Energy storage and dissipation associated with solar flare models has been at the core of solar and space physics research for at least 4 decades. These have been referred to in the context of “paradigms” i.e. the so-called E-J and B-v paradigms
In the first plasma configuration, the general emphasis is on currents and current systems, namely the “field aligned” current density J ‖ and how it can configure an energy balance in solar flare descriptions. In particular it derives its name given how the electric field (E) and current density (J) are emphasized. In the second, the magnetic field intensity B in conjunction with velocity field v come to the fore.
Long story short, it has been found that the B-v paradigm best accommodates and explains the energy changes in a potential flare region, while application of the space physics-based E-J paradigm produces a number of unphysical results. I examine why this is so in this post.
To be sure, so long as the E-J approach was limited to terrestrial magnetospheric substorms, little controversy developed. However, this altered once the substorm E-J models began to be extrapolated to solar conditions, and especially solar flares. Perhaps the first such effort was carried out by S.-I. Akasofu (1979, Nature, V. 284, 1980, p. 248) who attributed all flares as arising from a “photospheric dynamo process”. According to this narrative, the solar flare is a result of a progression that begins with increasing currents channeled through the photosphere via the solar wind. This leads to increased ionization and conductivity, which in turn leads to joule heating and a flare.
In a subsequent paper (Kan et al, 1983) this conjecture was much further developed into a “dynamo region” that generates flares, and which features “neutral winds” and V-, S-potentials. A double layer process was also invoked. The core equation that may be said to govern detailed energy balance in such a dynamo may be written (ibid.):
-Ñ·S = - Ñ· (E x b/ m0 ) = E· J
While these (space physics) dynamo-based models commendably incorporated both energy generation and dissipation, they exhibited a number of defects. In general, all such models overtax the similarity between magnetic substorms and flares while ignoring key aspects concerning the magnetic aspects of flares, including the well-established relationship between important flares and magnetic complexity, fluid dynamics. One also beheld constructs such as “neutral wind”, and “V-, S- potentials” that had no relevance in solar conditions.
In
the dynamo model of Kan et al ( op. cit.),
the “neutral wind” acts perpendicularly to the field –aligned ( J ‖ ) and cross-field (J ⊥ ) current (see Fig. 1 of Kan et al, 1983).
The wind is described in their paper as a “shear flow” (p. 154) However, there is no evidence of a “neutral shear flow”
in the region of the solar chromosphere or photosphere. Thus, it is an entirely
fabricated construct that bears no similarity to real solar conditions. More
accurately, in the regions wherein real magnetic loops reside, the physical
features of sunspots and their concentrated flux dominate. Thus, instead of
some vague “neutral wind’ one will expect for example, a convective downdraft
which helps to contain the individual flux tubes of a sunspot in one place
(e.g. Parker, 1979)[1].
An associated problem is the electron number density range proposed (107- 108 cm-3) is far too low for the solar corona. The better estimated range as given in the Table for Approximate Parameters of Astrophysical Plasmas (Zombeck) is 10 8-10 12 cm-3, with the latter applicable to the flare domain. This is important because the lower range will naturally underestimate the current density at the photosphere boundary (equation 11, Kan et al, and equation 25).
As for the “potentials” invoked by Kan et al (1983, e.g. see their Fig. 6), their V-potentials (or V-shaped potential structures or inverted- V events), actually refer to discrete auroral arcs in the ionosphere, at energies of several keV or more, obtained by space-based observations. However, the role of these sub storm artifacts is entirely vague in the context of the solar situation and moreover unobserved. Up to now no solar team or researcher has unambiguously identified a specific solar structure or process that might be tied to these. They are rather uniquely auroral structures because the energy vs. time plots (of particle fluxes associated with auroras made by space borne detectors) roughly mimic the shape of an inverted V. No similar solar flare energy vs. time plots do this.
The problem is that there is absolutely no observational analog of these structures on the Sun, and certainly not in solar flare regions. In other words, their use represents an artificiality or contrivance. This also applies to the “S-potentials”.
An implication of the E-J paradigm models is that adequate power for flares can be provided once sufficiently large field-aligned potential drops can occur (as in double layers) arising from sufficiently large longitudinal (J‖) current densities. (cf. Kan et al, 1983). Unfortunately, there seems to be no way to track these changes in the pre-flare phase, at least for specific active regions and sunspots. There is also, evidently, no physical significance to any “mean” longitudinal current density (Parker, 1996a)
Meanwhile, the unloading force-free field energy system, for the B- v paradigm, has become the centerpiece template for use in most solar physics applications. According to this view, convective fluid motions with characteristic velocity v warp and deform the magnetic field B, leading directly to:
Ñ X (B) = m 0 J
Ñ X B =
aB
and ( B·Ñ) a = 0
with a a scale factor (= (m0 J)/
B). For a potential (current-free) field a = 0 so
that Ñ X B = 0.. The use of methods to obtain magnetic
free energy are based upon the concept of magnetic energy accumulation arising
from shearing motions at the photosphere such that (e.g. Tanaka and Nakagawa,
1973):
¶ /¶t òv B 2
/
2m dx dy dz =
- òv |J | 2 / s dx dy dz
+ 1/ m
òv
[(v x B) x B]·dS
Here, the left hand side denotes the rate of magnetic free energy accumulation per unit volume while the right hand side denotes losses from joule heat dissipation and the change in magnetic energy arising from hydrodynamic motions (v) on a boundary surface (S) with magnetic induction B.
In my own flare modeling, and specifically with respect to predicting (with at least 50 % accuracy) a number of geo-effective flares over the Solar maximum year of 1980, I have found this ansatz particularly useful and with it the B- v paradigm.
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