Magnetospheric MHD Resonances and ULF Pulsations - Ultra and Extremely Low Frequency Electromagnetic Fields - page 235

6.3.3 Magnetospheric Plasma Instabilities

Instabilities of the internal magnetospheric plasma distributions can be another
mechanism for generation of the ULF pulsations. For one example, consider now
kinetic instabilities which result in the generation of MHD and ion-cyclotron waves
in the frequency range of Pc1, Pc2, and Pi1 pulsations. In a linear approximation the
ion-cyclotron instability arises from the energy exchange between the wave field and
charged particles. This interaction becomes the most effective under the resonance
condition (e.g., see the texts by Ginzburg ( 1970 ), and Trakhtengerts and Rycroft
( 2008 ) for detail)

! k z V z D n i ; (6.60)

where ! is the wave frequency, V z is projection of the thermal velocity of particles
on ambient magnetic field, k z is the same projection of wave vector, i is
gyrofrequency of the ions, and n is integer, that is n D 0; ˙ 1; ˙ 2;:::The kinematic
meaning of this condition can be understood in a local reference frame fixed at the
Larmor center of the particle. In this reference frame the wave frequency ! 0 D
! k z V z either equals zero .n D 0/ or a multiple of the ion gyrofrequency .n ¤ 0/.
Depending on the plasma particle distribution of the velocities the interaction
between the MHD wave and the resonant particles may result in either enhancement
or damping of the magnitude of oscillation.
This kind of the plasma instability can be due to the energetic protons
( 10-100 keV) of the ring current region (L 3-6) because of anisotropy of
the proton distributions with respect to the proton velocities (Cornwall 1965 ). The
kinetic energy of the plasma particles trapped in the ring current region can thus
serve as a source for energy transfer towards the ULF pulsations due to either
ion-cyclotron instability mechanism or collisionless Landau damping. Notice that
despite small concentration the helium ions present in plasma of the radiation
ring may greatly affect the ion-cyclotron instability in the frequency range of Pc1
(Dowden 1966 ).
The particle bounce motion between the mirror points above the northern and
southern ionospheres may cause the resonance interaction between the bounce
motion and the MHD waves. The bounce motion is accompanied by large-scale
drift of the plasma particles approximately perpendicular to the Earth magnetic field
lines. This drift caused by the gradient and curvature of the Earth magnetic field
take the particles entirely around the Earth as shown in Fig. 1.10 .TheMHDwave
field can resonate with the bounce and drift plasma motions as the wave frequency
is related to the bounce and drift frequencies through special resonance condition
(Karpman et al. 1977 ; Southwood 1980 ). Moreover, the deviation of the particle
distribution function from the equilibrium function is necessary to provide the drift-
bounce instability. It is believed that this mechanism is capable of explaining the
origin of small-scale (wave number m 50-100) azimuthal poloidal Pc4 pulsations
and giant pulsations Pg (Takahashi 1988 ).