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## 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

The problemof 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 beenstudiedinsufficiently. Itisquiteclear, however, thatinsomecasesregularrefractionthatleadstomultipathingandfocusingofradiowaves, mustinfluencethescatteringprocessandpromoteneweffectsduringthepropagationofradioemissionthrough a randomly-inhomogeneouscorona.

Questions

- Coronalsoundingwithspacecraftradio signals at small

elongations

- Coronalsounding with a pulsar at small elongations
- Scatteringofradioemissionfrom a solarsourceinthe

presenceoflarge-scaleelectrondensity inhomogeneities in

thecorona

Coronal sounding withspacecraft 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

isthecompleteintegraloftheeikonalequation:

whereisdielectricpermittivityofplasma, and

isthesolutionofthetransportequation:

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)

aisaparameterthatcharacterizesapartialwave

is the eikonal in the absence of statistical inhomogeneities;

is an addition introduced into the eikonal by the inhomogeneities;

Inthepresenceofelectrondensityinhomogeneitiesinthesolarcorona

theintegralrepresentationforthewavefieldcanbewrittenintheform:

(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 isthedepthofentryintotheshadow

zone;

point of

caustic

d

Sun

are the statistical

trajectory characteristicsdependingon

turbulentinhomogeneityparameters.

Earth’sorbit

Some numerical modeling results

Energy spectra for different depths of entry into the shadow zone

(for λ=3m)

Turbulent inhomogeneity parameters:

the density perturbation σN=1%;

the outer scale l0=106 km;

the inner scale q0=104 km;

the radial velocity of inhomogeneities

Vr=300 km/s.

l0=5 105km (curve 2)

l0=105km (curve 3)

Distortion of

the energy spectrum

with a change of the

velocity Vr of travel of

coronal inhomogeneities

Vr=300 km/s (curve 1)

Vr=800 km/s (curve 2)

λ=3 m

σN=1%;

l0=106 km;

q0=104 km;

Energy spectra for

different outer scales l0

of turbulent

inhomogeneities

λ=3 m

σN=1%;

q0=104 km;

Vr=300 km/s

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.

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

Ofinterest is to calculate the mean pulse profile in

the neighborhood of the regular caustic to analyse

the possibilities for the coronal turbulence diagnostics.

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

σN = 1%

σN = 3%

Turbulent inhomogeneity parameters:

the outer scale l0=106 km;

the inner scale q0=103 km.

The initial pulse parameters:

the carrier frequency f = 111 MHz;

the initial pulse half-width T = 1.510-3 s.

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)andJ(d2)are the values of the maxima of the mean pulse

profile in the caustic shadow zone at distances d1andd2 from

the caustic point;

(σa2) is a calculatedstatistical trajectory characteristic.

By measuring the maxima J(d1) andJ(d2) at the points d1andd2, and

calculating (σa2), one can estimate the value of the variance of

coronal plasma electron density fluctuations.

Conclusion

- The variation of the pulsar’s pulse energy in the caustic shadow
- zone can be treated as an indicator for turbulent inhomogeneity
- intensity in the solar corona

Scatteringofradioemissionfromasolarsourceinthepresenceoflarge-scaleelectrondensityinhomogeneitiesinthecoronaScatteringofradioemissionfromasolarsourceinthepresenceoflarge-scaleelectrondensityinhomogeneitiesinthecorona

Ofspecialinterestisthecombinedinfluenceofscatteringandstrongregularrefractiononcharacteristicsofradioemissionfromcoronalsources. Itisknownthataroundsuchsourcestherecanexistdifferentlarge-scaleregularelectrondensitystructures (coronalarches, streamers, andothers). Thesestructuresmaygiverisetoregularcausticsandmultipathingofradioemission.

Theappearingrefractioneffectsshouldbetakenintoaccountin

theanalysisoftheemissionstructureofsolarradioburstsand

theirgenerationmechanisms.

PartI.Solarmillisecondspikebursts

Examples of spikes

Amongthegreatvarietyofsolarradiobursts,millisecondspikeburstsrepresentoneofthelessunderstoodsolarphenomena.Spike burstsareintensenarrowband

(Δf / f < 1%) flashesofsubsecondduration,whichaccompanysolarflares. Theyareobservedindifferentwavelengthrangesfromcentimetrictodecametric.

Therearecurrentlyanumberofmodelsforthe

mechanismofradiospikegeneration.Nevertheless,

thequestionregardingtheoriginofspikesremains

tobeconclusivelyanswered.Onedifficultyisthatitisnotfullyclearastothe

particularinfluenceexertedbyaninhomogeneouspropagationmediumupon

observedcharacteristicsofradiospikes.

Considerationofthepropagationeffectsusuallyassumesthatthesolarcorona

isspherically-symmetricingeneral,theinfluenceofregularrefractionis

negligible,andthespikecharacteristicsaredeterminedbythescatteringand

diffractionofthewavesbyturbulentcoronalinhomogeneities.

Ontheotherhand, radiospikescanbegeneratedbysourceslocatedinhigh

coronalarches.Notonlythescatteringbutalsostrongregularrefractionofradio

emissioninthearchstructurecanbeimportantinthiscase.

A point radio source is located at the

coronal arch top and emits a δ-pulse

Geometry ofthe problem

Ray pattern of the field (f = 100 MHz)

Mean profile of the pulse after its passing through the corona

for different values of the density perturbation σN

(numerical modeling results)

σN = 1%

σN = 0.2%

Intensity

Intensity

Time, s

Time, s

σN = 2%

σN = 4%

Intensity

Time, s

Time, s

Time (UT)

The analysis of the event has shown that it is associated with

a coronal mass ejection which could be responsible for the

complex temporal structure of the pulses.

Time profile at 408 MHz of the radio burst observedwith the Trieste

Solar Radio System (Trieste Astronomical Observatory) on 15 April 2000 by J. Magdalenic, B. Vrsnak, P. Zlobec, and H. Aurass.

- 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.

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

f=25 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 Sun’s 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.

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

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

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 Sun’s own radio sources.

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