Приложения полно-волнового метода: излучение

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STANFORD
ELECTRICAL
E N G I N E E R I N G
Ïðèëîæåíèÿ ïîëíî-âîëíîâîãî ìåòîäà: èçëó÷åíèå
ìîäóëèðîâàííîãî ýêâàòîðèàëüíîãî ýëåêòðîäæåòà è
êîíâåðñèÿ ýëåêòðîìàãíèòíûõ Â× âîëí â
ëåíãìþðîâñêèå
Íèêîëàé Ëåõòèíåí
Ñòýíôîðäñêèé Óíèâåðñèòåò, Ñòýíôîðä, Êàëèôîðíèÿ, ÑØÀ
Íèæíèé Íîâãîðîä, ìàé 2013
STANFORD
ELECTRICAL
E N G I N E E R I N G
Ëåõòèíåí (Ñòýíôîðä)
Ïðèëîæåíèÿ StanfordFWM
Íèæíèé Íîâãîðîä, ìàé 2013
1
StanfordFWM
STANFORD
ELECTRICAL
E N G I N E E R I N G
Ïëàí
1
Ñòýíôîðäñêèé Ïîëíî-âîëíîâîé ìåòîä/Stanford Full-Wave Method
(StanfordFWM)
2
Èçëó÷åíèå ýêâàòîðèàëüíîãî ýëåêòðîäæåòà
Ïîñòàíîâêà çàäà÷è
Îáùèå ðåçóëüòàòû
Ãîðèçîíòàëüíûé ïîòîê ìîùíîñòè
3
Êîíâåðñèÿ Â× â Ëåíãìþðîâñêèå âîëíû
Ðàñïðîñòðàíåíèå Â× ñ õîëîäíûì StanfordFWM
Îáîáùåíèå íà ò¼ïëóþ ïëàçìó
Ñðàâíåíèå ñ ïðåäûäóùèìè ðàáîòàìè
Êîíâåðñèÿ ýëåêòðîìàãíèòíûõ Â× âîëí â Ëåíãìþðîâñêèå
4
Çàêëþ÷åíèå
Ëåõòèíåí (Ñòýíôîðä)
Ïðèëîæåíèÿ StanfordFWM
Íèæíèé Íîâãîðîä, ìàé 2013
2
StanfordFWM
STANFORD
ELECTRICAL
E N G I N E E R I N G
StanfordFWM â õîëîäíîé ïëàçìå
Âîçìîæíîñòè:
Ïðîèçâîëüíàÿ ïëîñêî-ñëîèñòàÿ ñðåäà: èîíîñôåðà (ãîðèçîíòàëüíî
ñòðàòèôèöèðîâàííàÿ íàìàãíè÷åííàÿ ïëàçìà ñ ïðîèçâîëüíûì
íàïðàâëåíèåì ìàãíèòíîãî ïîëÿ)
Ïðîèçâîëüíàÿ êîíôèãóðàöèÿ ãàðìîíè÷åñêèõ âî âðåìåíè òîêîâ
Îáåñïå÷èâàåò ïîëíî-âîëíîâîå 3D ðåøåíèå êàê äëÿ âèñòëåðîâ
èçëó÷¼ííûõ â èîíîñôåðó, òàê è äëÿ ÎÍ× âîëí èçëó÷¼ííûõ â
âîëíîâîä çåìëÿ-èîíîñôåðà
Ñòàáèëåí ïðîòèâ çàâàëèâàþùåé íåóñòîé÷èâîñòè çàòóõàþùèìè
âîëíàìè
Ýôôåêòèâíîå èñïîëüçîâàíèå âû÷èñëèòåëüíûõ ðåñóðñîâ, ëåãêî
ðàçáèâàåòñÿ íà ïàðàëëåëüíûå ïðîöåññû
Ïðèëîæåíèÿ:
Ðàñïðîñòðàíåíèå ñêâîçü èîíîñôåðó
Ðàñïðîñòðàíåíèå â âîëíîâîäå çåìëÿ-èîíîñôåðà
Ðàññåÿíèå íà âîçìóùåíèÿõ
Ëåõòèíåí (Ñòýíôîðä)
D -ñëîÿ
Ïðèëîæåíèÿ StanfordFWM
Íèæíèé Íîâãîðîä, ìàé 2013
3
StanfordFWM
z
STANFORD
ELECTRICAL
E N G I N E E R I N G
B
Ne
εk
y
zM
zk+1
zk
z2
z1=0
x
Ìû ðàáîòàåì â Ôóðüå-îáëàñòè ãîðèçîíòàëüíûõ âîëíîâûõ âåêòîðîâ
1
2
k⊥ :
k⊥ = const (çàêîí Ñíåëëèóñà) =⇒ íàõîäèì kz , E è
H â êàæäîì ñëîå äëÿ êàæäîãî èç 4 ðåøåíèé äëÿ ïëîñêèõ âîëí
(ìîä): 2 ââåðõ (u) è 2 âíèç (d)
Èñïîëüçóÿ íåïðåðûâíîñòü E⊥ è H⊥ ìåæäó ñëîÿìè, íàõîäèì
u,d è àìïëèòóäû ìîä u, d
êîåôôèöèåíòû îòðàæåíèÿ R
Äëÿ êàæäîãî
Íàïðàâëåíèå ðåêóðñèè
R̂uk +1 → R̂uk è uk → uk +1 îáåñïå÷èâàåò
ñòàáèëüíîñòü ïðîòèâ çàâàëèâàíèÿ ðåøåíèÿ ñïàäàþùèìè âîëíàìè
Ïðåäñòàâëÿåì òîêè èñòî÷íèêîâ â âèäå ãðàíè÷íûõ óñëîâèé ìåæäó
ñëîÿìè íà
3
E⊥ è H⊥
Îáðàòíîå ïðåîáðàçîâàíèå Ôóðüå
Ëåõòèíåí (Ñòýíôîðä)
k⊥ → r⊥
Ïðèëîæåíèÿ StanfordFWM
Íèæíèé Íîâãîðîä, ìàé 2013
4
Èçëó÷åíèå ýêâàòîðèàëüíîãî ýëåêòðîäæåòà
STANFORD
ELECTRICAL
E N G I N E E R I N G
Ïëàí
1
Ñòýíôîðäñêèé Ïîëíî-âîëíîâîé ìåòîä/Stanford Full-Wave Method
(StanfordFWM)
2
Èçëó÷åíèå ýêâàòîðèàëüíîãî ýëåêòðîäæåòà
Ïîñòàíîâêà çàäà÷è
Îáùèå ðåçóëüòàòû
Ãîðèçîíòàëüíûé ïîòîê ìîùíîñòè
3
Êîíâåðñèÿ Â× â Ëåíãìþðîâñêèå âîëíû
Ðàñïðîñòðàíåíèå Â× ñ õîëîäíûì StanfordFWM
Îáîáùåíèå íà ò¼ïëóþ ïëàçìó
Ñðàâíåíèå ñ ïðåäûäóùèìè ðàáîòàìè
Êîíâåðñèÿ ýëåêòðîìàãíèòíûõ Â× âîëí â Ëåíãìþðîâñêèå
4
Çàêëþ÷åíèå
Ëåõòèíåí (Ñòýíôîðä)
Ïðèëîæåíèÿ StanfordFWM
Íèæíèé Íîâãîðîä, ìàé 2013
5
Èçëó÷åíèå ýêâàòîðèàëüíîãî ýëåêòðîäæåòà
Ïîñòàíîâêà çàäà÷è
STANFORD
ELECTRICAL
E N G I N E E R I N G
Ýêâàòîðèàëüíûé ýëåêòðîäæåò
Èç-çà ãîðèçîíòàëüíîãî ìàãíèòíîãî ïîëÿ, ýôôåêòèâíàÿ ïðîâîäèìîñòü
äëÿ ãîðèçîíòàëüíîãî òîêà âûñîêàÿ (ïðîâîäèìîñòü Êàóëèíãà):
2
σCowling = σH
/σP + σP
160
150
140
130
σp
σh
σ||
σCowling
h, km
120
110
100
90
80
70
60 −15
10
−10
−5
10
10
0
10
σ, S/m
Ëåõòèíåí (Ñòýíôîðä)
Ïðèëîæåíèÿ StanfordFWM
Íèæíèé Íîâãîðîä, ìàé 2013
6
Èçëó÷åíèå ýêâàòîðèàëüíîãî ýëåêòðîäæåòà
Ïîñòàíîâêà çàäà÷è
STANFORD
ELECTRICAL
E N G I N E E R I N G
Ïðåäïîëîãàåìîå âîçìóùåíèå òîêà ýëåêòðîäæåòà
Ãîðèçîíòàëüíîå â
120
íàïðàâëåíèè
110
x̂
Çàïàä-Âîñòîê ( ,
∆σCowling )
100
èëè
ẑ
Papadopoulos,
âåðòèêàëüíîå ( ,
90
h, km
∆σH )
[
80
2006]
70
Ãàóññîâñêîå
ðàñïðåäåëåíèå ñ
60
50
0
øèðèíîé 23 êì
0.5
1
Ëåõòèíåí (Ñòýíôîðä)
1.5
∆ Ix, nA/m2
2
2.5
3
Ìîäóëèðîâàíî ñ
÷àñòîòîé
Ïðèëîæåíèÿ StanfordFWM
f
= 1875
Íèæíèé Íîâãîðîä, ìàé 2013
Ãö
7
Èçëó÷åíèå ýêâàòîðèàëüíîãî ýëåêòðîäæåòà
Ðåçóëüòàòû:
STANFORD
ELECTRICAL
E N G I N E E R I N G
E è B íà ïîâåðõíîñòè çåìëè
Ãåîìàãíèòíîå ïîëå
Òîê
Îáùèå ðåçóëüòàòû
∆I k x̂
B0 = 3 × 10−5 T, B0 k ŷ
Àñèììåòðèÿ ïîëÿ â íàïðàâëåíèè Çàïàä-ÂîñòîêEast-west
assymmetry in emission
B at the ground, pT
Ez at the ground, mV/m
⊥
500
500
y (S−N), km
0.1
1.2
1
0.05
0
0.8
0
0.6
0
0.4
0.2
−0.05
−500
−500
0
x (E−W), km
Ëåõòèíåí (Ñòýíôîðä)
500
−500
−500
Ïðèëîæåíèÿ StanfordFWM
0
x (E−W), km
500
Íèæíèé Íîâãîðîä, ìàé 2013
8
Èçëó÷åíèå ýêâàòîðèàëüíîãî ýëåêòðîäæåòà
Îáùèå ðåçóëüòàòû
STANFORD
ELECTRICAL
E N G I N E E R I N G
Ýíåðãèÿ íå ïðîõîäèò â èîíîñôåðó
Ïîñêîëüêó íà ýòèõ ÷àñòîòàõ ðàñïðîñòðàíÿåòñÿ òîëüíî ñâèñòîâàÿ
ìîäà (âèñòëåð), êîòîðàÿ íå ìîæåò ðàñïðîñòðàíÿòüñÿ
⊥ B0 ,
ýíåðãèÿ ïðàêòè÷åñêè íå ïðîõîäèò ââåðõ, â èîíîñôåðó. energy goes
upward into ionosphere.
Íåáîëüøîé ïîòîê ìîùíîñòè ââåðõ îáÿçàí íèæíå-ãèáðèäíûì
âîëíàì
120
110
h, km
100
90
80
70
60
50 −10
10
Ëåõòèíåí (Ñòýíôîðä)
−8
10
−6
−4
−2
10
10
10
Total upward energy flux, W
Ïðèëîæåíèÿ StanfordFWM
0
10
Íèæíèé Íîâãîðîä, ìàé 2013
9
Èçëó÷åíèå ýêâàòîðèàëüíîãî ýëåêòðîäæåòà
Ãîðèçîíòàëüíûé ïîòîê ìîùíîñòè
STANFORD
ELECTRICAL
E N G I N E E R I N G
Ãîðèçîíòàëüíûé ïîòîê ìîùíîñòè
f = 1875 Ãö, hsource = 79 êì
Ãîðèçîíòàëüíàÿ êîìïîíåíòà âåêòîðà Ïîéíòèíãà ïðîèíòåãðèðîâàííàÿ ïî
âûñîòå àñèììåòðè÷íà, â ïðîòèâîïîëîæíîì íàïðàâëåíèè äëÿ
I k x̂
I k ẑ
−6
x 10
I k x̂ è I k ẑ
−6
x 10
r= 75 km
r=100 km
r=200 km
r=300 km
2
1.5
r= 75 km
r=100 km
r=200 km
r=300 km
5
4
3
1
∫ Sy dz, W/m
∫ Sy dz, W/m
2
0.5
0
−0.5
1
0
−1
−2
−1
−3
−1.5
−4
−2
−5
−2
−1
0
∫ Sx dz, W/m
Ëåõòèíåí (Ñòýíôîðä)
1
2
−8
−6
x 10
Ïðèëîæåíèÿ StanfordFWM
−6
−4
−2
∫ S dz, W/m
0
x
Íèæíèé Íîâãîðîä, ìàé 2013
2
−6
x 10
10
Èçëó÷åíèå ýêâàòîðèàëüíîãî ýëåêòðîäæåòà
×àñòîòíàÿ çàâèñèìîñòü,
hsource = 79 êì
f
= 1000
f
Ãö
I
Ãîðèçîíòàëüíûé ïîòîê ìîùíîñòè
STANFORD
ELECTRICAL
E N G I N E E R I N G
k x̂
= 1875
f
Ãö
= 3000
Ãö
−7
x 10
−6
r= 75 km
r=100 km
r=200 km
r=300 km
3
−6
x 10
x 10
r= 75 km
r=100 km
r=200 km
r=300 km
2
1.5
1
1
0.5
0.5
−2
0
0
y
0
−1
∫ S dz, W/m
1
∫ Sy dz, W/m
∫ Sy dz, W/m
2
r= 75 km
r=100 km
r=200 km
r=300 km
2
1.5
−0.5
−0.5
−1
−1
−1.5
−1.5
−3
−2
−2
−3
−2
−1
0
1
∫ Sx dz, W/m
2
Ëåõòèíåí (Ñòýíôîðä)
3
−2
−7
x 10
−1
0
∫ Sx dz, W/m
1
2
−2
−6
x 10
Ïðèëîæåíèÿ StanfordFWM
−1
0
∫ Sx dz, W/m
1
2
−6
x 10
Íèæíèé Íîâãîðîä, ìàé 2013
11
Èçëó÷åíèå ýêâàòîðèàëüíîãî ýëåêòðîäæåòà
×àñòîòíàÿ çàâèñèìîñòü,
hsource = 79 êì
f
= 1000
f
Ãö
I
Ãîðèçîíòàëüíûé ïîòîê ìîùíîñòè
STANFORD
ELECTRICAL
E N G I N E E R I N G
k ẑ
= 1875
f
Ãö
= 3000
Ãö
−6
x 10
−6
x 10
5
r= 75 km
r=100 km
r=200 km
r=300 km
1.5
1
4
−0.5
−1
2
1
0
−1
−3
−2.5
−2
−1.5
−1
∫ Sx dz, W/m
−0.5
Ëåõòèíåí (Ñòýíôîðä)
−6
x 10
0
−1
−2
−3
−3
−4
−4
−5
−8
0
1
−2
−5
−1.5
3
∫ Sy dz, W/m
∫ Sy dz, W/m
y
∫ S dz, W/m
0
4
3
2
0.5
r= 75 km
r=100 km
r=200 km
r=300 km
5
r= 75 km
r=100 km
r=200 km
r=300 km
−6
x 10
−6
−4
−2
∫ Sx dz, W/m
0
−8
2
−6
x 10
Ïðèëîæåíèÿ StanfordFWM
−6
−4
∫ Sx dz, W/m
−2
0
−6
x 10
Íèæíèé Íîâãîðîä, ìàé 2013
12
Èçëó÷åíèå ýêâàòîðèàëüíîãî ýëåêòðîäæåòà
Ãîðèçîíòàëüíûé ïîòîê ìîùíîñòè
Çàâèñèìîñòü îò âûñîòû èñòî÷íèêà,
f = 1875 Ãö
hsource = 76 km
I
hsource = 82 êì
−7
x 10
r= 75 km
r=100 km
r=200 km
r=300 km
3
r= 75 km
r=100 km
r=200 km
r=300 km
2
1.5
4
−2
1
∫ S dz, W/m
0.5
0
0
y
∫ Sy dz, W/m
∫ Sy dz, W/m
0
r= 75 km
r=100 km
r=200 km
r=300 km
2
1
2
E N G I N E E R I N G
x 10
−6
6
ELECTRICAL
k x̂
hsource = 79 êì
−6
x 10
STANFORD
−0.5
−1
−1
−4
−2
−1.5
−6
−2
−6
−4
−2
0
2
∫ Sx dz, W/m
4
Ëåõòèíåí (Ñòýíôîðä)
6
−2
−6
x 10
−1
0
∫ Sx dz, W/m
1
−3
−3
2
−6
x 10
Ïðèëîæåíèÿ StanfordFWM
−2
−1
0
1
∫ Sx dz, W/m
2
3
−7
x 10
Íèæíèé Íîâãîðîä, ìàé 2013
13
Èçëó÷åíèå ýêâàòîðèàëüíîãî ýëåêòðîäæåòà
Ãîðèçîíòàëüíûé ïîòîê ìîùíîñòè
Çàâèñèìîñòü îò âûñîòû èñòî÷íèêà,
f = 1875 Ãö
hsource = 76 êì
I
ELECTRICAL
E N G I N E E R I N G
k ẑ
hsource = 79 êì
−5
STANFORD
hsource = 82 êì
x 10
2
r= 75 km
r=100 km
r=200 km
r=300 km
1.5
1
r= 75 km
r=100 km
r=200 km
r=300 km
4
1
1
0
0.5
0
y
∫ Sy dz, W/m
0
∫ S dz, W/m
2
−0.5
r= 75 km
r=100 km
r=200 km
r=300 km
1.5
3
0.5
y
∫ S dz, W/m
−6
x 10
−6
x 10
5
−1
−0.5
−2
−1
−3
−1.5
−2
−3
−1
−4
−1.5
−5
−2
−1
∫ Sx dz, W/m
Ëåõòèíåí (Ñòýíôîðä)
0
−8
−5
x 10
−6
−4
−2
∫ Sx dz, W/m
0
−1.5
2
−6
x 10
Ïðèëîæåíèÿ StanfordFWM
−1
−0.5
0
0.5
∫ Sx dz, W/m
1
1.5
−6
x 10
Íèæíèé Íîâãîðîä, ìàé 2013
14
Êîíâåðñèÿ Â× â Ëåíãìþðîâñêèå âîëíû
STANFORD
ELECTRICAL
E N G I N E E R I N G
Ïëàí
1
Ñòýíôîðäñêèé Ïîëíî-âîëíîâîé ìåòîä/Stanford Full-Wave Method
(StanfordFWM)
2
Èçëó÷åíèå ýêâàòîðèàëüíîãî ýëåêòðîäæåòà
Ïîñòàíîâêà çàäà÷è
Îáùèå ðåçóëüòàòû
Ãîðèçîíòàëüíûé ïîòîê ìîùíîñòè
3
Êîíâåðñèÿ Â× â Ëåíãìþðîâñêèå âîëíû
Ðàñïðîñòðàíåíèå Â× ñ õîëîäíûì StanfordFWM
Îáîáùåíèå íà ò¼ïëóþ ïëàçìó
Ñðàâíåíèå ñ ïðåäûäóùèìè ðàáîòàìè
Êîíâåðñèÿ ýëåêòðîìàãíèòíûõ Â× âîëí â Ëåíãìþðîâñêèå
4
Çàêëþ÷åíèå
Ëåõòèíåí (Ñòýíôîðä)
Ïðèëîæåíèÿ StanfordFWM
Íèæíèé Íîâãîðîä, ìàé 2013
15
Êîíâåðñèÿ Â× â Ëåíãìþðîâñêèå âîëíû
Õîëîäíîå Â× ðàñïðîñòðàíåíèå
 ïðîñòðàíñòâå âîëíîâûõ âåêòîðîâ
STANFORD
ELECTRICAL
E N G I N E E R I N G
k⊥
f=2fH; hreflO=229.2894 km; hattrZ=228.8355 km;
nx,w=−0.14163; nx,mz=−0.24531
E re Evac, dB
231
60
230.5
40
230
20
h, km
229.5
229
0
228.5
−20
228
−40
227.5
227
−0.3
−0.2
−0.1
0
nx=sin(θ)
0.1
0.2
0.3
−60
Îáûêíîâåííàÿ (Î) ìîäà êîíâåðòèðóåòñÿ â Z-ìîäó, ðàñïðîñòðàíÿþùóþñÿ ââåðõ èëè âíèç, â
nx
âåðõíåì (
= −0.14) èëè â íèæíåì (nx = +0.14) ðàäèî-îêíå Ýëëèñà (Ellis radio window),
ñîîòâåòñòâåííî. Îòìåòèì, ÷òî â õîëîäíîé ïëàçìå íåò Ëåíãìþðîâñêîé ìîäû.
Ëåõòèíåí (Ñòýíôîðä)
Ïðèëîæåíèÿ StanfordFWM
Íèæíèé Íîâãîðîä, ìàé 2013
16
Êîíâåðñèÿ Â× â Ëåíãìþðîâñêèå âîëíû
Õîëîäíîå Â× ðàñïðîñòðàíåíèå
STANFORD
ELECTRICAL
E N G I N E E R I N G
r
 êîíôèãóðàöèîííîì ⊥ -ïðîñòðàíñòâå
Upward window
h
f=2fH; RF window (P)
=228.8355 km; h =229.2894 km
attr
Downward window
h
E re max(E ), dB
refl
f=2fH; Downward RF window (Q)
=228.8355 km; h =229.2894 km
attr
i
231
E re max(E ), dB
refl
i
231
20
20
230.5
230.5
0
0
230
230
−20
−20
229.5
229.5
−40
h, km
h, km
−40
229
229
−60
−60
228.5
228.5
−80
228
−100
227.5
227
−50
−40
−30
−20
−10
0
x, km
10
20
30
40
50
−120
−80
228
−100
227.5
227
−50
−40
−30
−20
−10
0
x, km
10
20
30
40
50
−120
Budden The propagation of Radio Waves, 1985, Fig. 10.8
Ëåõòèíåí (Ñòýíôîðä)
Ïðèëîæåíèÿ StanfordFWM
Íèæíèé Íîâãîðîä, ìàé 2013
17
Êîíâåðñèÿ Â× â Ëåíãìþðîâñêèå âîëíû
Îáîáùåíèå íà ò¼ïëóþ ïëàçìó
STANFORD
ELECTRICAL
E N G I N E E R I N G
Ãèäðî-ýëåêòðî-äèíàìè÷åñêèå óðàâíåíèÿ
∂E
+ qnv
∂t
∂H
= −µ0
∂t
∇ × H = ε0
∇×E
m
d
pn−γ
dt
= 0
àäèàáàòà,
q = −e
γ=3
∇p
∂v
+ (v · ∇)v = −
+ q [E + v × (B0 + µ0 H)] − mν v
∂t
n
∂n
+ ∇ · (nv) = 0
∂t
Áåç èîíîâ
=⇒ ω ωLH
(Â× äèàïàçîí).
Ëèíåàðèçóåì äëÿ íåáîëüøèõ âîçìóùåíèé
E, H, v, p ∝ e −i ωt ;
E⊥ , H⊥ , vz and p íåïðåðûâíû ìåæäó ñëîÿìè;
3 àìïëèòóäû ââåðõ (u) and 3 âíèç (d);
6 êîìïîíåíò
Îáîáùàåì ñòàáèëüíûé ðåêóðñèâíûé àëãîðèòì äëÿ âû÷èñëåíèÿ
êîýôôèöèåíòîâ îòðàæåíèÿ
Ëåõòèíåí (Ñòýíôîðä)
R̂u,d (3 × 3)
Ïðèëîæåíèÿ StanfordFWM
è àìïëèòóä
u è d.
Íèæíèé Íîâãîðîä, ìàé 2013
18
Êîíâåðñèÿ Â× â Ëåíãìþðîâñêèå âîëíû
Îáîáùåíèå íà ò¼ïëóþ ïëàçìó
STANFORD
ELECTRICAL
E N G I N E E R I N G
Âàæíûå ïàðàìåòðû ïëàçìû
Ñêîðîñòü ýëåêòðîííîãî çâóêà
r
cs =
γ p0
mn0
Áåçðàçìåðíûå ïàðàìåòðû
X
=
q B0
q 2 n0
, Y=
, Z
2
m ε0 ω
mω
=
ν
,
ω
U = 1 + iZ ,
Γ=
c 2
s
c
Îòìåòèì ÷òî
X
= ωp2 /ω 2 , |Y| = |ωH | /ω ,
ãäå
ωp
and
ωH
ñîîòâåòñâåííî
ïëàçìåííàÿ è ãèðî-÷àñòîòà ýëåêòðîíîâ;
Γ = (2γ/3)(Eth /E0 ) = 2Eth /E0 , ãäå Eth òåïëîâàÿ ýíåðãèÿ
E0 = mc 2 ýíåðãèÿ ïîêîÿ ýëåêòðîíà. Ìû ðàññìàòðèâàåì
íåðåëÿòèâèñòñêóþ ïëàçìó, òàê ÷òî Γ 1.
Ëåõòèíåí (Ñòýíôîðä)
Ïðèëîæåíèÿ StanfordFWM
è
Íèæíèé Íîâãîðîä, ìàé 2013
19
Êîíâåðñèÿ Â× â Ëåíãìþðîâñêèå âîëíû
Ãðàäèåíò
Ñðàâíåíèå ñ ïðåäûäóùèìè ðàáîòàìè
STANFORD
ELECTRICAL
E N G I N E E R I N G
Ne
B0 , ν, Te = const =⇒ Y, Z , Γ =
const .
Ne = Ne (z ) =⇒ X = X (z ).
zmax
Âàæíûé áåçðàçìåðíûé ïàðàìåòð
k0 Λ, where
X
Λ=
dX /dz
Ãðàäèåíò ïëîòíîñòè ïëàçìû
0
zmin
ñèìóëèðóåòñÿ êàê ñèíóñîèäàëüíàÿ
ðàìïà â
Λ
X
âû÷èñëÿåòñÿ â òî÷êå
z =0
X1
Ëåõòèíåí (Ñòýíôîðä)
Ïðèëîæåíèÿ StanfordFWM
X0
X2
Íèæíèé Íîâãîðîä, ìàé 2013
20
Êîíâåðñèÿ Â× â Ëåíãìþðîâñêèå âîëíû
Ñðàâíåíèå ñ ïðåäûäóùèìè ðàáîòàìè
STANFORD
ELECTRICAL
E N G I N E E R I N G
Budden and Jones [1987, doi:10.1098/rspa.1987.0077]
f = 65 kHz, Y = 0.5, Z = 10−5 , Γ = 5 × 10−7 , k0 Λ = 53.5606, θB = 64.2◦
Èñïîëüçîâàëè ïîäîáíûé, íî íåóñòîé÷èâûé ïîëíî-âîëíîâîé àëãîðèòì
Êîíâåðñèÿ ýëåêòðîñòàòè÷åñêîé
Ne
â íåîáû÷íóþ ïðàâóþ
RX
ES
ìîäû ïàäàþùåé íà ãðàäèåíò ñ ðàñòóùåé
è îáû÷íóþ ëåâóþ
LO
ìîäû
Òðàåêòîðèÿ íà äèàãðàììå Êëåììîâà-Ìóëëàëè-Ýëëèñà (CMA diagram)
 òî÷êå
X1
(íèç):
LO , RX , ES ; â òî÷êå X2
(âåðõ): íåò ðàñïðîñòàíåíèÿ
ðàñïðîñòðàíÿþùèåñÿ âîëíû ñëàáî çàòóõàþò
Ëåõòèíåí (Ñòýíôîðä)
⇒
Ïðèëîæåíèÿ StanfordFWM
âûáîð
X1,2
ïðîèçâîëåí.
Íèæíèé Íîâãîðîä, ìàé 2013
21
Êîíâåðñèÿ Â× â Ëåíãìþðîâñêèå âîëíû
Ñðàâíåíèå ñ ïðåäûäóùèìè ðàáîòàìè
STANFORD
ELECTRICAL
E N G I N E E R I N G
Ñðàâíåíèå
Budden and Jones [1987, Fig 2]
Íàñòîÿùàÿ ðàáîòà
0
Power fraction, dB
−10
−20
−30
−40
ES to ES
−50
ES to RX
ES to LO
−60
−70
0.1
0.2
0.3
0.4
nx
0.5
0.6
0.7
0.8
Budden and Jones [1987, Fig 2], òàêèå
p
nx = Y /(1 + Y ) sin θB = 0.520. Îòðàæåíèå
ES → ES íåñêîëüêî íèæå, èç-çà çàòóõàíèÿ ES .
Ìû òàêæå ïîëó÷èëè ðåçóëüòàòû
êàê ðàäèî-îêíî íà
Ëåõòèíåí (Ñòýíôîðä)
Ïðèëîæåíèÿ StanfordFWM
Íèæíèé Íîâãîðîä, ìàé 2013
22
Êîíâåðñèÿ Â× â Ëåíãìþðîâñêèå âîëíû
Ñðàâíåíèå ñ ïðåäûäóùèìè ðàáîòàìè
STANFORD
ELECTRICAL
E N G I N E E R I N G
Mjølhus [1990, doi:10.1029/RS025i006p01321]
Mjølhus [1990] èíòåãðèðîâàë â êîìïëåêñíîé ïëîñêîñòè kz ;
Çàòóõàíèå A(p ) ìîäû LO ïðè îòðàæåíèè îò ðàñòóùåãî Ne
1/3 Y 1/2
Áåçðàçìåðíûé ïàðàìåòð p = (k0 Λ)
Mjølhus [1990, Fig 10]
Íàñòîÿùàÿ ðàáîòà
1
0.9
0.8
0.7
A(p)
0.6
0.5
0.4
0.3
0.2
0.1
0
0
1
2
3
4
5
p
Ðåçóëüòàòû ïîäîáíû, êðîìå
Ëåõòèíåí (Ñòýíôîðä)
A(p) 6= 0 ïðè p → ∞ (èç-çà ñòîëêíîâåíèé).
Ïðèëîæåíèÿ StanfordFWM
Íèæíèé Íîâãîðîä, ìàé 2013
23
Êîíâåðñèÿ Â× â Ëåíãìþðîâñêèå âîëíû
Ñðàâíåíèå ñ ïðåäûäóùèìè ðàáîòàìè
STANFORD
ELECTRICAL
E N G I N E E R I N G
Kim et al [2008, doi:10.1063/1.2994719]
Kim et al [2008] used a uid model
A(p, q ) çàòóõàíèå LO
1/3 n ,, p = (k Λ)1/3 Y 1/2
Ôàêòîðû Ìü¼ëõóñà (Mjølhus) q = (k0 Λ)
x
0
Kim et al [2008, Fig 6]
Íàñòîÿùàÿ ðàáîòà
1.4
0.8
1.2
q2
1
0.6
0.8
0.4
0.6
0.4
0.2
0.2
0
0.5
1
1.5
p
2
2.5
3
Ïîëîæåíèÿ ìàêñèìóìîâ ñîâïàäàþò!
Ëåõòèíåí (Ñòýíôîðä)
Ïðèëîæåíèÿ StanfordFWM
Íèæíèé Íîâãîðîä, ìàé 2013
24
Êîíâåðñèÿ Â× â Ëåíãìþðîâñêèå âîëíû
Êîíâåðñèÿ EM â ES
Äîïîëíèòåëüíûå ðåçóëüíàòû äëÿ óñëîâèé
Power, dB
0
0
−20
−40
−40
−60
−60
−80
−80
−100
−100
0
E N G I N E E R I N G
[1987]
RX
−20
−0.5
ELECTRICAL
Budden and Jones
LO
−1
STANFORD
0.5
1
−1
−0.5
0
0.5
1
ES
0
Power, dB
−20
into ES
−40
into RX
−60
into LO
−80
−100
−1
−0.5
0
n
0.5
1
x
ES → RX ýôôåêòèâíåå â âåðõíåì ðàäèî-îêíå ïðè nx = +0.520 ÷åì â íèæíåì
(nx = −0.520)
RX → ES íåýôôåêòèâíî, ìåíåå ýôôåêòèâíî â âåðõíåì ðàäèî-îêíå
LO → ES î÷åíü ýôôåêòèâíî â îáîèõ ðàäèî-îêíàõ
Ëåõòèíåí (Ñòýíôîðä)
Ïðèëîæåíèÿ StanfordFWM
Íèæíèé Íîâãîðîä, ìàé 2013
25
Êîíâåðñèÿ Â× â Ëåíãìþðîâñêèå âîëíû
Êîíâåðñèÿ EM â ES
STANFORD
ELECTRICAL
E N G I N E E R I N G
Ïîâåðõíîñòè ïîêàçàòåëÿ ïðåëîìëåíèÿ (Y
f = 5 ÌÃö
< 1,
X
≈ 1)
Òèïè÷íàÿ èîíîñôåðà,
X
103
0°
X
.1
LO
ES (θ<θres); Z (θ>θres)
100
30°
&1
Z
0°
30°
log10|n|
102
°
°
60
1
10
60
100
°
−1
10 −1
10
0
10
1
102
10
X=0.975
°
90
−1
10 −1
103
10
90
0
10
X=1.025
Y=0.2; Z=3.2e−05; Γ=4.4e−07
Êîíâåðñèÿ
1
2
LO â ES
ïðè
X
< 1 îáúÿñíÿåòñÿ
LO
Z
êîíâåðñèåé â ðàäèî-îêíå
→ ;
ìîäà íà ðåçîíàíñíîì êîíóñå ïåðåõîäèò â
Z
Çàìå÷àíèå:
Z
ìîäà ïðè
Ëåõòèíåí (Ñòýíôîðä)
θ 6= 0 íåïðåðûâíà ïðè
X
ES
ïîñêîëüêó ýòî òà æå ïîâåðõíîñòü.
= 1 ò.ê. îíà íåîáû÷íà.
Ïðèëîæåíèÿ StanfordFWM
Íèæíèé Íîâãîðîä, ìàé 2013
26
Çàêëþ÷åíèå
STANFORD
ELECTRICAL
E N G I N E E R I N G
Ïëàí
1
Ñòýíôîðäñêèé Ïîëíî-âîëíîâîé ìåòîä/Stanford Full-Wave Method
(StanfordFWM)
2
Èçëó÷åíèå ýêâàòîðèàëüíîãî ýëåêòðîäæåòà
Ïîñòàíîâêà çàäà÷è
Îáùèå ðåçóëüòàòû
Ãîðèçîíòàëüíûé ïîòîê ìîùíîñòè
3
Êîíâåðñèÿ Â× â Ëåíãìþðîâñêèå âîëíû
Ðàñïðîñòðàíåíèå Â× ñ õîëîäíûì StanfordFWM
Îáîáùåíèå íà ò¼ïëóþ ïëàçìó
Ñðàâíåíèå ñ ïðåäûäóùèìè ðàáîòàìè
Êîíâåðñèÿ ýëåêòðîìàãíèòíûõ Â× âîëí â Ëåíãìþðîâñêèå
4
Çàêëþ÷åíèå
Ëåõòèíåí (Ñòýíôîðä)
Ïðèëîæåíèÿ StanfordFWM
Íèæíèé Íîâãîðîä, ìàé 2013
27
Çàêëþ÷åíèå
STANFORD
ELECTRICAL
E N G I N E E R I N G
Èòîãè
Èçëó÷åíèå ýêâàòîðèàëüíîãî ýëåêòðîäæåòà:
Âñÿ èçëó÷¼ííàÿ ìîùíîñòü èä¼ò â âîëíîâîä Çåìëÿ-èîíîñôåðà
Ñëåäîâàòåëüíî, äëÿ òàêèõ æå òîêîâûõ âîçìóùåíèé ïîëó÷àåì áîëåå
ýôôåêòèâíîå èçëó÷åíèå ÷åì äëÿ âåðòèêàëüíîãî ãåîìàãíèòíîãî
ïîëÿ (30 Âò â ñðàâíåíèè ñ
∼1
Lehtinen and Inan, 2008])
Âò, [
Äèàãðàììà íàïðàâëåííîñòè àñèììåòðè÷íà â íàïðàâëåíèè
Çàïàä-Âîñòîê
Êîíâåðñèÿ Â×:
Àëãîðèòì StanfordFWM áûë îáîáùåí íà ñëó÷àé ò¼ïëîé ïëàçìû
Ðåçóëüòàòû ïðîâåðåíû ñðàâíåíèåì ñ ïðåäûäóùèìè ðàáîòàìè
LO → ES ýôôåêòèâíà áëàãîäàðÿ LO → Z → ES
Ïîãëîùåíèå ES îêîëî ïëàçìåííîãî ðåçîíàíñà ìîæåò âíåñòè âêëàä
â íàãðåâàíèå ýëåêòðîíîâ F -ðåãèîíà
Êîíâåðñèÿ
Ýòî ëèíåéíûé ìåõàíèçì, â îòëè÷èå îò ìåõàíèçìà
ïàðàìåòðè÷åêîãî çàòóõàíèÿ
Ëåõòèíåí (Ñòýíôîðä)
Ïðèëîæåíèÿ StanfordFWM
Íèæíèé Íîâãîðîä, ìàé 2013
28
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