A Geometric view of Magnetic Surfaces and Magnetic Curves

Year 2019, Volume: 12 Issue: 1, 126 - 134, 27.03.2019

Zehra Özdemir , İsmail Gök , F. Nejat Ekmekci

https://doi.org/10.36890/iejg.545865

Cited By: 3

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.

Keywords

Magnetic vector fields, magnetic curve, special surfaces

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.