電離層無線電課件目錄?1.1EM-wave

Force

on

a

charged

particle

in

free

space?1.2EM-wave

in

the

low-pressure

ionized

gas?1.3Plane

wave

in

ionized

gas

in

presence

of

externalmagneticfield?1.4The

Appleton(Appleton-Hartree;

Appleton-Lassen)

Formula?1.5

Some

properties

of

Appleton

formula?1.6True

height

analysis?1.7Doppler

frequency

shift?1.8Bragg’s

scattering?

1.9?

電波與介質(zhì)?

高頻:類全反射?

特高頻:布拉格散射?

超高頻:湯姆森散射1.1Force

on

a

charged

particle

in

free

space(vacuum)EM

wave

Electric

force:fE

=qE

Magnetic

force:fM

=qv

×BIncomparingtotheEarth’smagneticfieldBG,

theEMwaveBfieldisnegligible.When

interactingwithBG,

EMwaveswillsplitintoO-wave

andX-wave.Whentravelingintheionosphere,EMwave’sE-fieldscaneasilycouplewithelectrons.Duetothecollisionbetweenelectronsandneutralparticles,thecoupledelectronswilllossenergyandinturnresultintheabsorptionof

theEMwaves.q:chargeof

achargedparticlem:mass

ofa

charged

particleV:chargedparticlemotionBG:thegeomagneticfieldBandE:themagneticandelectricfieldsof

theEMwaveInfree

spacei.e.vacuum

Vp:phasevelocityVg:groupvelocityLetEMwavespropagateinthexdirectionk

=

kB

=

BE

=

EThechargedparticlemotion

(v

is

the

velocity

of

charged

particles.

x,

y,z

are

the

positions

ofparticles)FromLorentzforce,

^Y^x:

:

→

:

y^x^Let

E

=

E0

cos

wt:

→

=sin

wt:

x

y

Thus,invacuum,achargedparticlemotionisalmostdue

to

theelectricfield

LetE

=

E0eiwt

andlinearize

^y(thevelocityV

lagstheelectricfieldE

by

90。)微分令周期函數(shù)領(lǐng)先90。

.反之積分會落后90。?！?/p>

1.2EM-waveinthelow-pressureionizedgas(NoexternalBG

field)1.2.1collisionless(v=0)Lowpressure→collisionfrequencyv=0Ionizedgas→n+

(positiveions),n-

(negativeions),ne

(electrons)n+=n-+ne

=

σ

nα

qαVα

(summationof

αthspecies)Ve

?V+,

V-

(“momentum

conservation)

◎

→

(kiswavenumber)◎

→

Forelectron,(a)

w>wp

(i)collision=0

(invacuum)Vg

×

VP

=

C

2

(ii)inmedium

(b)w

<

wpVgand

VP

areimaginarynumber

(c)w

=

wpk=0Vp→∞

,Thewaveisreflected?

Plasma

frequencyAssume:(1)

Nomagnetic

field(2)No

thermal

motions

(i.e.

kT=0,

cold

plasma)(3)

Theionsarefixed

in

space

in

auniform

density(4)

Theplasmaisinfinite

in

extent(5)The

electron

motions

occur

only

in

the

x-direction

→

→

→

◎

FromMaxwell’s

equation,▽

→ε0

v

▽.E

dv=v

pdv

(v:volume)

→ε0

E

.d=

v

pdv→ε0EA

=neqexAA→◎Plasma

frequency

fp

∝n

→fp

?

8.98n,where

n

is

in

mks

unit.i.e.#/m3.++++++++++++++++++++E

x

θ2θ

1Vertical:Z

=

tVg

dt

trueheight

virtualheight

Oblique:S

=

tVg

dttruepath

phase

path?

1.2.2collisional

condition(v

≠

0)→inthelowerionosphere(not

lowpressure)

Inthecollisionalcase,aparticledoesnotmakeacycle

aboutthemagneticfieldbeforeacollisiontakesplace

[Kelly,2009]

From

Ampere-Maxwellequation,

(H

=

B?μ

0

;

D

=

Let

ik

=

α

+

iβ

Power;

damping

as

x↑

Phase

1.3Plane

wave

in

ionized

gas

in

presence

of

externalmagnetic

field

(B0)Radiowavesareelectromagneticwaves,andtheirpropagationinamediummustsatisfy

two

sets

of

conditions:(i)

Maxwell’sequations(ii)The

response

of

the

medium

to

the

wave

fieldsTheconstituti-

-verelationsD=εE=ε0E+

PB=

μ0Hε:the

dielectric

permittivity

of

the

mediumε0:thepermittivityof

freespace,8.85x

10-12

Fm-1μ0:

magneticpermittivityof

vacuum,4π

x

10-7

Hm-1▽.

εE=P

P:

totalcharge

▽.

B

=

0

→▽

Setthedirectionof

propagationinthex-directionLinear

equations

in(w,

k)

domain:

Let

P

=0▽.

D=0→Dx

=ε0Ex

+

PX

=0▽.

H

=0→

Hx

=0

—ikHy

+ikHz

=iwDx

+iwDy

+iwDz

→

▽×

E

=—iwμ0H

→

If

R

is

real→

linear

polarizedIf

Riscomplex→

ellipsespolarized^Y^X^YAssumptions:1.

Waveproperties(i)

Smallwaveamplitude(ii)Steady-state

solution(iii)Planewaves2.Propertiesof

themedium(i)Electricalneutral(ii)Noresultantspacecharges(iii)UniformexternalmagneticfieldTheMagnetoionictheory?

1.4The

AppletonformulaThe

Appleton(Appleton-Hartree;

Appleton-Lassen)formula(iv)Electron

collisions

independent

of

electron

energy(v)

Coldplasma(vi)Magnetic

properties

of

free

spaceX

(upward)B0

:geomagneticfiledk:a

plane

EM

waveY

(northward)InthemagneticfiledB,theforceonamoving

electronwhichhas

avelocitycanbeexpressedas

Lorentzforce→The

equation

of

motion

of

an

electron

is

given

by

Forrectangularcoordinatesystemmx…

=

eEx

—

ez.BT

—mνx.my…

=

eEy

+

ez.BL

—

mνy.mz…=

eEz

+

ex.BT

—

ey.BL

—

mνz.(i)MultiplebyNe

∵P=Neγ(ii)

→

→

—ω2Ne2Ex

=

—mω2Px

+iωeBTPz

+

iωmνPxNe2Ey

=

—mω2Py

—

iωeBLPz

+

iωmνPyNe2Ez

=

—mω2Pz

—

iωeBTPx

+

iωeBLPy

+iωmνPZ

--------------

(1)

ε0ΧEx

=

—px

1

—

iz+

ipzYT

-----------------------------

(1a)

→ε0ΧEy

=

—pY

1

—

iz

—

ipzYL

-----------------------------

(1b)

ε0ΧEz

=

—pz

1

—

iz

—

ipxYT

+

ipyYL

----------------

(1c)

YL

=

Y

cosθ

YT

=

Y

sinθT:transversecomponentL:longitudinalcomponent

Y

=

devidedbymω2WHsubstitute

ε0Ex

+Px

=

0into(1a)ε0ΧEx

=

—Px

1

—

iz+

iPzyT

(1a）→

—Px

1

—

X

—

iz=

iPzyT

---------------------------------------(2)substitute(2)into(1c)

ε0ΧEz

=

—Pz

1

—

iz

—

iPxyT

+

iPyyL

(1c)→ε0Χ

=

—

1

—

iz

—

-

+

iyL

------------------------(3)

Rearrange

→

ε0ΧEy

=—Py

1

—

iz

—

iPzyL

(1b)→

∵Eq.(3a)=Eq.(4a)

PP

Let

U

=

1

—

iz→

n2

=

1

—

Appleton-Hartree

formula

from

{

—

y

0HDzμwiw=

izHikE—ikn2

=

(μ

—

iχ)2(i)

Thecollisionsarenegligible(intheF2

region)Z=0→

U=1n2

=

1

一

2(1-X)-YT2

±YT4

+4YL2

(1-X)2

2(ii)Themagneticfieldisnegligible(i.e.Y<<1)Veryhighaltitude?

Whenν2

>>

ω2

(iii)

Bothcollisionsandthemagneticfieldeffectsarenegligibleμ2

=

1

一

X

=

1

一

一

N:electrondensityf:radiowavefrequency

1.5Somepropertiesof

AppletonformulaIn

the

ionosphere

0

≤

μ

≤

1(i)For

a

fixed

sounding

frequency

f

(radio

wave

frequency)f

=constant=>N

↑→

μ

↓(ii)For

a

fixed

plasma

frequency

fNfN

=constant=>

f

↑→

μ

↑Reflectioncondition(i)Be

=

0Asthewavepenetratesintothelayertheelectrondensityincreasesandthewavenormalchangesaccordingto

Snell’slaw:μsinφ=

μ0sinφ0

μ0

andφ0

arethecorrespondingvaluesatthebaselayer→

μ0

=

1(1)at

reflection,φ=90→

μr

=

sinφ0(2)if

φ0=0→

μr=0→f

=fN。(ii)Be

≠

0(Reflectionconditionforverticalpropagation)

μ

=

01→

2X1

—X=

2(1

—X)

—

YT2

±YT4

+4YL2

(1

—X)22‘+

,

sign1→YT2

—

2(1

—X)2

=YT4

+

4YL2

(1

—X)

2→

X=1→

W

=

WN

Ordinary

wave(o-wave)‘—

,sign1→

YT2

—

2(1

—X)2

=

—YT4

+4YL2

1

—X2

2→

YT4

—

4YT

1

—X2

+41

—X4

=

YT4

+4YL2

1

—X2

→

4

1

—

X

4

=

4Y2

1

—

X

2→

1

—

X

2

=

Y2

Extraordinary

wave(x-wave)(1)Y

<

1

→X

=

1

±YX

=

1

—

Y

(x-wave)X

=

1

+Y

(z-wave)(2)Y

>

1

→X

=

1

+Y電磁波的頻譜3536折射指數(shù)

(refractiveindex)

37折射指數(shù)

(refractive

index)38394042/vr2ls/knowings/radiowave/radiowave.html43Time(Period

=T)tt+Tt+2T44/vr2ls/knowings/radiowave/radiowave.html4546Planewave等相位處

是個平面474816505152--

》無解53如何設(shè)計電離層探測

儀器？回波會長怎樣？refractive

index先考慮由地表垂直往上

發(fā)射頻率為

f

的電磁波忽略地球磁場時：隨著高度改變54由地表垂直往上發(fā)射頻率為

f

的電磁波

,

當(dāng)發(fā)射的電磁波到

達(dá)某個高度

,

其發(fā)射頻率

f

等于該高度當(dāng)?shù)氐碾姖{頻率

fN

時

,

該電磁波將發(fā)生反射,

在地面將會接收到該電磁回波若以

“掃頻”形式

改變發(fā)射頻率時：55565758μ0

sinφ0

=

μ

sinφμ0

sinφ0

=

μ1

sinφ1μ1

sinφ1

=

μ2

sinφ2

:μi-1

sinφi-1

=

μi

sinφiμi

sinφi

=

μr

sinφrAtthe

reflection

point→

μ0

sinφ0

=

μr

sinφr

sinφ0

=

μr

sin90。

sinφ0

=

μr忽略地球磁場時n2

=(μ-

ix)2

=1

-

1

Y2

「

Y4

7

22(1

-

X-

iZ)|L4(1

-

X

-

iZ)2

L

」|WithobliquePropagationSnell’slaw施乃爾定律1

-

iZ

-

T

±

T

+

Y259XIonosonde垂直探測時各層回波頻率約為多少？60Question：（1）利用

傾斜發(fā)射的ionosonde，發(fā)射頻率為18

MHz的電磁波，若要

得到電漿濃度為106

el/cm3

處的回波，在地面應(yīng)以何角度發(fā)射電波？（2）若垂直發(fā)射電波，當(dāng)如何取得回波？折射指數(shù)

(refractive

index)6263

n2theAppletonformula折射指數(shù)(refractive

index)/laptag-website/Lectures/Appleton.pdfSomepropertiesof

the

Appletonformula65Considerageometrywith

propagation

ofan

e-

mwave

(kdirection)

atsome

angle

θfromthe

magneticfield,

anddefinethe

planecontainingkand

B

asthex-y

plane.theAppletonformula折射指數(shù)(refractive

index)

6667Therefore,abovetheE-region,we

usuallycan

neglecttheabsorption

owingto

collisions.

WhenthemagneticfieldisnegligibleBE

=

0

(i.e.Y<<

1)Whencollisionsarenegligibleν=0,

therefore

Z

=

0μ0

sinφ0

=

μ

sinφμ0

sinφ0

=

μ1

sinφ1μ1

sinφ1

=

μ2

sinφ2

:μi-1

sinφi-1

=

μi

sinφiμi

sinφi

=

μr

sinφrAtthe

reflection

point→

μ0

sinφ0

=

μr

sinφr

sinφ0

=

μr

sin90。

sinφ0

=

μrSnell’slaw施乃爾定律70Whenbothcollisionsandmagneticfieldeffectsarenegligible

N

：

,

f

=

Hz

goodfortheF-region10m3≤e/μ電磁波頻率越高越能穿透電離層，可避免電離層效應(yīng)，

但是仍會受到大氣效應(yīng)的影響WithverticalPropagationφ0

=0。μ0

sin

φ0

=μr

sin

φr

→

1×

0

=μrverticalsounding：f

≤f0F2

→

echosf

>f0F2

→penetration??！

(直接穿透了)→

μr

=

0:

→

fN

=

f忽略地球磁場時：X

=

1μ0

sinφ0

=

μ

sinφμ0

sinφ0

=

μ1

sinφ1μ1

sinφ1

=

μ2

sinφ2

:μi-1

sinφi-1

=

μi

sinφiμi

sinφi

=

μr

sinφrWithobliquePropagationAside-viewofpropagation

pathsofSuperDARN

rays

intheionosphereatafrequencyof12.45

MHzforelevation

angles

from5to50.Thedashed

line

indicatesthe

electron

density

profile.74。ElectronGyro-frequencyfH

isabout

1.4

MHz(8.8x106

rad/s).Collisionfrequency

=

1.75

kHz(at

100

kmaltitude)

Transmitfrequency

=

1~20

MHzrad'sEMwaveBEMagneticequatorMiddle

latitudeMiddle

latitude76reflectioncondition:μ

=0

代入2X(1

-

X)=2(1

-

X)-

YT2

±[YT4

-

4(1

-

X)2

YL2

-

2(1

-

X)2

=-YT2

±[YT4

+

4(1

-

X)2

YL2

]考慮地球磁場時：Thereflectionconditionforverticalsoundingwiththe

external(Earth’s)magneticfield固定發(fā)射頻率反射條件：

μ=00,

BE

≠

0

,

V→00

≤μ

≤1φ

=ie.12“─”

sign

二邊半方：YT4

-

4YT2

(1

-

X)2

+

4

(1

-

X)4

=YT4

+

4YL2

(1

-

X)2→

4

(1

-

X)4

-

4

(1

-

X)2

Y2

=

0→

(1

-

X)2

-

Y2

=0

→X

=1

±

Y不是在f

=fN時反射Theordinarywavereflectioncondition,f

=

fN

X=

1

且取

“+

”sign(Theextra

ordinarywave)先找

0=0的解Thereflectionconditionforverticalsoundingwiththeexternal

(Earth’s)magneticfield固定發(fā)射頻率會在三個不同高度反射：“─”sign

X

=1±

YTheextra-ordinary

wave;

Theirheightof

reflection

isindependentoftheangleθand,hence,ofthemagnetic

dip.“

+”sign

X

=

1Theordinarywave

;

(as

nomagneticfield)79O-wave:261

kmX-wave:223

kmZ-wave:298

kmThereflectionconditionforverticalsoundingwiththeexternal(Earth’s)magneticfieldO-wave:9

MHzX-wave:9.42

MHzZ-wave:8.58MHzX

=

1±

Y}X=1,foF2

:Critical

frequency

ofF2Whenthelevelof

maximum

electronconcentrationinasinglethick

layer

is

reached,

thefrequencyatwhichthis

occurs

is

calledcritical

frequencyof

thislayer.82IonogramparametersFRegionfoF2:critical

frequency

of

the

ordinary

trace

of

the

highest

layer

of

theFregion,calledtheF2

layerwhentheF1

layerispresent.fxI:highest

frequency

recorded

by

a

reflection

from

the

F

region.foF1:critical

frequency

of

the

ordinary

trace

of

the

F1

layer

when

present.

h’F2:minimum

virtual

height

of

the

ordinary

trace

of

the

F2layer.h’F:lowest

virtual

height

of

the

ordinary

trace

of

the

F

region.ERegionfoE:critical

frequency

of

the

ordinary

trace

of

the

E

region.h’E:minimum

virtual

height

of

the

ordinary

trace

of

the

E

region.SporadicElayer(Es)foEs:highest

frequency

of

the

ordinary

trace

of

the

continuous

sporadic

E

layer.

h’Es:minimum

virtual

height

of

the

ordinary

trace

of

the

Es

layer.fmin:lowest

frequency

recorded

in

the

ionogram.8384h,=

virtual

heightf=

radiofrequencyμ,

=

1/μ,

μ

=group

refractive

indexN=

electron

densityB=geomagneticfield

strengthLiu

et

al.

[TAO

1992]Thetrue

height

(real

height)analysish,-f-

-

-

>

z-NMethodsofthetrue

height

analysis?

Model

Method?

Integral

Method?

Direct?

Lamination?

PolynomialLiu

et

al.

[TAO

1992]Advantages:simpleand

quickDisadvantages:

notsatisfyall

casesModel

methodChapman

layer

modelParabola

layer

modelLinear

layer

modelh,=

virtual

heightf=

radiofrequencyμ,

=

1/μ,

μ

=group

refractive

index

N=

electron

densityB=geomagneticfield

strengthAdvantages:1.No

a

priori

assumptions

are

made

about

the

shape.2.

Earth,s

magneticfield

istaken

intoaccount.Integral

methodIntegral

method-

Laminationrealheightvirtual

height[Liu,

1988]Integral

method-

PolynomialPOLANh,=

B

α

h

=

(A

B-1)

h,h

=

A

αassumptionGetfrom

ionogram91MUF(maximum

usablefrequency)

:thehighestfrequencyforionospherictransmissionover

anoblique

path,foragivensystem

performance92M(3000)F2:Thisparameterrepresentstheoptimumfrequencyatwhichtobroadcastasignalthatistobereceivedatadistanceof

3000km.NCU

HF

CW

Doppler

soundingsystemNCCU

FBELiyutanNCNUYiLanNTTUHCS

V丄

=

VD

COSθDoppler

FrequencyShift

Dopplerfrequencyshiftsofsoundingfrequency1.9

MHz

at

NCCU

during

16-20

October

2019Dopplerfrequencyshiftsofsoundingfrequency

5.5

MHz

at

NCCU

during

16-20

October

2019Dopplerfrequencyshiftsofsoundingfrequency1.9

MHz

at

5

stations

during

3

May

2020Dopplerfrequencyshiftsofsoundingfrequency

5.5

MHz

at

5

stations

during

3

May

2020Ionosphericgeomagnetic

pulsationsof

Dopplerfrequencyshiftsobserved

atChung-Li

on

24

March

1991.Liu

et

al.

(JGG

1993)Magnetosphere-IonospherecouplingIonospheric

solarflareeffectsof

Doppler

FrequencyShiftsLiu

et

al.

(JGR

1996)Ionospheric

disturbances

induced

byseismicwavesofthe2004

M9.3Sumatra

earthquake(left)Locationsof

the

epicenter(red

star)and

faultrupturearea

(black

box)

of

the

M9.3

Sumatra

earthquake,

the

broadband

seismic

station

PSI,

andtheionosonde

stations

HSS

(21.7N,

121.0E;

3580

km

to

the

epicenter),YAM

(31.7N;

130.6E,4810

km),and

KOK

(35.9N;

140.

1E,

5800

km).

The

possible

distance

to

thesource

fromHSS

(yellow

rings),

YAM

(blue

rings)

andKOK

(red

rings).

(right)

ObservationalsitesinTaiwan,includingtheionospheric

reflection

pointsofthedigital

Dopplersounderreceivingstations

NCNU

(21.

1N;

120.8E),

DHIT

(21.2N;

121.2E),

and

NCU(21.7N;

121.0E),digital

ionosonde

station

HSS,

and

broadbandseismicstation

NACB.(top)

Enlarged

portion

of

the

Doppler

sounder

record

obtained

at

DHIT,showingoscillatoryionosphericdisturbances.

(bottom)Time

histories

of

the

vertical

ground

velocity

obtained

atNACB.

The

arrival

times

of

P,

S,

and

LR

(Rayleigh)

waves

are

marked

onthe

trace.(top)DigitalDopplersounderrecordsof

theionosphericdisturbance

obtained

at

stationsNCNU,DHIT,

and

NCU.

The

circledportions

of

NCU

and

DHIT

are

enlarged

in

Figures

3

and

4,

respectively.

(bottom)

Ionosoderecordsobtainedatstation

HSSat

04:00

UT

and

04:15

UT.

1730MHzRadarImaging

ArrayR4R2R6T12

T11

T10

T930MHz4x1TXArray48

47

46

45

44

43

42

4140

39

38

37

36

35

34

3324

23

22

21

2019

18

1708

07

06

05

04

03

02

0132

31

30

29

28

27

26

25STArray64

63

62

61

60

59

58

5756

55

54

53

52

51

50

4916

15

14

13

12

11

1009

32

31

30

29

12

11

10

09

28

27

26

25

08

07

06

05

04

03

02

01

24

23

22

2116