Tomography of force-free fields
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 18 (2015) no. 3, pp. 237-253.

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

In order to investigate the force-free fields it is proposed to use the computerized tomography methods. For the inversion of the ray transformation, the method of multipole fields expansion has been developed. This method is based on the expansion of a vector field and the ray transformation over the special basis of vector-functions. Analytical expressions for the ray transform of the basis vector-functions and the results of computer simulation are given.
@article{SJVM_2015_18_3_a0,
     author = {A. L. Balandin},
     title = {Tomography of force-free fields},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {237--253},
     publisher = {mathdoc},
     volume = {18},
     number = {3},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2015_18_3_a0/}
}
TY  - JOUR
AU  - A. L. Balandin
TI  - Tomography of force-free fields
JO  - Sibirskij žurnal vyčislitelʹnoj matematiki
PY  - 2015
SP  - 237
EP  - 253
VL  - 18
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJVM_2015_18_3_a0/
LA  - ru
ID  - SJVM_2015_18_3_a0
ER  - 
%0 Journal Article
%A A. L. Balandin
%T Tomography of force-free fields
%J Sibirskij žurnal vyčislitelʹnoj matematiki
%D 2015
%P 237-253
%V 18
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJVM_2015_18_3_a0/
%G ru
%F SJVM_2015_18_3_a0
A. L. Balandin. Tomography of force-free fields. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 18 (2015) no. 3, pp. 237-253. http://geodesic.mathdoc.fr/item/SJVM_2015_18_3_a0/

[1] Moffat G., Vozbuzhdenie magnitnogo polya v provodyashchej srede, Mir, M., 1980

[2] Chandrasekhar S., Kendall P. C., “On force-free magnetic fields”, Astrophys. J., 126 (1957), 457–460 | DOI | MR

[3] Chandrasekhar S., “On force-free magnetic fields”, Proc. Nat. Acad. Sci. of USA, 42:1 (1956), 1–5 | DOI | MR | Zbl

[4] Bellan P. M., Fundamentals of Plasma Physics, Cambridge University Press, Cambridge, 2006

[5] Chandrasekhar S., Hydrodynamic and Hydromagnetic Stability, Oxford University Press, Oxford, 1961 | MR | Zbl

[6] Freire G. F., “Force-free magnetic-field problem”, Amer. J. Phys., 34 (1966), 567–570 | DOI

[7] Marsh G. E., Force-Free Magnetic Fields: Solution, Topology and Applications, World Scientific Publishing Co. Pte. Ltd, Singapore, 1996

[8] Howard J., “Vector tomography applications in plasma diagnostics”, Plasma Physics and Control Fusion, 38 (1996), 489–503 | DOI

[9] Balandin A. L., Ono Y., “Tomographic determination of plasma velocity with the use of ion Doppler spectroscopy”, Eur. Phys. J. D, 17 (2001), 337–344 | DOI

[10] Winters K. B., Rouseff D., “Tomographic reconstruction of stratified fluid flow”, IEEE Trans. Ultrason., Ferroelectr. Freq. Control, UFFC-40:1 (1993), 26–33 | DOI

[11] Norton S. J., “Tomographic reconstruction of 2-D vector fields: application to flow imaging”, J. Geophysics, 97 (1987), 161–168 | DOI

[12] Schuster Th., “An efficient mollifier method for three-dimensional vector tomography: convergence analysis and implementation”, Inverse Problems, 17:4 (2001), 739–766 | DOI | MR | Zbl

[13] Sparr G., Strahlen K., Lindstrom K., Persson H. W., “Doppler tomography for vector field”, Inverse Problems, 11:5 (1995), 1051–1061 | DOI | MR | Zbl

[14] Osman N. F., Prince J. L., “3D vector tomography on bounded domains”, Inverse Problems, 14:1 (1998), 185–196 | DOI | MR | Zbl

[15] Derevtsov E., Kazantsev S., Schuster T., “Polynomial bases for subspaces of potential and solenoidal vector fields in the unit ball of R3”, J. Inv. Ill-Posed Prob., 15:1 (2007), 19–55 | DOI | MR | Zbl

[16] Varshalovich D. A., Moskalev A. N., Khersonskij V. K., Kvantovaya teoriya uglovogo momenta, Nauka, L., 1975

[17] Blatt D. Zh., Vajskopf V., Teoreticheskaya yadernaya fizika. Prilozhenie II, IL, M., 1954 | Zbl

[18] Moses H. E., “The use of vector spherical harmonics in global meteorology and aeronomy”, J. Atmospheric Sci., 31 (1974), 1490–1500 | 2.0.CO;2 class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI | MR

[19] Hill E. H., “The theory of vector spherical harmonics”, Amer. J. Phys., 22 (1953), 211–214 | DOI | MR

[20] Hansen W. W., “A new type of expansion in radiation problem”, Phys. Rev., 47 (1935), 139–143 | DOI | Zbl

[21] Stratton J. A., Electromagnetic Theory, McGraw-Hill, New York, 1941 | Zbl

[22] Colton D., Kress R., Inverse Acoustic and Electromagnetic Scattering Theory, Springer-Verlag, Berlin, 1992 | MR | Zbl

[23] Edmonds A. R., Angular Momentum in Quantum Mechanics, Princeton University Press, Princeton, NJ, 1974 | MR

[24] Cantarella J., DeTurck D., Gluck H., “Vector calculus and the topology of domains in 3-space”, Amer. Math. Month., 109:5 (2002), 409–442 | DOI | MR | Zbl

[25] Mors F. M., Feshbakh G., Metody teoreticheskoj fiziki, v. 1, 2, IL, M., 1958

[26] Bejtmen G., Erdeji A., Vysshie transtsendentnye funktsii, v. 2, Nauka, M., 1974

[27] Erdelyi A., Magnus W., Oberhettinger F., Tricomi F. G., Higher Transcendental Functions, v. 1, 2, McGraw-Hill, New York, 1953 | Zbl

[28] Natterer F., Matematicheskie aspekty komp'yuternoj tomografii, Mir, M., 1990 | MR

[29] Gradshtejn I. S., Ryzhik I. M., Tablitsy integralov, summ, ryadov i proizvedenij, IFML, M., 1962

[30] Natterer F., Wubbeling F., Mathematical Methods in Image Reconstruction, SIAM, Philadelphia, 2001 | MR | Zbl

[31] Bidenkharn L., Lauk Dzh., Uglovoj moment v kvantovoj fizike. Teoriya i prilozheniya, v. 1, Mir, M., 1984