Magnetic Fluctuations Close to Io: Ion Cyclotron and Mirror Mode Wave Properties

C. T. Russell, M. G. Kivelson, K. K. Khurana and D. E. Huddleston

  Institute of Geophysics and Planetary Physics, University of California,
Los Angeles, CA 90095-1567

Originally published in:
Planet. Space. Sci., 41, 143-150, 1999.

 

Abstract

As Galileo approached Io on December 7, 1995 and passed through the Io wake it passed from a region of ion cyclotron waves at the SO2+ gyrofrequency into a region of strong compressional waves at the edge of the wake region and through a region of waves linearly polarized transverse to the magnetic field in the center of the wake region. As the Io wake was approached the properties of the ion cyclotron waves changed as if there was a change in the wave generating region. The cyclotron waves were also significantly weaker outbound than inbound. We interpret the compressional waves to be mirror mode waves generated by the anisotropic pick-up distribution of SO2+. The appearance of the mirror mode waves at the edges of the wake suggests that the magnetic field or plasma gradient plays a role in limiting the growth rate of the ion cyclotron instability in this region, in addition to the disappearance of the isotropic warm torus plasma that stabilizes the mirror mode outside of the wake region.

 

Introduction

Magnetic fluctuations are important phenomena in planetary magnetospheres as they are both agents for change in the plasma and energetic particle distributions and they are diagnostic of the processes occurring therein. Despite the passage of five previous spacecraft through the Jovian magnetosphere we still know little about the wave processes occurring in the inner magnetosphere and especially in the Io torus, the region we believe is responsible for supplying the mass of the Jovian magnetodisk, a unique feature of the solar system's largest planetary magnetosphere.

Previous measurements have shown Jupiter to have an unsteady magnetosphere. Khurana and Kivelson [1989] reported 10-20 minute period waves in the middle magnetosphere, at a distance of 10 to 35 RJ, from Voyager 2 magnetometer measurements. Glassmeier et al. [1989] found 13-20 minute waves in the Io torus from about 5.5 to 7.5 RJ using Voyager 1 magnetometer measurements. Balogh et al. [1992] also reported an unsteady magnetic field using the Ulysses data. All authors find that the waves have transverse and compressional components. Other than these approximately 15 minute oscillations, the only other activity reported are ion cyclotron waves in the middle magnetosphere near the current sheet [Dougherty et al., 1997].

Fig. 1. Sketch of the trajectory of Io for the 22 minutes surrounding the crossing of the Io wake. The coordinate system is such that the ordinate is increasingly positive in the direction of the corotating plasma. The abscissa increases toward Jupiter. Indicated along the trajectory are the times corresponding to the panels of Figure 4 (L, LC, RC, R) and Figure 5 (a, b, c).

On December 7, 1995 the Galileo spacecraft passed through the Io torus returning particles and fields data from 1521 to 1820 UT as the spacecraft moved from 7.7 RJ to 5.5 RJ and a local time of 1040 to 1240. The trajectory had been chosen to remain close to the midplane of the Io torus. The magnetometer returned magnetic measurements at a rate of 4.5 16-bit vectors per second using the tape recorder for later transmission. As shown in Figure 1 1745:30 UT the Galileo spacecraft passed through the center of the Io wake at a distance of 0.5 Io radii above the surface of Io and almost precisely through the geometric center of the wake. The initial observations of the magnetic fields investigation have been described by Kivelson et al. (1996). As Io was approached by Galileo a relatively narrow band of ion cyclotron waves near the SO2+ gyrofrequency was encountered. The amplitude of these waves grew as Io was approached and diminished as Galileo left Io, but in the vicinity of the wake they disappeared, only to be replaced by new wave phenomena a strong compressional wave on the edges of the wake and a linear transverse wave in the center of the wake. The source of these ion cyclotron waves have been discussed by Warnecke et al. [1997] and by Huddleston et al. [1997]. It is the purpose of this paper to provide a more detailed description of the properties of the waves close to Io and in the vicinity of Io's wake.

 

Observations

The measurements during the Io flyby were made with the inboard magnetometer in its 16,000 nT range. Each of the three orthogonal sensors is sampled at 30 samples per second with a 12-bit analog-to-digital converter that is accurate to 1/8 of the least significant bit [Kivelson et al., 1992]. The digital noise associated with this process is 0.36 nT2/Hz and is independent of frequency [Russell, 1972]. The data are then digitally filtered to prevent aliasing and resampled to provide 4.5 16-bit samples per second. The digital noise level introduced by this 16-bit resampling is negligible relative to the noise introduced during the first digitization. The rms noise associated with the 0.36 nT2/Hz digital noise is 0.9 nT. Thus during the Io encounter the magnetometer should be able to resolve waves with amplitudes down to about 1 nT.

Fig. 2. Dynamic spectrum of the power observed in the radial (top), azimuthal (middle) and theta (bottom) directions from 1736 to 1756 as Galileo traversed the Io wake. The radial direction points radially outward from Jupiter; the azimuthal direction points in the direction of the corotating flow; and the theta direction is southward. See text for the details of the construction of the dynamic spectrum.

Figure 2 shows dynamic spectra of the waves in the frequency band 0.01 to 2.25 Hz for the 20 minutes surrounding closest approach for each of the three components. This figure covers almost all of the portion of the trajectory shown in Figure 1. In these plots the data were Fourier analyzed in 256-point samples overlapped by 32. This corresponds to samples of length 57 seconds, each one taken 7 seconds later. The frequency estimates have been averaged in bands of 15. The vertical scale displays the logarithm of the frequency. The color scale goes from 80 nT2/Hz (blue) to 8000 nT2/Hz (red). The coordinate system in which the data are displayed has BR radially outward from Jupiter, B southward, and B in the direction of corotation. During the flyby the magnetic field was predominantly in the theta direction so that compressional fluctuations are seen most clearly in the B measurements and transverse fluctuations most clearly in the Br and B measurements.

These spectra clearly show the transition on either side of the wake region from the transverse ion cyclotron waves seen in BR and B at about 0.2 Hz (log f of about -0.7) both inbound and outbound from Io and to the compressional waves seen in B. The strong burst of activity seen in BR and B from 1742-1743 UT signals the end of the transverse wave activity. This activity appears to have begun at 1740 UT at a somewhat higher frequency (about 0.4 Hz) than the pre-Io cyclotron waves (at about 0.3 Hz at 1740 UT). The SO2+ ion cyclotron frequency here is 0.4 Hz. Since the magnetic field is principally in the B direction, this component records the compressional activity and is fairly insensitive to the transverse waves. The B component, like BR is mainly transverse to the main field and generally mirrors the activity in BR. We note that the burst of waves at 1741 is much stronger in B than BR and thus is not circularly polarized. The region of compressional activity extends from about 1743 to 1749 UT or from 1.65 RIo before the center of the wake to 1.17 RIo post wake. (Note that the spacecraft is crossing the wake at 0.47 RIo per minute and thus there is some spreading of the wave energy due to the finite width of our time window). On exit from the Io wake the compressional fluctuations and the transverse fluctuations are both weaker than upon entry. Moreover, there seems to be a clear gap centered at 1749:15 between the two types of activity. Finally, we note the weakening of activity in all three components in the center of the wake centered on 1746:15 UT. The B component weakens the least in the center of the wake due to the presence of a linearly polarized signal almost completely restricted to B in the region.

Fig. 3. Dynamic spectrum of the coherence and phase between pairs of components during the Io flyby: Br-B coherence (top), Br-B coherence (middle), Br-B phase (bottom). See text for the details of the construction of the dynamic spectrum.

Dynamic spectra of the coherence of the waves shown in the upper two panels of Figure 3 reveal a strikingly different pattern. The cross spectrum of the two transverse components shows strong coherence in the frequency band around 0.5 Hz on either side of the wake but little coherence at any frequency within the wake. The low amplitude waves (barely visible on the color scale of Figure 2) from 1736:1739 UT and from 1755-1756 are quite coherent while the strongest (compressional) waves from 1743 to 1749 UT do not appear in Figure 3 at all. The bottom panel of Figure 3 shows the phase spectrum between Br and B , with a mask covering any estimates for which the coherence is less than 0.5. The waves that have been identified as transverse ion cyclotron waves are clearly at 90o as expected for cyclotron waves. However, there is a small burst of signal at 1740 UT that has a 120o phase difference. This is a real effect, not an artifact.

Fig. 4. Spectra of the transverse (thin trace) and compressional (thick trace) wave power at four times during the Io encounter from: 1740 to 1744 just prior to the wake encounter; from 1745 to 1746 during the first period of mirror mode waves; from 1746 to 1747 during the period when mirror mode waves were not present in the wake; and from 1755 to 1758 UT just after the wake encounter.

The dynamic spectra in Figure 2 illustrate the trends in the data well but do not illustrate clearly the spectral shape or the absolute amplitudes. Figure 4 shows slices through the spectrum prior to the wake from 1740-1744 (L); during the wake passage from 1745-1746 (LC) and 1746-1747 (RC) and after the wake from 1755-1758 (R). The periods over which these spectra were obtained are shown in Figure 1. The upper curve shows the transverse power and the lower curve the compressional power in each panel. While there is a band of frequencies present, the wave amplitude outside the wake clearly peaks right at the ion cyclotron frequency. However, inside the wake the spectrum is totally featureless and very steep. The transverse power always dominates over the compressional power except for frequencies below 0.2 Hz when the mirror mode waves are present. We note that the ion cyclotron waves have a significant compressional component. This is consistent with the combined elliptical polarization of these waves and their non-parallel propagation.

Fig. 5. Time series of the magnitude of the magnetic field during the Io wake passage. The bottom panel shows the full wake passage. The top three panels show segments of the wake crossings on an expanded scale. Temporal resolution is 0.222 seconds in all panels.

We emphasize that the compressional waves in the wake are quite strong. This can be seen in the power spectra shown in Figure 4 but we make this point again in Figure 5 that shows the time series of the total field. The bottom trace here shows the overall field profile across the wake while the upper three panels illustrate sections of the traversal. These intervals are also illustrated in Figure 1 by the levels a, b, c corresponding to the top three panels of Figure 4. The dips in the field strength at the two edges of the wake are about 500 nT inbound and 200 nT on exit. Even in the center of the wake there are 30 nT peak-to-peak compressional variations.

 

Wave Properties

The dynamic spectra shown in Figure 2 illustrate the presence of ion cyclotron waves on either side of the wake and both compressional and transverse waves within the wake region. However, these spectra per se do not provide the quantitative measurements of wave properties that one would need to compare with theory or simulations of the wave growth process.

Table 1. Ion cyclotron waves properties

Time RIo p/<f>
(o)
kB %Po1 Amp
(nT)
CompAmp
(nT)
B/Bo
(%)
1707-12 18 51 11 -0.95 41 2.9 0.9 0.19
1714-21 14 56 16 -0.73 75 3.9 1.1 0.25
1717-24 12 53 11 -0.82 76 4.4 1.1 0.28
1724-31 9 53 4 -1.00 90 6.1 1.3 0.37
1728-34 8 57 5 -0.96 92 7.2 1.4 0.43
1734-37 5 56 8 -0.88 96 15 3.0 0.89
1736-41 4 54 15 -0.87 85 20 5.7 1.19
1740-44 2 67 6 -0.72 89 32 8.3 1.93
1749-52 3 73 6 -0.76 93 27 4.3 1.06
1752-55 4 48 16 -0.51 64 14 3.6 0.08
1755-58 5 44 15 -0.62 81 5.9 1.4 0.03
1758-01 7 41 38 -0.32 71 2.8 0.8 0.01


Notes: RIo is the distance of the observation point from the center of Io; p/<f> is the observed wave period measured in terms of the proton gyro period; kB is the angle of the wave normal to the magnetic field direction; is the wave ellipticity; %Po1 is the percentage polarization; Amp is the rms wave amplitude; CompAmp is the rms amplitude of the compressional fluctuations; B/Bo is the amplitude of the wave normalized by the background magnetic field strength.

The properties of the ion cyclotron waves are summarized in Table 1 using the wave analysis technique of Means [1972] that is optimum for circularly polarized waves such as these. The wave period shown is given in proton gyro periods derived from the power weighted average frequency of the peak. This technique differs from that employed by Kivelson et al. [1996] and by Warnecke et al. [1997], who calculate an instantaneous frequency whose power is averaged over 30s. The column labeled kB gives the direction of propagation determined from the quadrature portion of the signal and hence is appropriate for nearly circularly polarized waves as we have here. The column labeled indicates how circular, =+1, or linear, =0, are the waves. A positive sign indicates right-handed polarization. Perhaps surprisingly, the waves' phase velocities are most closely aligned with magnetic field lines and are most circularly polarized about 1730 UT, not closer to Io. After Io closest approach the waves have a lower percent polarization than before closest approach, the waves are more linearly polarized, and the angle of propagation less field aligned. These properties and the greater wave amplitude suggest that the mass loading was stronger on the inbound leg over the sunlit hemisphere of Io. In the outbound region the minimum variance direction differs from the direction of the wave normal calculated from the Means' quadrature technique [Means, 1972]. The minimum variance direction remains close to the field line. Thus in order to obtain the direction of the k-vector for the cyclotron waves in this region it is necessary to use the Means technique.

The amplitudes shown are the square root of the total power summed over the three orthogonal directions. The compressional amplitude is usually about 1/4 the transverse, and is clearly non-zero. In fact immediately post encounter the compressional amplitude is one-half the transverse, when the wave amplitudes are near their largest values. The last column shows the ratio of the wave amplitude to the background field strength. Even though these are intense ion cyclotron waves, they remain in the linear regime at all times with amplitudes no greater than about 2% of the background magnetic field strength. The growth of these waves is examined by both Huddleston et al. [1997] and Warnecke et al. [1997]. Basically, the damping by the Io torus plasma dominates over the wave growth stimulated by the newly added ions at all frequencies except near the SO2+ gyrofrequency because the SO2+ in the torus has dissociated. However, very close to Io the newly added plasma eventually dominates over the torus plasma and a new class of waves appears.

Table 2. Wake wave mode properties
Time RIo Frequency
(Hz)
kB %Po1 Amp
(nT)
CompAmp
(nT)
B/Bo
(%)
1744-45 1.7 .09-.26 84 0.12 40 122 93.3 11.8
.27-.50 88 0.05 51 67.3 53.8 6.5
1745-46 1.5 .11-.39 87 0.63 73 89.7 67.7 7.8
.43-.97 17 -0.11 59 21.4 8.1 1.9
1746-47 1.5 .13-.35 7 -0.03 81 42.2 4.0 3.0
.39-.81 4 -0.06 71 24.1 2.0 1.7
1747-48 1.7 .07-.29 82 0.25 34 99.4 75.7 7.4
1748-49 1.9 .15-.31 83 0.33 31 43.6 26.6 3.1


Notes: Here kB is the angle of the minimum variance direction from that of the magnetic field.

Table 2 presents a summary of the wake wave properties using the technique of Rankin and Kurtz [1970] patterned after optical methods. This technique is optimum for linearly polarized signals. We begin the analysis at 1744 UT where the compressional waves in the wake first begin and end the analysis at 1749 UT where ion cyclotron waves appear again. The table shows the frequency band analyzed in Hz, the angle between the minimum variance direction in that frequency band and the magnetic field direction, the eccentricity of the ellipse made by the magnetic fluctuations, the percent polarization of the signals, the rms amplitude of the waves adding the power of all three components, the amplitude of the compressional part of the wave, and the ratio of the wave amplitude to the background field strength.

Examining first the column labeled, kB, we find that the minimum variance direction at the edges of the wake is close to orthogonal to the background magnetic field. However, in the middle of the wake region at all frequencies the minimum variance direction is along the field. In other words the waves have become transverse. This can be confirmed by inspecting the second and third last columns of the table that show the compressional amplitude and total amplitude of the waves. Entering and exiting from the wake the compressional amplitude is a major fraction of the total wave amplitude but in the center of the wake the compressional amplitude is about 10% of the total wave strength. The large wave normal angle implied by the large kB of the compressional waves can be checked using what amounts to an application of the coplanarity theorem applied to the fast mode shock wave [Russell et al., 1987]. The magnetic perturbations of compressional waves are perpendicular to the direction of propagation and lie in the plane containing the background magnetic field and the propagation vector. Thus the triple vector cross-product of the field change, the background field and the field change is parallel to the propagation direction. Applying this formula to the compressional dips in the field strength we obtain angles of propagation of close to 70o. Thus the direction of propagation implied by the minimum variance direction is qualitatively correct, but not quantitatively correct. The reason for this difference is that the minimum variance direction aligns with the wave normal only for circularly or elliptically polarized waves. These waves are very linearly polarized.

Examining the column labeled , we see that the waves in the wake region are generally quite linearly polarized. Finally, we note that the percent polarization of the waves remains high throughout the wake passage indicating that the waves are due to a single coherent source.

 

Discussion and Conclusions

The compressional waves on the edges of the wake resemble mirror mode waves seen in the coma of comet Halley and in planetary magnetosheaths [Russell et al., 1987; Tsurutani et al., 1982] and are quite distinct from the properties of the ion cyclotron waves seen before and after the fly by. The appearance of the dips and their derived directions of propagation are very similar to those previously observed mirror mode waves. The plasma analyzer [Frank et al. 1996] does not have sufficient temporal resolution to follow any density increase in these structures to confirm the expected anti-phase relationship present between the magnetic field and the plasma density [see e.g. Vaisberg et al. 1989] but the other properties of these fluctuations are very similar to those seen in situations where we had that verifying information such as at Comet Halley [Vaisberg et al. 1989]. This includes the steep spectrum, and the depth of field minima and their random overlapping occurrence.

Mirror mode waves arise in the presence of a strong pitch angle anisotropy, the same anisotropy as responsible for the growth of ion cyclotron waves. We would not expect these waves to arise in the Io torus where the warm torus plasma is quasi-isotropic and will stabilize the mirror mode. When these particles disappear in the wake it is natural that the mirror mode arises in the presence of the newly picked up ions gyrating perpendicular to the field. Thus, the question these waves present to us is why do we not see ion cyclotron waves in the wake region. What prevents the ion cyclotron waves from growing at the edge of the wake is not clear. One clue is in the dimensions of the structures. The gyro radius of SO2+ gyrating in the Jovian field at Io with a velocity equal to the corotational velocity is about 20 km. The velocity of Galileo as it passed through the Io wake was about 14 km/sec and the plasma velocity several 10's of km/s. Thus the dips in field strength associated with the mirror mode waves, that last 2-3 seconds are a few gyro radii in width with the precise thickness dependent on the orientation of the mirror mode wave fronts. The gradient in field strength and by inference the gradient in the plasma density and pressure are clearly similar but perhaps several times larger as illustrated in the bottom panel of Figure 5. If the gradients in the field strength are large, the phasing of the cyclotron motion of the particles will be randomized and the coherent motion of the ions associated with ion cyclotron waves will be upset. The mirror mode, however, does not require coherent ion gyro motion. In the center of the tail the ion beta drops as the temperature decreases and the mirror mode is stable even though a large anisotropy could be present.

The transverse linearly polarized waves in the center of the tail have no obvious explanation in terms of wave-particle instabilities. There is no obvious source of free energy that would cause these waves to grow. We note that this is the region in which field-aligned electron beams were seen [Williams et al. 1996] but we would not expect these waves to be resonant with because the electron velocities are much higher than the ULF wave velocity. These waves may, however, be associated with unsteadiness in the massloading process. The polarization observed would be expected if the bending or draping of the jovian field associated with the slowing down of the material closest to Io varied with time.

This brief examination of the ion cyclotron waves closest to Io also reveals complexity in their generation process. The most obvious feature is the inbound/outbound asymmetry signaling a strong source region of SO2+ ion pickup on the dayside. The ion cyclotron waves occur in bursts and those bursts have different characteristics. The phase differences between the components is not always 90o, nor are the waves always circularly polarized.

In conclusion, while the pick-up process seems to dominate the growth of waves in the vicinity of Io, the nature of these waves differs markedly depending on the properties of the background plasma. In the torus proper ion cyclotron waves appear but the edges of Io's wake promote strong mirror mode growth. Only 1.5 RIo downstream of the center of Io the waves have grown to a large fraction of the background field. The dimensions of these features are several ion gyro radii whether one uses the spacecraft velocity or the observed plasma velocity to convert from the temporal signature to the spatial dimensions. In the center of the wake a new wave mode appears. This wave is linearly polarized transverse to the magnetic field and has a steep, featureless spectrum.

 

Acknowledgements

The authors wish to thank R. J. Strangeway for many discussions about wave dispersion relations and Steve Joy for his assistance with Galileo data acquisition. This work was supported by the National Aeronautics and Space Administration through the Jet Propulsion Laboratory's grant JPL 958510.

 

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