volume | PIER Journals

Abstract

In this work we describe a model for the computation of the scalar and vector potentials associated with known electric and magnetic fields, as well as for the inverse problem. The formulation is general, but the applications motivating our study are related to the requirements for advanced modeling of charged particle dynamics in plasma-driven electromagnetic environments. The dependence of the electromagnetic field and its potentials in space and time is assumed to be separable, where the spatial part is connected to established solutions of the static problem, and the temporal part is derived from a phenomenological description based on time-series of measurements. We benchmark our model in the simple problem of a finite current-carrying conductor, for which an analytical solution is feasible, and then present numerical results from simulations of a magnetospheric disturbance in geospace.

1. Jackson, J. D., Classical Electrodynamics, 3rd Ed., Wiley, New York, 1999.

2. Goldstein, H., Classical Mechanics, 2nd Ed., Addison-Wesley, Boston, 1980.

3. Griffiths, D. J., Introduction in Electrodynamics, 4th Ed., Addison-Wesley, Boston, 2012.

4. Parks, G. K., Physics of Space Plasmas: An Introduction, Addison-Wesley, New York, 1991.

5. Jackson, J. D., "From Lorenz to Coulomb and other explicit gauge transformations," Am. J. Phys., Vol. 70, 917-928, 2002.
doi:10.1119/1.1491265 Google Scholar

6. Carpenter, C. J., "Electromagnetic energy and power in terms of charges and potentials instead of fields," IEE Proc. A, Vol. 136, 55-65, 1989. Google Scholar

7. Tsironis, C. and L. Vlahos, "Anomalous transport of magnetized electrons interacting with EC waves," Plasma Phys. Control. Fusion, Vol. 47, 131-144, 2005.
doi:10.1088/0741-3335/47/1/008 Google Scholar

8. Anastasiadis, A., I. A. Daglis, and C. Tsironis, "Ion heating in an auroral potential structure," Astron. Astrophys., Vol. 419, 793-799, 2004.
doi:10.1051/0004-6361:20034513 Google Scholar

9. Pulkkinen, T. I., N. A. Tsyganenko, H. Reiner, and W. Friedel, The Inner Magnetosphere: Physics and Modeling, American Geophysical Union, Washington, 2005.
doi:10.1029/GM155

10. Tsironis, C., A. Anastasiadis, C. Katsavrias, and I. A. Daglis, "Modeling of ion dynamics in the inner geospace during enhanced magnetospheric activity," Ann. Geophys., Vol. 34, 171-185, 2016.
doi:10.5194/angeo-34-171-2016 Google Scholar

11. Arfken, G. B. and H.-J. Weber, Mathematical Methods for Physicists, 6th Ed., Academic Press, 2005.

12. Rostocker, G., "Geomagnetic indices," Rev. Geophys., Vol. 10, 935-950, 1972.
doi:10.1029/RG010i004p00935 Google Scholar

13. Tsyganenko, N. A., "Data-based modelling of the Earth’s dynamic magnetosphere: A review," Ann. Geophys., Vol. 31, 1745-1772, 2013.
doi:10.5194/angeo-31-1745-2013 Google Scholar

14. Goldston, R. J. and P. J. Rutherford, Introduction to Plasma Physics, CRC Press, Florida, 1995.
doi:10.1887/075030183X

15. Abramowitz, M. and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Ninth Printing), Dover Publications, New York, 1970.

16. Press, W. H., S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran 90, 2nd Ed., Cambridge University Press, New York, 1996.

17. Akasofu, S. I., "Energy coupling between the solar wind and the magnetosphere," Space Sci. Rev., Vol. 28, 121-190, 1981.
doi:10.1007/BF00218810 Google Scholar

18. Russell, C. T., "The solar wind interaction with the Earth’s magnetosphere," IEEE Trans. Plasma Sci., Vol. 28, 1818-1830, 2000.
doi:10.1109/27.902211 Google Scholar

19. Metallinou, F.-A., "Growth and decay of magnetic storms in geospace,", Ph.D. Thesis, Aristotle University of Thessaloniki, 2008. Google Scholar

20. Delcourt, D. C., "Particle acceleration by inductive electric fields in the inner magnetosphere," J.A.S.T.P., Vol. 64, 551-559, 2002. Google Scholar

21. Arykov, A. A. and Yu. P. Maltsev, "Contribution of various sources to the geomagnetic storm field," Geomag. Aeron., Vol. 33, 67-74, 1993. Google Scholar

22. Volland, H., "A semiempirical model of large-scale magnetospheric electric fields," J. Geophys. Res., Vol. 78, 171-180, 1973.
doi:10.1029/JA078i001p00171 Google Scholar

23. Boyle, C. B., P. H. Reiff, and M. R. Hairston, "Empirical polar cap potentials," J. Geophys. Res., Vol. 102, 111-125, 1997.
doi:10.1029/96JA01742 Google Scholar

24. Weimer, D. R., "Improved ionospheric electrodynamic models and application to calculating Joule heating rates," J. Geophys. Res., Vol. 110, A05306, 1997. Google Scholar

Prof. Christos Tsironis