Calculation of Geomagnetic Cutoff Rigidity Using Tracing Based on the Buneman–Boris Method

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Abstract

The work includes the development of a method for determining the rigidity of geomagnetic cutoff based on tracing charged particles in the Earth’s magnetic field using the particle-in-cell method, implemented in the Buneman–Boris scheme. To test the method, calculations of the geomagnetic cutoff rigidity were carried out in the field of an ideal dipole and in the field specified by the IGRF model. In the first case, the obtained data were compared with analytical values. The calculation accuracy in this case was 3 MV. In the second case, the penumbra pattern was reproduced at different geographical points for different periods, and the stability of the method to small perturbations of the initial parameters was also investigated. As the main results of the work, maps of geomagnetic cutoff rigidity at the altitudes of low-orbit satellites for different directions in space, as well as their variations from 1900 to 2015, were constructed and analyzed.

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About the authors

P. A. Kruchinin

Moscow Engineering Physics Institute

Author for correspondence.
Email: kruchinin_01@inbox.ru
Russian Federation, Moscow

V. V. Malakhov

Moscow Engineering Physics Institute

Email: vvmalakhov@mephi.ru
Russian Federation, Moscow

V. S. Golubkov

Moscow Engineering Physics Institute

Email: vlad10433@mail.ru
Russian Federation, Moscow

A. G. Mayorov

Moscow Engineering Physics Institute

Email: agmayorov@mephi.ru
Russian Federation, Moscow

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Supplementary files

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2. Fig. 1. Map of the LGE deviations of the modelled particle relative to the value obtained from the Störmer formula for the geomagnetic latitude λ = 30°. The distance is 5 Earth radii from the centre of the dipole.

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3. Fig. 2. Dependence on latitude of the relative difference between the calculated and theoretical values of the LGE. Distance: 5 Earth radii from the centre of the dipole.

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4. Fig. 3. Illustration of the penumbra of geomagnetic clipping. Sioux Falls. IGRF-13 model (left). 1975. Altitude 30 km. The zenith angle of the particle arrival is 5°. On the right is the result of Smart and Shea [D.F. Smart and M.A. Shea, 2009]. White denotes the allowed regions, black denotes the forbidden regions.

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5. Fig. 4. Study of the stability of the geomagnetic clipping penumbra from the initial parameters of particle arrivals.

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6. Fig. 5. Geomagnetic clipping stiffness map for (a) vertical particle arrival direction; (b) zenith angle 15°, azimuth angle 200°; (c) zenith angle 30°, azimuth angle 200°. Model IGRF-13. 2006. Altitude 500 km.

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7. Fig. 6. LCA maps for azimuthal angles from 0° to 350° in 50° increments. Zenith angle = 30°. 2006. Altitude 500 km.

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8. Fig. 7. (a) Map of relative deviations of geomagnetic clipping stiffness values in 1903 and 2023; (b) time dependence of geomagnetic clipping stiffness (crosses) and magnetic field strength (squares) [Gelvam et al., 2009] in the region of the South Atlantic magnetic anomaly (40° S; 50° W).

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