Instrumentation and Data

Both the ISEE 1 electric field and magnetic field data are examined for studying phase skips and the Poynting flux of magnetospheric pulsations. The magnetic fields are measured by the fluxgate magnetometer [Russell, 1978]. The instrument has two commandable ranges, $\pm 8192$ and $\pm 256$ nT. At 16-bit digitization these ranges give 1/4 and 1/128 nT resolution.

The electric fields are measured by the spherical double probe experiment [Mozer et al., 1978]. Measurements are made of the potential difference between a pair of 8-cm-diameter vitreous carbon spheres. The instrument measures the component of the electric field 8 times per second along the boom direction in the spin plane, which is very close to the ecliptic plane. In the spacecraft coordinate system the components of DC electric fields in the sunward (x) direction and the dawn-to-dusk direction (y) can be determined by least squares fitting of the data over one spin period 3 s. The magnetic fields used in this study also have a time resolution of 3 s.

In general, the electric fields in the magnetosphere can be determined by the precision with an uncertainty less than $1.0\rm\,mV/m$under average conditions, and the electric field in the dawn-to-dusk direction, E_y, can be measured with somewhat better accuracy than $0.5\rm\,mV/m$ because the symmetry between two probes is better in this direction [Cattell et al., 1986]. However, for pulsation events, the errors are expected to be much smaller since the wave signatures can well be described without the exact knowledge of nearly constant offsets [Pedersen et al., 1984].

The pulsations events analyzed are selected when the waves of the same frequency can be seen in both electric field and magnetic field data. Figure 1 shows an example of Pc3-4 waves observed by the ISEE 1 spacecraft on November 24 (day 328), 1977, when the spacecraft was located approximately at $(8.5, -4.5, 3.9)\,R_E$ in GSM coordinates.

Figure 1. An example of Pc3-4 waves observed on November 24 (day 328), 1977. The measurements are presented in the spacecraft coordinates that x is sunward, y is roughly duskward, and z is along the spin axis.

The short data gaps are caused by the sounder experiment on board the spacecraft [Harvey et al., 1978], which interfered with the electric field experiment. The average wave frequency for this event is 24 mHz. Another Pc3-4 example observed on November 3 (day 307), 1977, when ISEE 1 was located at $(9.3, 1.0, 4.1)\,R_E$is shown in, Figure 2 where the solid lines are the linearly detrended values and the dashed lines are the band-pass filtered values over the frequency range 20-35 mHz. The Hanning window is applied to the filter in order to reduce the ringing effect. The data gaps are first treated by an interpolation, and the data in the interpolated region are removed after the filtering process. It can be seen that, for both the electric field and magnetic field data, the filter preserves the phase of the original wave signals. In addition, the similarity of the amplitude envelope of these two independently measured signals (E_x and B_y) attests to the reality of the signal as a natural phenomenon.

Figure 2. Another example of Pc3-4 waves observed on November 3 (day 307), 1977. The solid lines show the detrended values, and the dashed lines show filtered values. The frequency band for the filter is 20-35 mHz.

The full three-dimensional (3-D) electric field vectors are required to perform the Poynting flux calculation. Having two components of the electric field and three components of the magnetic field, we may calculate the electric field along the direction of spacecraft's spin axis ($\mathbf{z}$) by assuming that the MHD condition $\mathbf{E} \cdot \mathbf{B}$ = 0 is conserved, that is, E_z = -(E_xB_x + E_yB_y) / B_z. Since this calculation may produce large errors when B_z is comparatively small, we adopt the criterion suggested by Pedersen et al. [1984] that the full 3-D electric field vectors are calculated only when the angle between $\mathbf{B}$ and $\mathbf{z}$ is less than 80.