Coronal scattering under strong regular refraction

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Coronal scattering under strong regular
refraction
Alexander Afanasiev Institute of
Solar-Terrestrial Physics Irkutsk, Russia
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• The problem of accounting for the combined
  influence exerted by the regular inhomogeneity of
  background corona and by random coronal
  inhomogeneities upon the propagation of radio
  emission has been studied insufficiently. It is
  quite clear, however, that in some cases regular
  refraction that leads to multipathing and
  focusing of radio waves, must influence the
  scattering process and promote new effects during
  the propagation of radio emission through a
  randomly-inhomogeneous corona.
• Questions
• Coronal sounding with spacecraft radio signals
  at small
• elongations
• Coronal sounding with a pulsar at small
  elongations
• Scattering of radio emission from a solar source
  in the
• presence of large-scale electron density
  inhomogeneities in
• the corona

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Coronal sounding with spacecraft radio signals
at small elongations
Schematic plot of ray trajectories in a regular
(i.e. without random inhomogeneities)
spherically-symmetric solar corona
When a spacecraft is at rather small angular
distance from the Sun, the observer on the Earth
may be in the illuminated zone, close to the
caustic or may get in the caustic shadow
zone.
spacecraft
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The interference integral method (proposed by
Yu. I. Orlov in 1972)
The scalar wave field U (for example, a component
of the electric vector) at any given point r is
represented as an integral over partial waves
(1)
a is a parameter that characterizes a partial
wave

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In the presence of electron density
inhomogeneities in the solar corona the integral
representation for the wave field can be written
in the form
(2)
In the shadow zone near the caustic boundary, the
following expression for the energy spectrum
R(?) can be obtained
shadow zone
is the parabolic cylinder function
d is the depth of entry into the shadow
zone
point of caustic
d
Sun
are the statistical
trajectory characteristics depending on
turbulent inhomogeneity parameters.
Earths orbit
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Some numerical modeling results
Energy spectra for different depths of entry into
the shadow zone (for ?3m)
Turbulent inhomogeneity parameters the density
perturbation sN1 the outer scale l0106
km the inner scale q0104 km the radial
velocity of inhomogeneities Vr300 km/s.
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Distortion of the energy spectrum with a change
of the velocity Vr of travel of coronal
inhomogeneities
Vr300 km/s (curve 1) Vr800 km/s (curve 2)
?3 m sN1 l0106 km q0104 km
Energy spectra for different outer scales l0 of
turbulent inhomogeneities
?3 m sN1 q0104 km Vr300 km/s
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Conclusion

• The form of the energy spectrum in the caustic
  shadow zone differs
• from a Gaussian and depends critically on the
  properties of the
• turbulent inhomogeneities. Therefore
  measurements of the radio
• energy spectrum in the neighborhood of the
  caustic can be used
• for the coronal plasma diagnostics.

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Coronal sounding with a pulsar at small
elongations
For investigating the properties of the
near-solar plasma, natural distant radio
sources when they are occulted by the corona, are
also used. In particular, pulsars that are
virtually point pulsed sources are applied for
this purpose. Coronal inhomogeneities cause the
temporal broadening of the pulses and distort
their shapes. Therefore the mean time profile of
the pulse is a useful characteristic that
contains information on coronal turbulent
inhomogeneities.
Qualitative ray picture of radio emission
propagation from a pulsar through the corona
Of interest is to calculate the mean pulse
profile in the neighborhood of the regular
caustic to analyse the possibilities for the
coronal turbulence diagnostics.
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If the radiated (initial) pulse from a pulsar is
specified by the Gaussian form, the following
expression for the mean pulse profile in the
neighborhood of the caustic boundary can be
obtained
d is the depth of entry into the shadow zone
Mean pulse profiles for different points of
observation in the caustic shadow zone
sN 1
sN 3
Turbulent inhomogeneity parameters the outer
scale l0106 km the inner scale q0103 km.
The initial pulse parameters the carrier
frequency f 111 MHz the initial pulse
half-width T 1.5?10-3 s.
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Using the asymptotic representation for the
parabolic cylinder function
one can obtain an expression for estimating the
variance of relative fluctuations in the
electron density
where J(d1) and J(d2) are the values of the
maxima of the mean pulse profile in the caustic
shadow zone at distances d1 and d2 from the
caustic point (sa2)? is a calculated statistical
trajectory characteristic. By measuring the
maxima J(d1) and J(d2) at the points d1 and d2,
and calculating (sa2)?, one can estimate the
value of the variance of coronal plasma electron
density fluctuations.
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Conclusion

• The variation of the pulsars pulse energy in
  the caustic shadow
• zone can be treated as an indicator for
  turbulent inhomogeneity
• intensity in the solar corona

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Scattering of radio emission from a solar source
in the presence of large-scale electron density
inhomogeneities in the corona
Of special interest is the combined influence of
scattering and strong regular refraction on
characteristics of radio emission from coronal
sources. It is known that around such sources
there can exist different large-scale regular
electron density structures (coronal arches,
streamers, and others). These structures may give
rise to regular caustics and multipathing of
radio emission.
The appearing refraction effects should be taken
into account in the analysis of the emission
structure of solar radio bursts and their
generation mechanisms.
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Part I. Solar millisecond spike bursts
Examples of spikes
Among the great variety of solar radio bursts,
millisecond spike bursts represent one of the
less understood solar phenomena. Spike bursts are
intense narrowband (?f / f lt 1) flashes of
subsecond duration, which accompany solar flares.
They are observed in different wavelength ranges
from centimetric to decametric.

• There are currently a number of models for the
• mechanism of radio spike generation.
  Nevertheless,
• the question regarding the origin of spikes
  remains
• to be conclusively answered. One difficulty is
  that it is not fully clear as to the
• particular influence exerted by an inhomogeneous
  propagation medium upon
• observed characteristics of radio spikes.

Consideration of the propagation effects usually
assumes that the solar corona is
spherically-symmetric in general, the influence
of regular refraction is negligible, and the
spike characteristics are determined by the
scattering and diffraction of the waves by
turbulent coronal inhomogeneities. On the other
hand, radio spikes can be generated by sources
located in high coronal arches. Not only the
scattering but also strong regular refraction of
radio emission in the arch structure can be
important in this case.
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A point radio source is located at the coronal
arch top and emits a d-pulse
Geometry of the problem
Ray pattern of the field (f 100 MHz)
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Mean profile of the pulse after its passing
through the corona for different values of the
density perturbation sN (numerical modeling
results)
sN 1
sN 0.2
Intensity
Intensity
Time, s
Time, s
sN 2
sN 4
Intensity
Time, s
Time, s
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Time profile at 408 MHz of the radio burst
observed with the Trieste Solar Radio System
(Trieste Astronomical Observatory) on 15 April
2000 by J. Magdalenic, B. Vrsnak, P. Zlobec, and
H. Aurass.
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Conclusions

• When the spike emission is propagating in the
  solar corona, strong
• regular refraction due to large-scale regular
  electron density
• structures such as coronal arches can lead to
  the formation of
• multipathing and regular caustics. These
  phenomena promote
• formation of a multi-component mean time
  profile of the radio spikes.
• To understand the causes of formation of the
  complex time
• profiles of spikes associated with the
  propagation effects, it is
• necessary to consider the data concerning the
  large-scale structure
• of the solar corona (CME, arches, etc). This
  would create the
• conditions for a more correct investigation of
  spike generation caused
• by physical processes occurring within the
  solar radio source.

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Part II. Type IIId solar decameter radio bursts
with echo-components
One important feature of type IIId radio
bursts (which was revealed by Abranin, Baselyan,
and Tsybko Astron. Rep. 1996, V. 40, 853 during
the solar observations with the UTR-2 radio
telescope) is that as the burst source approaches
the central solar meridian, a temporal splitting
of the bursts is developed and thus an additional
burst component is produced.
Examples of time profiles of type
IIId bursts f25 MHz
DB
additional component
Time profiles of some type IIId burst events
contain several additional components.
What is more, position observations showed that
the positions of visible sources of the initial
burst and its additional component usually do
not coincide and can be spaced by a distance
comparable to the Suns optical diameter.
To explain this observational evidence, Abranin,
Baselyan, and Tsybko suggested that the
additional components represent echoes of the
original burst in the corona, which are produced
due to strong regular refraction of radio
emission on large-scale structures lying at
heights of the middle corona.
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The observed radio burst echo-components with
long delays can be explained by the production
of additional radio emission propagation modes
within a transverse refraction waveguide
arising between the localized electron density
nonuniformity and deeper layers in the corona. As
these additional modes are reflected from the
streamers, they can reach the Earth.
Ray pattern illustrating formation of the
refraction waveguide in the corona (f 25 MHz)
direct signal
source
photosphere
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Mean time profiles for the radio pulse for
different values of intensity of the large-scale
localized nonuniformity forming the refraction
waveguide
f 25 MHz
direct signal
echo-components
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Conclusions
The results of the theoretical analysis and
numerical modeling, presented here reveal the
importance of the regular refraction phenomenon
in the solar corona. On the one hand, analysing
statistical characteristics of radio emission
from distant non-solar sources in
the neighborhood of the regular caustic is useful
for coronal turbulence diagnostics. On the other
hand, strong regular refraction due to
large-scale coronal structures can influence
substantially the emission from Suns own radio
sources.