In this study it is found that the phase skipping phenomenon in pulsation signals is directly related to the directional change of the Poynting flux. This is not an unexpected result since the Poynting flux is a function of the relative phase of the magnetic and electric oscillations and phase skips are due to changes of phase relative to the reference signal. Although these two properties do not have an absolute relationship, it is very likely that phase skips in either dE or dB, or both, will be observed when a series of wave energy impulses with different propagating directions come into the system.
When discussing the impulsive wave energy that seems to be consistent with our observations, it is important to assess how field line and cavity-like resonances play a role in this picture. There is observational evidence of field line resonances in the magnetosphere [e.g., Greenwald and Walker, 1980; Takahashi et al., 1984; Engebretson et al., 1986, 1987]. Mier-Jedrzejowicz and Hughes  conjecture that an impulse initiates the wave packets in phase at all stations, and then the local field lines act as resonators in which the signals drift out of phase due to the slight differences in magnetic field geometry or particle populations at the different field lines. A new impulse brings the signals back in phase again. In this picture the impulse and the resonance should have comparable importance in terms of wave energy.
First, we may obtain some information from the simultaneous Poynting vectors as shown in Figures 5 and 6. If we consider a transverse wave causing field line oscillations, the Poynting vectors behave very differently depending on whether the wave is traveling or standing. Figure 9 is a diagram of the Poynting vectors for the two different schemes. Even though the wave amplitudes for both conditions are set to be the same and the magnitude of Poynting vector oscillations is consequently the same, the traveling wave propagates energy, while the standing wave produces no net energy flux. The Poynting vectors in Figures 5 and 6 more resemble the traveling wave pattern. Thus for the Pc3-4 wave activities in our observations the traveling wave component is stronger. We may also estimate the resonant condition by examining the phase difference between dE and dB [e.g., Singer et al., 1982]. If the phase difference is 90, the wave is standing and a resonant condition is reached.
|Figure 9. The schematic diagrams of the product of E and B for the (left) traveling wave case and the (right) standing wave case. T is the wave period.|
Figure 10 compares the orthogonal components of dE and dB for the Pc3-4 event on day 328, 1977. The phase difference is a strong function of time and it suggests that the spacecraft was not observing a fine standing wave structure.
|Figure 10. The phase comparison between dE and dB for the Pc3-4 event on day 328, 1977.|
A Pc5 event is also studied here for comparison. The ISEE 1 spacecraft observed a 4-mHz wave event both in the electric field and magnetic field (Figure 11) when the spacecraft was located at in GSM coordinates. The waveforms are clearly seen in the raw data. The waves are mainly in the transverse components and they are linearly polarized (not shown).
|Figure 11. The Pc5 event observed by the ISEE 1 spacecraft on November 3 (day 307), 1977.|
Figure 12 shows the phase comparison between dE and dB for this event. It is clear that the spacecraft was seeing a standing wave and the structure persisted for approximately 45 min. This Pc5 event has a very different appearance from the two Pc3-4 events presented, and it suggests that the two classes of pulsations have different nature.
|Figure 12. The phase comparison between dE and dB for the Pc5 event on day 307, 1977.|
While many studies have shown evidence of Pc3-4 field line resonances in spacecraft observations [e.g., Takahashi et al., 1984; Cahill et al., 1986; Engebretson et al., 1986, 1987], the observations in this study present a different result. It is possible that the inconsistence arises because the locations of observations are different. In this study, the observations were mainly made in the region outside the geosynchronous orbit where the fundamental model frequency is likely in the Pc5 band. However, this outer part of the magnetosphere contains strong broadband Pc3-4 waves that are strongly influenced by the foreshock's upstream waves. The Pc3-4 events presented by Cahill et al.  are observed at lower L shells (L = 2.5-5.7), where the fundamental mode frequency shifts to a higher value in the Pc3-4 band. Therefore the impulsive nature of the Pc3-4 in the outer magnetosphere found by this study does not necessarily conflict with the early works which find the resonant behavior of Pc3-4 at inner L shells.
In Figure 7 we see that most of the time average Poynting vectors, or equivalently the energy flow of the pulsations, have a strong field-aligned component. If an Alfvén wave is traveling along the field line toward the ionosphere, the high conductivity in the dayside ionosphere will result in a reflected wave traveling back into the magnetosphere.
The Alfvénic travel time is calculated in the Appendix. For the Pc3-4 event on day 328, 1977, as seen in Figure 5, the ISEE 1 spacecraft was located at in GSM coordinates, or , (latitude) = 7.3, (longitude) = in SM coordinates equivalently. Although ISEE 1 density data are not available for this event, the Fast Plasma Experiment [Bame et al., 1978] on ISEE 2 recorded the ion charge density of approximately . At that time, ISEE 1 was following the ISEE 2 trajectory and only behind by 4 min, and therefore we may take this density as what would have been observed by ISEE 1 since the two spacecraft were very close to each other. Substituting the density and spacecraft locations into (A6) (assuming m = 3), we obtain that s and s. In Figure 5 the time for the field-aligned component of the Poynting vector changing from minimum (negative) to maximum (positive) is about 3 min (e.g., from 2056 UT to 2059 UT; from 2105 UT to 2108 UT). This time is comparable to the calculated value, which represents the time for an Alfvén wave to travel from the spacecraft location following the field line to the southern ionosphere and then travel back through the same path. It should be noted that the above calculation is only a rough estimate since the density model and magnetic field model may be simplistic, and the density of heavy ions has not been included in the calculation. However, it is suggestive that one wave packet could produce multiple phase skips in the wave signals by being reflected from the ionosphere.
Of course one cannot totally ignore the role of wave beating in interpreting phase skipping. Even when a strong impulse of wave energy comes into the system, there must be a certain amount of interference between the incoming wave and the preexisting wave. However, it can be seen in Figure 5 that the wave energy can come from many different directions within 50 min (or 25 min for Figure 6). Therefore the phase skipping phenomenon must be more complicated than the beating of two sinusoidal waves.
From Figures 5 and 6 it can be seen that the phase skipping phenomenon, or the impulses of wave energy, occurred approximately every 5-10 min. One might speculate that these energy impulses are associated with the flux transfer events (FTEs) on the dayside magnetopause since the average time interval between FTE signatures is about 8 min [e.g., Lockwood and Wild, 1993; Kuo et al., 1995]. First of all, as we have described previously, one Alfvénic wave packet could produce multiple phase skips and therefore it is difficult to compare the recurrence of FTEs with the separation time of two phase skips. Second, the statistical result of Berchem and Russell  indicates that FTEs occur almost exclusively during southward IMF conditions, while Table 1 shows that only 6 out of 23 events occurred during the time when the IMF was southward. In addition, Kawano and Russell  also show that statistically the occurrence of FTEs is not associated with the foreshock geometry, which is important in controlling the Pc3-4 activities in the magnetosphere [e.g., Russell et al., 1983].
Our results could also address some apparent inconsistencies in the early work on this topic. Lanzerotti et al.  and Ansari and Fraser  studied the phase skips of low-latitude ( for the former study and for the latter one) pulsations measured by ground magnetometer arrays. Both studies found that the phase skips seldom occur simultaneously at all latitudes, and they concluded that the impulsive process suggested by Mier-Jedrzejowicz and Hughes  could generally not be responsible for their observations. Since few Poynting vectors in our observations (see Figure 7) are perpendicular to the L shells, that is, and , it is possible that only a few examples of globally impulsive events would be found in multistation observations. However, the source of wave energy can still be considered impulsive. A caveat of this argument is that our study is based on the spacecraft observations at high L shells, whereas the aforementioned studies made their observations at low L shells.
Our statistical result of Poynting flux directions shows that most of the Poynting vectors for Pc3-4 pulsations are approximately tangential to the L shells, that is, they are mainly field aligned or in the azimuthal direction. A small portion of Poynting vectors do show a strong component perpendicular to L shells (Figure 7). The simulation work of Junginger  shows that near the resonant region a strong field-aligned Poynting flux flowing toward the closer ionosphere due to the finite ionospheric conductivities. However, Junginger's results cannot be applied to our observations here since he discusses a steady process opposed to the impulsive nature of the field-aligned Poynting flux in our observations, where the orientation of the Poynting flux can change from being parallel to antiparallel to the ambient field in several minutes (Figures 5 and 6). In addition, our observations of Pc3-4 waves show a traveling wave pattern, whereas Junginger simulated the conditions for field line resonances. It is also not likely that these changes are due to the fast variation of ionospheric conductivities and therefore the separation point (or the ``null point'' as given by Allan ) for the Poynting flux flowing to different ionospheres moves northward and southward rapidly along the field line. Table 2 indicates that when the ISEE 1 spacecraft was located in either the northern or southern hemisphere, the numbers of northward Poynting vectors and southward Poynting vectors are in fact comparable.
Therefore our observations suggest the importance of the impulsive process and the reflection of Alfvén waves from the ionosphere, rather than the ionospheric dissipation. This is expected for the dayside region where the ionosphere acts as a good reflector for incident Alfvén waves [see, e.g., Hughes, 1974]. It is also possible that the fast-mode waves may be reflected at some inner boundary, such as the plasmapause, and this reflection may explain some outward propagating Poynting vectors shown in Figure 7. Figure 13 qualitatively sketches the propagation of the Pc3-4 wave packets as observed in this study.
|Figure 13. Sketch of Pc3-4 impulses in the outer part of the magnetosphere.|
We find from the single-spacecraft measurements here that the propagation of Pc3-4 wave energy is not simply propagating inward from an external energy source. The IMF conditions seem to support the model of the upstream wave source for Pc3-4 waves, but the propagation pattern is too complicated to be resolved by this study. The sources for outward propagating wave energy also requires further investigations, although it is possible that the ion drift instability may act as the internal generation mechanism [Anderson et al., 1990]. Future work, possibly by multiple spacecraft observations, might provide understanding of these issues.