On March 18, 1996 POLAR crossed the dayside cusp at a low altitude (0.81Re from Earth's surface) at a magnetic latitude of 11:00 and while moving towards the high latitude polar cap. At the cusp TIMAS observed O+ and H+ conics. The O+ conic with highest energy was seen at the spin centered at 08:37:48. The H+ conic with highest energy was seen at the spin centered at 08:37:48.
The EFI instrument observed very high amplitude waves during this cusp crossing and thus the burst mode was triggerred. The raw field data are shown in the despun frame X-Y, Z, 56 in Figure EFI_RAW (System: X-Y is crosssection of spin plane and ecliptic pointing to SUN, Z is on spin plane pointing northward, 56 is along spin axis completing an orthogonal system). The top panel shows the E-field transmitted at 40 Hz, while the bottom panel shows the E-field transmitted at 1600 Hz with a 500 Hz filter.
We have transformed the E-field in the Parallel/Perpendicular components relative to the instantaneous magnetic field. This transformation is currently good to within 5% and will improve significantly in the next few weeks. It is evident from Figure EParEPerp that the E-field fluctuations are perpendicular to the B-field to within the current accuracy of the transformation.
The waveform during the presense of the O+ conic is shown in Figure EParEPerp_Detail1. The waveform during the H+ conic is shown in Figure EParEPerp_Detail2.
The power spectrum during the two minute interval 08:37-08:39 UT is shown in Figure EParEPerp_Total. The power spectrum during the O+ conic is shown in Figure PwrSpc_Detail1. The power spectrum during the H+ conic is shown in Figure PwrSpc_Detail2. Note that some differences in the low frequency power computed from the low res. and burst mode data do exist. They are due to aliasing as the waves are not monochromatic but are due to bipolar structures and spikes in the E-field. This is why the spectrum is quite broadbanded.
The magnetic field during the period was ~9370 nT, in agreement with the T95 model. The O+ and H+ gyrofrequencies are approximately 9 Hz and 140 Hz respectively. The power at those frequencies is 100 and 10 (mV/m)^2/Hz respectively. A dynamic power spectrum of the 2 minute interval is shown in Figure EFIParPerPSD.
More careful analysis of the probe potential indicates that the two probes V1 and V2 do not measure the potential with the same phase: There is a small phase shift between them indicating finite wavelength effects (wavelength comparable to the boom separation). V1 sees the potential first and V2 later at some times: (V1beforeV2) whereas at other times the reverse is true: (V1afterV2)
One can demonstrate that clearly by plotting the correlation of the E-field measured as the difference of probe V1-Vsc and -V2+Vsc. This was doen in figure (Correlator). For Vsc we use Vsc=0.5*(V5+V6)*factor, where factor is something to account for the fact that the probes 5 and 6 do not measure the full SC potential as they are not completely in the sheath. The cross correlation between V1-Vsc and -V2+Vsc exhibits a periodic oscillation that is due to the rotation of the double probe with spin. When the probe is aligned to the field no lag is observed. When V1 is behind the SC along is motion then a positive lag is seen, as V1 lags behind V2. When V1 is ahead of the SC in its motion the lag is negative. The same behavior with a 90 degrees shift is seen by spheres V3 and V4. The lack of a shift in V5 and V6 shows that the motion of the spacecraft is the one controlling these lags. The amplitude of the oscillation indicates a maximum lag of ~7.5 msec. For a boom center separation of 55 m, we get a phase speed of the waves in the SC frame of 7.3 km/s. This is the sc velocity. The analysis indicates that zero frequency structures are passing by the sc.
However, if you look at the power spectrum of V1-V2 and V3-V4 it does not exhibit a "fingerprint signature" like one would expect for such waves, if the waves have a specific wavelength. Is it possible that the waves have a mixture of wavelenths? We are still investigating that.
Regarding the O+ waves: They do not exhibit a finite wavelength effect, One can then decompose the waves in parallel and perpendicular components, and the perpendicular components into two: One on the spin plane and another out of the spin plane. They are mutually orthogonal. They are termed Eperon, Eperoff, Epar. They turned out to be close to EXY, E56 and -Z. The E field then looks like: (EFIParPerMake). The left hand component will be gotten out of the fourier transform of Eperon and Eperoff, and will be E+ = (Eperon + i Eperoff) in fourier space. The magnitude of that is the power of the left hand component. The power spectrum of that in the ~9 Hz range will be the power of the left hand waves that are important for O+ heating. The power spectrum of Eperon, Eperoff (and Epar); as well as E_left_hand, E_right_hand (and Epar) is shown in the plot (Eper_RH_LH_power_spectrum_total). It is evident that the power distribution in the Eperon and Eperoff is almost exactly the same in all frequencies, and similarly the power distribution in right hand and left hand waves is also the same. Thus, there is no preference in left hand waves during this interval.
However, significant power exists in both RH and LH modes. The power spectrum at the time of the O+ conic observations is given at (Eper_RH_LH_power_spectrum_detail_O+). The power at 9 Hz at that time is approximately 80-100 (mV/m)^2/Hz. The spectra have low variability because they are composed of 9 spectra averages to reduce noise (less averaging will give more data points around 9 Hz but higher fluctuation level). The time series detail and the hodogram of the components perpendicular to the field Eperon and Eperoff, are given in (Eperonoff_detail_O+).
What about the proton gyrofrequency modes? These cannot be observed in the low sampling rate data, but they can be observed in the high resolution, burst data. The power in these waves is shown in figure (powspec_before). The left part of the figure is low sampling rate (up to 40 Hz) and the right part of the figure is high sampling rate (up to 1600 Hz) data. As before the data are shown in Epar, Eperon, Eperoff components, while also shown is the power in the L- and R-hand mode.
Note that the Eperon spectrum does not match the Eperoff spectrum. In addition, a frequency of 100 Hz is (if due to H+ waves) subject to finite wavelength effects, as it corresponds to wavelengths of rho_i which are comparable to the boom length. In addition, as we saw before, high frequencies are subject to corrections due to finite scalelengths convected past the spacecraft.
We first correct for the spacecraft speed. The cross-correlation between the different modes gives a speed that (as evident in the plot Correlator mentioned above) is varying sinusoidaly with spin phase. Modelling the spin dependence of the time lag, we can find an amplitude commensurate with the satellite speed, and then model it with a pure sine/cosine. We then subtract a time-dependent time lag from the prove V1, V2, V3 and V4 data and reference all times to the time the structures would hit the spacecraft. The effect is to make the V1, V2 traces have maximum correlation at zero lag. Proof that this was done properly is that there is no sinusoidal dependence of the time lag between V1,V2 and V3,V4 in the figure unlagged.
If the spheres were to measure the potential locally, they would respond to infinitesimal wavelength structures, and our E-field measurements would be good to very high frequencies (low wavelengths). They don't. They respond to potential differences between sphere and satellite. Thus our measurements are good to wavelengths as small as the boom size (i.e., half the sphere separation distance). Our technique references the center point of the boom to the spacecraft. Thus our electric field is responsive to wavelengths equal to the boom size. Before the subtraction of the time lag, we were responding to E-field from wavelengths as short as the sphere separation. Thus our technique has reduced the wavelength to which we respond by a factor of two. A comparison of the power spectra before and after the subtraction of the time lag is shown in figure powspec_beforeandafter. The arrows indicate the highest frequency booms 12, 34 and 56 are responding to, given their length and the spacecraft velocity. For example, boom 34 is 100 meters and the E-field measurements when 34 is along the SC velocity (7.5 km/s) are responsive to frequencies as high as (7.5km/s)/(0.1 km)=75 Hz. Boom 12 (129 meters) has a similar wavelength/frequency to which it is responsive. This pertains to the Eperon component, since that component is derived from booms 12 and 34 and is along the SC velocity on the spin plane. After the time-lag removal, boom 34 gives measurements responsive to wavelengths as low as 50 meters, which means frequencies as high as 150 Hz. Thus Eperon is good up to that frequency.
Notice that the spectrum of Eperon, after tlag removal, is identical to the spectrum of Eperoff (essentially spin axis direction) in the new frequency range that Eperon is not responsive to. This gives us confidence that the Eperoff spectrum is a good measure of the E-field structures. Eperoff should be good up to 500 Hz (or 13 meter wavelengths). How can we be certain of that?
There is a range of spin phases during which boom 12 or 34 are nearly perp to Vsc, and also to B. Then the projection of the boom perpendicular to B is small. Since the waves are perp to B, our boom will respond to wavelengths, lower than the boom length, equal to the boom projection of the plane perp. to B. By boom length we mean (since the tlag has been subtracted) one half of interprobe separation. We can take the measurements from one rotating boom pair, and the E56, and compute Eperp. If the angle between the rotating boom 34 and V is more than 70 degrees we will be responsive to wavelegths as low as cos(70)*boom length = 17 meters (boom 34 length=50 meters). The approach will work as long as we are not too close to B to have problems computing Eperp. Figure FinWavEff_line2 shows the part of the spin phase when the angle between 34 boom and Vsc is 50-90 degrees. The red line corresponds to the actual 3-D measurements of the E-field, whereas the black line corresponds to the E-field computed from one rotating probe (34) and the spin axis one (56). The agreement is quite good, except for some small corrections that result in zeroing out Eparallel completely, by virtue of the procedure. The only problems occur very close to B, when a spike in the data (black line) shows unpphysical E-field due to the proximity of the boom to the B direction. If we avoid that region we are OK. We set the angle of avoidance to 16 degrees. We also limit our angle to V to greater than 70 degrees. This makes our sensitive wavelengths to as low as 17 meters (see above). When we do that we limit the phase to only 4 degrees on either side of B. The data are shown in Figure FinWavEff_line1. Wehn we include the same range of angles but from both probes (34 and 12) we get from the full duration of the burst the Figure FinWavEff_line0. Note the very good agreement between the black and red lines (2D and 3D measurements) except for small corrections that are due to increased sensitivity to wavelengths as low as 17 meters.
The difference in the power spectra is dramatic. If you use the part of the spin phase when boom 34 is between 70 and 10 degrees away from the Vsc you get in figure FinWavEff_pwrspc2 the same dissagreement between Eperon and Eperoff as we had seen before. The Eperon is below Eperoff because it cannot respond to small wavelengths. If you use the part of the spin phase when boom 34 (or 12) are between 76 and 70 degrees from Vsc you get in figure FinWavEff_pwrspc1 an agreement between the two power spectra. The agreement continues if you reduce the angle to 3 or 2 degrees. It does not continue if you increase the angle to go too close to B (as close as 15 degrees to B). In that case we get spurious fields resulting from noise in determination of the third field component from the E*B=0 approximation.
In short: we now trust the E56 measurement as being real as it is reproduced from the 12 and 34 booms when they respond to the same wavelengths. This means that the wave power is uniform on the plane perpendicular to B. The analysis is consistent with 2D zero-frequency turbulence. Notice that there is a knee to the spectrum that resembles 2D hydrodynamical turbulence of Kraichnan. Although the wavelengths are quite short in this case to consider the system a hydrodynamical one, the analogy may be instructive. In 2D MHD turbulence the wavelength at the knee of the spectrum is the feeding wavelength at which energy is provided to the system. By analogy, the wavelength in which energy is fed here is 50 meters, or 150 Hz. The wavelength corresponds to ion cyclotron waves of protons with temperature 5 eV. This is typical H+ temperature at these altitudes.
Bill Peterson, Harry Collin: Do you see background 5-10 eV temperature plasma? What density? What is the total density you observe? Thanks.
