Electron Pitch-Angle Distribution in Earth's Magnetotail: Pancake, Cigar, Isotropy, Butterfly, and Rolling-Pin

Electron pitch-angle distributions, including isotropy, pancake, cigar, butterfly, and recently discovered rolling-pin distributions, are crucial to understanding electron dynamics in the magnetotail. However, occurrence rates of these distributions remain unclear. Here, for the first time, we reveal the occurrence rates of these distributions in the magnetotail by using Cluster data during 2001–2009, with special focus on the newly reported rolling-pin distribution. We find that percentages of these distributions are 44.7% (isotropy), 31.3% (pancake), 17.5% (cigar), 4.9% (rolling-pin), and 1.6% (butterfly), respectively. We find that in the XY_GSM plane, occurrence rates of these PADs peak near: [X_GSM ≈ −11 R_E, Y_GSM ≈ −5 R_E] (isotropy), [X_GSM ≈ −15 R_E, Y_GSM ≈ −11 R_E] (pancake), [X_GSM ≈ −11 R_E, Y_GSM ≈ −5 R_E] (cigar), [X_GSM ≈ −11 R_E, Y_GSM ≈ −3 R_E] (rolling-pin), and [X_GSM ≈ −11 R_E, Y_GSM ≈ −4 R_E] (butterfly), respectively; and along the r direction, where r is the distance to the center of the Earth in the XY_GSM plane, their occurrence rates peak near: −18 R_E < r < −12 R_E (isotropy), −20 R_E < r < −12 R_E (pancake), −16 R_E < r < −10 R_E (cigar), r ≈ −13 R_E (rolling-pin), and −14 R_E < r < −10 R_E (butterfly), respectively. Such rates indicate that the rolling-pin and cigar distributions have similar occurrence rates, supporting previous studies suggesting that rolling-pin distributions arise from cigar distributions. All distributions have maximum occurrences near the equator but at different subregions. We cannot find any statistical correlation between magnetic structures and the rolling-pin distributions, different from previous studies suggesting a close connection between them.