“…For Liouville phase‐space mapping, we assume conserved first and second adiabatic invariants, that is, both plasma wave scattering and field‐line curvature scattering effects have been neglected here (Artemyev, Angelopoulos, et al.,
2022; Artemyev, Neishtadt, et al.,
2022; Sergeev et al.,
1983; Shen et al.,
2022). We then have the following relation:
where E is the electron energy, α eq is the pitch angle at the equator, μ is the first adiabatic invariant, B ( s , t ) is the magnetic field intensity along the field line s with B (0, t ) representing the value at the equator, and l 1 and l 2 are the magnetic mirror latitudes in the northern and southern hemisphere, respectively.…”