Magnetospheric MHD Resonances and ULF Pulsations - Ultra and Extremely Low Frequency Electromagnetic Fields - page 225

6.2.5 Wave Polarization

As we have noted above, near the resonance the phase of the resonance components
changes by abruptly, so one may expect a corresponding change in the wave
polarization in the vicinity of the resonance point. From Eq. ( 6.131 ) it follows that
the amplitudes of E x and E y are related through

E x
E y

ik y
k A k n k y

dE y
dx

1
E y :

(6.55)

In the region x<the sense of polarization depends on only the signs of k y and
dE y =dx. In other words, the sense of polarization is a function of the direction of
propagation in y, and it depends on whether the amplitude increases or decreases
with the radial distance (Southwood 1974 ).
In the vicinity of the resonance point x D Eq. ( 6.55 ) is reduced to

E x
E y

i
k y

dE y
dx

1
E y :

(6.56)

This implies that the sense of polarization switches on each side of a maximum and
or minimum in amplitude. For example, consider an eastward propagating MHD
wave, which corresponds to k y >0. In the region where dE y =dx < 0 the wave is
the clockwise-polarized and vice versa. We recall that the y axis corresponds to the
west-east direction, while x axis is in radial direction. In this picture the expected
polarization and the wave amplitude as a function of L for magnetic equator plane
is schematically shown at the upper panel of Fig. 6.4 . For the resonance shell
the polarization tends to be linear. In the case of a westward propagating wave

k y <0 the sense of polarization is reversed. Looking down on the Earth from
above in the northern hemisphere, this wave would have clockwise polarization
south of the resonant site and anticlockwise polarization north of the resonance.
These properties of the polarization would thus be expected to be valid on the ground
despite the influence of the conducting E layer of the ionosphere.
On the basis of data recorded at a chain of stations at geomagnetic latitudes
between 59 ı N and 77 ı N within 2 ı of longitude 302 ı E Samson et al. ( 1971 )have
studied the diurnal and latitude variations of the amplitude and polarization of
the long-period pulsation. Their basic results for fixed frequency of 5 mHz are
schematically shown in Fig. 6.5 . The pulsation amplitude reaches a peak value at
the line which belongs to auroral zone. Across this line the rotation sense of the
horizontal polarization changes from counterclockwise to clockwise or vice versa at
midday.
It is generally believed that the ULF pulsations in the frequency range
10 2 -10 3 Hz originate from the interaction between the solar wind and planetary
magnetosphere. In this picture an FMS wave propagating in the magnetosphere
can build up as a result of Kelvin-Helmholtz instability at the magnetopause.