The relationship between Pc3-4 pulsations and the solar wind parameters were obtained by com- paring Pc3-4 periods with solar wind parameters (Gringauz et al., 1970) measured on Venus 2 (1965), Venus 4 (1967) and Venus 5 and 6 (1969). The purpose of this section is to describe the main source of Pc3 pulsations and highlight their propagation path in the magnetosphere.
Extensive theoretical and observational studies of ULF pulsations available in the literature in- form and drastically improve our knowledge and understanding of pulsation source mechanisms.
Observational evidence suggesting that these geomagnetic pulsation are controlled, if not ac- tually generated by the solar wind, has been mounting in the literature. This supported the formulation of the problem of diagnosing the magnetosphere by means of ULF waves (Troit- skaya, 1961; Troitskaya and Melnikova, 1959; Troitskaya et al., 1962). Upstream waves asso- ciated with the quasi-parallel shock have been linked to both compressional Pc3 and toroidal multi-harmonic field line resonance (Anderson, 1994). The ULF upstream waves with a typ- ical period of 20-30 s are large amplitude waves found almost everywhere in the Earth fore- shock region (Greenstadt et al., 1968) generated by ion-cyclotron resonant instability caused by ions backstreaming along the magnetic field to generate Alfv´en waves in the interplanetary medium (Fairfield, 1969; Thomsen, 1985). The ion cyclotron waves are subsequently convected downstream across the bowshock to the magnetopause and couple energy into magnetosphere (Barnes, 1970; Greenstadt et al., 1968; Le and Russell, 1996).
The ULF waves observed in the upstream region from the Earth’s bow shock, appear with different wave forms depending on their locations in the foreshock: nearly monochromatic transverse waves near the foreshock boundary, compressional waves with steepening edges deep into the foreshock, and very irregular nonlinear waves near the bow shock (Le and Russell,
(a) (b)
Figure 2.8: a) SW speed control of UW mean compressional power. b) IMF cone angle control of UW compressional power. (Adopted from Heilig et al. (2007).)
1994, 1996).
2.9.1 Upstream wave path
Engebretson et al. (1991) reviewed models of upstream wave entry into the Earth’s magneto- sphere, focusing on the direct entry of wave energy across the magnetopause, followed by mode conversion to generate resonant transverse pulsations. The Earth’s foreshock is the region up- stream from the bow shock where the interplanetary magnetic field intersects the bow shock and is characterised by backstreaming electrons, ions and associated waves (Le and Russell, 1994). ULF waves generated in the region upstream of the bow shock are convected down- stream by the solar wind into the magnetosheath. When the IMF cone angle is small, waves in the subsolar upstream region are carried to the magnetopause boundary. The magnetopause re- sponds to these pressure fluctuations and transfers wave energy into the dayside magnetosphere where they can excite field line resonances. Upstream waves have a broad-band spectrum, and when propagating through the magnetosphere, different parts of this spectrum correspond to local field line resonances and excite them (Varga, 1980). It is generally agreed that upstream waves are the major source for dayside Pc3 and 4 magnetic pulsations (Le and Russell, 1994).
However, the wave structure observed may be affected by cavity modes (Menk et al., 2000).
2.9.2 The observable relationship between the upstream wave and Pc3-4 pulsations
The frequency of UWs is proportional to the magnitude of the interplanetary magnetic field (Troitskaya et al., 1971) and the UW occurrence rate is controlled by IMF direction, namely the
Figure 2.9: The relationship between UW peak frequency and the IMF strength. (Adopted from Heilig et al. (2007)).
IMF cone angle (Bolshakova, 1966; Bolshakova and Troitskaya, 1968; Greenstadt and Olson, 1977; Russell et al., 1983). A small cone angle creates a favourable condition for the generation of upstream waves (Le and Russell, 1996). The relationship between IMF strength and wave frequency is explained by linear theory (Fairfield, 1969) since the majority of the waves are believed to be generated by resonant interactions coming from the bow shock (Barnes, 1970;
Gary et al., 1981). The dominant frequency of Pc3-4 pulsations observed on the ground was shown to be controlled by the strength of the IMF (Green et al., 1983). The relationship between upstream wave frequency and the IMF was suggested as:
fU W(mHz) = 6 IM F(nT). (2.27)
Heilig et al. (2007) used magnetic field measurements from the CHAMP satellite to investi- gate upstream waves (UW) in the topside ionosphere and made suggestions concerning the entry mechanism of UW’s from the foreshock region into the magnetosphere. They compared their comprehensive observations of UW in the topside ionosphere observed by CHAMP with pulsations observed on the ground. The mean signal power of compressional wave activity in CHAMP data for the group of waves confined to the dayside (06:00-18:00 LT) was shown to be highest over the equator and lowest around 400 latitude.
Heilig et al. (2007) tested the effect of solar wind speed, interplanetary magnetic field (IMF) and cone angle on the UWs, since these parameters are known to control the generation of UWs (Saito, 1964; Troitskaya et al., 1971). They confirmed that high solar wind speed pro- vided higher power input to UWs and that a smaller cone angle creates a favourable condition for the generation of upstream waves as shown in Figures 2.8(a) and 2.8(b) respectively; also
that the frequency of the UWs is proportional to the IMF strength (see Figure 2.9). They also provided the first observational verification of the Doppler shift of the UW frequency relative to the satellite frame, caused by the super Alfv´enic solar wind.