Electron Scattering Due To Asymmetric Drift-Orbit Bifurcation: Geometric Jumps of Adiabatic Invariant

Radial transport of energetic electrons is one of the key processes responsible for the variability of the outer radiation belt. This transport amounts to a violation of the drift motion. One of the mechanisms that can lead to such violation and associated radial transport is drift-orbit bifurcation. This arises naturally from solar wind compression of the dayside magnetosphere, which results in a local maximum of the field strength at the equator and two off-equatorial minima at the north and south segments of the field line. Azimuthally drifting, near-equatorially mirroring electrons can be trapped, bouncing along the field line in either of those minima for a portion of their drift orbit around Earth. Trapping and the ensuing de-trapping are associated with jumps of the second adiabatic invariant, making the third adiabatic invariant undefined and the drift orbit open. Drift-orbit bifurcation has been previously investigated for north-south and dawn-dusk symmetric configurations of the magnetospheric magnetic field. Here we study the implications of an asymmetry in the drift-orbit bifurcation due to a large IMF $B_y$ field. Using the theory of separatrix crossings in Hamiltonian systems with a slow and a fast variable, we demonstrate that there are geometric (in phase space) jumps of adiabatic invariants due to the asymmetry of the magnetic field configuration. These jumps have magnitudes comparable to the initial invariant magnitudes and are dictated by the topology of the magnetic field. We develop a technique that allows estimation of the jumps in a given magnetic field configuration. We also assess the radial transport expected from asymmetric drift-orbit bifurcation. We find that such transport can reach $\pm 1$ $R_E$ (Earth's radius) per drift period, depending on the magnitude of the IMF $B_y$.