Geodesic
The simulation of high energy charged particles motion in the summary dipole magnetic field and uniform magnetic field
Matematičeskoe modelirovanie, Tome 7 (1995) no. 6, pp. 32-53.

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The model of charged particles motion in the summary dipole and external uniform, parallel to dipole, field is considered. External field associates with the effect of magnetic perturbation. Such problem appeares, for example, for protons in the geomagnetic field during the magnetic storm. In contrast to traditional model, not the line of force, but the so-called central trajectory (СТ- trajectory, passes through the dipole center) is used as the leading centers trajectory. It allows to save the basic ideas of adiabatic theory for the non-adiabatic case in modified form. The characteristics of СТ are discribed with the help of numerical experiment and the modification of Puankare mapping, extending the range of discrete model of motion, is build. 
@article{MM_1995_7_6_a1,
     author = {I. V. Amirkhanov and Yu. G. Dzuba and E. P. Zhidkov and A. N. Il'ina and V. D. Il'in},
     title = {The simulation of high energy charged particles motion in the summary dipole magnetic field and uniform magnetic field},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {32--53},
     publisher = {mathdoc},
     volume = {7},
     number = {6},
     year = {1995},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_1995_7_6_a1/}
}
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I. V. Amirkhanov; Yu. G. Dzuba; E. P. Zhidkov; A. N. Il'ina; V. D. Il'in. The simulation of high energy charged particles motion in the summary dipole magnetic field and uniform magnetic field. Matematičeskoe modelirovanie, Tome 7 (1995) no. 6, pp. 32-53. http://geodesic.mathdoc.fr/item/MM_1995_7_6_a1/