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 10 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.