Geodesic
Mathematical modeling of voltage harmonicsfor current-voltage characteristics with singularities
Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 19 (2017) no. 4, pp. 68-78.

Voir la notice de l'article provenant de la source Math-Net.Ru

In the paper mathematical modeling of the voltage harmonics occurring in superconductor is performed. It is assumed that the superconductoris in the resistive state when an alternating harmonic current passes through them. In such the I-V characteristics of a superconductor are nonlinear and often have singularities caused by instability. For this reason, the I-V characteristics of superconductors obtained for alternating and direct currents are very different. Analytical expressions for the voltage amplitude of the first harmonic for wide films of type-II superconductors with singularitiesof jump-type and break-type in the current dependence of the I-V characteristics are obtained. The dependences of the amplitudes of the 1st, 2nd, 3rd and the 5th voltage harmonics on the value of the constant current and on the amplitude of the alternating current are calculated numerically. It is shown that the positions of the current dependencies’ singularities determine important characteristics of the superconductor. The experimental I-V characteristic of the first harmonic of YBCO single crystal is considered. Basing on the mathematical modeling performed, it is shown that at currents above the critical one, the single crystal overheats because of poor heat transfer. The resistance of a single crystal depends on the temperature and increases in proportion to the current; the I-V characteristic has a parabolic relationship.
Keywords: current-voltage characteristic of superconductors, singularities of the current-voltage characteristic, current-voltage characteristic of the voltage harmonics, critical current.
Mots-clés : amplitude voltage of harmonic 
@article{SVMO_2017_19_4_a5,
     author = {N. D. Kuzmichev and M. A. Vasyutin and E. A. Lapshina and D. A. Shilkin},
     title = {Mathematical modeling of voltage harmonicsfor current-voltage characteristics with singularities},
     journal = {\v{Z}urnal Srednevol\v{z}skogo matemati\v{c}eskogo ob\^{s}estva},
     pages = {68--78},
     publisher = {mathdoc},
     volume = {19},
     number = {4},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SVMO_2017_19_4_a5/}
}
TY  - JOUR
AU  - N. D. Kuzmichev
AU  - M. A. Vasyutin
AU  - E. A. Lapshina
AU  - D. A. Shilkin
TI  - Mathematical modeling of voltage harmonicsfor current-voltage characteristics with singularities
JO  - Žurnal Srednevolžskogo matematičeskogo obŝestva
PY  - 2017
SP  - 68
EP  - 78
VL  - 19
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SVMO_2017_19_4_a5/
LA  - ru
ID  - SVMO_2017_19_4_a5
ER  - 
%0 Journal Article
%A N. D. Kuzmichev
%A M. A. Vasyutin
%A E. A. Lapshina
%A D. A. Shilkin
%T Mathematical modeling of voltage harmonicsfor current-voltage characteristics with singularities
%J Žurnal Srednevolžskogo matematičeskogo obŝestva
%D 2017
%P 68-78
%V 19
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SVMO_2017_19_4_a5/
%G ru
%F SVMO_2017_19_4_a5
N. D. Kuzmichev; M. A. Vasyutin; E. A. Lapshina; D. A. Shilkin. Mathematical modeling of voltage harmonicsfor current-voltage characteristics with singularities. Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 19 (2017) no. 4, pp. 68-78. http://geodesic.mathdoc.fr/item/SVMO_2017_19_4_a5/

[1] L. Solimar, Superconducting Tunneling and Application, Izd. Mir, Moscow, 1974 (In Russ.)

[2] N. D. Kuzmichev, “The behavior of the magnetization of polycrystalline YBa$_{2}$Cu$_{3}$O$_{7-x}$ samples in weak magnetic fields”, Technical Physics Letters, 17 (1991), 56 (In Russ.)

[3] N. D. Kuzmichev, “Hysteresis magnetization and harmonic generation by magnetic materials: analysis of the magnetization harmonic spectrum by the example of high-temperature superconductors”, Technical Physics. The Russian Journal of Applied Physics, 64 (1994), 63 (In Russ.)

[4] N. D. Kuzmichev, “The modulation technique for reconstructing the original dependencies and their derivatives in the case of arbitrary modulation amplitudes”, Technical Physics Letters, 20 (1994), 39 (In Russ.)

[5] N. D. Kuzmichev, “Application of the Taylor-Fourier series for numerical and experimental calculation of investigation dependance derivatives”, SVMO, 13 (2011), 70 (In Russ.) | Zbl

[6] M. A. Vasyutin, A. I. Golovashkin, N. D. Kuzmichev, “Nonlinearity of the current-voltage characteristics for YBa$_{2}$Cu$_{3}$O$_{7-x}$ single crystals and the Berezinskii-Kosterlitz-Thouless transition”, Physics of the Solid State, 48 (2006), 2128 (In Russ.)

[7] N. D. Kuzmichev, M. A. Vasyutin, A. I. Golovashkin, “YBCO single crystals I-V characteristics nonlinearity and Nelson-Kosterlitz jump”, Physica C, 849 (2007), 460-462

[8] M. A. Vasyutin, N. D. Kuzmichev, “Nonlinearity of the current-voltage characteristics of high-temperature superconductivity YBa$_{2}$Cu$_{3}$O$_{7-x}$, determined by the modulation technique”, Technical Physics Letters, 18 (1992), 5 (In Russ.)

[9] L. G. Aslamazov, S. V. Lempickiy, “Resistive state in broad superconducting films”, JETP, 84 (1983), 2216

[10] B. Yu. Blok, S. V. Lempickiy, Physics of the Solid State, 26 (1984), 457 (In Russ.)

[11] N. D. Kuzmichev, M. A. Vasyutin, E. A. Lapshina, D. A. Shilkin, “Mathematical modeling of temperature dependence of the second critical field of thin films of niobium nitride”, SVMO, 18 (2016), 134 (In Russ.)

[12] N. D. Kuzmichev, M. A. Vasyutin, D. A. Shilkin, “Upper critical field of niobium nitride thin films”, Physics of the Solid State, 58 (2016), 231 (In Russ.)

[13] N. D. Kuzmichev, M. A. Vasyutin, D. A. Shilkin, “Experimental determination of the derivative of the current–voltage characteristic of a nonlinear semiconductor structure using modulation Fourier analysis”, Semiconductors, 50 (2016), 830 (In Russ.)