Plain language summary
The high temperature of the corona by heat energy from the photosphere
seems to be difficult. Thus, the ionization process by energetic
electrons is proposed. A dynamo process in the photosphere produces
field-aligned currents along magnetic loops in the corona, in which a
double layer (an electric field) along magnetic field lines might form.
The resulting ionization rate is semi-quantitatively estimated.
Keywords: solar corona. coronal temperature. double layer
ionosphere
e-mail address:
sakasofu@alaska.edu
Introduction
After the high temperature, 2x106 K, of the solar
corona was discovered in the 1940s in terms of emissions from highly
ionized FeXII atoms (ionization potential, 250 eV)
others, there have been a very large number of attempts to explain the
coronal high temperature in the past (cf. Van de Hulst, 1953; Zirn,
1988).
However, in one of the most recent reviews examining various past
efforts, Van Doorsselaere at al. (2020) summarized the
difficulties of heating the corona by MHD waves.
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In the past, it had been considered that highly ionized ions must
be caused by the ionization of the corona by energetic
electrons (Stix, 2002), but the responsible process of the acceleration
of electrons in the coronal environment have not been known.
In this paper, we suggest a field-aligned current system along
coronal magnetic loops, which is driven by a photospheric
dynamo process for the field-aligned currents; field-aligned currents
are essential in developing a double layer, which can accelerate both
electrons and ions.
Acceleration of electrons of auroral electrons
The coronal situation is somewhat similar to the ionospheric one. The
auroral green line oxygen atoms (their excitation potential 4 ev, the
corresponding temperature being 4.5 x 104° K) is
caused by the excitation of oxygen atoms by secondary
electrons, which are produced by the ionization of energetic
current-carrying electrons in the field-aligned currents. They
are accelerated by the double layer in the magnetosphere-
Ionosphere coupling circuit.
However, the ambient temperature of the ionosphere is known
to be at most 2000K, not 4.5 x 104 K. This ambient
high
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temperature is caused by the additional ionization by solar X-rays in
daylight hours.
In auroral processes, the presence of the electric field of the double
layer, consisted of a U-shaped potential, along magnetic field lines was
suggested by Alfven (cf.1981, 1986) on the ground that current-carrying
electrons cannot cause the aurora
without being accelerated (from 100-300 ev in the magnetosphere to more
than 10 KeV to penetrate into the
ionosphere) and that the magnetospheric current
system has to close (current continuity) by connecting to the
ionospheric currents.
In auroral research, the presence of a U-shaped potential structure in
field-aligned currents is observationally well confirmed by many
satellite observations. In the earth’s auroral conditions, various
observed values related to the
double layer are summarized by (Karlsson, 2012): Field-aligned potential
drops of the order of 6 KV or more, field-aligned currents of
10-1-101 µA/cm2,
and the acceleration of magnetospheric electrons from 300 eV to 10 KeV
and more, an
estimated thickness of the double layer 10 KV per 1 km, located between
0.5-2.0 Re above the ionosphere (Re = the earth’s radius).
The equation for the ionization rate by a beam of energetic electrons in
the ionosphere is given by (cf. Rees 1989):
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q (cm3s) = F E ρd/ (RE2x30 ev ).
A typical set of observed values for the ionosphere by assuming that the
field-aligned current intensity of 1µA and the double
layer of 10 KV potential drop:
The ionization rate q at the height of 110 km is:
F = electron flux (108/cm2s),
E = electron energy (10 Kev),
ρ = mass density (1.6 x 10-12 g =
1012/cm3 x 1.6 x
10-24g),
d= depth/distance (107 cm),
RE2= effective range (5.34 x 102g/cm2),
q= 1.9 x106/cm3s,
where the number density is taken to be
1011/cm3.
This value of q is well within the accepted values Rees, 1989).
Coronal ionization by energetic electrons
In the past, a double layer has been considered for solar flares
and its effect on coronal processes (Li et al., 2013, 2014).
However, no estimate of the ionization rate by a double layer
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has been made for a given current intensity and its potential drop.
Here, we consider a loop of magnetic field lines in the corona as the
circuit.
The ionization rate of the middle level of the corona by field-
aligned currents of 0.001 A (103 µA), supposing that
the
double layer provides a potential drop of 1KV:
F = 6.2 x 1011/cm2s-1,
E = 1 Kev,
ρ = 1.6 x 10-13g (=
1011/cm3 x 1.6
x10-24 g),
d = 109cm (assuming about 102collisions/s),
RE2 = 5.6 g/cm2,
q = 6.3 x 108/cm3s,
where the number density is taken to be
1011/cm3 at the height of 2 x
103 km (Aschwanden (2005, his figure 1.19).
Field-aligned currents produced by a dynamo process
The currents must be generated by a photospheric dynamo process. An
example of the dynamo-induces field-aligned currents under a magnetic
arcade is shown in Figure 1. The
dynamo process is considered here with a set of B = 12 G and the
speed of 2 km/s along the neutral line under a typical
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magnetic arcade (Choe and Lee, 1996)); the intensity of
the field-aligned currents 0.5 x
10-4A/m2 (5 x 10
µA/m2) in
this case.