Geoscience Reference
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transport as a function of time and energy. A striking feature here is the
formation of bands of enhanced flux that gradually evolve with time. This
effect is obtained for low-initial temperature (top right panel) and vanishes
at higher initial temperatures (center right panel). The reason for this effect
may be understood by examining the
κ
variations in the bottom right panel
of Fig. 4. Indeed, it is apparent from this latter panel that electrons with
energies up to a few hundreds of eV have
κ
much large than unity. They
accordingly behave in an adiabatic (magnetic moment conserving) manner.
These test electrons however experience a different parallel energization
depending upon bounce phase at the dipolarization onset (violation of the
second adiabatic invariant), and Liouville theorem that states conservation
of the particle density in phase space leads to higher flux for those electrons
that experience larger energy gains.
On the other hand, it can be seen in the bottom right panel of Fig. 4
that, above a few hundreds of eV, electrons have
κ
of the order of unity
or below. These are accordingly subjected to magnetic moment scattering
which hampers the build-up of the above structuring due to differential
parallel energization. In other words, for
T
0
= 30 eV (top right panel), most
of the electrons are found to behave adiabatically with respect to the first
invariant but non-adiabatically with respect to the second one, whereas
for
T
0
= 1 keV (center right panel) the bulk of the electron population
behaves non-adiabatically with respect to the first invariant. Finally, note
that at high energies (several tens of keV), electrons are less sensitive to
the convection surge induced by the dipolarization and that they drift in
the immediate vicinity of the planet; hence their large
κ
parameter.
In the Earth's magnetosphere, Mauk
20
demonstrated that the bouncing
ion clusters frequently observed in the inner plasma sheet (e.g., Refs. 21 and
22) likely follows from such differential parallel energy gains and consequent
violation of the second adiabatic invariant during substorm dipolarization.
At Earth, reconfiguration of the magnetic field lines typically occurs on
time scales of the order of a few minutes and the above flux modulation
accordingly affect essentially ions that have comparable bounce periods.
In contrast, at Mercury, it is apparent from Fig. 4 that, because of small
temporal scales, such a flux modulation may be obtained for electrons and
it may be speculated that, in a like manner to bouncing ion clusters at
Earth, the build-up of bouncing electron clusters will provide information
on the dynamics of the magnetotail.
Finally, it was shown in Ref. 18 that, in the Earth's magnetosphere, the
first adiabatic invariant may not be conserved during dipolarization which
allows for enhanced perpendicular energization. Given the relaxation time
