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A Geometric view of Magnetic Surfaces and Magnetic Curves

Year 2019, Volume: 12 Issue: 1, 126 - 134, 27.03.2019
https://doi.org/10.36890/iejg.545865

Abstract

In the present paper, we approach the magnetic surfaces geometrically. For this aim, we study the
problem of constructing a family of magnetic surfaces from a given magnetic field line. We obtain
a parametric representation for the surfaces family whose members share the same magnetic field
lines and magnetic curves. We investigate the trajectory of charged particles moving related to
these surfaces. Moreover, we give various examples of these surfaces and illustrate their figures.

References

  • [1] Barros, M., Romero, A., Magnetic vortices. EPL, 77(2007) 1-5.
  • [2] Barros, M., Cabrerizo, J.L., Fernandez,M., Romero, A., Magnetic vortex filament flows. J. Math. Phys.,48(8) (2007) 082904.
  • [3] Barros, M. General helices and a theorem of Lancret. Proc. Am.Math. Soc.,125, 1503-1509, 1997.
  • [4] Bird, B.R., Stewart, W.E., Lightfoot, E. N., Transport Phenomena. Wiley. ISBN 0-471-07392-X, 1960.
  • [5] Boozer, A.H., Physics of magnetically confined plasmas. Rev. Mod. Phys., DOI:https://doi.org/10.1103/RevModPhys.76.1071, 2005.
  • [6] Bozkurt, Z.,Gök, İ., Yaylı Y., Ekmekci, F.N., A new Approach for Magnetic Curves in Riemannian 3D􀀀Manifolds. J. Math. Phys., 55(2014), 1-12.
  • [7] Cabrerizo, J.L., Magnetic fields in 2D and 3D sphere. J. Nonlinear Math. Phys., 20(3)(2013), 440-4503.
  • [8] Dru¸t-Romaniuc, S.L., Munteanu, M.I., Magnetic curves corresponding to Killing magnetic fields in E3. J. Math. Phys.,52(2011), 113506,
  • [9] Hazeltine, R.D., Meiss, J. D. Plasma Confinement. Dover publications. inc. Mineola, New York, 2003.
  • [10] Pedersen, T.S., Boozer, A.H., Confinement of nonneutral plasmas on magnetic surfaces. Phys. Rev. Lett., 88 (2002), 205002.
  • [11] Wang, G.J., Tang, K., Tai, C.L., Parametric representation of a surface pencil with a common spatial geodesic. Computer-Aided Design, 36(5)(2004), 447-459.
  • [12] Illert, C., Formulation and solution of the classical problem, II Tubular three dimensional surfaces. Nuovo Cimento, 11(1989), 761-780.
Year 2019, Volume: 12 Issue: 1, 126 - 134, 27.03.2019
https://doi.org/10.36890/iejg.545865

Abstract

References

  • [1] Barros, M., Romero, A., Magnetic vortices. EPL, 77(2007) 1-5.
  • [2] Barros, M., Cabrerizo, J.L., Fernandez,M., Romero, A., Magnetic vortex filament flows. J. Math. Phys.,48(8) (2007) 082904.
  • [3] Barros, M. General helices and a theorem of Lancret. Proc. Am.Math. Soc.,125, 1503-1509, 1997.
  • [4] Bird, B.R., Stewart, W.E., Lightfoot, E. N., Transport Phenomena. Wiley. ISBN 0-471-07392-X, 1960.
  • [5] Boozer, A.H., Physics of magnetically confined plasmas. Rev. Mod. Phys., DOI:https://doi.org/10.1103/RevModPhys.76.1071, 2005.
  • [6] Bozkurt, Z.,Gök, İ., Yaylı Y., Ekmekci, F.N., A new Approach for Magnetic Curves in Riemannian 3D􀀀Manifolds. J. Math. Phys., 55(2014), 1-12.
  • [7] Cabrerizo, J.L., Magnetic fields in 2D and 3D sphere. J. Nonlinear Math. Phys., 20(3)(2013), 440-4503.
  • [8] Dru¸t-Romaniuc, S.L., Munteanu, M.I., Magnetic curves corresponding to Killing magnetic fields in E3. J. Math. Phys.,52(2011), 113506,
  • [9] Hazeltine, R.D., Meiss, J. D. Plasma Confinement. Dover publications. inc. Mineola, New York, 2003.
  • [10] Pedersen, T.S., Boozer, A.H., Confinement of nonneutral plasmas on magnetic surfaces. Phys. Rev. Lett., 88 (2002), 205002.
  • [11] Wang, G.J., Tang, K., Tai, C.L., Parametric representation of a surface pencil with a common spatial geodesic. Computer-Aided Design, 36(5)(2004), 447-459.
  • [12] Illert, C., Formulation and solution of the classical problem, II Tubular three dimensional surfaces. Nuovo Cimento, 11(1989), 761-780.
There are 12 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Zehra Özdemir

İsmail Gök

F. Nejat Ekmekci

Publication Date March 27, 2019
Published in Issue Year 2019 Volume: 12 Issue: 1

Cite

APA Özdemir, Z., Gök, İ., & Ekmekci, F. N. (2019). A Geometric view of Magnetic Surfaces and Magnetic Curves. International Electronic Journal of Geometry, 12(1), 126-134. https://doi.org/10.36890/iejg.545865
AMA Özdemir Z, Gök İ, Ekmekci FN. A Geometric view of Magnetic Surfaces and Magnetic Curves. Int. Electron. J. Geom. March 2019;12(1):126-134. doi:10.36890/iejg.545865
Chicago Özdemir, Zehra, İsmail Gök, and F. Nejat Ekmekci. “A Geometric View of Magnetic Surfaces and Magnetic Curves”. International Electronic Journal of Geometry 12, no. 1 (March 2019): 126-34. https://doi.org/10.36890/iejg.545865.
EndNote Özdemir Z, Gök İ, Ekmekci FN (March 1, 2019) A Geometric view of Magnetic Surfaces and Magnetic Curves. International Electronic Journal of Geometry 12 1 126–134.
IEEE Z. Özdemir, İ. Gök, and F. N. Ekmekci, “A Geometric view of Magnetic Surfaces and Magnetic Curves”, Int. Electron. J. Geom., vol. 12, no. 1, pp. 126–134, 2019, doi: 10.36890/iejg.545865.
ISNAD Özdemir, Zehra et al. “A Geometric View of Magnetic Surfaces and Magnetic Curves”. International Electronic Journal of Geometry 12/1 (March 2019), 126-134. https://doi.org/10.36890/iejg.545865.
JAMA Özdemir Z, Gök İ, Ekmekci FN. A Geometric view of Magnetic Surfaces and Magnetic Curves. Int. Electron. J. Geom. 2019;12:126–134.
MLA Özdemir, Zehra et al. “A Geometric View of Magnetic Surfaces and Magnetic Curves”. International Electronic Journal of Geometry, vol. 12, no. 1, 2019, pp. 126-34, doi:10.36890/iejg.545865.
Vancouver Özdemir Z, Gök İ, Ekmekci FN. A Geometric view of Magnetic Surfaces and Magnetic Curves. Int. Electron. J. Geom. 2019;12(1):126-34.