt/∂~x0has a large singular value that

increases exponentially in time and a small singular value

that is the inverse of the large singular value.

Allen Boozer has published a number of articles

on the fundamental importance of chaos to magnetic

reconnection and that show that the magnetic ﬁelds

must have a non-trivial dependence on all three spa-

tial dimensions for chaos to be important. Two re-

cent articles are [7, 8]. He and Todd Elder also pub-

lished [9] a simple example, Figure 1, of corona-like

footpoint motions directly driving magnetic ﬁeld line

arXiv:2210.02209v1 [physics.plasm-ph] 14 Sep 2022

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JudgmentofparadigmsformagneticreconnectionincoronalloopsAllenHBoozerColumbiaUniversity,NewYork,NY10027ahb17@columbia.edu(Dated:October6,2022)Thetraditionalparadigmformagneticeldlineschangingconnectionsignoresmagneticeldlinechaosandrequiresanextremelylargecurrentdensity,jmax/Rm,owinginthinsheetsoft...

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Judgment of paradigms for magnetic reconnection in coronal loops Allen H Boozer Columbia University New York NY 10027

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