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Matsumoto & Omura 1981
Matsumoto, H. and Omura, Y. (1981). Cluster and channel effect phase bunchings by whistler waves in the nonuniform geomagnetic field. Journal of Geophysical Research 86: doi: 10.1029/JA086iA02p00779. issn: 0148-0227.

A test particle simulation has been carried out on the characteristic behavior of resonant electrons in a monochromatic whistler wave propagating along the nonuniform geomagnetic field. The geomagnetic field is approximately by a parabolic field around the equator. In addition to a phase bunching of untrapped electrons due to the inhomogeneity of the magnetic field, found by Vomvoridis and Denavit (1979), another type of phase bunching of initially untrapped and later trapped electrons is found to take place in the parabolically nonuniform magnetic field. The former is called channel effect phase bunching, and the latter is called cluster effect phase bunching. The difference of the cluster effect phase bunching from the channel effect bunching as well as from the conventional phase bunching in a uniform magnetic field is discussed. The relative importance of these phase bunchings in forming resonant currents in the generation process of VLF-triggered emissions is also discussed.

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Journal of Geophysical Research
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