Plasmastatic models of Galateya magnetic traps

K. V. Brushlinsky ; A. S. Goldich ; A. S. Desyatova

Matematičeskoe modelirovanie, Tome 24 (2012) no. 8, pp. 81-96.

Résumé

Equilibrium plasma configurations in the magnetic field are considered for three types cylindrical Galateya-traps with conductors immersed in the plasma. Mathematical models of configurations having any symmetry are based on boundary value problems with the two-dimensional semilinear Grad–Shafranov equation of elliptic type. Plasma, magnetic field and electric current spreading in the trap and their properties are investigated in computation. As a common property of all configurations, the electric current vanishes where the plasma pressure is maximum. The maximum current is located near the plasma configuration boundary.

Détail

Keywords: magnetic traps galateyas, plasma equilibrium, Grad–Shafranov equation.

Bibliographie

[1] Morozov A. I., “O galateyakh-plazmennykh lovushkakh s omyvaemymi plazmoi provodnikami”, Fiz. plazmy, 18:3 (1992), 305–316

[2] Morozov A. I., Savelev V. V., “O galateyakh-lovushkakh s pogruzhennymi v plazmu provodnikami”, Usp. fiz. nauk, 168:11 (1998), 1153–1194 | DOI

[3] Shafranov V. D., “O ravnovesnykh magnitogidrodinamicheskikh konfiguratsiyakh”, ZhETF, 33:3(9) (1957), 710–722 | Zbl

[4] Grad H., Rubin H., “Hydromagnetic equilibria and force-free fields”, Proc. 2${}^{\mathrm{nd}}$ United Nations Int. Conf. on the Peaceful Uses of Atomic Energy (Geneva), v. 31, Columbia Univ. Press, N.Y., 1959, 190

[5] Brushlinskii K. V., Matematicheskie i vychislitelnye zadachi magnitnoi gazodinamiki, BINOM. Laboratoriya znanii, M., 2009

[6] Brushlinskii K. V., Savelev V. V., “Magnitnye lovushki dlya uderzhaniya plazmy”, Matem. modelirovanie, 11:5 (1999), 3–36 | MR

[7] Kostomarov D. P., Medvedev S. Yu., Sychugov D. Yu., “Matematicheskoe modelirovanie MGD-ravnovesiya plazmy”, Matem. modelirovanie, 20:5 (2008), 3–34 | MR | Zbl

[8] Johnson J. L., Oberman C. R., Kulsrud R. M., Frieman E. A., “Some stable hydromagnetic equilibria”, Phys. Fluids, 1:4 (1958), 281–296 | DOI | MR | Zbl

[9] Brushlinskii K. V., Chmykhova N. A., “O ravnovesii plazmy v magnitnom pole lovushek-galatei”, Matem. modelirovanie, 22:6 (2010), 3–14 | MR

[10] Morozov A. I., Frank A. G., “Toroidalnaya magnitnaya lovushka-galateya s azimutalnym tokom”, Fiz. plazmy, 20:11 (1994), 982–989

[11] Brushlinskii K. V., Ignatov P. A., “Plazmostaticheskaya model magnitnoi lovushki “galateya-poyas””, Zh. vychisl. matem. i matem. fiz., 50:12 (2010), 2184–2194 | MR | Zbl

[12] Morozov A. I., Murzina M. V., “Prosteishie ravnovesnye konfiguratsii galatei tipa “Poyas””, Fiz. plazmy, 22:6 (1996), 551–563

[13] Brushlinskii K. V., Zaborov A. M., Syrovatskii S. I., “Chislennyi analiz tokovogo sloya v okrestnosti magnitnoi nulevoi linii”, Fiz. plazmy, 6:2 (1980), 297–311

[14] Morozov A. I., Pustovitov V. D., “O stellaratore s levitiruyuschimi obmotkami”, Fiz. plazmy, 17:10 (1991), 1276

[15] Brushlinskii K. V., Zueva N. M., Mikhailova M. S., Morozov A. I., Pustovitov V. D., Tuzova N. B., “Chislennoe modelirovanie pryamykh vintovykh shnurov s provodnikami, pogruzhennymi v plazmu”, Fiz. plazmy, 20:3 (1994), 284–292

[16] Brushlinskii K. V., Morozov A. I., Petrovskaya N. B., “Chislennoe modelirovanie ravnovesnoi vintovoi konfiguratsii s plazmoi na separatrise”, Matem. modelirovanie, 10:11 (1998), 29–36

[17] Brushlinskii K. V., Zueva N. M., Mikhailova M. S., Petrovskaya N. B., “Zavisimost svoistv vintovykh plazmennykh shnurov ot shaga vinta”, Fiz. plazmy, 21:3 (1995), 221–225

[18] Brushlinskii K. V., Zueva N. M., Mikhailova M. S., Petrovskaya N. B., “O edinstvennosti i ustoichivosti reshenii dvumernykh zadach plazmostatiki”, Matem. modelirovanie, 7:4 (1995), 73–86 | MR