Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://www.kosmofizika.ru/model/nymmik_2.8a.doc Äàòà èçìåíåíèÿ: Wed Nov 30 12:41:21 2005 Äàòà èíäåêñèðîâàíèÿ: Tue Oct 2 00:33:23 2012 Êîäèðîâêà: koi8-r

Ïîëóýìïèðè÷åñêàÿ äèíàìè÷åñêàÿ ìîäåëü ïîòîêîâ ÷àñòèö ãàëàêòè÷åñêèõ
êîñìè÷åñêèõ ëó÷åé (âåðñèè ISO è 2005 ã)


Ð.À.Íûììèê
Îòäåë êîñìîôèçè÷åñêèõ èññëåäîâàíèé, ÍÈÈ ÿäåðíîé ôèçèêè èì. Ä.Â.Ñêîáåëüöûíà,
Ìîñêîâñêèé ãîñóäàðñòâåííûé óíèâåðñèòåò èì. Ì.Â.Ëîìîíîñîâà


Àííîòàöèÿ





Êëþ÷åâûå ñëîâà
Èçëàãàþòñÿ îñíîâíûå âîïðîñû ìåòîäîëîãèè, êîòîðûå ëåãëè â îñíîâó
ïîëóýìïèðè÷åñêîé äèíàìè÷åñêîé ìîäåëè ïîòîêîâ ÷àñòèö ãàëàêòè÷åñêèõ
êîñìè÷åñêèõ ëó÷åé. Ìîäåëü ðàçðàáîòàíà â ÍÈÈ ÿäåðíîé ôèçèêè ÌÃÓ è îäíà èç åå
âåðñèè â íàñòîÿùåå âðåìÿ óòâåðæäåíà â êà÷åñòâå ìåæäóíàðîäíîãî ñòàíäàðòà ISO-
15390, 2004 .

Ãàëàêòè÷åñêèå êîñìè÷åñêèå ëó÷è, ïîëóýìïèðè÷åñêàÿ ìîäåëü, ïðîãíîç ïîòîêîâ
÷àñòèö 1˜Z˜92.



1. ÂÂÅÄÅÍÈÅ

 ïðàêòèêå ïëàíèðîâàíèÿ ïîëåòîâ è êîíñòðóèðîâàíèÿ êîñìè÷åñêèõ àïïàðàòîâ,
îðáèòàëüíûõ è ìåæïëàíåòíûõ ñòàíöèè îñîáîå ìåñòî çàíèìàþò âîïðîñû
ðàäèàöèîííîãî âîçäåéñòâèÿ âûñîêîýíåðãåòè÷åñêèõ ÷àñòèö êîñìè÷åñêîé ðàäèàöèè
- Ãàëàêòè÷åñêèõ êîñìè÷åñêèõ ëó÷åé (ÃÊË) è Ñîëíå÷íûõ êîñìè÷åñêèõ ëó÷åé
(ÑÊË), à íà îêîëîçåìíûõ îðáèòàõ - ÷àñòèö ðàäèàöèîííûõ ïîÿñîâ Çåìëè (ÐÏÇ).
×àñòèöû ÃÊË îáðàçóþò â ìåæïëàíåòíîì ïðîñòðàíñòâå ìåäëåííî èçìåíÿþùååñÿ ñ
èçìåíåíèåì ñîëíå÷íîé àêòèâíîñòè (ÑÀ) ðàäèàöèîííîå ïîëå, êîòîðîå ëèøü
èçðåäêà è íà êîðîòêîå âðåìÿ (äî ñóòîê) óìåíüøàåòñÿ (äî 50% â ìåæïëàíåòíîì
ïðîñòðàíñòâå) âñëåäñòâèå Ôîðáóø ýôôåêòîâ. Â ñîîòâåòñòâèè ñî ñâîåé
æåñòêîñòüþ, ÷àñòèöû ÃÊË ïðîíèêàþò òàêæå â îêîëîçåìíîå ïðîñòðàíñòâî íà
îðáèòû ñïóòíèêîâ Çåìëè.
Ðàçðàáîòàííûå íà íà÷àëüíîì ýòàïå èññëåäîâàíèè êîñìè÷åñêèõ ëó÷åé
ýìïèðè÷åñêèå ìîäåëè ÃÊË - ÃÎÑÒ 25645.(122, 123, 124, 125)-85; ÃÎÑÒ
25645.144-88 ÃÎÑÒ 25645.150-90 è CREME-81 (Adams et al., 1981), â îñíîâó
êîòîðûõ áûëè çàëîæåíû âåëè÷èíû ïîòîêîâ ÷àñòèö âî âðåìÿ ìàêñèìóìà è ìèíèìóìà
ÑÀ, à òàêæå ñèíóñîèäàëüíàÿ çàâèñèìîñòü ïîòîêîâ ÷àñòèö ñ 11-ëåòíèì ïåðèîäîì
ÑÀ, ê íàñòîÿùåìó âðåìåíè èñ÷åðïàëè ñåáÿ ïîëíîñòüþ. C äðóãîé ñòîðîíû,
ðàçðàáîòàííûå ê íàñòîÿùåìó âðåìåíè òðàíñïîðòíûå ìîäåëè, îïèñûâàþùèå
ñîëíå÷íóþ ìîäóëÿöèþ ÷àñòèö ÃÊË, ïðîíèêàþùèõñÿ èç ãàëàêòè÷åñêîãî
êîñìè÷åñêîãî ïðîñòðàíñòâà â ãåëèîñôåðó (Adams et al., 1991; Badhwar and
O'Neill, 1992, 1994, 1996; Davis et al., 2000, 2001a,b), â áîëüøåé ÷àñòè â
ñâîåé îñíîâå â êà÷åñòâå èñõîäíîãî ïàðàìåòðà èñïîëüçóþò èçìåíÿþùóþñÿ ñ ÑÀ
âåëè÷èíó äèôôóçèîííîãî êîýôôèöèåíòà, âåëè÷èíà êîòîðîãî âû÷èñëÿåòñÿ èç
íàáëþäàòåëüíûõ äàííûõ, êàê ïðàâèëî, îòíîñÿùèõñÿ ê íåéòðîííûì ìîíèòîðàì
(Climax). Ýòî îçíà÷àåò, ÷òî òàêèå ìîäåëè ïîçâîëÿþò îïèñàòü óæå
çàðåãèñòðèðîâàííûå ïîòîêè ÷àñòèö è íå îáëàäàþò ñïîñîáíîñòüþ ïðîãíîçèðîâàòü
ïîâåäåíèå ïîòîêîâ â áóäóùåì âðåìåíè. Áîëåå òîãî, àâòîðû ýòèõ ìîäåëåé
äåìîíñòðèðóþò òî÷íîñòü ñâîèõ ìîäåëåé íà ýêñïåðèìåíòàëüíûõ äàííûõ,
îòíîñÿùèõñÿ ê ìèíèìóìó ÑÀ è èçáåãàþò ýòî äåìîíñòðèðîâàòü íà äàííûõ,
îòíîñÿùèõñÿ ê ìàêñèìóìó ñîëíå÷íîé àêòèâíîñòè, êîãäà ðåçóëüòàòû ìîäåëüíûõ
ðàñ÷åòîâ íàìíîãî õóæå ñîãëàñóþòñÿ ñ ýêñïåðèìåíòàëüíûìè äàííûìè.
Ïåðå÷èñëåííûå äâà îáñòîÿòåëüñòâà: îòñóòñòâèå âîçìîæíîñòè ïðîãíîçà è
íåóäîâëåòâîðèòåëüíîå îïèñàíèå ìîäåëüþ ýêñïåðèìåíòàëüíûõ äàííûõ ïðè
ìàêñèìóìå ÑÀ, ÿâëÿþòñÿ ïðè÷èíîé òîãî, ÷òî â êà÷åñòâå ìåæäóíàðîäíîãî
ñòàíäàðòà áûëà ïðèíÿòà íå òåîðåòè÷åñêàÿ, à ïîëóýìïèðè÷åñêàÿ ìîäåëü ÃÊË. Ýòà
ìîäåëü áûëà â òå÷åíèå ðÿäà ëåò ðàçðàáîòàíà â ÌÃÓ (Ñóñëîâ è Íûììèê, 1988,
1989; Suslov and Nymmik, 1989; Nymmik and Suslov 1989, 1995, 1996; ÃÎÑÒ
25645.150-90; Íûììèê è äð. 1991; Nymmik et al. 1992, 1994, 1995; Beliaev et
al., 1996; Nymmik 1998a,b, 1999a,b,c; ISO 15390-2004). Ñëåäóåò îñîáî
ïîä÷åðêíóòü, ÷òî â òîé ÷àñòè ìîäåëè CREME-96 (Tylka et al. 1997), êîòîðàÿ
îòíîñèòñÿ ê ÃÊË, ìîäåëü ÿâëÿåòñÿ îäíîçíà÷íîé êîïèåé ðàáîòû Nymmik et al.
(1995). Âñå ïåðå÷èñëåííûå ïóáëèêàöèè â ðàçíîé ñòåïåíè ðàñêðûâàþò
ìåòîäîëîãèþ îäíîé è òîé æå ïîëóýìïèðè÷åñêîé ìîäåëè â åå ðàçâèòèé, ðàçíûå
âàðèàíòû êîòîðîé èìåþò è íåêîòîðûå ðàçëè÷èÿ.
Îñíîâíîå ðàçëè÷èå ðàçíûõ âàðèàíòîâ ìîäåëè èìååò â îñíîâå ñïîðíóþ òî÷êó
çðåíèÿ î ïðèðîäå íèçêîýíåðãåòè÷åñêîé êîìïîíåíòû êîñìè÷åñêèõ ëó÷åé. Ïîä ýòèì
îïðåäåëåíèåì ìû èìååì â âèäó ïîòîêè ÷àñòèö ñ æåñòêîñòüþ R<0,25•A/Z à(À -
ìàññîâîå ÷èñëî; Z- çàðÿä ÿäðà), îáùàÿ âåëè÷èíà êîòîðûõ âîçðàñòàåò ñ
óâåëè÷åíèåì ÑÀ è óìåíüøàþòñÿ ñ åå óìåíüøåíèåì. Ïîòîêè ýòèõ ÷àñòèö ðåçêî
âîçðàñòàþò ñ óìåíüøåíèåì ýíåðãèè ÷àñòèö.  ÃÎÑÒ 25645.150-90 ýòè ïîòîêè
áûëè âêëþ÷åíû â ñîñòàâ ìîäåëè ÃÊË, à â ñòàíäàðòå ISO-15390, (2002) è CREME-
96 (Tylka et al, 1997) îíè èç ìîäåëè ÃÊË áûëè èñêëþ÷åíû. Îñíîâàíèåì ýòîãî
ÿâëÿåòñÿ òî, ÷òî óêàçàííûå ÷àñòèöû èìåþò ñîëíå÷íîå ïðîèñõîæäåíèå è èõ
äèíàìèêà ïðîòèâîïîëîæíî èçìåíåíèþ âåëè÷èíû ïîòîêîâ ÃÊË â èõ çàâèñèìîñòè îò
ÑÀ.
Íèçêîýíåðãåòè÷åñêèé êîìïîíåíò î÷åâèäíî ÿâëÿåòñÿ ôîíîâûì èçëó÷åíèåì
áîëüøîãî ÷èñëà î÷åíü ìàëûõ ñîáûòèé ÑÊË, îïèñàíèå êîòîðûõ òðåáóåò äðóãèõ
ìåòîäîâ, ÷åì òå, êîòîðûå ïðèìåíÿþòñÿ â âåðîÿòíîñòíîé ìîäåëè ÑÊË. Ïîñêîëüêó
ìîäåëè, îïèñûâàþùèå êîìïîíåíò íèçêîýíåðãåòè÷åñêèõ ÷àñòèö ïîêà íå
ðàçðàáîòàíû, â ñëó÷àÿõ, êîãäà íåîáõîäèìî îöåíèòü ðàäèàöèîííûå ýôôåêòû â
ïîâåðõíîñòíîì ñëîå âåùåñòâà (d < 1 ìì) ìû äîïóñêàåì èñïîëüçîâàíèå äëÿ
îïèñàíèÿ ïîòîêîâ ýòèõ ÷àñòèö ìîäåëè, çàëîæåííîé â îñíîâó ÃÎÑÒ 25645.150-
90.


2. ÎÁÙÈÅ ÕÀÐÀÊÒÅÐÈÑÒÈÊÈ ÌÎÄÅËÈ ÃÊË.


Ìîäåëü ïðåäíàçíà÷åíà äëÿ êîëè÷åñòâåííîãî îïèñàíèÿ ïîòîêîâ ÷àñòèö
Ãàëàêòè÷åñêèõ êîñìè÷åñêèõ ëó÷åé (ÃÊË) íà îðáèòå Çåìëè çà åå ìàãíèòîñôåðîé â
õîäå ìîäóëÿöèè, îáóñëîâëåííîé 11-ëåòíåé âàðèàöèåé ñîëíå÷íîé àêòèâíîñòè è 22-
ëåòíèì öèêëîì èçìåíåíèÿ êðóïíîìàñøòàáíîãî ìàãíèòíîãî ïîëÿ Ñîëíöà.
Ìîäåëüþ îïèñûâàþòñÿ ïîòîêè ÷àñòèö ñ çàðÿäîì îò 1 äî 92 (âêëþ÷àÿ ýëåêòðîíû)
â äèàïàçîíå ýíåðãèè îò 5 äî 105 ÌýÂ/íóêëîí.
 ìîäåëè îáîáùåíû èìåþùèåñÿ ñîâðåìåííûå ýêñïåðèìåíòàëüíûå äàííûå î ïîòîêàõ
÷àñòèö íà îðáèòå Çåìëè â èõ çàâèñèìîñòè îò:
1. óðîâíÿ ñîëíå÷íîé àêòèâíîñòè, îïðåäåëÿåìîãî êàê óñðåäíåííîå ïî 12
ìåñÿöàì ÷èñëî ñîëíå÷íûõ ïÿòåí (÷èñëà Âîëüôà) è
2. âåëè÷èíû è íàïðàâëåíèÿ êðóïíîìàñøòàáíîãî ìàãíèòíîãî ïîëÿ ãåëèîñôåðû
(îòîæäåñòâëÿåìîãî êàê ïîëÿðíîå ìàãíèòíîå ïîëå Cîëíöà).
 ìîäåëè ó÷òåíû ýôôåêòû çàïàçäûâàíèÿ èçìåíåíèÿ ïîòîêîâ ÷àñòèö ïðè
èçìåíåíèè óðîâíÿ ñîëíå÷íîé àêòèâíîñòè, çàâèñÿùèå êàê îò æåñòêîñòè ÷àñòèö
òàê è îáóñëîâëåííûå ðàçíèöåé ïóòåé (è âðåìåíè) äèôôóçèè ÷àñòèö ïðè ðàçíîì
íàïðàâëåíèè ãåëèîñôåðíîãî ìàãíèòíîãî ïîëÿ.
Ïðèâåäåíû ôîðìóëû è ÷èñëåííûå ïàðàìåòðû, ïîçâîëÿþùèå ïðîâîäèòü ðàñ÷åòû
ïîòîêîâ ÷àñòèö íà ïåðèîä ñ 1954 äî 2010 ãîäà.
Òî÷íîñòü äîëãîâðåìåííîãî ïðîãíîçà âåëè÷èí ïîòîêîâ ÷àñòèö çàâèñèò ãëàâíûì
îáðàçîì îò òî÷íîñòè ïðîãíîçà ÷èñëà ñîëíå÷íûõ ïÿòåí íà ïðîãíîçèðóåìûé ïåðèîä
ñîëíå÷íîé àêòèâíîñòè.
 îñíîâó ìîäåëè ëåæàò ïðèíöèïû ïîëóýìïèðè÷åñêîé äèíàìè÷åñêîé ìîäåëè
ïîòîêîâ ÷àñòèö ÃÊË, öåëèêîì ðàçðàáîòàííàÿ â ÍÈÈßÔ ÌÃÓ (ïóáëèêàöèè
ïåðå÷èñëåíû âûøå). Îäèí èç âàðèàíòîâ ýòîé ìîäåëè áûë óòâåðæäåí â âèäå ÃÎÑÒ
25645.150-90.
Îäèí èç ïîñëåäíèõ âåðñèè ìîäåëè óòâåðæäåí ìåæäóíàðîäíûì ñòàíäàðòîì ISO
15390. Íèæåïðèâåäåííîå îïèñàíèå ìîäåëè îòðàæàåò êàê ðàç ìåòîäîëîãèþ ýòîãî
ñòàíäàðòà.


2.1 Îáùèé ïðèíöèï


Ìîäåëü óñòàíàâëèâàåò âåëè÷èíó ïîòîêîâ ÷àñòèö "i" ñîðòà íà îðáèòå Çåìëè çà
åå ìàãíèòîñôåðîé â n-òîì 11-ëåòíåì öèêëå ñîëíå÷íîé àêòèâíîñòè ïðè
óñðåäíåííîì ÷èñëå Âîëüôà [pic] - [pic] [÷àñòèö/(ì2•ñð•ñ•ÌýÂ/íóêëîí)],
èñõîäÿ èç âåëè÷èíû ïîòîêîâ ÷àñòèö â áëèæíåì ìåæçâåçäíîì ïðîñòðàíñòâå (ÁÌÏ)
- [pic]:

[pic], (1)

ãäå [pic] - åäèíàÿ äëÿ âñåõ ÷àñòèö ïîëóýìïèðè÷åñêàÿ ìîäóëÿöèîííàÿ ôóíêöèÿ,
çàâèñÿùàÿ îò ìàãíèòíîé æåñòêîñòè ÷àñòèö R, óðîâíÿ ñîëíå÷íîé àêòèâíîñòè è
÷åòíîñòè-íå÷åòíîñòè ñîëíå÷íîãî öèêëà. Âèä ìîäóëÿöèîííîé ôóíêöèè îïðåäåëåí
èç òðåáîâàíèÿ íàèáîëåå òî÷íîãî îïèñàíèÿ èìåþùåéñÿ ñîâîêóïíîñòè
ýêñïåðèìåíòàëüíûõ äàííûõ î ïîòîêàõ ÿäåð ÃÊË íà îðáèòå Çåìëè. Îäíîâðåìåííî,
âèä èñïîëüçóåìîé ìîäóëÿöèîííîé ôóíêöèè ïîçâîëÿåò îïèñûâàòü è èçìåíåíèÿ
ïîòîêîâ ýëåêòðîíîâ íà îðáèòå Çåìëè, èñõîäÿ èç èçâåñòíîé ôîðìû
ýíåðãåòè÷åñêîãî ñïåêòðà ýëåêòðîíîâ â Ãàëàêòèêå, îïðåäåëåííîé ïî
ðàäèîàñòðîíîìè÷åñêèì äàííûì ñîãëàñíî Webber et al., (1980)
[pic], ãäå [pic] GV. (2)



2.2 Ñïåêòðû ÷àñòèö â áëèæíåì ìåæçâåçäíîì ïðîñòðàíñòâå è îáùèé âèä
ìîäóëÿöèîííîé ôóíêöèè


Ýíåðãåòè÷åñêèå ñïåêòðû âñåõ ÷àñòèö (êðîìå ýëåêòðîíîâ) â áëèæíåì
ìåæçâåçäíîì ïðîñòðàíñòâå (ÁÌÏ) â ìîäåëè ïðåäñòàâëåíû ÷åðåç æåñòêîñòíûå
ñïåêòðû [pic] ÷àñòèö â âèäå:

[pic], (3)

ãäå [pic] è [pic] - ïîñòîÿííûå, ïðèâåäåííûå â ñòàíäàðòe. Óêàçàííàÿ åäèíàÿ
ôîðìà ïðåäñòàâëåíèÿ äàííûõ î ïîòîêàõ ÷àñòèö ÁÌÏ (ïðè îïðåäåëåííûõ íèæå
ïàðàìåòðàõ [pic] è [pic]) íå ðàñõîäèòñÿ ñ ðåçóëüòàòàìè áîëüøèíñòâà
èññëåäîâàíèé, â êîòîðûõ, îäíàêî, íå ñòàâèëñÿ âîïðîñ àïïðîêñèìàöèè ñïåêòðà
àíàëèòè÷åñêîé ôóíêöèåé ýíåðãèè-æåñòêîñòè.
Èç âûðàæåíèÿ (3) âèäíî, ÷òî ïðè ðåëÿòèâèñòñêèõ ýíåðãèÿõ (?=1) êîýôôèöèåíò
Ñ(i) è ñïåêòðàëüíûé èíäåêñ [pic] îïðåäåëÿþòñÿ îäíîçíà÷íî èç
ýêñïåðèìåíòàëüíûõ äàííûõ.
Äëÿ ìîäóëÿöèîííîé ôóíêöèè ìû íàøëè ñëåäóþùåå ôóíêöèîíàëüíîå âûðàæåíèå,
êîòîðîå âìåñòå ñî ñïåêòðîì (3) õîðîøî îïèñûâàåò ýíåðãåòè÷åñêèå ñïåêòðû
÷àñòèö ïðè ëþáîì óðîâíå ñîëíå÷íîé àêòèâíîñòè (W(?T) ñ ó÷åòîì çàïàçäûâàíèÿ
?T èçìåíåíèÿ ïîòîêà ÷àñòèö îòíîñèòåëüíî õîäà ÑÀ) è íàïðàâëåíèÿ è âåëè÷èíû
îáùåãî ãåëèîñôåðíîãî ìàãíèòíîãî ïîëÿ (?):
[pic] (4)
Óñëîâíî ìû èìååì 3 ýêñòðåìàëüíûõ ýíåðãåòè÷åñêèõ ñïåêòðà äëÿ êàæäîãî ñîðòà
÷àñòèö (ìàêñèìóì, ÷åòíûé è íå÷åòíûé ìèíèìóìû ÑÀ). Ëåãêî ïîêàçàòü, ÷òî,
èñïîëüçóÿ ýòè ñïåêòðû äëÿ ïðîòîíîâ, ÿäåð ãåëèÿ è ýëåêòðîíîâ ìû èìååì 9
óðàâíåíèé - ïî 3 óðàâíåíèÿ äëÿ êàæäîãî ñîðòà ÷àñòèö i:
[pic]
[pic] (5)
[pic]

Èç 9-òè óðàâíåíèé ñ èçáûòî÷íîé òî÷íîñòüþ îïðåäåëÿþòñÿ íåêîòîðûå èç
îñíîâíûõ ïàðàìåòðîâ ìîäåëè - Rmax, Romin(=0,375), ?ïðîò (=2,85),
?He(=3,12), ?(=5,5) è ?(=1,13).
Íà ðèñ. 1 ïðèâåäåí âû÷èñëåííûé íàìè ýíåðãåòè÷åñêèé ñïåêòð ïðîòîíîâ â ÁÌÏ,
êîòîðûé ñîâïàäàåò èëè áëèçîê ê ñïåêòðàì, îïðåäåëåííûì â ðàáîòàõ Garcia-
Munoz et al. (1991), Webber et al, (1987, íî çíà÷èòåëüíî îòëè÷àåòñÿ îò
ñïåêòðà, ïðåäëîæåííîãî â ðàáîòå Badhwar&O'Neil, (1992) (íà Ðèñóíêå 1 íå
ïðèâåäåí).

[pic]

Ðèñóíîê 1. Ðåçóëüòàòû èçìåðåíèÿ ïîòîêîâ ïðîòîíîâ íà îðáèòå Çåìëè
(êðåñòèêè) è ïåðåñ÷èòàííûå ïî ôîðìóëå (6) ê óñëîâèÿì ÁÌÏ (òî÷êè).
Ïóíêòèðíûå ëèíèè - ðàñ÷åò ïî íàñòîÿùåé ìîäåëè äëÿ óñëîâèé 1977, 1987, 1981
è 1969 ãîäà äëÿ îðáèòû Çåìëè. Ñïëîøíûå êðèâûå - ñïåêòðû äëÿ óñëîâèè
áëèæíåãî ìåæçâåçäíîãî ïðîñòðàíñòâà ñîãëàñíî:
1 - íàñòîÿùåé ìîäåëè; 2- Garcia-Munoz, (1991); 3- Webber, (1987).

Òðåòèé ïàðàìåòð ýíåðãåòè÷åñêèõ ñïåêòðîâ îñòàëüíûõ ÿäåð (3 z 96) - ?i, â
ÁÌÏ áûë îïðåäåëåí èç òðåáîâàíèÿ î òîì, ÷òîáû ôóíêöèÿ (1) îïèñûâàëà âñå
ýêñïåðèìåíòàëüíûå äàííûå î ïîòîêàõ ÷àñòèö íà îðáèòå Çåìëè ïðè îäèíàêîâûõ
ïàðàìåòðàõ ìîäóëÿöèîííîé ôóíêöèè (4):
[pic] (6)
Ïðè ýòîì ïîëó÷åííûå ðÿäû Fo(i)(R) äàííûõ, îòíîñÿùèåñÿ ê ðàçíûì
ýêñïåðèìåíòàì áûëè àïïðîêñèìèðîâàíû ôóíêöèåé (3) ñ èñïîëüçîâàíèåì ìåòîäà
íàèìåíüøèõ êâàäðàòîâ, âñëåäñòâèå êîòîðîãî áûëè ïîëó÷åíû ïàðàìåòðû ñïåêòðîâ
ÿäåð "i' â ÁÌÏ.
Íåðåäêè ñëó÷àè, êîãäà â ýêñïåðèìåíòàõ íå îïðåäåëÿþò âåëè÷èíû ïîòîêîâ ÿäåð
îäíîãî ñîðòà, à îòíîøåíèÿ äâóõ ñîðòîâ ÿäåð, ïîòîêè îäíîãî èç êîòîðûõ "|i"
èçâåñòíû ëó÷øå, ÷åì ïîòîêè äðóãîãî (íàïðèìåð He, O, Si , Fe).  ýòîì ñëó÷àå
ìåòîäîì íàèìåíüøèõ êâàäðàòîâ âû÷èñëÿëàñü ôóíêöèÿ:
[pic] (7)
îòêóäà îïðåäåëÿëèñü ïàðàìåòðû ñïåêòðà ÷àñòèö ñîðòà "j" â ÁÌÏ.


2.3 Ñòðóêòóðà ìîäóëÿöèîííîé ôóíêöèè


Âèä ìîäóëÿöèîííîé ôóíêöèè â ìîäåëè íå ñîîòâåòñòâóåò ðåøåíèþ òðàäèöèîííîé
äèôôóçèîííî-êîíâåêöèîííîé ìîäåëè, ò.ê. ðåøåíèå òîé ìîäåëè â âèäå
ýêñïîíåíöèàëüíîé çàâèñèìîñòè îò æåñòêîñòè ÷àñòèö ïðè ýíåðãèÿõ 300
ÌýÂ/íóêëîí íå ïîçâîëÿåò ñîãëàñîâàòü èìåþùèåñÿ äàííûå î ñïåêòðàõ ÷àñòèö â
ÁÌÏ è ñîâîêóïíîñòü ýêñïåðèìåíòàëüíûõ äàííûõ î ïîòîêàõ ÷àñòèö íà îðáèòå
Çåìëè. Ìîäóëÿöèîííàÿ ôóíêöèÿ â íàñòîÿùåé ìîäåëè [pic] ÿâëÿåòñÿ ðåçóëüòàòîì
ïðîèçâåäåíèÿ äâóõ ïîëóýìïèðè÷åñêèõ ôóíêöèè ìîäóëÿöèîííîãî ïàðàìåòð[pic],
îäíà èç êîòîðûõ îïèñûâàåò ðåçóëüòàò íåçàâèñèìûõ, äðóãàÿ - çàâèñèìûõ îò
çíàêà çàðÿäà ÷àñòèöû ìîäóëÿöèîííûõ ýôôåêòîâ:

[pic], (8)

ãäå [pic] (9)
à [pic] - âåëè÷èíà ïîëÿðíîãî (îáùåãî) ìàãíèòíîãî ïîëÿ Ñîëíöà, [pic] -
ôóíêöèÿ, îïèñûâàþùàÿ çàâèñèìîñòü âåëè÷èíû ìîäóëÿöèîííîãî ýôôåêòà îò çíàêà
çàðÿäà ÷àñòèöû

2.3.1 Ìîäóëÿöèîííûé ïîòåíöèàë

Ìîäóëÿöèîííûé ïîòåíöèàë ãåëèîñôåðû â ìîäåëè ÿâëÿåòñÿ ôóíêöèåé îáùåãî óðîâíÿ
ñîëíå÷íîé àêòèâíîñòè, õàðàêòåðèçóåìûì óñðåäíåííûì (ïî 12 ìåñÿöàì)
êîëè÷åñòâîì ñîëíå÷íûõ ïÿòåí [pic]:

[pic] (10)

Ïðè ýòîì ñîïîñòàâëåíèå èçìåíåíèÿ ïîòîêîâ ÷àñòèö ðàçíîé ìàãíèòíîé
æåñòêîñòè ñ èçìåíåíèåì êîëè÷åñòâà ñîëíå÷íûõ ïÿòåí îáíàðóæèâàåò ýôôåêò
ìåíÿþùåéñÿ ñî âðåìåíåì è çàâèñÿùåé îò æåñòêîñòè ÷àñòèö çàäåðæêè [pic]
(Garcia-Munoz et al. 1991.
, Badhwar and O'Neil, 1993; Suslov and Nymmik, 1995; Nymmik 2000):

[pic] [ìåñÿöåâ], (11)

ãäå àìïëèòóäû çàäåðæêè â ÷åòíûõ öèêëàõ (n) ñîãëàñíî Nymmik&Suslov (1996) íå
çàâèñèò îò ñîëíå÷íîé àêòèâíîñòè
[pic] [ìåñÿöåâ] (12a)
ïðàêòè÷åñêè íå çàâèñèò îò æåñòêîñòè ÷àñòèö, â íå÷åòíûõ öèêëàõ
[pic] [ìåñÿöåâ]. (12b)
Ýòè âåëè÷èíû çàëîæåíû â ñòàíäàðò ISO 15390.
Áîëåå íîâûå ýêñïåðèìåíòàëüíûå äàííûå î çàâèñèìîñòè àìïëèòóä çàäåðæêè
[pic] è [pic]îò æåñòêîñòè ïðèâåäåíû íà ðèñ.2 (Nymmik, 2000), êîòîðûå
öåëåñîîáðàçíî âêëþ÷èòü â íîâóþ âåðñèþ ìîäåëè..


[pic]

Ðèñóíîê 2. Àìïëèòóäû çàïàçäûâàíèÿ T÷åòíûé è Òãíå÷åòíûé èçìåíåíèÿ ïîòîêîâ
÷àñòèö ÃÊË ïî ñðàâíåíèþ ñ èçìåíåíèåì ñîëíå÷íîé àêòèâíîñòè êàê ôóíêöèè
æåñòêîñòè ÷àñòèö. Ýêñïåðèìåíòàëüíûå äàííûå èç àíàëèçà âðåìåííûõ ðÿäîâ
ïîòîêîâ: ïðîòîíîâ (êðóæî÷êè), ÿäåð ãåëèÿ (êâàäðàòû) è ïîòîêîâ
âûñîêîýíåðãýòè÷åñêèõ ÷àñòèö â ñòðàòîñôåðå íàä Ìóðìàíñêîì, íåéòðîííûõ
ìîíèòîðîâ Äèèï-Ðèâåð è Êëàéìàêñ (òðåóãîëüíèêè ñëåâà íàïðàâî).

Âðåìåííàÿ ñîñòàâëÿþùàÿ âåëè÷èíû çàäåðæêè [pic] â (7) âûðàæàåòñÿ â âèäå
ôóíêöèè êîëè÷åñòâà ñîëíå÷íûõ ïÿòåí:

[pic], (13)

ãäå [pic] è [pic] åñòü ìèíèìàëüíîå è ìàêñèìàëüíîå êîëè÷åñòâî ñîëíå÷íûõ
ïÿòåí â n-îì öèêëå ñîëíå÷íîé àêòèâíîñòè, à [pic] ìåñÿöåâ.
Ìîäóëÿöèîííûé ïîòåíöèàë ÿâëÿåòñÿ åäèíñòâåííûì àðãóìåíòîì ïåðâîãî
ñëàãàåìîãî ìîäóëÿöèîííîé ôóíêöèè, îïèñûâàþùåãî ðåçóëüòàò ïðîöåññîâ
êîíâåêöèè, àäèàáàòè÷åñêîãî çàìåäëåíèÿ è íåçàâèñèìûõ îò çíàêà çàðÿäà
äðåéôîâ.

2.3.2 Ýôôåêò ìîäóëÿöèè çàâèñèìûõ îò çíàêà çàðÿäà äðåéôîâ.

Âåëè÷èíà ýôôåêòà ìîäóëÿöèè çàâèñèìûõ îò çíàêà çàðÿäà ÷àñòèöû äðåéôîâ,
îïðåäåëÿåòñÿ ïîêàçàòåëåì ñòåïåíè ìîäóëÿöèîííîé ôóíêöèè, êîòîðûé çàâèñèò îò
äâóõ ñëàãàåìûõ:
i. îò âåëè÷èíû îáùåãî ìàãíèòíîãî ïîëÿ ãåëèîñôåðû èëè, â äðóãèõ ñëîâàõ,
ïîëÿðíîãî ìàãíèòíîãî ïîëÿ Ñîëíöà - [pic] (14) è,
ii. ÿâëÿåòñÿ ôóíêöèåé ñêîðîñòè äðåéôà ÷àñòèö â ìàãíèòíîì ïîëå, êîòîðàÿ
ïðîïîðöèîíàëüíà ïðîèçâåäåíèþ îòíîñèòåëüíîé ñêîðîñòè ÷àñòèöû íà åå ìàãíèòíóþ
æåñòêîñòü [pic] (15).
Àíàëèç âðåìåííûõ ðÿäîâ ýêñïåðèìåíòàëüíûõ äàííûõ ïîòîêîâ ÷àñòèö ÃÊË
ïðèâîäèò ê âûâîäó, ÷òî íàáëþäàåìûå èçìåíåíèÿ ïîòîêîâ ìîãóò áûòü îïèñàíû,
åñëè èçìåíåíèÿ îáùåãî (ýôôåêòèâíîãî) ìàãíèòíîãî ïîëÿ ãåëèîñôåðû èìåþò âèä
ñëåäóþùåé ôóíêöèè ñãëàæåííîãî ÷èñëà ñîëíå÷íûõ ïÿòåí:
[pic], (14)
ãäå S=1 ïðè [pic] (èíà÷å S=-1); [pic] åñòü ìîìåíò ïåðåìåíû çíàêà ïîëÿðíîãî
ìàãíèòíîãî ïîëÿ â n-îì öèêëå ñîëíå÷íîé àêòèâíîñòè. Äåéñòâèòåëüíî, èìåííî
òàêèì è ÿâëÿåòñÿ âðåìåííàÿ çàâèñèìîñòü ïîëÿðíîãî ìàãíèòíîãî ïîëÿ Ñîëíöà,
ñîãëàñíî ðàáîòå (Hoeksema, 1996) (ñì. ðèñ.3).

[pic]

Ðèóíîê 3. Íîðìèðîâàííàÿ ê åäèíèöå çàâèñèìîñòü îò âðåìåíè îáùåãî ìàãíèòíîãî
ïîëÿ ãåëèîñôåðû ñîãëàñíî íàñòîÿùåé ìîäåëè (ëèíèÿ) è ïîëÿðíîãî ìàãíèòíîãî
ïîëÿ Ñîëíöà ñîãëàñíî ðàáîòå Hoeksema, (1996) (êðåñòèêè).

Âèä ôóíêöèè ñêîðîñòè äðåéôà â ïîêàçàòåëå âòîðîãî ñëàãàåìîãî ìîäóëÿöèîííîé
ôóíêöèè (3) îïðåäåëåí èç óñëîâèÿ íàèëó÷øåãî ñîãëàñèÿ ðåçóëüòàòîâ ðàñ÷åòîâ
ïî ìîäåëè ñ ýêñïåðèìåíòàëüíûìè äàííûìè î ôîðìå ñïåêòðîâ ÷àñòèö è áûë íàéäåí
â ñëåäóþùåì âèäå:
[pic] (15)
 èòîãå âèä ïîêàçàòåëÿ âòîðîãî ñëàãàåìîãî ìîäóëÿöèîííîé ôóíêöèè èìååò âèä
ïðîèçâåäåíèÿ ñîìíîæèòåëåé (14) è (15) c íîðìèðîâî÷íûì êîýôôèöèåíòîì 1.13
ñì. (9).

3. ÏÎÒÎÊÈ ×ÀÑÒÈÖ ÃÊË ÂÍÅ ÏÐÅÄÅËΠÎÐÁÈÒÛ ÇÅÌËÈ

 ðàìêè âûøåèçëîæåííîé ìîäåëè ïîçâîëÿþò îöåíèòü ïîòîêè ÷àñòèö ÃÊË è âíå
îáëàñòè îðáèòû Çåìëè â ìåæïëàíåòíîì ïðîñòðàíñòâå â ïëîñêîñòè ýêëèïòèêè.
Òàêàÿ îöåíêà áûëà ïðèâåäåíà â ðàáîòå Nymmik and Suslov (1992). Ñ ó÷åòîì
ñîâðåìåííûõ äàííûõ îá óñëîâíûõ ðàçìåðàõ ãåëèîñôåðû, ïîòîêè ÷àñòèö ÃÊË ìîãóò
áûòü âû÷èñëåíû ïðè ïîìîùè âûøåïðèâåäåííûõ ôîðìóë ïðè èçìåíåíèè âåëè÷èíû
ïîòåíöèàëà ñîãëàñíî ôîðìóëå (16):

[pic], (16)
ãäå r - ðàññòîÿíèå îò Ñîëíöà â àñòðîíîìè÷åñêèõ åäèíèöàõ, à ro - ðàäèóñ
îáëàñòè ìîäóëÿöèè (ro—90 à.å.).


4. ÒÎ×ÍÎÑÒÜ ÌÎÄÅËÈ


Îòíîñèòåëüíàÿ ïîãðåøíîñòü ìîäåëè ïðè îïèñàíèè èçìåíåíèé ïîòîêîâ ÷àñòèö ÃÊË
ñ E10 ÌýÂ/íóêëîí â õîäå èçìåíåíèÿ ïàðàìåòðîâ ñîëíå÷íîé àêòèâíîñòè íå
ïðåâîñõîäèò 15%, ÷òî â 3 ðàçà âûøå, ÷åì äëÿ ìîäåëè CREME (Adams et al.
1981), ÷òî íàãëÿäíî äåìîíñòðèðóþò ãðàôèêè ðèñ.4.


[pic]

[pic]


Ðèñóíîê.4. Îïèñàíèå ýêñïåðèìåíòàëüíûõ äàííûõ îá èçìåíåíèè ïîòîêîâ ÿäåð
ãåëèÿ ÃÊË âî âðåìåíè (IMP-8) è ðåçóëüòàòû ðàñ÷åòà ïîòîêîâ ÷àñòèö ñîãëàñíî
ìîäåëÿì CREME (Adams et al.1981) è íàñòîÿùåé ðàáîòû.

Àíàëèç äðóãèõ ýêñïåðèìåíòàëüíûõ ðÿäîâ äàííûõ äëÿ ÷àñòèö ðàçíîé æåñòêîñòè
è ïðèðîäû ïîêàçûâàåò, ÷òî ñòàíäàðòíîå îòêëîíåíèå ðåçóëüòàòîâ ðàñ÷åòà íå
ïðåâîñõîäèò 20%.
Ñëåäóåò îòìåòèòü, ÷òî îáúÿâëåííàÿ äëÿ ìîäåëè ÃÊË, ðàçðàáîòàííîé â ðàáîòàõ
(Davis et al. 2000, 2001a,b) òî÷íîñòü 10% îòíîñèòñÿ ê ñëó÷àþ, êîãäà
âåëè÷èíû ïîòîêîâ ÷àñòèö ÃÊË îïðåäåëÿþòñÿ íå ïî ïàðàìåòðàì ñîëíå÷íîé
àêòèâíîñòè, à ïî ðåçóëüòàòàì àíàëèçà óæå çàðåãèñòðèðîâàííîãî ïîòîêà ÷àñòèö
ÃÊË (íåéòðîííîãî ìîíèòîðà) è íå îòíîñèòñÿ ê ïðîãíîçó ïîòîêîâ ÷àñòèö.


5. ÐÅÀËÈÇÀÖÈß ÐÀÑ×ÅÒÍÎÉ ÌÎÄÅËÈ


Ðàñ÷åòíàÿ ìîäåëü ïîòîêîâ ÷àñòèö ÃÊË áóäåò âûñòàâëåíà äëÿ ïîëüçîâàòåëåé â
ñåòè ÈÍÒÅÐÍÅÒ íà ïåðèîä àïðîáàöèè ìîäåëè ïî àäðåñó:
http://www.npi.msu.su/gcrf/form.html
è äîïóñêàåò ðàñ÷åò ïîòîêîâ ÷àñòèö íà ïåðèîä ñ 1954 ãîäà ïî íàñòîÿùåå âðåìÿ,
à òàêæå ïðîãíîç ïîòîêîâ íà øåñòü ëåò â ïåðèîä â ñîîòâåòñòâèè ñ ïðîãíîçîì
÷èñëà ñîëíå÷íûõ ïÿòåí ïî ñïðàâî÷íûì èçäàíèÿì (ÃÎÑÒ 25645.302-83; Niehuss,
1966; www/sec.noaa.gov ).
Ðàñ÷åòíàÿ ìîäåëü â ñåòè "ÈÍÒÅÐÍÅÒ" äîïóñêàåò ðàñ÷åò ýíåðãåòè÷åñêèõ
ñïåêòðîâ óêàçûâàåìûõ êëèåíòîì ÷àñòèö â óêàçûâàåìîì èíòåðâàëå ýíåðãèè â
óêàçàííûé ïåðèîä âðåìåíè (ãîä, ìåñÿö). Ðåçóëüòàò ðàñ÷åòà âûäàåòñÿ êëèåíòó â
âèäå òàáëèöû èëè ãðàôèêà.
Ñî âñåìè çàìå÷àíèÿìè è ïðåäëîæåíèÿìè ïî ïîâîäó ìåæäóíàðîäíîãî ñòàíäàðòà è
ïî ðàáîòå ñ åãî ðàñ÷åòíûì âàðèàíòîì â ñåòè ÈÍÒÅÐÍÅÒ îáðàòèòüñÿ ïî àäðåñó:
Ð.À. Íûììèê
ÍÈÈ ßäåðíîé Ôèçèêè Ìîñêîâñêîãî Óíèâåðñèòåòà; Ìîñêâà 119899 ,
e-mail: nymmik@srdlan.npi.msu.su

6. Ëèòåðàòóðà


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www.sec.noaa.gov/ftpdir/weekly/predict.txt