Figure A1. The shape of the aurora borealis and the regions of radiation. (a) Point O is the origin of the three coordinate systems: Oxyz, the mobile axes system of IAG, the geographic system Ox′y′z′, and the geomagnetic system Ox 1 y 1 z 1 . EP and ES with R = 1 were represented. The P′OE′ triangle is equal to PFE, and they have surfaces proportional to the negative algebraic energy generated by the absolute speed Ω 2 . On the terrestrial surface, the three types of areas with radiation and ion characteristics important for our study include the following: Region R1 at ±78.5°-90° MLAT, determined by herpolhodic cones; Region R2 at ±56°-79° MLAT, generated by the polhodic cones; and Region R3 at ±0°-56° MLAT, generated by the PCA singularities. N g was used to note the geographic North Pole and N m was used to note the magnetic North Pole and N was used to note the EP North Pole. (b) The oval shape of the aurora borealis in geographical coordinates with the origin O 2 (N m ), where a is the major semiaxis and b the minor semiaxis. Each dotted circle represents 10° of latitude. (c) The representation of the geometric situation of point C in the plane (scale 2:1). (Geophysicochemical model of an ionospheric auroral gyroscope)

















