Abstract
In the paper, inhomogeneous differential equations are obtained to reconstruct the average differential susceptibility of type-II superconductors from the in-phase (real) component of the magnetization’s first harmonic in the hysteresis case. Basing on the second-order differential equation, mathematical modeling of the average differential susceptibility for the theoretical and experimental dependence of the real part of the magnetization’s first harmonic is performed. The Cauchy problem was solved numerically by the Runge-Kutta method of the fourth order of accuracy. To do this, the differential equation for the restoration of the average susceptibility was reduced to a system of differential equations. On the basis of the method developed in the work, the average differential susceptibility of a disc-shaped polycrystalline superconductor YBa2Cu3O7−x was reconstructed from the experimentally obtained first harmonic of magnetization in interval of magnetic fields from 0 to 800 Oe.
Highlights
The dierential equation for the restoration of the average susceptibility was reduced to a system of dierential equations
On the basis of the method developed in the work, the average dierential susceptibility of a disc-shaped polycrystalline superconductor Y Ba2Cu3O7−x was reconstructed from the experimentally obtained rst harmonic of magnetization in interval of magnetic elds from 0 to 800 Oe
Çäåñü êðóæêàìè îáîçíà÷åíû ýêñïåðèìåíòàëüíûå äàííûå äåéñòâèòåëüíîé ÷àñòè ïåðâîé ãàðìîíèêè íàìàãíè÷åííîñòè íîðìèðîâàííîé íà àìïëèòóäó ìîäóëÿöèè h è ñïëîøíàÿ êðèâàÿ ïîêàçûâàåò ðåçóëüòàòû âîññòàíîâëåíèÿ íà îñíîâå óðàâíåíèÿ (2.7)
Summary
Äèôôåðåíöèàëüíûå óðàâíåíèÿ äëÿ âîññòàíîâëåíèÿ ñðåäíåé äèôôåðåíöèàëüíîé âîñïðèèì÷èâîñòè ñâåðõïðîâîäíèêîâ èç èçìåðåíèé ïåðâîé ãàðìîíèêè íàìàãíè÷åííîñòè  ðàáîòå ïîëó÷åíû íåîäíîðîäíûå äèôôåðåíöèàëüíûå óðàâíåíèÿ äëÿ âîññòàíîâëåíèÿ ñðåäíåé äèôôåðåíöèàëüíîé âîñïðèèì÷èâîñòè ñâåðõïðîâîäíèêîâ âòîðîãî ðîäà èç ñèíôàçíîé (äåéñòâèòåëüíîé) ñîñòàâëÿþùåé ïåðâîé ãàðìîíèêè íàìàãíè÷åííîñòè â ãèñòåðåçèñíîì ñëó÷àå. Íà îñíîâå äèôôåðåíöèàëüíîãî óðàâíåíèÿ 2-ãî ïîðÿäêà âûïîëíåíî ìàòåìàòè÷åñêîå ìîäåëèðîâàíèå ñðåäíåé äèôôåðåíöèàëüíîé âîñïðèèì÷èâîñòè äëÿ òåîðåòè÷åñêîé è ýêñïåðèìåíòàëüíîé çàâèñèìîñòè äåéñòâèòåëüíîé ÷àñòè ïåðâîé ãàðìîíèêè íàìàãíè÷åííîñòè. Äëÿ ýòîãî äèôôåðåíöèàëüíîå óðàâíåíèå äëÿ âîññòàíîâëåíèÿ ñðåäíåé âîñïðèèì÷èâîñòè ñâîäèëîñü ê ñèñòåìå äèôôåðåíöèàëüíûõ óðàâíåíèé.
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