VLF chorus emissions modeling with EPOCH PIC code: Analysis of the fine structure of chorus elements

Fine structure of chorus elements, which may consist of several subpackets, is studied. This structure is seen in experimental data from satellites and confirmed by numerical simulations. We use a recently developed numerical model for the generation of VLF chorus emissions in the Earth's magnetosphere based on the one-dimensional EPOCH PIC code. We use the parameter Ntr that quantifies the number of oscillations of the electron velocity in the quasi-monochromatic electromagnetic wave field, as it passes through a subpacket, and study its relation with chorus emission properties. This parameter represents the nonlinear nature of chorus emission generation, including the nonlinear mechanism of subpackets formation. We show that the relation between the parameter Ntr and the maximum wave field amplitude in a subpacket Bsub obeys a power law dependence, and that this relation is the same along the entire generation region. The latter property confirms and quantifies the fact that subpackets are formed together with the chorus element, and their characteristics do not change significantly during chorus propagation within the generation region. We obtain that Ntr≲1 on average, i.e., a typical subpacket has a duration corresponding to about one electron oscillation in the wave field. These results clarify previously formulated ideas regarding the nature of subpacket formation.