Currently, seven mechanisms have been proposed to explain the formation of the butterfly PAD during magnetic activities: (a) wave-particle interaction with magnetosonic waves and chorus waves, (b) nonlinear resonance with oblique electromagnetic ion cyclotron waves, (c) wave-particle interaction with hiss waves, lightening-generated whistlers and ground VLF transmitters, (d) outward adiabatic transports, (e) magnetopause shadowing effect, (f) substorm injection combined with drift shell splitting, and (g) nonadiabatic scattering due to the field line curvature scattering and adiabatic effect caused by ring current through the conservation of electron's magnetic moment. During magnetic activities, the observation of butterfly PAD can be located within L = 6 at all magnetic local time (MLT). This mechanism is called as magnetopause shadowing effect. The 90° electrons can drift further than electrons of smaller pitch angles and will be lost when their drift orbits come across the magnetopause. It is produced by the drift shell splitting effect due to the day-night asymmetry of the Earth magnetic field. During the quiet time, electron's butterfly PAD usually takes place at nightside with L = 5–9. The butterfly PAD can be observed during geomagnetic quiet times and disturbances. As for the butterfly distribution, the generation mechanisms are relatively complicated and incomplete. The flat-top distribution can be treated as the transition between pancake and butterfly PAD. The pancake distribution is frequently observed in the radiation belts and can be produced by inward radial diffusion and wave-particle interaction with electron cyclotron harmonic waves and chorus waves. The radiation belt electron's PADs can be classified into three categories: 90° peak (also known as pancake distribution), flat-top distribution, and butterfly distribution with a peak at off 90°.

High time and pitch angle resolution data from Van Allen Probes (VAP) provide us a great opportunity to investigate the relativistic electron's PADs in radiation belts. On the other hand, different PADs can affect the loss and energization of the radiation belt electrons.

Different types of pitch angle distributions (PADs) can provide important information about the underlying physical processes that electron experienced, including wave-particle interaction and radial transport processes. The variation of the relativistic electron's pitch angle distributions is also of great importance in radiation belt physics. Violation of these invariants can lead to the change of electron energy, pitch angle, and drift shell.Įlectron's pitch angle is a key parameter to describe the motion and distribution of particles in phase space. Radiation belts electrons have three quasiperiodic motions: gyration around the ambient magnetic field, bounce along the background magnetic field, and drift around the Earth, each of which can be associated with an adiabatic invariant. The outer belt is very dynamic and dramatically changes during magnetic disturbances. The inner belt is relatively stable compared to the outer belt. The radiation belts generally consist of two distinct zones, the inner belt ( L = 1–2) and the outer belt ( L = 3–8), separated by a low flux “slot” region. The magnetic trapped energetic electrons encircling our planet form the Earth's electron radiation belts.

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