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
